ability in problem solving 2021

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How to Solve Problems

• Laura Amico

To bring the best ideas forward, teams must build psychological safety.

Teams today aren’t just asked to execute tasks: They’re called upon to solve problems. You’d think that many brains working together would mean better solutions, but the reality is that too often problem-solving teams fall victim to inefficiency, conflict, and cautious conclusions. The two charts below will help your team think about how to collaborate better and come up with the best solutions for the thorniest challenges.

• Laura Amico is a former senior editor at Harvard Business Review.

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Problem-Solving Skills: Think Beyond the Whiteboard Test

Mastering technical problem-solving skills involving data sets and algorithms are all fine and good, but getting a handle on these other problem-solving skills are equally important.

Are you technically brilliant? Even a rock star? 

Sorry, that may not be good enough to get you hired or promoted, said Philippe Clavel, senior director of engineering at Roblox, a game development platform company based in San Mateo, California.

Mastering technical problem-solving skills involving data sets and algorithms are all fine and good, but getting a handle on these non-technical problem-solving skills are equally important, according to hiring managers.

Prior to joining Roblox, Clavel managed a technically brilliant engineer who had a toxic personality that constantly challenged others and failed to let them think, Clavel said. After giving feedback to the engineer about his behavior, Clavel paired him with someone more senior to ensure he and his teammates worked together in solving problems.

This engineer eventually started to change and realized it wasn’t so hard to temper his comments and even say hello to people. 

“The outcome was much better. He could do more with other people than what he could do alone,” Clavel told Built In. “It definitely speeded up the collaboration process by 20 percent because there was more discussion on the front end.”

More on people Management How to Make Your Next Meeting the Best Ever

How You Sabotage Yourself

Without possessing non-technical problem-solving skills, you are likely to miss out on landing your dream job or securing that promotion you’ve been seeking.

“Technical skills can be acquired. What I’m looking for when I hire someone is can they learn quickly? Technology changes very quickly and you have to stay on top of it,” said Igor Grinkin, a DevOps manager at San Francisco-based Newfront Insurance.

Roughly 50 to 60 percent of job candidates that come through Roblox’s door believe their technical prowess is the only thing of importance to land the job, Clavel said. He noted this belief is especially prevalent among new college graduates. However, Roblox’s interview process tends to weed people who lack non-technical problem-solving skills by the time they reach Clavel for an interview, he said.

“I would say a lot of people think these skills aren’t important. But I will be honest, they are wrong. We especially see this in new engineers, but even senior engineers think this way. They think, ‘I’m so good at technology, there’s nothing else I need to know.’ But, what this does is it prevents you from having the job you really want, because that will be one of the differentiators with you as a candidate. Or, if you get the job, it will block you in your career,” he warned.  

Amazon Web Services (AWS) also places a high importance on non-technical problem-solving skills, according to Caitlyn Shim, a general manager and director of AWS Organizations and Accounts at the Seattle-based company. “We don’t want brilliant jerks,” said Shim.

“You can be extremely smart, but if you can’t work with others, you’re gonna have a really hard time in the end. Ultimately, we’re trying to tackle problems that one person can’t solve alone.”

She added if you can’t work in a group, then you’re limiting yourself to solving one-person-sized problems and limiting your career. 

More on People Management Why Are Companies Still Offering Unpaid Internships?

Why These Non-Technical Problem-Solving Skills Are Needed

Effective communication and collaboration skills are an “absolute must” for any job at autonomous vehicle maker Waymo, said Annie Cheng, engineering director at Mountain View, California-based Waymo. She, like other hiring managers, notes that solving big problems takes more than one person.  

You also need to learn from your mistakes, as well as have an open mind, when tackling problems, Cheng added, noting these attributes rank high in non-technical problem-solving skills.

“Being able to think out of the box, looking at things from different angles and considering alternative solutions is an important problem-solving skill, especially if you’re working on a novel, or a moonshot project,” Cheng said.

10 Critical Non-Technical Problem-Solving Skills

• Active listener
• Good communicator
• Collaborator
• Open mindedness
• Accepts feedback
• Learns quickly and from mistakes
• Attains consensus
• Drive to see problems through

Making mistakes is not only inevitable but it’s a key part to developing your problem-solving ability, said Cheng, noting it leads to learning from one’s mistakes.

Driving consensus is another non-technical problem-solving skill you should master, said hiring managers.

“We have passionate people who have really strong opinions but you also have to listen to each other. Then, you have to be able to figure out how to pull the right things from everyone’s ideas so that you can all come to a good consensus in the end,” Shim said. “That’s a skill in and of itself.”

Embracing feedback will grease your problem-solving skills and prevent you from becoming stuck to one idea, no matter how much you love it and believe it smacks of brilliant innovation, said Shim, noting it’s a tough but important skill to develop.

Drive is also critical to problem-solving skills, especially complex ones.

“In computer science and software development, you have to push to the finish line. But there’s a lot of complexity that may get in your way. While it’s easy to say you want to finish, you need to go the extra mile,” Clavel said.

Curiosity is also needed for problem-solving, he added. Engineers progress by wanting to learn more and that, in turn, adds to the bench of tools you can call on to solve problems.

These non-technical problem-solving skills are important for all technical roles, hiring managers said, but they note some skills, like effective communication , have greater weight for some positions.

Engineers who work in the product feature area at Roblox, for example, need to have good communication skills because they are working closely with designers in determining what users want. Excellent communication skills can help explain your vision to product managers and designers, said Clavel.

Actionable Steps to Develop These Problem-Solving Skills

“There’s no silver bullet, as every person is unique,” Cheng said. “While some people naturally have good soft problem-solving skills, others might need to invest quite some time to develop those.”

Emotions also often overshadow the core problems you are trying to express, Cheng observed.

“One piece of advice I gave to a direct report years ago is first learn to detect whether they are in an emotional state and see if they can control their emotion while trying to express the core problem. When they find it challenging, use different communication methods, such as writing, so they can filter out emotions and focus on bringing clarity to the key problem statement,” Cheng said.

Talking to lay people in words they can understand can bolster your technical communication skills. This skill can also be developed by teaching courses or explaining your work to a fifth-grader, she added.

There are many different ways to develop your problem-solving skills — consider these five steps from authors John Bransford and Barry Stein detailed in their book, “The IDEAL Problem Solver: A Guide to Improved Thinking, Learning, and Creativity.”

IDEAL Steps

• Identify the problem
• Define the challenges
• Examine potential strategies
• Act on the strategies
• Look at the results and evaluate whether other actions are needed

Broaden your collaboration skills by going beyond the day-to-day scope of your work and try collaborating with coworkers outside your team on projects across the company, such as forming an ERG group or working with interest-based groups like a cycling or yoga group, Cheng said. She added these efforts may also improve your communication skills too.

Matching employees with other employees to help them grow is an effective solution to develop their non-technical problem-solving skills, Clavel said. 

Managers can also take other steps to help employees develop their non-technical problem-solving skills too.

Rather than telling your employee, ‘Hey, you need to focus on communicating better or improving your creativity,’ try giving examples over time, Clavel said. The combination of knowing they need to change and having examples as a framework leads to more realistic outcomes where they can develop these problem-solving skills, Clavel said.

“Engineers are smart and it’s a matter of learning how to apply your smartness to other areas.”

“You may not get all of the skills at once, but that’s OK. You may not be very good at communication, but you can compensate by your drive or creativity, or other of those skills.”

Self-discovery in developing non-technical problem-solving skills yields the best results, hiring managers said. 

That is what Shim saw at AWS.

“Someone used to present their ideas with a bunch of attitude and was kind of aggressive. But he saw when someone else would restate his ideas in a more open way, others would listen to it and were far more receptive,” Shim said. “That really helped him see it’s not necessarily what you say, but how you say it. He started to experiment with different presentation styles and found one that worked and felt natural for him.”

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• Open access
• Published: 12 November 2021

Interleaved practice enhances memory and problem-solving ability in undergraduate physics

• Joshua Samani   ORCID: orcid.org/0000-0001-8774-6646 1 &
• Steven C. Pan   ORCID: orcid.org/0000-0001-9080-5651 2  

npj Science of Learning volume  6 , Article number:  32 ( 2021 ) Cite this article

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• Human behaviour

We investigated whether continuously alternating between topics during practice, or interleaved practice, improves memory and the ability to solve problems in undergraduate physics. Over 8 weeks, students in two lecture sections of a university-level introductory physics course completed thrice-weekly homework assignments, each containing problems that were interleaved (i.e., alternating topics) or conventionally arranged (i.e., one topic practiced at a time). On two surprise criterial tests containing novel and more challenging problems, students recalled more relevant information and more frequently produced correct solutions after having engaged in interleaved practice (with observed median improvements of 50% on test 1 and 125% on test 2). Despite benefiting more from interleaved practice, students tended to rate the technique as more difficult and incorrectly believed that they learned less from it. Thus, in a domain that entails considerable amounts of problem-solving, replacing conventionally arranged with interleaved homework can (despite perceptions to the contrary) foster longer lasting and more generalizable learning.

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Introduction.

In virtually all learning domains, different topics or skills need to be mastered. Examples include derivatives and integrals in calculus, body systems in physiology, and the forehand, backhand, and serve in tennis. An intuitive approach to achieving mastery in such cases is to focus on learning one topic or skill at a time, which cognitive scientists refer to as blocking or massing (e.g., given concepts A, B, and C, studying three examples of each concept according to an “A 1 A 2 A 3 B 1 B 2 B 3 C 1 C 2 C 3 ” schedule). Blocking is ubiquitous throughout education, including in mathematics, science, and language curricula 1 , 2 , 3 . Its use is consistent with the common assumptions that human beings learn best when topics are introduced in isolation 4 , the learning of concepts is facilitated by exposure to successive examples of the same concept 5 , and that repetition practice fosters the development of expertize 6 (although there are varying perspectives as to the veracity of these assumptions). In contrast, researchers have recently begun investigating an alternative approach known as interleaved practice (henceforth, interleaving ). Interleaving involves switching between topics (or skills, concepts, categories, etc.) during learning (e.g., studying concepts A, B, and C using an “A 1 B 1 C 1 A 2 B 2 C 2 A 3 B 3 C 3 ” schedule) 7 . Consequently, to-be-learned materials are learned in juxtaposition to one another, rather than one at a time. Interleaving may improve attention 8 , induce memory retrieval processes 9 , prompt mental comparison processes 10 , foster relational processing 3 , and simulate the unpredictability of real-world situations 9 , all of which may be beneficial for learning. However, the benefits of interleaving have not yet been extensively explored in authentic educational contexts 11 , and the technique is not generally well known as an effective learning technique among students or instructors 9 . Hence, interleaving is currently rarely used in pedagogical settings 1 , 2 , 3 .

To date, most research on interleaving involves laboratory studies wherein perceptual categories such as artists’ painting styles 12 , 13 , 14 , biological taxonomic classifications 15 , 16 , 17 , or artificial shapes 18 , 19 , 20 are learned. In these studies, example images of to-be-learned categories are studied in blocked or interleaved fashion, followed by a classification test wherein new images that were drawn from the previously learned categories are shown. Typically, categories that were interleaved are classified more accurately than categories that were blocked 7 , 20 . A recent meta-analysis found that the typical benefit of interleaving for perceptual category learning is Hedges’ g (effect size) = 0.67, 95% confidence interval (CI) [0.57, 0.77] for artists’ paintings and g  = 0.31, 95% CI [0.17, 0.54] for artificial shapes 8 . The largest interleaving benefits have usually been observed for groups of categories that are perceptually similar (e.g., evolutionarily-related bird families), which implies that interleaving is more effective when to-be-learned materials are confusable with one another 8 , 21 . Mechanistically, benefits of interleaving for perceptual category learning have been attributed to the temporal spacing between category exemplars that occurs during such interleaving, which constitutes a form of distributed practice (which over a century of research has established can improve memory 22 ), as well as learners’ attention being focused on differences between categories (i.e., the attention bias and discriminative contrast framework, wherein interleaving-induced focused attention may yield improvements in the ability to discriminate between perceptually similar categories) 12 , 13 , 23 , 24 .

Based on the aforementioned research, recent reviews have defined the “interleaving effect” as improved inductive learning — that is, the mental process of acquiring conceptual knowledge from the study of exemplars—that stems from interleaving exemplars of visual or other perceptual categories 8 , 11 , 25 . A question left largely unanswered, however, is whether the interleaving effect extends beyond inductive learning tasks wherein the only determination of category membership is needed. In particular, it has yet to be fully established (a) whether interleaving enhances memory for to-be-learned facts as opposed to perceptual categories, (b) whether interleaving is effective for tasks that require substantial problem-solving, and (c) whether interleaving is effective in authentic educational settings and across extended time intervals 3 , 9 , 21 . These questions pertain to many contexts wherein interleaving could be used. As one example, an instructor might choose to interleave a series of different homework problems that require factual knowledge and the execution of stepwise procedures. Initial efforts to address these questions have involved interleaving in such domains as mathematics 21 , 26 , 27 , second language instruction 2 , 28 , 29 , and other areas 30 .

