National Academies Press: OpenBook

How People Learn: Brain, Mind, Experience, and School: Expanded Edition (2000)

Chapter: 2 how experts differ from novices, 2 how experts differ from novices.

People who have developed expertise in particular areas are, by definition, able to think effectively about problems in those areas. Understanding expertise is important because it provides insights into the nature of thinking and problem solving. Research shows that it is not simply general abilities, such as memory or intelligence, nor the use of general strategies that differentiate experts from novices. Instead, experts have acquired extensive knowledge that affects what they notice and how they organize, represent, and interpret information in their environment. This, in turn, affects their abilities to remember, reason, and solve problems.

This chapter illustrates key scientific findings that have come from the study of people who have developed expertise in areas such as chess, physics, mathematics, electronics, and history. We discuss these examples not because all school children are expected to become experts in these or any other areas, but because the study of expertise shows what the results of successful learning look like. In later chapters we explore what is known about processes of learning that can eventually lead to the development of expertise.

We consider several key principles of experts’ knowledge and their potential implications for learning and instruction:

Experts notice features and meaningful patterns of information that are not noticed by novices.

Experts have acquired a great deal of content knowledge that is organized in ways that reflect a deep understanding of their subject matter.

Experts’ knowledge cannot be reduced to sets of isolated facts or propositions but, instead, reflects contexts of applicability: that is, the knowledge is “conditionalized” on a set of circumstances.

Experts are able to flexibly retrieve important aspects of their knowledge with little attentional effort.

Though experts know their disciplines thoroughly, this does not guarantee that they are able to teach others.

Experts have varying levels of flexibility in their approach to new situations.


One of the earliest studies of expertise demonstrated that the same stimulus is perceived and understood differently, depending on the knowledge that a person brings to the situation. DeGroot (1965) was interested in understanding how world-class chess masters are consistently able to out-think their opponents. Chess masters and less experienced but still extremely good players were shown examples of chess games and asked to think aloud as they decided on the move they would make if they were one of the players; see Box 2.1 . DeGroot’s hypothesis was that the chess masters would be more likely than the nonmasters to (a) think through all the possibilities before making a move (greater breadth of search) and (b) think through all the possible countermoves of the opponent for every move considered (greater depth of search). In this pioneering research, the chess masters did exhibit considerable breadth and depth to their searches, but so did the lesser ranked chess players. And none of them conducted searches that covered all the possibilities. Somehow, the chess masters considered possibilities for moves that were of higher quality than those considered by the lesser experienced players. Something other than differences in general strategies seemed to be responsible for differences in expertise.

DeGroot concluded that the knowledge acquired over tens of thousands of hours of chess playing enabled chess masters to out-play their opponents. Specifically, masters were more likely to recognize meaningful chess configurations and realize the strategic implications of these situations; this recognition allowed them to consider sets of possible moves that were superior to others. The meaningful patterns seemed readily apparent to the masters, leading deGroot (1965:33–34) to note:

We know that increasing experience and knowledge in a specific field (chess, for instance) has the effect that things (properties, etc.) which, at earlier stages, had to be abstracted, or even inferred are apt to be immediately perceived at later stages. To a rather large extent, abstraction is replaced by perception, but we do not know much about how this works, nor where the borderline lies. As an effect of this replacement, a so-called ‘given’ problem situation is not really given since it is seen differently by an expert than it is perceived by an inexperienced person….

DeGroot’s think-aloud method provided for a very careful analysis of the conditions of specialized learning and the kinds of conclusions one can draw from them (see Ericsson and Simon, 1993). Hypotheses generated from think-aloud protocols are usually cross-validated through the use of other methodologies.

The superior recall ability of experts, illustrated in the example in the box, has been explained in terms of how they “chunk” various elements of a configuration that are related by an underlying function or strategy. Since

there are limits on the amount of information that people can hold in short-term memory, short-term memory is enhanced when people are able to chunk information into familiar patterns (Miller, 1956). Chess masters perceive chunks of meaningful information, which affects their memory for what they see. Chess masters are able to chunk together several chess pieces in a configuration that is governed by some strategic component of the game. Lacking a hierarchical, highly organized structure for the domain, novices cannot use this chunking strategy. It is noteworthy that people do not have to be world-class experts to benefit from their abilities to encode meaningful chunks of information: 10- and 11-year-olds who are experienced in chess are able to remember more chess pieces than college students who are not chess players. In contrast, when the college students were presented with other stimuli, such as strings of numbers, they were able to remember more (Chi, 1978; Schneider et al, 1993); see Figure 2.3 .

Skills similar to those of master chess players have been demonstrated for experts in other domains, including electronic circuitry (Egan and Schwartz, 1979), radiology (Lesgold, 1988), and computer programming (Ehrlich and Soloway, 1984). In each case, expertise in a domain helps people develop a sensitivity to patterns of meaningful information that are not available to novices. For example, electronics technicians were able to reproduce large portions of complex circuit diagrams after only a few seconds of viewing; novices could not. The expert circuit technicians chunked several individual circuit elements (e.g., resistors and capacitors) that performed the function of an amplifier. By remembering the structure and function of a typical amplifier, experts were able to recall the arrangement of many of the individual circuit elements comprising the “amplifier chunk.”

Mathematics experts are also able to quickly recognize patterns of information, such as particular problem types that involve specific classes of mathematical solutions (Hinsley et al., 1977; Robinson and Hayes, 1978). For example, physicists recognize problems of river currents and problems of headwinds and tailwinds in airplanes as involving similar mathematical principles, such as relative velocities. The expert knowledge that underlies the ability to recognize problem types has been characterized as involving the development of organized conceptual structures, or schemas, that guide how problems are represented and understood (e.g., Glaser and Chi, 1988).

Expert teachers, too, have been shown to have schemas similar to those found in chess and mathematics. Expert and novice teachers were shown a videotaped classroom lesson (Sabers et al., 1991). The experimental set-up involved three screens that showed simultaneous