Thus far, the emerging literature on such uses of interleaving has yielded promising results and especially in the domain of middle-school mathematics. For example, in a 2014 classroom study, the use of interleaved homework assignments to practice algebra and graphing problems (e.g., solving for x in an equation; graphing an equation in the form of y  =  mx  +  b ) yielded subsequent surprise test performance that was nearly double that relative to a condition using blocked homework assignments 21 . Such benefits occurred even for materials that were not necessarily confusable with one another (as featured in most studies of interleaving and perceptual category learning). Even more impressively, a recent randomized controlled trial of interleaved algebra and graphing homework assignments in 54 classrooms (constituting the largest-ever investigation of interleaving to date) reported improvements of Cohen’s d (effect size) = 0.83, 95% CI [0.68, 0.97] on surprise delayed tests 31 . These and other results 27 , 32 , 33 raise the prospect that the interleaving effect encompasses more than inductive learning, with potentially broad implications for theories of learning, skill acquisition, and curriculum design.

To further explore the different types of learning that interleaving may promote, the present study examined the effects of interleaving on factual knowledge and problem-solving ability in a previously unexplored domain, namely undergraduate physics. Physics is one of the most popular academic subjects (in the United States alone, ~350,000 undergraduate students take introductory physics courses and over 280,000 high school students take Advanced Placement Physics exams each year) 34 , 35 . Physics is required not just for physics majors, but also for aspiring professionals in such fields as engineering, medicine, and other areas. Due to the extensive problem-solving skills that are needed, physics is a difficult subject to master, and owing to that difficulty, physics test scores are often among the lowest of all science subjects 34 (which can cause students to abandon the pursuit of science, technology, engineering, and math (STEM) careers) 36 . Accordingly, there is a pressing need to develop and investigate learning techniques that can be highly effective in physics courses.

The present study addressed that need by conducting a real-world, reasonably well-controlled test of interleaving in undergraduate physics. This test took the form of a preregistered experiment in two large lecture sections of an introductory-level undergraduate physics course (“Physics for Life Science Majors”) at a major US public university. The experiment spanned the first 8 weeks of the 10-week course, during which conventionally blocked homework assignments (wherein, only one problem type is practiced at a time) were replaced with interleaved assignments (involving switching between problem types). Importantly, rather than constructing or selecting materials specifically for research purposes, only the arrangement of homework problems during the course of normal instruction was manipulated and no other aspects of the course were altered. Hence, this test of interleaving occurred in an otherwise “business-as-usual” learning environment, which should increase confidence in its generalizability to real-world settings.

Across both lecture sections, 350 students participated in a counterbalanced, within-subjects design. During weeks 1–4 (Stage 1), students in the first and second sections (henceforth, Lecture 1 and Lecture 2) received blocked and interleaved homework assignments, respectively, whereas during weeks 5–8 (Stage 2), the assignment types were reversed (see Fig. 1 ). In other words, Lecture 1 students experienced blocking during Stage 1 and interleaving during Stage 2, whereas Lecture 2 students experienced the reverse. This arrangement ensured that each student in each section ultimately experienced both practice types.

In each of the two stages of the course, students completed 84 practice problems across 10 homework assignments. Blocked assignments typically featured three successive problems for each of three topics, whereas interleaved assignments typically featured only one problem per topic. In the figure, letters represent topics and subscripts represent the problem number for a given topic (1, 2, or 3). Different topics are also assigned different colors so that it is easier to visually tell them apart. Reflecting the relative simplicity of practicing one topic at a time, topics in each row of the blocked condition correspond perfectly to the assignment subject labeling that row, but this is not the case for the interleaved condition. Topics addressed on the criterial tests are also listed. Due to course time constraints, the last two blocked assignments of each stage include only two problems per topic instead of three. Topics from these assignments were not included in criterial tests.

During the course, each of the three weekly lectures was accompanied by a homework assignment. With blocked assignments, each topic was repeatedly practiced in succession with no intervening topics, whereas with interleaved assignments, each successive problem involved a change in the topic (for a list of topics, see Table 1 ). Of the nine problems per assignment, blocked assignments had three successive isomorphic problems per topic (i.e., having the same underlying problem-solving structure with contrasting surface features), which resembles the arrangement of practice exercises that occurs in many educational contexts 1 , whereas interleaved assignments had only one problem per topic, thus requiring students to engage in switching between topics (with the second and third problems per topic appearing on subsequent assignments). Crucially, within each stage, all students completed the same 84 total problems, with only the arrangement of those problems differing.

To measure the potential effects of interleaving, we administered an in-class surprise criterial test at the conclusion of each stage. These tests followed the approach taken in recent studies of interleaving and mathematics 31 , 33 and avoided contaminating effects of cramming, study group activities, and other events that can occur with increasing frequency in the period leading up to pre-announced exams. Both tests featured three novel problems that were more difficult than those included in the homework assignments. The first two problems required integrating concepts and procedures from two separate topics, whereas the third problem required applying a single topic in a new scenario. All three problems required recall and application of factual content conveyed in formulas (see Fig. 1 ). To derive answers, students had to correctly recognize the topics involved, all of which were last encountered more than 1 week prior; recall relevant formulas, rules, and principles; and in two of three problems, integrate and apply that information to devise a new solution strategy 37 (which could be viewed as requiring higher-order reasoning, integration, and constructive thought processes as opposed to simply recalling and repeating previously learned information) 38 , 39 .

As an example, one criterial test problem required recognizing the relevance of both Faraday’s Law and torque on a current loop in a magnetic field, recalling corresponding relevant formulas, and combining them in a novel way to compute the torque on a current loop in the magnetic field of an magnetic resonance imaging machine. Importantly, this combination of problem-solving processes was not included in any of the homework assignments and had not been specifically taught in the course. This type of problem also differed from the isomorphic problems commonly used in prior research on interleaving and problem-solving skills 26 , 31 , 32 , 33 , 40 .

How did students perform on interleaved versus blocked homework assignments—and how did they perceive both practice types?

Across both lecture sections, 290 students in stage 1 (83% of the total enrolled) and 286 students in Stage 2 (82% of total enrolled) experienced the experimental manipulation in its entirety by completing and turning in all of the homework assignments. Per our preregistered inclusion criteria, only data from those students were analyzed. Although that analysis revealed disparities between interleaving and blocking in terms of student performance, judgments of difficulty, and judgments of pedagogical effectiveness, there was no advance indication of any interleaving benefit.

With respect to overall performance, students correctly solved more blocked than interleaved homework problems (Table 2 ), with a mean deficit on interleaved assignments of 0.05 and 0.09 proportion correct in Stages 1 and 2, respectively. When interpreting these results, it is important to consider that there were nine different problem types on most interleaved assignments, with each type requiring a different problem-solving strategy, whereas, with most blocked assignments, there were only three problem types. Hence, the expectation that the blocked assignments would be easier was confirmed by student performance.

When asked at the end of each assignment to make metacognitive judgments—that is, to evaluate their own process of learning—students tended to rate interleaved assignments as more challenging and yielding less mastery (Table 2 ). For both practice types, the largest proportion of students’ judgments of difficulty spanned from the “medium” to “difficult” categories, but a higher proportion of those ratings occurred at the conclusion of interleaved assignments. Correspondingly, for both practice types, the largest proportion of students’ judgments of learning spanned from “well” to “extremely well,” but a higher proportion of those ratings occurred at the conclusion of blocked assignments. Thus, on interleaved assignments, students performed more poorly, experienced greater difficulty, and perceived fewer learning benefits. On the basis of these findings, one might predict that student performance on a delayed test of the practiced topics would suffer.

How did interleaving and blocking affect learning as measured on the criterial tests?

Belying the patterns observed on the homework assignments, however, students who had completed interleaved assignments well outperformed those who had completed blocked assignments on the surprise criterial tests. Interleaving yielded higher criterial test scores than blocking in Stage 1, d  = 0.40, 95% CI [0.17, 0.65], t (288) = 3.41, p  = 0.0008, and in Stage 2, d  = 0.91, 95% CI [0.66, 1.20], t (284) = 7.68, p  < 0.0001. Thus, interleaving improved the ability to correctly recall and use prior knowledge in an attempt to generate solutions to novel problems. Inspection of the full distributions of test scores further confirms the occurrence of strong interleaving benefits (see Fig. 2 ). Specifically, interleaving improved median test scores over-blocking by 50% and 125% in Stages 1 and 2, respectively (i.e., interleaving improved learning across both halves of the course and in both counterbalanced groups). In Stage 2, when students had twice as much course content to draw upon (including topics that were arguably more difficult than those that were presented during Stage 1), the effect size of the interleaving advantage was larger.

Each histogram displays the distributions of criterial test scores in a given stage, with green representing performance in the interleaved condition and purple representing performance in the blocked condition. The median score in each condition is included as a vertical bar of the corresponding color. Histograms are normalized so that in each condition, the sums of values of all bins equals 1. Mean performance in Stages 1 and 2, respectively, was 0.43 and 0.27 in the blocked condition and 0.54 and 0.47 in the interleaved condition.

For additional insights into the effects of interleaving, we examined two distinct sub-measures of test performance: (a) whether students were able to correctly recall necessary formulas, which relies on long-term memory, and (b) whether students’ solution strategies yielded an exact match to the correct answer both in numerical value and in units, which is a more stringent measure of problem-solving ability (as it necessitated devising a multi-step problem-solving strategy and executing its associated computations without making a single error). It should be noted, however, that producing precisely correct answers is uncommon in many introductory-level physics courses due to the inherent conceptual difficulty and computational complexity of the material; in line with that expectation, the mean rate of correct answers, across both conditions, was no >0.34 proportion correct. Sub-measure analyses revealed that interleaving improved long-term memory in Stage 1, d  = 0.41, 95% CI [0.17, 0.66], t (288) = 3.49, p  = 0.006, and in Stage 2, d  = 0.96, 95% CI [0.70, 1.24], t (284) = 8.05, p  < 0.0001. Further, interleaving improved the correctness of answers in Stage 1, d  = 0.25, 95% CI [0.02, 0.48], t (288) = 2.17, p  = 0.0311, and in Stage 2, d  = 0.40, 95% CI [0.16, 0.64], t (284) = 3.32, p  = 0.0010. Thus, interleaving enhanced both memory and problem-solving accuracy.

Results at the level of individual problems (Table 3 ) also showed the advantages of interleaving. These advantages were the most consistent (i.e., across both sub-measures) for the easiest problem in each stage (which addressed one as opposed to two topics). Overall, interleaving yielded at least a numerical advantage on both sub-measures for all three problems on both criterial tests.

How did interleaving and blocking affect learning and study behaviors in the remainder of the course?

On high-stakes midterm exams occurring 3 days after each criterial test, scores did not significantly differ between the blocked and interleaved conditions (post-Stage 1 midterm, d  = 0.20, 95% CI [−0.04, 0.43], t (288) = 1.68, p  = 0.0944), and post-Stage 2 midterm, d  = 0.02, 95% CI [−0.21, 0.25], t (284) = 0.16, p  = 0.8758). Only in Stage 1 was there a hint of an interleaving benefit on the high-stakes exams (as most students did not complete the final exam due to a pandemic-induced campus closure, that exam was not analyzed). Although these patterns suggest a possible limitation on the efficacy of interleaving, there were factors that called into question the diagnosticity of the midterm exams, and these factors led us to include surprise criterial tests as our primary outcome measures. Specifically, exit surveys confirmed that most students engaged in extensive cramming prior to the midterms, but not before the criterial tests (Table 4 ). Further, the criterial tests were a potentially powerful learning event that previewed the problem format and scope on the midterms and likely influenced students’ study behaviors. These observations are consistent with the fact that the mean proportion correct on midterms (0.74) was high compared with the criterial tests (0.42). Thus, although the benefits of interleaving were not detected on midterm exams, any such benefits may have been occluded by cramming and practice testing.

With respect to the potential effects of interleaving and blocking on study behaviors, there were no significant self-reported study time differences between the two conditions (Table 3 ). Rather, the most common pattern across both conditions involved minimal studying prior to the criterial test (≤3 h over 4 weeks) and intense studying between the criterial tests and midterms (≥10 h over 3 days). Such cramming is almost universal among student study behaviors 41 . These patterns suggest that the benefits of interleaving on the criterial tests cannot be attributed to interleaving-induced changes in the volume of studying, but rather to qualitative changes in the learning that occurred during the completion of the homework assignments.

The present results reveal that interleaving can indeed enhance memory and problem-solving ability in the domain of undergraduate physics. Specifically, the use of homework assignments wherein problem types were interleaved, as opposed to conventionally blocked, generated learning improvements on two surprise criterial tests that were comprised of novel and more challenging problems. Such improvements were, in effect size terms, relatively large compared with other pedagogical techniques 42 , 43 (despite some variation across stages and across problems) and comparable to interleaving-induced improvements in such domains as middle-school mathematics 31 , 33 and second language learning 2 , 28 . Further, learning benefits were observed (a) for the case of long-term memory for factual content, (b) for the correctness of answers, (c) after retention intervals of at least one to several weeks, and (d) on surprise criterial tests but not on subsequent high-stakes exams. From the perspective of the literature on interleaving and related techniques (e.g., variability during practice) 44 , 45 , 46 , the present results bolster the conclusion that the benefits of alternating between topics or skills during learning extend well beyond the ability to classify perceptual category exemplars; these benefits can also encompass certain problem-solving skills. Moreover, the present results suggest that the avoidance of supposed preconditions for effective learning—including learning topics in isolation 4 , successive exposures to the same concept 5 , and single-session repetition practice 9 —may not be detrimental for learning. Rather, in line with pedagogical perspectives that encourage variability of practice 1 , 2 , violating those preconditions may in fact enhance learning. That tentative conclusion may validate the practices of instructors that already incorporate some form of interleaving in their homework assignments, but may not necessarily be aware of it as an evidence-supported learning technique.

Several theoretical mechanisms may account for the observed benefits of interleaving. Here, we summarize five candidates. These explanatory accounts are not necessarily mutually exclusive and have been largely drawn from the literature on interleaving, with some adaptations to problem-solving in introductory physics.

First, interleaving may have facilitated inductive learning of problem categories defined by specific physical concepts or principles. These categories, whose correct identification was necessary to solve criterial test problems, are often easily confusable to novice physics learners, who tend to base their problem representations on literal features instead of abstract principles 47 . The course progressed in a hierarchical manner whereby problems across topics commonly shared literal features, but problem classification was never explicitly discussed; hence, any inductive learning of problem categories would most likely have occurred during practice on homework sets. As has been repeatedly demonstrated in the literature (e.g., the attention bias and discriminative contrast framework), inductive learning of confusable perceptual categories is a context wherein interleaving can excel relative to blocking 12 , 13 , 23 , 24 . It is plausible that the interleaved homework sets, which provided more opportunities to compare non-isomorphic problem categories than the blocked homework sets, yielded similar benefits. However, it is important to note that the criterial tests required additional problem-solving steps, including memory retrieval of formulas. As such, inductive learning of problem categories alone might not be sufficient to explain the observed results.

Second, as previously noted, interleaving incorporates distributed practice (i.e., learning spread out over multiple sessions), which is known to improve long-term memory 10 . According to the study-phase retrieval account of the spacing effect, distributed practice during homework sets may have forced students to engage in repeated long-term memory retrieval processes, which are known to enhance the durability and accessibility of memories 3 . In contrast, with blocking, every successive set of three homework problems involved the same topic, thus allowing students to bypass memory retrieval in favor of knowledge temporarily held in working memory (i.e., repeatedly reusing the same solutions). Hence, productive memory retrieval processes may have been attenuated in the blocked condition, potentially reducing the rate of successfully recalling correct formulas on criterial tests, even in the case that the problem solver had achieved a correct conceptual classification of the problem. Other cognitive processes that distributed practice may engage, such as increased encoding of varied contextual cues, may have also had a facilitative effect on learning 48 .

Relatedly, there is evidence in the interleaving literature to support both minimal and major roles of distributed practice depending on the learning context. In the case of perceptual category learning, conditions that feature extensive amounts of distributed practice in the absence of interleaving have failed to yield similar learning benefits 13 , 15 , which suggests a minimal role, whereas, in studies involving mathematics or second language learning, interleaving schedules that incorporate substantial amounts of distributed practice have yielded larger benefits, which suggests a major role 2 , 24 . It is important to note, however, that differences in experimental and task design across studies may have also been factors.

A third explanation involves reduced lag-to-test—that is, elapsed time from practice to assessment—in the interleaved versus blocked conditions. In the present study, each interleaved topic was practiced across a 1-week period following its introduction, whereas each blocked topic was practiced only shortly after its introduction. The interleaved condition, therefore, had more recent exposure (by up to 1 week) on at least one topic per problem at the time of the criterial test, although the lags in both conditions were still at least 1–3 weeks long. It should be noted, however, that having students review to-be-tested topics shortly before a criterial test, which might be expected to attenuate differences in lag-to-test, has not eliminated the interleaving benefit in recent math learning studies 33 .

Fourth, by allowing students to mentally compare different types of problems, interleaving may have fostered more relational processing 3 , potentially improving the ability to integrate concepts from superficially distinct problem categories in order to solve criterial test problems that combined non-isomorphic problem types (see Fig. 1 ). These problem types were merged through shared concepts, such as emitted radiation power, and not recognizing these connections would have rendered the problems unsolvable. Recognition of common concepts may have been more likely in the interleaved condition due to the inclusion of non-isomorphic problem types on each homework assignment, whereas in the blocked condition, students would have had to deliberately juxtapose different homework sets in order to find the relevant connections. The potential for increased relational processing in the interleaved condition might also be described as an instance of material-appropriate processing — that is, cognitive processes that match that needed to perform well on a criterial test 49 (in the present case, integrating non-isomorphic problem types via specific, connecting concepts) and are not redundant with other processes that may already be occurring.

Finally, given that every successive problem on the interleaved homework assignments involved a different topic, interleaving may have given students practice in strategy selection—that is, choosing the correct solution for a given problem from a range of possible options 3 , 21 , 50 . In contrast, the predictability of blocked assignments obviated any need to engage in strategy selection (as students could repeatedly use the same solutions with a high degree of success). Proficiency in strategy selection was crucial for all criterial test problems.

It should be reiterated, however, that none of the accounts presented here are mutually exclusive (e.g., improvements in inductive learning of problem categories and/or relational processing may have facilitated better strategy selection), nor was it the purpose of the present study to adjudicate between them. Any or all of these mechanisms may have jointly contributed to the efficacy of interleaving.

Although the present results are quite clear with respect to an interleaving benefit for memory, the results for “far” transfer of learning 37 —which in the present case involved combining information across topics in order to devise new solution strategies—are more equivocal. If such transfer is to be judged based on numerical and unit correctness, then there was, in effect size terms, a smaller benefit of interleaving relative to the recall of relevant formulas and principles. However, a high level of correct responding was not expected, and the correctness sub-measure could not fully capture the degree to which students were able to successfully transfer their learning (i.e., that measure could not account for better, but imperfect, solution strategies). In our view, further research using more fine-grained measures of problem-solving ability (e.g., having students delineate each solution step, which would have required longer test sessions, and then subjecting those steps to analysis) is needed to clarify the potential of interleaving for far transfer and whether the technique is competitive with other transfer-enhancing approaches 47 , 51 .

The disparity between homework and criterial test data—wherein interleaving initially yielded poorer performance and lower difficulty and efficacy ratings, yet better criterial test performance—illustrates a metacognitive illusion 52 that may complicate student acceptance of interleaving. That illusion reflects the tendency of human beings to be inaccurate at judging the progress of their own learning and the relative utility of contrasting pedagogical activities (with more effective techniques being judged as less beneficial and vice versa) 53 . In response, instructors might consider additional measures, such as explaining the long-term benefits of interleaving prior to administering homework assignments 54 . Fortunately, there did not seem to be an overtly hostile reception towards interleaving, at least as conveyed to the course instructor, and student evaluations of the course were also relatively unchanged versus prior iterations of the course taught by the same instructor.

From an application standpoint, it is promising that the methods used in the present study were relatively simple and could be adapted to other contexts wherein multiple topics are learned using blocked homework assignments. Simply interleaving those assignments in a similar fashion may greatly enhance their effectiveness. We wish to caution, however, that instructors and researchers will need to be careful in generalizing the present results to cases wherein assignments do not contain multiple isomorphic or nearly isomorphic problems for each topic, and it is unclear whether such interleaving benefits will be apparent on high-stakes exams after extensive cramming (especially when considering the tendency of some laboratory-developed learning interventions to “wash out” in classroom contexts) and practice exams 55 . If no such benefits reliably occur, then that would constitute a notable limitation, particularly if enhancing exam performance was the sole objective. However, it remains to be determined whether a larger interleaving benefit would be observed in cases where practice exams were more substantially different than subsequent high-stakes exams, as well as after high-stakes exams, during which any benefits of cramming may have dissipated. Finally, implementation issues 56 such as the relative predictability of interleaving schedules 28 and the point during the learning process that interleaving is introduced 2 , 21 remain to be resolved. Given the incipient state of the classroom-focused interleaving literature, real-world uses of interleaving will inevitably involve a certain amount of trial-and-error.

From the perspective of undergraduate physics education and other forms of STEM learning, the present results serve as a proof-of-concept for a relatively low-cost learning intervention (in terms of time required and necessary equipment) that has the potential to yield sizeable learning benefits. The finding that interleaving benefits learning for one of the most challenging subjects that college students have to master, and does so for the case of relatively difficult problem-solving materials, invites a reevaluation of conventional instructional approaches and a greater appreciation for the influence of practice schedules in the development of skills and expertise. Indeed, it is becoming increasingly apparent that there are a variety of educationally authentic contexts in which human learners benefit more from practicing multiple topics from a given domain at one time, rather than practicing one topic at one time.

Preregistration

The study design and analysis plan were preregistered prior to data collection at: https://osf.io/8t4e5/ . Of the analyses described in the main text, the preregistered analysis plan contains the only comparison of overall criterial test and midterm exam performance across conditions. All other analyses, including performance on course assignments, accompanying judgments of learning, and exit survey analysis, were planned after preregistration but before data collection and should be regarded as exploratory.

Participants

Participants were 350 undergraduate students enrolled in either of two back-to-back lecture sections of Physics 5 C (“Physics for Life Sciences Majors: Electricity, Magnetism, and Modern Physics”) at the University of California, Los Angeles (UCLA) in Winter 2020, which began on 6 January 2020 and ended on 20 March 2020. Per the preregistered inclusion criteria, any student that did not complete any homework assignment during Stage 1 (weeks 1–4) or Stage 2 (weeks 5–8) or that did not take the associated criterial test was removed from the data analyses for the corresponding stage of the study. Consequently, in Stage 1, analyses were performed using data from 139 students in the first lecture section and 151 students in the second lecture section (henceforth, referred to as Lecture 1 and Lecture 2, respectively). In Stage 2, 137 students in Lecture 1 and 149 students in Lecture 2 were included in the analyses. Demographic information for all students included in the data analyses is listed in Supplementary Table 1 . It should be noted that there was no significant difference in mean GPA between students in Lecture 1 and Lecture 2. Thus, despite the fact that students enrolled in the lecture section of their choice (often based on their schedule of availability and preference for time-of-day), any potential differences in academic aptitude between the students in the two lecture sections were likely to have been negligible.

The study was approved by the UCLA Human Research Protection Program as exempt from formal review. No written informed consent was required for data collected during the course of normal instruction and reported in a fully anonymous and summary fashion as occurs in this manuscript. Informed consent was obtained for any individually identifiable reporting of data, of which there are none in this manuscript.

Course description

Physics 5 C is a 10-week lower-division course that is the third in a sequence of required physics courses for life sciences majors at UCLA. The official description of the course states that it addresses: “Electrostatics in vacuum and in water. Electricity, circuits, magnetism, quantum, atomic and nuclear physics, radioactivity, with applications to biological and biochemical systems.” In Winter 2020, the course involved thrice-weekly lecture sections of 50 min each (Lecture 1 from 10 to 10:50 AM and Lecture 2 from 11 to 11:50 AM; each student was enrolled in either of those sections), a weekly discussion section with a duration of 50 min, and a weekly laboratory section with a duration of 110 min. Both lecture sections were taught by the first author of this manuscript (J.S.), a faculty member in the Department of Physics and Astronomy at UCLA, on Mondays, Wednesdays, and Fridays. The discussion and laboratory sections, of which there were multiple sections available each week, were taught by graduate teaching assistants and collaborative problem-solving therein was further facilitated by undergraduate learning assistants.

Grading in Physics 5 C during Winter 2020 was determined via participation questions administered during the lecture sections (5%), discussion section assignments (5%), thrice-weekly homework assignments (20%), laboratory activities (15%), and two midterm exams (22.5% each). Participation questions and homework assignments were completed individually, whereas the remaining graded components were completed entirely or partly in groups. A cumulative final exam was originally scheduled and intended to be the most heavily-weighted aspect of the course (30%); however, that exam was removed from the required list of graded components and was made optional due to COVID-19 pandemic-induced suspension of all in-person instruction at UCLA on 11 March 2020. Importantly, the experimental manipulation and all primary measures of interest (i.e., the criterial tests) had been completed and were unaffected by the time in-person instruction was suspended.

Study materials are archived at the Open Science Framework (OSF): https://osf.io/8t4e5/ . Course materials were drawn from the assigned textbook (University Physics for the Life Sciences by Knight, Jones and Field), which is a common textbook for undergraduate physics courses in the United States. A list of topics covered during weeks 1–8 of the course is presented in Table 1 . There were 30 topics per experimental stage. Each lecture covered topics that roughly corresponded to between 1 and 3 sections of the course textbook. Each lecture began with an outline of what was to be learned followed by explanations of key concepts, worked examples, and clicker questions that were often accompanied by peer instruction. Discussion sections consisted of a short review of relevant topics from that week followed by a group exercise involving a single, reasonably challenging corresponding problem on a worksheet. Students were given credit for attending discussion sections and for demonstrating a reasonable level of effort and completion on the weekly problem as judged by their teaching assistant, but discussion worksheets were not scored for correctness. Weekly labs gave students hands-on experience applying course concepts to real physical systems and typically involved materials that had already been covered a week or two beforehand in lecture and on homework assignments.

Both experimental stages featured 10 homework assignments each spread across 4 weeks. There were nine problems per assignment (exceptions included the last two assignments of the blocked condition as well as the first two and last three assignments of the interleaved condition), for a total of 84 homework problems (see Fig. 1 and the main text). There were three isomorphic problems for a given topic (excepting six topics per experimental stage, for which there were two isomorphic problems). It should be noted that given the constraints used to define blocking and interleaving, the interleaved condition had fewer problems on the first two assignments per cycle (given the number of topics introduced to date), and on the final week of a given cycle, the interleaved condition had one additional problem per assignment and up to two problems per topic (but not presented adjacent to one another), with the blocked condition also having fewer than nine problems each. Given the proximity to the end of each cycle and variations in assignment length, topics that appeared on the final week of assignments were not included on the criterial tests.

Each assignment took the form of a multi-page PDF uploaded to Gradescope (a web application for turning in and scoring assignments) on a Monday, Wednesday, or Friday of a given week. Each assignment contained instructions reminding students to complete each assignment on their own, avoid skipping problems, always show their work in the provided spaces (so as to receive completion credit), and clearly indicate their final answers in provided boxes. Each problem type consisted of using a concept and related formulas to compute the values of one or more physical quantities. Isomorphs for each problem type was generated by varying superficial features that left the underlying computational and conceptual structure invariant, such as by changing values for given physical quantities or changing the context in which the given information was presented.

The final page of each assignment contained three multiple-choice survey questions: (a) How difficult did you find the questions on this assignment?; (b) Over how many days did you complete this assignment?; and (c) How well do you think you have learned the concepts and procedures addressed by these problems?

There were three assignments each week except in weeks 3 and 7, during which there was no class on Monday owing to a holiday. This holiday fell on precisely the same day in the practice schedule during each stage, so the two stages had identical problem set schedules despite the holidays.

Both criterial tests were intended to be completed within a 50-min lecture period and contained three questions each. The formatting of the tests, which were administered in pen (or pencil)-and-paper form, mirrored the homework assignments in that there were provided spaces and boxes to show work and to indicate final answers. Critically, however, the criterial test problems required integrating knowledge from two separately-learned topics, or applying knowledge regarding a previously learned topic in a new way (as described in the main text). The topics addressed on the criterial tests are noted in Fig. 1 of the main text. Given the deviations in the number of problems per assignment in the final week of each cycle, as well as the proximity in time between instruction and the criterial test, all topics addressed in that week were not covered on the criterial tests.

Two midterm exams were administered (both occurring on the first Monday after the end of an experimental stage and ~72 h after the criterial test). Each midterm exam contained five problems that were of a similar type as those presented on the criterial tests.

At the end of the course, students were asked to complete an online exit survey in exchange for extra credit. The survey contained questions addressing (a) how the homework assignments were completed; (b) study activities that occurred prior to the surprise and midterm exams; (c) level of surprise in the surprise exams, and (d) prior physics courses. Questions addressing (a–c) were posed separately for Stages 1 and 2. A complete copy of the exit survey is archived at the aforementioned OSF link.

Design and procedure

A 2 × 2 counterbalanced design was used with within-subjects factors of condition (blocked vs. interleaved) and Stage (1 vs. 2). Blocking versus interleaving was manipulated by having one lecture section experience blocking and interleaving during Stages 1 and 2, respectively, whereas the other section experienced the reverse of that arrangement. The experiment was implemented as part of regular course activities as follows. On the first day of class, the instructor outlined course expectations as described in the syllabus. The substantial contribution of homework assignments to the course grade was emphasized (and to further incentivize completion of homework assignments, an additional 1% extra credit bonus was promised to all students that completed every single homework assignment). Homework assignments were then released regularly online on each Monday, Wednesday, and Friday (during weeks 1–4 and 5–8, and excepting the Friday of weeks 4 and 8). Each assignment was to be completed within 72 h of it being made available, and finished assignments were to be scanned and uploaded to Gradescope for grading. Fully worked solutions and answers for each assignment were posted each Sunday evening. Grades, rubrics, and answer keys for each assignment were posted on Gradescope within roughly 1 week of the due date. All other course activities, including the lectures, discussion sections, and lab sections, proceeded as per standard practice. The course instructor delivered identical lecture content to both sections throughout the entire course.

During the lecture sections on the Fridays of weeks 4 and 8, the surprise criterial test was administered. That lecture had been billed as a “review session” addressing the content covered over the preceding 4 weeks, with students incentivized to attend by a promise of 1% extra credit. In place of a review session, however, the test was handed out, students were told that they would get up to 1% extra credit according to their performance on the test (although during the actual assignment of grades, all students were given the full 1% extra credit), and students were then given the full 50-minute lecture period to complete the test. Aside from increasing every student’s final grade by 1%, the criterial tests did not impact student grades. The test was proctored by the course instructor and teaching assistants. Survey data revealed that the majority of students were surprised that the “review session” actually entailed a criterial test (see Table 4 ).

Performance on the blocked and interleaved homework assignments was analyzed to provide insights into the relative difficulty of the two learning schedules used. To facilitate analysis, each students’ intended answers, as indicated by entry into provided answer boxes, were transcribed into an electronic spreadsheet, and the answers were then computer-scored against a correct answer list. In all cases, the transcription of homework data was conducted by research assistants that were blind to the condition. In addition, the answers to the three multiple-choice survey questions on each assignment were also transcribed by hand.

Performance on the criterial tests was the primary outcome of interest given that the criterial tests were the purest measures of the effects of the experimental manipulation (i.e., uncontaminated by any additional study or review activities, or foreknowledge of the question types). Every problem on the criterial tests required (a) recognizing which mathematical relationships (often equations) were relevant for solving that problem, (b) writing those relationships down, and (c) appropriately combining them with given values of physical quantities to compute a single final numerical answer with a corresponding physical unit. A rubric based on that employed throughout lower-division physics courses at UCLA was used to score the criterial tests and allowed for inferring whether steps (a–c) were successfully completed. The rubric items per problem fell into two mutually exclusive, exhaustive categories: In the first, “memory” category, each item indicated whether or not one of the necessary equations was recalled and written down correctly; in the second, “correctness” category, each item indicated whether or not the final numerical answer and unit were correct. Criterial tests were each scored by at least two trained raters that were blind to the condition. Each rubric item for each problem was first scored independently by two scorers, after which a third scorer independently scored only those items on which the original two scorers differed. For each rubric item, inter-rater reliability (IRR) between the original two raters was assessed. In Stages 1 and 2, the mean IRR across all rubric items on the criterial test was Cohen’s κ  = 0.81 and 0.83, respectively.

Null hypothesis significance testing of criterial test data was conducted using t tests as per our preregistered analysis plan. All tests were two-tailed. Effect sizes were reported in terms of Cohen’s d as defined in prior work 57 . As a supplement to the t tests, permutation tests (which do not require the assumption of normality of underlying population distributions) were also conducted. The permutation tests yielded negligibly different p values relative to the t tests and are not detailed further for simplicity.

Performance on the midterm and final exams were originally to be analyzed separately. Performance on these exams would have reflected the effects of the experimental manipulation as well as review and study activities, including cramming, prior to the exams. However, as the final exam was made optional (and switched to take-home format) due to the COVID-19 pandemic, data for that exam were not available for the vast majority of students. Hence, the analysis of that exam was dropped. Per procedures that the instructor had used in prior physics courses, the midterm exams—which were completed at separate exam periods outside of normal lecture hours—were completed in individual and group stages (i.e., students first attempted the questions on their own, they were organized into groups to share ideas and revise their answers). The results reported in the main text reflect data from the individual stages. The midterm exams were scored by teaching assistants that were also blind to condition.

The exit surveys, which provided additional context for interpreting the study results, were transcribed by research assistants that were blind to condition.

Reporting summary

Further information on research design is available in the Nature Research Reporting Summary linked to this article.

Data availability

Data and materials are archived at the OSF: https://osf.io/8t4e5/ .

Code availability

Analysis code is available upon request.

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Acknowledgements

Thanks to the UCLA Teaching and Learning Lab for helpful discussions and Casey Shapiro for helpful advice. Thanks to Shirley Zhang, Quynh Tran, Chester Li, and Nam Phuong Nguyen for assisting with the scoring of criterial tests, and to Jeana Wei and other members of the UCLA Bjork Lab for assisting with transcription of homework assignments. This research was supported by the UCLA Division of Physical Sciences.

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Joshua Samani

Department of Psychology, University of California, Los Angeles, CA, USA

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J.S. and S.C.P. conceptualized and designed the study, J.S. conducted the study and analyzed the data, and J.S. and S.C.P. wrote and edited the manuscript.

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Correspondence to Joshua Samani or Steven C. Pan .

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The Skills We Need to Face the Challenges of 2021

Part 2: we certainly have a lot to deal with this year..

Posted March 10, 2021 | Reviewed by Chloe Williams

In a previous post , we talked about the role of optimism and pessimism in being able to determine the future. How we look at things does have a major impact on what we do and how things turn out in our lives. When we talk to ourselves in an optimistic way we are giving ourselves positive self instructions and predictions about how things will go for us in the future. When we talk to ourselves in a pessimistic way, we are usually making negative predictions about the future and our ability to manage the future. Generally speaking, positive self-instructions work better than negative ones.

We also talked about the importance of remembering that most things, either good or bad, are not permanent. This too will pass. We also discussed the reality that most things do not have a pervasive effect on our lives but a specific one, and that accountability is important but blaming is different and not helpful.

We certainly have a lot to deal with this year. Getting the virus under control and bringing our divided nation together are two of the major issues facing us in 2021. We need to be resilient, remembering that resilience is the power to adapt well to adversity. It is the process of coping with and managing tragedy and crisis in our lives. Resilience is a set of skills and attitudes that we can learn. It is not genetically determined or inherited.

We need each other in this country. In order to come together, we need to be able to communicate well with others and problem solve, both individually and with others. This involves listening and problem-solving skills with the goal being to work as a team member within our community.

We also need to be able to make realistic plans and take action to carry them out. Being able to see what is rather than what we would like to see is part of the skill. Being proactive rather than reactive, being assertive rather than aggressive or passive are all important components of this skill.

Perhaps one of the most important things that we can do to move things forward in this country is to find purpose and meaning in doing it. We need to be able to make sense of what is happening and to find meaning in it. We are a country in crisis. Spiritual and religious practices can often help us create this meaning and purpose. Covid-19 is a crisis, but it's also created opportunities for us. It has forced many of us to break old patterns of behavior and try different ways of dealing with the problems that we are facing. Trying in a different way rather than trying harder in the same way is often the key to making positive change.

There are other skills and attitudes that we need to exercise and to get better at. We will talk more about these in the next post. But for now, remember that being connected to others and being able to communicate with others is critical if we are going to move our lives and our country forward. As we indicated in our earlier post, we need to deal with the strong feelings that come up in this crisis and find ways to express them in a positive way so that they do not cloud our thinking. And we need to find purpose and meaning in the present. Being able to see the big picture is critical as is remembering that few things are permanent and pervasive and to be blamed for the present.

Ron Breazeale, Ph.D. , is the author of Duct Tape Isn’t Enough: Survival Skills for the 21st Century as well as the novel Reaching Home .

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Effects of Online Problem-Solving Instruction and Identification Attitude Toward Instructional Strategies on Students' Creativity

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• 1 College of International Relations, Huaqiao University, Xiamen, China.
• PMID: 34721247
• PMCID: PMC8552024
• DOI: 10.3389/fpsyg.2021.771128

Problem-solving ability is an essential part of daily life. Thus, curiosity and a thirst for knowledge should be cultivated in students to help them develop problem solving and independent thinking skills. Along with positive attitudes and an active disposition, these abilities are needed to solve problems throughout the lifespan and develop -confidence. To achieve educational objectives in the context of globalization, creative ability is necessary for generating competitive advantages. Therefore, creative thinking, critical thinking, and problem-solving ability are important basic competencies needed for future world citizens. Creativity should also be integrated into subject teaching to cultivate students' lifelong learning and a creative attitude toward life. A questionnaire was distributed to 420 students in colleges and universities in Fujian, China. After removing invalid and incomplete responses, 363 copies were found to be valid yielding a response rate of 86%. Findings indicate that the new generation requires high levels of support to develop creativity and integrate diverse subjects such as nature, humanities, and technology. A rich imagination is needed to root creativity in the new generation.

Keywords: affective component; creativity; identification attitude; instructional strategies; online problem.

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Original research article, mathematical problem-solving through cooperative learning—the importance of peer acceptance and friendships.

• 1 Department of Education, Uppsala University, Uppsala, Sweden
• 2 Department of Education, Culture and Communication, Malardalen University, Vasteras, Sweden
• 3 School of Natural Sciences, Technology and Environmental Studies, Sodertorn University, Huddinge, Sweden
• 4 Faculty of Education, Gothenburg University, Gothenburg, Sweden

Mathematical problem-solving constitutes an important area of mathematics instruction, and there is a need for research on instructional approaches supporting student learning in this area. This study aims to contribute to previous research by studying the effects of an instructional approach of cooperative learning on students’ mathematical problem-solving in heterogeneous classrooms in grade five, in which students with special needs are educated alongside with their peers. The intervention combined a cooperative learning approach with instruction in problem-solving strategies including mathematical models of multiplication/division, proportionality, and geometry. The teachers in the experimental group received training in cooperative learning and mathematical problem-solving, and implemented the intervention for 15 weeks. The teachers in the control group received training in mathematical problem-solving and provided instruction as they would usually. Students (269 in the intervention and 312 in the control group) participated in tests of mathematical problem-solving in the areas of multiplication/division, proportionality, and geometry before and after the intervention. The results revealed significant effects of the intervention on student performance in overall problem-solving and problem-solving in geometry. The students who received higher scores on social acceptance and friendships for the pre-test also received higher scores on the selected tests of mathematical problem-solving. Thus, the cooperative learning approach may lead to gains in mathematical problem-solving in heterogeneous classrooms, but social acceptance and friendships may also greatly impact students’ results.

Introduction

The research on instruction in mathematical problem-solving has progressed considerably during recent decades. Yet, there is still a need to advance our knowledge on how teachers can support their students in carrying out this complex activity ( Lester and Cai, 2016 ). Results from the Program for International Student Assessment (PISA) show that only 53% of students from the participating countries could solve problems requiring more than direct inference and using representations from different information sources ( OECD, 2019 ). In addition, OECD (2019) reported a large variation in achievement with regard to students’ diverse backgrounds. Thus, there is a need for instructional approaches to promote students’ problem-solving in mathematics, especially in heterogeneous classrooms in which students with diverse backgrounds and needs are educated together. Small group instructional approaches have been suggested as important to promote learning of low-achieving students and students with special needs ( Kunsch et al., 2007 ). One such approach is cooperative learning (CL), which involves structured collaboration in heterogeneous groups, guided by five principles to enhance group cohesion ( Johnson et al., 1993 ; Johnson et al., 2009 ; Gillies, 2016 ). While CL has been well-researched in whole classroom approaches ( Capar and Tarim, 2015 ), few studies of the approach exist with regard to students with special educational needs (SEN; McMaster and Fuchs, 2002 ). This study contributes to previous research by studying the effects of the CL approach on students’ mathematical problem-solving in heterogeneous classrooms, in which students with special needs are educated alongside with their peers.

Group collaboration through the CL approach is structured in accordance with five principles of collaboration: positive interdependence, individual accountability, explicit instruction in social skills, promotive interaction, and group processing ( Johnson et al., 1993 ). First, the group tasks need to be structured so that all group members feel dependent on each other in the completion of the task, thus promoting positive interdependence. Second, for individual accountability, the teacher needs to assure that each group member feels responsible for his or her share of work, by providing opportunities for individual reports or evaluations. Third, the students need explicit instruction in social skills that are necessary for collaboration. Fourth, the tasks and seat arrangements should be designed to promote interaction among group members. Fifth, time needs to be allocated to group processing, through which group members can evaluate their collaborative work to plan future actions. Using these principles for cooperation leads to gains in mathematics, according to Capar and Tarim (2015) , who conducted a meta-analysis on studies of cooperative learning and mathematics, and found an increase of .59 on students’ mathematics achievement scores in general. However, the number of reviewed studies was limited, and researchers suggested a need for more research. In the current study, we focused on the effect of CL approach in a specific area of mathematics: problem-solving.

Mathematical problem-solving is a central area of mathematics instruction, constituting an important part of preparing students to function in modern society ( Gravemeijer et al., 2017 ). In fact, problem-solving instruction creates opportunities for students to apply their knowledge of mathematical concepts, integrate and connect isolated pieces of mathematical knowledge, and attain a deeper conceptual understanding of mathematics as a subject ( Lester and Cai, 2016 ). Some researchers suggest that mathematics itself is a science of problem-solving and of developing theories and methods for problem-solving ( Hamilton, 2007 ; Davydov, 2008 ).

Problem-solving processes have been studied from different perspectives ( Lesh and Zawojewski, 2007 ). Problem-solving heuristics Pólya, (1948) has largely influenced our perceptions of problem-solving, including four principles: understanding the problem, devising a plan, carrying out the plan, and looking back and reflecting upon the suggested solution. Schoenfield, (2016) suggested the use of specific problem-solving strategies for different types of problems, which take into consideration metacognitive processes and students’ beliefs about problem-solving. Further, models and modelling perspectives on mathematics ( Lesh and Doerr, 2003 ; Lesh and Zawojewski, 2007 ) emphasize the importance of engaging students in model-eliciting activities in which problem situations are interpreted mathematically, as students make connections between problem information and knowledge of mathematical operations, patterns, and rules ( Mousoulides et al., 2010 ; Stohlmann and Albarracín, 2016 ).

Not all students, however, find it easy to solve complex mathematical problems. Students may experience difficulties in identifying solution-relevant elements in a problem or visualizing appropriate solution to a problem situation. Furthermore, students may need help recognizing the underlying model in problems. For example, in two studies by Degrande et al. (2016) , students in grades four to six were presented with mathematical problems in the context of proportional reasoning. The authors found that the students, when presented with a word problem, could not identify an underlying model, but rather focused on superficial characteristics of the problem. Although the students in the study showed more success when presented with a problem formulated in symbols, the authors pointed out a need for activities that help students distinguish between different proportional problem types. Furthermore, students exhibiting specific learning difficulties may need additional support in both general problem-solving strategies ( Lein et al., 2020 ; Montague et al., 2014 ) and specific strategies pertaining to underlying models in problems. The CL intervention in the present study focused on supporting students in problem-solving, through instruction in problem-solving principles ( Pólya, 1948 ), specifically applied to three models of mathematical problem-solving—multiplication/division, geometry, and proportionality.

Students’ problem-solving may be enhanced through participation in small group discussions. In a small group setting, all the students have the opportunity to explain their solutions, clarify their thinking, and enhance understanding of a problem at hand ( Yackel et al., 1991 ; Webb and Mastergeorge, 2003 ). In fact, small group instruction promotes students’ learning in mathematics by providing students with opportunities to use language for reasoning and conceptual understanding ( Mercer and Sams, 2006 ), to exchange different representations of the problem at hand ( Fujita et al., 2019 ), and to become aware of and understand groupmates’ perspectives in thinking ( Kazak et al., 2015 ). These opportunities for learning are created through dialogic spaces characterized by openness to each other’s perspectives and solutions to mathematical problems ( Wegerif, 2011 ).

However, group collaboration is not only associated with positive experiences. In fact, studies show that some students may not be given equal opportunities to voice their opinions, due to academic status differences ( Langer-Osuna, 2016 ). Indeed, problem-solvers struggling with complex tasks may experience negative emotions, leading to uncertainty of not knowing the definite answer, which places demands on peer support ( Jordan and McDaniel, 2014 ; Hannula, 2015 ). Thus, especially in heterogeneous groups, students may need additional support to promote group interaction. Therefore, in this study, we used a cooperative learning approach, which, in contrast to collaborative learning approaches, puts greater focus on supporting group cohesion through instruction in social skills and time for reflection on group work ( Davidson and Major, 2014 ).

Although cooperative learning approach is intended to promote cohesion and peer acceptance in heterogeneous groups ( Rzoska and Ward, 1991 ), previous studies indicate that challenges in group dynamics may lead to unequal participation ( Mulryan, 1992 ; Cohen, 1994 ). Peer-learning behaviours may impact students’ problem-solving ( Hwang and Hu, 2013 ) and working in groups with peers who are seen as friends may enhance students’ motivation to learn mathematics ( Deacon and Edwards, 2012 ). With the importance of peer support in mind, this study set out to investigate whether the results of the intervention using the CL approach are associated with students’ peer acceptance and friendships.

The Present Study

In previous research, the CL approach has shown to be a promising approach in teaching and learning mathematics ( Capar and Tarim, 2015 ), but fewer studies have been conducted in whole-class approaches in general and students with SEN in particular ( McMaster and Fuchs, 2002 ). This study aims to contribute to previous research by investigating the effect of CL intervention on students’ mathematical problem-solving in grade 5. With regard to the complexity of mathematical problem-solving ( Lesh and Zawojewski, 2007 ; Degrande et al., 2016 ; Stohlmann and Albarracín, 2016 ), the CL approach in this study was combined with problem-solving principles pertaining to three underlying models of problem-solving—multiplication/division, geometry, and proportionality. Furthermore, considering the importance of peer support in problem-solving in small groups ( Mulryan, 1992 ; Cohen, 1994 ; Hwang and Hu, 2013 ), the study investigated how peer acceptance and friendships were associated with the effect of the CL approach on students’ problem-solving abilities. The study aimed to find answers to the following research questions:

a) What is the effect of CL approach on students’ problem-solving in mathematics?

b) Are social acceptance and friendship associated with the effect of CL on students’ problem-solving in mathematics?

Participants

The participants were 958 students in grade 5 and their teachers. According to power analyses prior to the start of the study, 1,020 students and 51 classes were required, with an expected effect size of 0.30 and power of 80%, provided that there are 20 students per class and intraclass correlation is 0.10. An invitation to participate in the project was sent to teachers in five municipalities via e-mail. Furthermore, the information was posted on the website of Uppsala university and distributed via Facebook interest groups. As shown in Figure 1 , teachers of 1,165 students agreed to participate in the study, but informed consent was obtained only for 958 students (463 in the intervention and 495 in the control group). Further attrition occurred at pre- and post-measurement, resulting in 581 students’ tests as a basis for analyses (269 in the intervention and 312 in the control group). Fewer students (n = 493) were finally included in the analyses of the association of students’ social acceptance and friendships and the effect of CL on students’ mathematical problem-solving (219 in the intervention and 274 in the control group). The reasons for attrition included teacher drop out due to sick leave or personal circumstances (two teachers in the control group and five teachers in the intervention group). Furthermore, some students were sick on the day of data collection and some teachers did not send the test results to the researchers.

FIGURE 1 . Flow chart for participants included in data collection and data analysis.

As seen in Table 1 , classes in both intervention and control groups included 27 students on average. For 75% of the classes, there were 33–36% of students with SEN. In Sweden, no formal medical diagnosis is required for the identification of students with SEN. It is teachers and school welfare teams who decide students’ need for extra adaptations or special support ( Swedish National Educational Agency, 2014 ). The information on individual students’ type of SEN could not be obtained due to regulations on the protection of information about individuals ( SFS 2009 ). Therefore, the information on the number of students with SEN on class level was obtained through teacher reports.

TABLE 1 . Background characteristics of classes and teachers in intervention and control groups.

Intervention

The intervention using the CL approach lasted for 15 weeks and the teachers worked with the CL approach three to four lessons per week. First, the teachers participated in two-days training on the CL approach, using an especially elaborated CL manual ( Klang et al., 2018 ). The training focused on the five principles of the CL approach (positive interdependence, individual accountability, explicit instruction in social skills, promotive interaction, and group processing). Following the training, the teachers introduced the CL approach in their classes and focused on group-building activities for 7 weeks. Then, 2 days of training were provided to teachers, in which the CL approach was embedded in activities in mathematical problem-solving and reading comprehension. Educational materials containing mathematical problems in the areas of multiplication and division, geometry, and proportionality were distributed to the teachers ( Karlsson and Kilborn, 2018a ). In addition to the specific problems, adapted for the CL approach, the educational materials contained guidance for the teachers, in which problem-solving principles ( Pólya, 1948 ) were presented as steps in problem-solving. Following the training, the teachers applied the CL approach in mathematical problem-solving lessons for 8 weeks.

Solving a problem is a matter of goal-oriented reasoning, starting from the understanding of the problem to devising its solution by using known mathematical models. This presupposes that the current problem is chosen from a known context ( Stillman et al., 2008 ; Zawojewski, 2010 ). This differs from the problem-solving of the textbooks, which is based on an aim to train already known formulas and procedures ( Hamilton, 2007 ). Moreover, it is important that students learn modelling according to their current abilities and conditions ( Russel, 1991 ).

In order to create similar conditions in the experiment group and the control group, the teachers were supposed to use the same educational material ( Karlsson and Kilborn, 2018a ; Karlsson and Kilborn, 2018b ), written in light of the specified view of problem-solving. The educational material is divided into three areas—multiplication/division, geometry, and proportionality—and begins with a short teachers’ guide, where a view of problem solving is presented, which is based on the work of Polya (1948) and Lester and Cai (2016) . The tasks are constructed in such a way that conceptual knowledge was in focus, not formulas and procedural knowledge.

Implementation of the Intervention

To ensure the implementation of the intervention, the researchers visited each teachers’ classroom twice during the two phases of the intervention period, as described above. During each visit, the researchers observed the lesson, using a checklist comprising the five principles of the CL approach. After the lesson, the researchers gave written and oral feedback to each teacher. As seen in Table 1 , in 18 of the 23 classes, the teachers implemented the intervention in accordance with the principles of CL. In addition, the teachers were asked to report on the use of the CL approach in their teaching and the use of problem-solving activities embedding CL during the intervention period. As shown in Table 1 , teachers in only 11 of 23 classes reported using the CL approach and problem-solving activities embedded in the CL approach at least once a week.

Control Group

The teachers in the control group received 2 days of instruction in enhancing students’ problem-solving and reading comprehension. The teachers were also supported with educational materials including mathematical problems Karlsson and Kilborn (2018b) and problem-solving principles ( Pólya, 1948 ). However, none of the activities during training or in educational materials included the CL approach. As seen in Table 1 , only 10 of 25 teachers reported devoting at least one lesson per week to mathematical problem-solving.

Tests of Mathematical Problem-Solving

Tests of mathematical problem-solving were administered before and after the intervention, which lasted for 15 weeks. The tests were focused on the models of multiplication/division, geometry, and proportionality. The three models were chosen based on the syllabus of the subject of mathematics in grades 4 to 6 in the Swedish National Curriculum ( Swedish National Educational Agency, 2018 ). In addition, the intention was to create a variation of types of problems to solve. For each of these three models, there were two tests, a pre-test and a post-test. Each test contained three tasks with increasing difficulty ( Supplementary Appendix SA ).

The tests of multiplication and division (Ma1) were chosen from different contexts and began with a one-step problem, while the following two tasks were multi-step problems. Concerning multiplication, many students in grade 5 still understand multiplication as repeated addition, causing significant problems, as this conception is not applicable to multiplication beyond natural numbers ( Verschaffel et al., 2007 ). This might be a hindrance in developing multiplicative reasoning ( Barmby et al., 2009 ). The multi-step problems in this study were constructed to support the students in multiplicative reasoning.

Concerning the geometry tests (Ma2), it was important to consider a paradigm shift concerning geometry in education that occurred in the mid-20th century, when strict Euclidean geometry gave way to other aspects of geometry like symmetry, transformation, and patterns. van Hiele (1986) prepared a new taxonomy for geometry in five steps, from a visual to a logical level. Therefore, in the tests there was a focus on properties of quadrangles and triangles, and how to determine areas by reorganising figures into new patterns. This means that structure was more important than formulas.

The construction of tests of proportionality (M3) was more complicated. Firstly, tasks on proportionality can be found in many different contexts, such as prescriptions, scales, speeds, discounts, interest, etc. Secondly, the mathematical model is complex and requires good knowledge of rational numbers and ratios ( Lesh et al., 1988 ). It also requires a developed view of multiplication, useful in operations with real numbers, not only as repeated addition, an operation limited to natural numbers ( Lybeck, 1981 ; Degrande et al., 2016 ). A linear structure of multiplication as repeated addition leads to limitations in terms of generalization and development of the concept of multiplication. This became evident in a study carried out in a Swedish context ( Karlsson and Kilborn, 2018c ). Proportionality can be expressed as a/b = c/d or as a/b = k. The latter can also be expressed as a = b∙k, where k is a constant that determines the relationship between a and b. Common examples of k are speed (km/h), scale, and interest (%). An important pre-knowledge in order to deal with proportions is to master fractions as equivalence classes like 1/3 = 2/6 = 3/9 = 4/12 = 5/15 = 6/18 = 7/21 = 8/24 … ( Karlsson and Kilborn, 2020 ). It was important to take all these aspects into account when constructing and assessing the solutions of the tasks.

The tests were graded by an experienced teacher of mathematics (4 th author) and two students in their final year of teacher training. Prior to grading, acceptable levels of inter-rater reliability were achieved by independent rating of students’ solutions and discussions in which differences between the graders were resolved. Each student response was to be assigned one point when it contained a correct answer and two points when the student provided argumentation for the correct answer and elaborated on explanation of his or her solution. The assessment was thus based on quality aspects with a focus on conceptual knowledge. As each subtest contained three questions, it generated three student solutions. So, scores for each subtest ranged from 0 to 6 points and for the total scores from 0 to 18 points. To ascertain that pre- and post-tests were equivalent in degree of difficulty, the tests were administered to an additional sample of 169 students in grade 5. Test for each model was conducted separately, as students participated in pre- and post-test for each model during the same lesson. The order of tests was switched for half of the students in order to avoid the effect of the order in which the pre- and post-tests were presented. Correlation between students’ performance on pre- and post-test was .39 ( p < 0.000) for tests of multiplication/division; .48 ( p < 0.000) for tests of geometry; and .56 ( p < 0.000) for tests of proportionality. Thus, the degree of difficulty may have differed between pre- and post-test.

Measures of Peer Acceptance and Friendships

To investigate students’ peer acceptance and friendships, peer nominations rated pre- and post-intervention were used. Students were asked to nominate peers who they preferred to work in groups with and who they preferred to be friends with. Negative peer nominations were avoided due to ethical considerations raised by teachers and parents ( Child and Nind, 2013 ). Unlimited nominations were used, as these are considered to have high ecological validity ( Cillessen and Marks, 2017 ). Peer nominations were used as a measure of social acceptance, and reciprocated nominations were used as a measure of friendship. The number of nominations for each student were aggregated and divided by the number of nominators to create a proportion of nominations for each student ( Velásquez et al., 2013 ).

Statistical Analyses

Multilevel regression analyses were conducted in R, lme4 package Bates et al. (2015) to account for nestedness in the data. Students’ classroom belonging was considered as a level 2 variable. First, we used a model in which students’ results on tests of problem-solving were studied as a function of time (pre- and post) and group belonging (intervention and control group). Second, the same model was applied to subgroups of students who performed above and below median at pre-test, to explore whether the CL intervention had a differential effect on student performance. In this second model, the results for subgroups of students could not be obtained for geometry tests for subgroup below median and for tests of proportionality for subgroup above median. A possible reason for this must have been the skewed distribution of the students in these subgroups. Therefore, another model was applied that investigated students’ performances in math at both pre- and post-test as a function of group belonging. Third, the students’ scores on social acceptance and friendships were added as an interaction term to the first model. In our previous study, students’ social acceptance changed as a result of the same CL intervention ( Klang et al., 2020 ).

The assumptions for the multilevel regression were assured during the analyses ( Snijders and Bosker, 2012 ). The assumption of normality of residuals were met, as controlled by visual inspection of quantile-quantile plots. For subgroups, however, the plotted residuals deviated somewhat from the straight line. The number of outliers, which had a studentized residual value greater than ±3, varied from 0 to 5, but none of the outliers had a Cook’s distance value larger than 1. The assumption of multicollinearity was met, as the variance inflation factors (VIF) did not exceed a value of 10. Before the analyses, the cases with missing data were deleted listwise.

What Is the Effect of the CL Approach on Students’ Problem-Solving in Mathematics?

As seen in the regression coefficients in Table 2 , the CL intervention had a significant effect on students’ mathematical problem-solving total scores and students’ scores in problem solving in geometry (Ma2). Judging by mean values, students in the intervention group appeared to have low scores on problem-solving in geometry but reached the levels of problem-solving of the control group by the end of the intervention. The intervention did not have a significant effect on students’ performance in problem-solving related to models of multiplication/division and proportionality.

TABLE 2 . Mean scores (standard deviation in parentheses) and unstandardized multilevel regression estimates for tests of mathematical problem-solving.

The question is, however, whether CL intervention affected students with different pre-test scores differently. Table 2 includes the regression coefficients for subgroups of students who performed below and above median at pre-test. As seen in the table, the CL approach did not have a significant effect on students’ problem-solving, when the sample was divided into these subgroups. A small negative effect was found for intervention group in comparison to control group, but confidence intervals (CI) for the effect indicate that it was not significant.

Is Social Acceptance and Friendships Associated With the Effect of CL on Students’ Problem-Solving in Mathematics?

As seen in Table 3 , students’ peer acceptance and friendship at pre-test were significantly associated with the effect of the CL approach on students’ mathematical problem-solving scores. Changes in students’ peer acceptance and friendships were not significantly associated with the effect of the CL approach on students’ mathematical problem-solving. Consequently, it can be concluded that being nominated by one’s peers and having friends at the start of the intervention may be an important factor when participation in group work, structured in accordance with the CL approach, leads to gains in mathematical problem-solving.

TABLE 3 . Mean scores (standard deviation in parentheses) and unstandardized multilevel regression estimates for tests of mathematical problem-solving, including scores of social acceptance and friendship in the model.

In light of the limited number of studies on the effects of CL on students’ problem-solving in whole classrooms ( Capar and Tarim, 2015 ), and for students with SEN in particular ( McMaster and Fuchs, 2002 ), this study sought to investigate whether the CL approach embedded in problem-solving activities has an effect on students’ problem-solving in heterogeneous classrooms. The need for the study was justified by the challenge of providing equitable mathematics instruction to heterogeneous student populations ( OECD, 2019 ). Small group instructional approaches as CL are considered as promising approaches in this regard ( Kunsch et al., 2007 ). The results showed a significant effect of the CL approach on students’ problem-solving in geometry and total problem-solving scores. In addition, with regard to the importance of peer support in problem-solving ( Deacon and Edwards, 2012 ; Hwang and Hu, 2013 ), the study explored whether the effect of CL on students’ problem-solving was associated with students’ social acceptance and friendships. The results showed that students’ peer acceptance and friendships at pre-test were significantly associated with the effect of the CL approach, while change in students’ peer acceptance and friendships from pre- to post-test was not.

The results of the study confirm previous research on the effect of the CL approach on students’ mathematical achievement ( Capar and Tarim, 2015 ). The specific contribution of the study is that it was conducted in classrooms, 75% of which were composed of 33–36% of students with SEN. Thus, while a previous review revealed inconclusive findings on the effects of CL on student achievement ( McMaster and Fuchs, 2002 ), the current study adds to the evidence of the effect of the CL approach in heterogeneous classrooms, in which students with special needs are educated alongside with their peers. In a small group setting, the students have opportunities to discuss their ideas of solutions to the problem at hand, providing explanations and clarifications, thus enhancing their understanding of problem-solving ( Yackel et al., 1991 ; Webb and Mastergeorge, 2003 ).

In this study, in accordance with previous research on mathematical problem-solving ( Lesh and Zawojewski, 2007 ; Degrande et al., 2016 ; Stohlmann and Albarracín, 2016 ), the CL approach was combined with training in problem-solving principles Pólya (1948) and educational materials, providing support in instruction in underlying mathematical models. The intention of the study was to provide evidence for the effectiveness of the CL approach above instruction in problem-solving, as problem-solving materials were accessible to teachers of both the intervention and control groups. However, due to implementation challenges, not all teachers in the intervention and control groups reported using educational materials and training as expected. Thus, it is not possible to draw conclusions of the effectiveness of the CL approach alone. However, in everyday classroom instruction it may be difficult to separate the content of instruction from the activities that are used to mediate this content ( Doerr and Tripp, 1999 ; Gravemeijer, 1999 ).

Furthermore, for successful instruction in mathematical problem-solving, scaffolding for content needs to be combined with scaffolding for dialogue ( Kazak et al., 2015 ). From a dialogical perspective ( Wegerif, 2011 ), students may need scaffolding in new ways of thinking, involving questioning their understandings and providing arguments for their solutions, in order to create dialogic spaces in which different solutions are voiced and negotiated. In this study, small group instruction through CL approach aimed to support discussions in small groups, but the study relies solely on quantitative measures of students’ mathematical performance. Video-recordings of students’ discussions may have yielded important insights into the dialogic relationships that arose in group discussions.

Despite the positive findings of the CL approach on students’ problem-solving, it is important to note that the intervention did not have an effect on students’ problem-solving pertaining to models of multiplication/division and proportionality. Although CL is assumed to be a promising instructional approach, the number of studies on its effect on students’ mathematical achievement is still limited ( Capar and Tarim, 2015 ). Thus, further research is needed on how CL intervention can be designed to promote students’ problem-solving in other areas of mathematics.

The results of this study show that the effect of the CL intervention on students’ problem-solving was associated with students’ initial scores of social acceptance and friendships. Thus, it is possible to assume that students who were popular among their classmates and had friends at the start of the intervention also made greater gains in mathematical problem-solving as a result of the CL intervention. This finding is in line with Deacon and Edwards’ study of the importance of friendships for students’ motivation to learn mathematics in small groups ( Deacon and Edwards, 2012 ). However, the effect of the CL intervention was not associated with change in students’ social acceptance and friendship scores. These results indicate that students who were nominated by a greater number of students and who received a greater number of friends did not benefit to a great extent from the CL intervention. With regard to previously reported inequalities in cooperation in heterogeneous groups ( Cohen, 1994 ; Mulryan, 1992 ; Langer Osuna, 2016 ) and the importance of peer behaviours for problem-solving ( Hwang and Hu, 2013 ), teachers should consider creating inclusive norms and supportive peer relationships when using the CL approach. The demands of solving complex problems may create negative emotions and uncertainty ( Hannula, 2015 ; Jordan and McDaniel, 2014 ), and peer support may be essential in such situations.

Limitations

The conclusions from the study must be interpreted with caution, due to a number of limitations. First, due to the regulation of protection of individuals ( SFS 2009 ), the researchers could not get information on type of SEN for individual students, which limited the possibilities of the study for investigating the effects of the CL approach for these students. Second, not all teachers in the intervention group implemented the CL approach embedded in problem-solving activities and not all teachers in the control group reported using educational materials on problem-solving. The insufficient levels of implementation pose a significant challenge to the internal validity of the study. Third, the additional investigation to explore the equivalence in difficulty between pre- and post-test, including 169 students, revealed weak to moderate correlation in students’ performance scores, which may indicate challenges to the internal validity of the study.

Implications

The results of the study have some implications for practice. Based on the results of the significant effect of the CL intervention on students’ problem-solving, the CL approach appears to be a promising instructional approach in promoting students’ problem-solving. However, as the results of the CL approach were not significant for all subtests of problem-solving, and due to insufficient levels of implementation, it is not possible to conclude on the importance of the CL intervention for students’ problem-solving. Furthermore, it appears to be important to create opportunities for peer contacts and friendships when the CL approach is used in mathematical problem-solving activities.

Data Availability Statement

The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.

Ethics Statement

The studies involving human participants were reviewed and approved by the Uppsala Ethical Regional Committee, Dnr. 2017/372. Written informed consent to participate in this study was provided by the participants’ legal guardian/next of kin.

Author Contributions

NiK was responsible for the project, and participated in data collection and data analyses. NaK and WK were responsible for intervention with special focus on the educational materials and tests in mathematical problem-solving. PE participated in the planning of the study and the data analyses, including coordinating analyses of students’ tests. MK participated in the designing and planning the study as well as data collection and data analyses.

The project was funded by the Swedish Research Council under Grant 2016-04,679.

Conflict of Interest

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Publisher’s Note

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.

Acknowledgments

We would like to express our gratitude to teachers who participated in the project.

Supplementary Material

The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/feduc.2021.710296/full#supplementary-material

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Keywords: cooperative learning, mathematical problem-solving, intervention, heterogeneous classrooms, hierarchical linear regression analysis

Citation: Klang N, Karlsson N, Kilborn W, Eriksson P and Karlberg M (2021) Mathematical Problem-Solving Through Cooperative Learning—The Importance of Peer Acceptance and Friendships. Front. Educ. 6:710296. doi: 10.3389/feduc.2021.710296

Received: 15 May 2021; Accepted: 09 August 2021; Published: 24 August 2021.

Reviewed by:

Copyright © 2021 Klang, Karlsson, Kilborn, Eriksson and Karlberg. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

*Correspondence: Nina Klang, [email protected]

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Effects of Self-Esteem, Problem-Solving Ability, and Professional Nursing Values on the Career Identity of Nursing College Students in South Korea: A Cross-Sectional Study

1 Graduate Program in System Health Science and Engineering, Ewha Womans University, Seoul 03760, Korea; moc.revan@19sedocsjm

Hyunlye Kim

2 Department of Nursing, College of Medicine, Chosun University, Gwangju 61452, Korea; rk.ca.nusohc@ooygnoyeaj

Jaeyong Yoo

In Korea, the number of admissions to nursing colleges has greatly increased over the past 20 years to address the shortage of nurses. However, many nursing students have unclear career identities during college and stop working in healthcare after graduation. This study aimed to examine the effects of self-esteem, problem-solving ability, and professional nursing values on career identity. The participants were 140 third- and fourth-year nursing students recruited from a university in South Korea. Data were collected between September and October 2019 using a self-administered questionnaire. Data were analyzed using descriptive statistics, t -test, ANOVA, Pearson’s correlation, and multiple linear regression. The results showed significant correlations between satisfaction with college life and major subject, subjective academic achievement, self-esteem, problem-solving ability, professional nursing values, and career identity. The factors that significantly affected career identity were self-esteem and professional nursing values. Nursing educators can support the career development of nursing students by enhancing their self-esteem and professionalism, along with efforts to improve satisfaction with their college life and major.

1. Introduction

The current shortage of nurses is a global health concern, especially during the coronavirus disease (COVID)-19 pandemic. Many countries are making efforts to improve nursing education and working conditions to overcome the undersupply of nurses. However, a more systematic solution is needed [ 1 ]. In South Korea over the past 20 years, the health policy of increasing the number of admissions to nursing colleges had led to an increased supply of licensed nurses. However, there is still a shortage of nurses in the field to such an extent that the number of working nurses per 1000 population remains below 50% of the OECD (Organization for Economic Cooperation and Development) average [ 2 ]. According to OECD statistics 2018, the level of nursing workforce production is at or above the OECD average, while the ratio of clinically working nurses to licensed nurses is about 34.5%, which is only half of the OECD average (65.3%) [ 3 ]. As this extremely low nurse retention rate is related to the high nurse turnover rate, active efforts from various angles are required [ 2 , 4 ]. In particular, the high resignation rate of new nurses suggests that nursing education can play a significant role in this problem.

The COVID-19 pandemic is not only a healthcare crisis, but also an opportunity to reshape the professional identity of nursing students [ 5 ]. A nationwide study conducted in China found that the professional identities of nursing students were strengthened during the COVID-19 pandemic [ 6 ]. Another study examined the professional identity and intention to leave the profession of nursing students during the COVID-19 pandemic. Participants with stronger professional identities intended to remain in nursing and reported an increase in enthusiasm during the pandemic [ 5 ]. Professional identity is important for the education, career development, and retention of students [ 7 , 8 ]. The career identity of college students was found to be closely related to occupational decision-making [ 9 , 10 ]. Therefore, career identity for nursing students is important to produce nurses who can contribute positively to healthcare.

Career identity is a component of self-image, and can be defined as a dynamic multiplicity of internal mental positions or “voices” regarding work [ 11 ]. Career identity is associated with a student’s competence, learning motivation and outcomes, and quality of choices [ 12 ]. The motivation, learning experiences, work performance, and career plans of nursing students are affected by their conceptualization of nursing practice and reasons for choosing the profession [ 13 ]. In a cross-sectional study of nursing students in South Korea, low nursing professionalism, such as a lack of understanding of the roles and responsibilities of nurses or having a negative occupational view, was associated with negative career-related identity and behavior [ 14 ]. Nursing educators should aim to enhance career identity to improve job satisfaction, and support nursing students in their career choices and planning. This study aimed to identify factors that influence career identity, and the results could be used to develop strategies to enhance career identity.

In previous studies of the career identity of nursing students, variables studied included self-esteem, problem-solving ability, professional values/professionalism, and learning experiences in nursing college. Several studies demonstrated that self-esteem correlated positively with the professional self-concept and values of nursing students [ 15 , 16 ]. In recent studies, self-esteem influenced the career identity of Korean nursing students [ 17 , 18 , 19 ]. Self-esteem also predicted the career preparation of nursing students [ 20 ]. Problem-solving ability was related to the maturity and motivation of Korean nursing students [ 21 , 22 ]. Problem-solving ability is one of the essential competencies for nursing students [ 23 ], but it is unclear how it relates to career identity. Another factor that may influence career identity is the conceptualization of the nursing profession. Professional values are the general behavioral principles that determine how well a profession suits an individual and their goals. These values are closely related to career choices [ 24 ]. In previous studies, professional values/professionalism were found to be related to career identity [ 14 , 25 ], and predicted the career plans of nursing students [ 26 ]. Finally, satisfaction with learning activities and academic achievement affected the career identity of nursing students in many previous studies [ 8 , 17 , 19 , 27 , 28 ].

This study evaluated the career identity of nursing students, with the goal of formulating a nursing education strategy to produce nurses who can play an active role during healthcare crises subsequent to the COVID-19 pandemic. We aimed to evaluate the effects of self-esteem, problem-solving ability, and professional values on the career identity of nursing students. The hypothetical model of the variables analyzed in this study is shown in Figure 1 .

A hypothetical model for factors affecting career identity.

2. Materials and Methods

2.1. samples.

The sample of this study was nursing students with an average age of 21.84 years, who were mainly female. This cross-sectional descriptive study used convenience sampling. Students enrolled in a 4-year clinical nursing program were recruited from a university in G city. We included third- and fourth-year nursing students. The sample size required for regression analysis was calculated using G*Power software (version 3.1.9.2; Franz Faul, Universität Kiel, Germany). The required sample size was 119 for three predictors, with a medium effect size of 0.15, significance level of 0.05, and statistical power of 0.95. Only 6 of the 146 questionnaires were excluded because of incomplete responses or missing information, such that 140 were included in the final analysis.

2.2. Data Collection

Data were collected between September and October 2019. This study was approved by the institutional review board of C University (approval No.: 2-1041055-AB-N-01-2019-35; 4 September 2019). We explained the study objectives and procedures to the director of the nursing college and requested their cooperation. The survey was conducted directly by the first author in the classroom with the permission of the educator in charge. Participants were informed regarding the ethical principles of confidentiality, use of data for study purposes only, and freedom to withdraw from the study at any time. All participants gave written consent and completed the self-administered questionnaire, which took 15–20 min. The completed questionnaires were sealed in an envelope. The final enrolled participants were students in the third (56.6%) and fourth (43.4%) years of nursing colleges with similar proportions.

2.3. Variables

2.3.1. general characteristics.

The questionnaire included questions about demographics (age, sex, and years of education), motives for enrolling in nursing college, satisfaction with college life, satisfaction with major subject at the time of admission to nursing college, current satisfaction with major subject, subjective academic achievement, desired career path after graduation, experiences related to college life, and major activities.

2.3.2. Self-Esteem

Self-esteem was measured using the Korean version of the Rosenberg Self-esteem Scale [ 29 , 30 ]. This tool consists of 10 items rated on a five-point Likert scale (1–5: strongly disagree to strongly agree), with higher scores reflecting more positive feelings about the self. Items 3, 5, and 8–10 were reverse-scored. The internal consistency (Cronbach’s α) of this tool was 0.85 in a previous study [ 30 ] and 0.84 in the current study.

2.3.3. Problem-Solving Ability

Problem-solving ability was assessed using the Problem Solving Scale developed by the Korea Educational Development Institute [ 31 ]. This tool is composed of nine sub-components with five items each: problem recognition, information collection, analysis, divergent thinking, decision-making, planning, execution and risk taking, performance evaluation, and feedback. This scale consists of 45 items rated on a five-point Likert scale (1–5: very rarely to very often), with higher scores reflecting greater problem-solving ability. The Cronbach’s α for this tool was 0.94 (0.63–0.77 for sub-components) [ 31 ] at the time of its development and 0.91 (0.58–0.81) in this study. An example of a scale item included in this instrument is as follows: “I first check what the problem is to be solved”.

2.3.4. Professional Nursing Values

Professional nursing values were measured using the Nursing Professional Values Scale, which was developed in Korea and consists of 29 items [ 32 ] and five sub-domains: self-concept of the profession (nine items), social awareness (eight items), nursing professionalism (five items), roles of nursing service (four items), and nursing originality (three items). Each question is rated on a five-point Likert scale (1–5: not at all to very much), with higher scores reflecting greater nursing professionalism. Items 16, 20, and 24 were reverse-scored. The Cronbach’s α for this tool was 0.92 (0.53–0.86 for sub-domains) [ 32 ] at the time of its development and 0.89 (0.46–0.83) in this study. Examples of items on the scale included in this instrument are as follows: “Nurses are considered to be trusted by patients” and “Nurses are known to perform tasks independently and autonomously”.

2.3.5. Career Identity

Career identity was measured using the identity subscale of the Korean version of the My Vocational Situation (MVS) scale [ 33 , 34 ], modified for Korean nursing students [ 34 ]. The scale consists of 14 items, rated on a four-point Likert scale (1–4: strongly disagree to strongly agree). The responses for all items, except question 6, were reverse-scored. Higher scores correlated with a greater sense of career identity. The Cronbach’s α for this tool was 0.88 in a previous study [ 35 ] and 0.87 in this study. An example of a scale item included in this instrument is as follows: “I’m not sure I’ll do well for my chosen nursing profession”.

2.4. Statistical Analyses

Data analyses were performed using SAS statistical software (version 9.4; SAS Institute, Cary, NC, USA). Descriptive statistics, including means, standard deviations, frequencies, and percentages, were used to describe the baseline characteristics and study variables. Differences in variables based on the general characteristics of participants were analyzed using independent t -tests and analysis of variance (ANOVA) with Scheffé post-hoc tests. The relationships between variables were analyzed using Pearson’s correlation coefficient. However, non-parametric tests were performed for self-esteem that was not normally distributed by the Shapiro‒Wilk test ( p = 0.017) and the Q‒Q plot: Mann‒Whitney U test, Kruskal‒Wallis test with Bonfferoni post-hoc tests, and Spearman rank correlation. After the basic assumptions of regression analysis were assessed, multiple linear regression was used to determine the factors that predicted career identity.

3.1. General Characteristics

The average age of the participants was 21.84 ± 1.24 years, and most participants were female (82.5%). The participants were enrolled in the third (56.6%) or fourth (43.4%) year of nursing college. The reasons cited for choosing nursing college were its high employment rate (46.2%), academic performance (20.4%), and interests and aptitudes (19.4%). Satisfaction with college life was reported by 41.4% of participants, and satisfaction with the major subject was reported by 41.4% of participants at the time of admission and 42.1% currently. In terms of subjective academic achievement, a significant proportion of participants (65.0%) reported that they were at an intermediate level. Most participants (75.5%) wanted to work as a hospital nurse after graduation ( Table 1 ).

General characteristics of the participants ( N = 140).

M = mean; SD = standard deviation; n = number of participants. * Includes duplicate responses.

3.2. Descriptive Statistics of Study Variables

Table 2 presents the descriptive statistics of the variables of interest and its subcomponents. The mean score was 3.80 ± 0.67 out of 5 for self-esteem, 3.54 ± 0.38 out of 5 for problem-solving ability, 3.62 ± 0.44 out of 5 for professional nursing values, and 2.52 ± 0.55 out of 4 for career identity.

Descriptive statistics for variables ( N = 140).

M = mean; SD = standard deviation; n = number.

3.3. Differences in Variables According to General Participant Characteristics

Table 3 presents the differences in the variables according to the participants’ general characteristics. There were statistically significant differences in self-esteem, problem-solving ability, professional nursing values, and career identity according to college life satisfaction, satisfaction with major subject, and subjective academic achievement. In addition, self-esteem differed significantly between grades, and career identity differed between sexes and grades.

Differences in variables according to the participants’ general characteristics ( N = 140).

M = mean; SD = standard deviation; IQR = interquartile range; In the variables of College life satisfaction, Major satisfaction at admission, Satisfaction with current major, “a” is the Satisfied category, “b” is the Normal category, and “c” is the Unsatisfied category. In the Subjective academic achievement variable, “a” is the High category, “b” is the Middle category, and “c” is the Low category.

3.4. Correlations between Variables

Spearman’s correlation analysis and Pearson’s correlation analysis showed that career identity had a significantly positive correlation with self-esteem (Spearman’s rho = 0.49, p < 0.001), problem-solving ability (r = 0.31, p < 0.001), and professional nursing values (r = 0.37, p < 0.001). In addition, professional nursing values positively correlated with self-esteem (Spearman’s rho = 0.30, p < 0.001) and problem-solving ability (r = 0.44, p < 0.001). Problem-solving ability was positively correlated with self-esteem (Spearman’s rho = 0.42, p < 0.001) ( Table 4 ).

Correlations between variables ( N = 140).

3.5. Factors Affecting Career Identity

In the initial regression model, self-esteem, problem-solving ability, and professional nursing values were set as independent variables. Considering the high significance in the correlation between independent variables, a regression diagnosis was made to identify the problem of endogeneity. All correlation coefficients were less than 0.5 (0.30–0.49), tolerances were more than 0.1 (0.76–0.89), and variance inflation factor (VIF) was less than 10 (1.12–1.32). However, low eigenvalues (0.009), a high condition index (21.114), and simultaneously a high proportion of variance (31.8%; 77.6%) were observed in self-esteem and professional nursing values, indicating collinearity. After removing the problem-solving ability to explain less the dependent variable among these, multiple regression analysis was then performed.

Table 5 shows the results of multiple regression analysis, with self-esteem and professional nursing values as independent variables. The Durbin‒Watson value was 1.749, indicating no auto-correlation. The tolerances were more than 0.1 (0.93), and the VIF was less than 10 (1.07), indicating no multicollinearity. The regression model was fit (F = 32.89, p < 0.001), and the explanatory power was 31.5%, slightly higher than that (31.0%) of the initial model. The factors affecting career identity were self-esteem (β = 0.450, p < 0.001) and professional nursing values (β = 0.252, p = 0.001).

Factors that affect career identity ( N = 140).

4. Discussion

This study presented significant associations with college life and career-related characteristics, self-esteem, problem-solving ability, professional nursing values, and career identity of Korean nursing students. In particular, it was confirmed that self-esteem and professional nursing value were predictors of career identity.

First, the characteristics of the participants’ college life and career are as follows. In this study, many nursing students reported that they were motivated to study nursing because of the high employment rates, and many wanted to work in a general hospital after graduation. These findings were similar to those of a study conducted by Seong et al. (2012) in Korea [ 14 ]. However, nurses in many countries, including Korea, often stop working as clinical nurses after graduation. Healthcare crises similar to the COVID-19 pandemic may occur again in the future. Nursing educators should help nursing students who wish to become professional nurses by playing an active role as guardians to promote a better healthcare environment.

The self-esteem of our participants (rated as 3.80 out of 5 points overall) was significantly higher among the fourth-year (4.02) compared with third-year students (3.62). Similar results were reported by a descriptive longitudinal study conducted in Turkey that explored the effects of a 4-year nursing college educational program on self-esteem [ 36 ]. Self-esteem was higher among students satisfied with their college life and major subject, and among those with higher subjective academic achievement, consistent with the results of earlier studies [ 19 , 28 , 37 , 38 , 39 , 40 , 41 ]. Educational interventions to strengthen self-esteem should help to ensure that nursing students are satisfied with their college life and major subjects, and achieve high academic performance.

In this study, problem-solving ability (rated as 3.54 out of 5 points) correlated positively with satisfaction with college life and the major subject, and with academic achievement, consistent with the results of previous studies of Korean nursing students [ 21 , 41 , 42 , 43 ]. Luo et al. (2019) emphasized the importance of the problem-solving skills of nursing students in the context of self-directed learning, because nurses must be able to respond quickly using reasoning [ 23 ]. Nursing education curricula should be based on problem-solving instead of rote-learning to enhance knowledge accumulation.

In this study, the professional nursing values (rated as 3.62 out of 5 points overall) with the lowest scores were social awareness (3.27) and nursing originality (3.58). This pattern was consistent with the results of a study by Kim & Kim (2019), who used the same tools for assessing Korean nursing students [ 44 ]. These results suggest that efforts are needed to enhance social awareness among nurses and emphasize the uniqueness of nursing, in order to enhance the professional intuition of nursing students. In addition, professional nursing values differed significantly by college life satisfaction, satisfaction with the major subject, and academic achievement. In many previous studies, scores for professional nursing values were higher among students who were satisfied with their university life or major subject, and among students with high academic achievement [ 44 , 45 , 46 , 47 ]. Poorchangizi et al. (2019) emphasized that the professional values of nursing students vary based on the educational strategy of their institution, and that these values should be enhanced by integrating them into the curriculum [ 48 ].

Career identity (rated as 2.52 out of 4 points) was significantly greater in our female students and students in the fourth year. Studies of differences in career identity among students according to sex and grade showed inconsistent results [ 18 , 49 , 50 ]. Career identity was relatively strong in our study population, as evidenced by high college life satisfaction, major subject satisfaction, and academic achievement. Similar results were found in many previous studies [ 10 , 27 , 49 , 50 , 51 , 52 , 53 ]. Nursing educators can help students establish their career identity through career development programs, and by adjusting the curriculum beginning in the junior year.

We observed positive correlations among self-esteem, problem-solving ability, professional nursing value, and career identity. Many previous studies have also reported correlations among these variables [ 14 , 17 , 18 , 19 , 25 , 28 , 39 , 42 , 43 , 54 ]. These factors could be used to establish an effective career development strategy and enhance career identity.

In multiple regression analysis, self-esteem and professional nursing values predicted career identity. An effect of self-esteem on career identity has also been identified in previous studies [ 17 , 19 , 28 ]. According to a qualitative study of young Australians, subjective achievement affected the formation of career identity [ 55 ]. Therefore, a career development program with activities and experiences promoting positive self-evaluation may be effective. Previous studies have reported effects of professional nursing values among nursing students on career identity [ 53 ], and of nursing professionalism on career plans [ 14 ]. In addition, a qualitative study of career identity among Vietnamese nursing students reported that personal values, needs, plans regarding future career, and sociocultural values significantly affected career identity [ 56 ]. A study of the professional identity of U.K. nursing students using focus group interviews demonstrated that the students had “dualistic” attitudes, expressing both idealism and cynicism; they also expressed anxiety about nursing work, and perceived nurses to be in a “powerless position” within the professional healthcare hierarchy [ 57 ]. These results suggest that individual nursing values and perceptions of the realities of nursing have important influences on career identity and future career paths. Nursing educators should help nursing students understand how professional nursing values contribute to a healthy life, and help them to formulate career plans.

A major limitation of this study is the difficulty of generalization owing to the small sample size from a single university. Future studies should include larger and more diverse samples, and assess different interventions to definitively determine the factors that most affect career development.

5. Conclusions

In this study, self-esteem and professional nursing value were factors influencing career identity, along with their association with college life/major satisfaction and problem-solving ability. Nursing educators need to devise a career development program that can enhance students’ self-esteem and professionalism, along with efforts to improve satisfaction with their college life and major. Health officials should support the establishment of a quality education and career development system for expanded nursing college students. These proactive measures would help nurses to lead a satisfactory college life, develop nursing competencies, and be motivated to continue to work in healthcare after graduation.

Author Contributions

Conceptualization, J.M., H.K. and J.Y.; methodology, J.M., H.K. and J.Y.; formal analysis, J.M. and J.Y.; investigation, J.M., H.K. and J.Y.; data curation, J.M.; writing—original draft preparation, J.M., H.K. and J.Y.; writing—review and editing, J.M. and H.K.; supervision, H.K.; project administration, J.M.; funding acquisition, J.M. All authors have read and agreed to the published version of the manuscript.

This research received no external funding.

Institutional Review Board Statement

The study was conducted according to the guidelines of the Declaration of Helsinki, and approved by the Institutional Review Board (or Ethics Committee) of Chosun University (2-1041055-AB-N-01-2019-35; 4 September 2019).

Informed Consent Statement

Informed consent was obtained from all subjects involved in the study.

Conflicts of Interest

The authors declare no conflict of interest.

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Nature of Home

Top 10 Smartest Animals: Geniuses of the Animal Kingdom

Posted: April 27, 2024 | Last updated: April 27, 2024

Have you ever wondered which creatures are the brightest in the animal world? While humans may be at the top of the class, many of our fellow animals exhibit remarkable intelligence in their own unique ways.

From problem-solving skills to complex communication, these brainy beasts continue to amaze scientists and animal lovers alike.

1. Chimpanzee

Chimpanzees, our closest living relatives, are known for their exceptional intelligence. These clever primates have been observed using tools, such as sticks to fish for termites or rocks to crack open nuts. They also display advanced problem-solving abilities and can learn sign language to communicate with humans.

What’s more, chimpanzees have a remarkable memory and can recall the faces of individual humans and other chimps for years. Their complex social structures and ability to cooperate and strategize during hunts further demonstrate their cognitive prowess.

2. Dolphins

Dolphins are the brainiacs of the ocean, with a brain-to-body-size ratio second only to humans. These marine mammals are known for their playful nature and impressive communication skills, using a variety of clicks, whistles, and body language to convey information to their pod mates.

In addition to their social smarts, dolphins have demonstrated problem-solving abilities and self-awareness. They can recognize themselves in mirrors, a trait shared by only a few other species ( ref ). Dolphins have also been observed using tools, such as sponges to protect their snouts while foraging for food on the ocean floor.

3. Elephants

Elephants are not only the largest land mammals but also among the most intelligent. These gentle giants have exceptional memories, able to remember the locations of water sources and the faces of individual humans and other elephants for years.

Elephants also display complex social behaviors, such as grieving over the loss of a family member and cooperating to care for their young. They can problem-solve and use tools, such as branches to swat flies or scratch hard-to-reach places. Some elephants have even been observed creating art with paint and brushes!

4. Crows & Ravens

Don’t let their spooky reputation fool you; crows and ravens are among the smartest birds on the planet. These clever corvids have problem-solving skills that rival those of primates. They can use tools, such as bending wire to create hooks for retrieving food, and even solve multi-step puzzles.

Crows and ravens also have impressive memories, able to remember human faces and hold grudges against those who have wronged them. They engage in social learning, teaching their young and even other species new skills.

Some have been observed placing nuts on roads, allowing cars to crack them open for an easy meal.

Pigs are often underestimated, but these barnyard brainiacs are smarter than you might think. Studies have shown that pigs can solve complex mazes, recognize themselves in mirrors, and even manipulate joystick-controlled video games with their snouts.

Pigs also have excellent long-term memories and can remember the location of food sources and the faces of individual humans and other pigs. They are highly social animals, capable of forming strong bonds with their family members and even showing empathy towards others in distress.

6. Octopuses

Octopuses are the masterminds of the invertebrate world, with a intelligence that rivals that of some mammals. These cephalopods are known for their incredible problem-solving abilities, able to navigate mazes, open jars, and even escape from aquarium tanks.

They also have the ability to change color and texture to blend in with their surroundings ( ref ), a skill that requires a complex nervous system. They can use tools, such as coconut shells for shelter, and have been observed engaging in play behavior, a sign of advanced cognitive abilities.

7. African Grey Parrots

African grey parrots are not just talented mimics but also highly intelligent birds. These feathered geniuses have been shown to have cognitive abilities similar to those of a 5-year-old human child. They can understand complex concepts, such as same vs. different and absence vs. presence.

One famous African grey parrot, named Alex, was trained by animal psychologist Irene Pepperberg. Alex could identify over 100 objects, recognize quantities up to six, and even understand the concept of zero. He also had a vocabulary of over 100 words and could combine them to form simple sentences ( ref ).

8. Squirrels

Don’t let their small size fool you; squirrels are surprisingly smart. These bushy-tailed rodents have excellent spatial memory, able to remember the locations of thousands of buried food caches for months. They also engage in deceptive behavior, pretending to bury food to throw off potential thieves.

Squirrels have been observed solving complex puzzles to obtain food rewards and even using tools, such as sticks to reach objects that are out of their reach ( ref ). They also display social intelligence, communicating with each other through a variety of vocalizations and body language.

Man’s best friend is also one of the smartest animals around. Dogs have been domesticated for thousands of years, and their cognitive abilities have evolved alongside their close relationship with humans. They can understand human gestures, facial expressions, and even some words.

Dogs also have excellent problem-solving skills and can be trained to perform a wide variety of tasks, from guiding the blind to detecting drugs and explosives. They have a keen sense of smell and can use it to track scents over long distances. Some dogs have even been trained to detect diseases, such as cancer, in humans.

10. Raccoons

Raccoons may be known for their mischievous behavior, but these masked bandits are also highly intelligent. They have excellent problem-solving skills and can open complex locks and latches to obtain food. They also have a keen sense of touch, using their sensitive front paws to explore their environment.

They have been observed engaging in social learning, watching and imitating the behaviors of their peers. They also have excellent spatial memory, able to remember the locations of food sources and navigate complex environments with ease.

Remarkable Beings

The animal kingdom is full of intelligent creatures that continue to surprise and amaze us. From the problem-solving skills of chimpanzees and octopuses to the social smarts of elephants and dogs, these animals demonstrate that intelligence comes in many forms.

As we continue to study and learn from these remarkable beings, we gain a greater appreciation for the diversity and complexity of life on Earth.

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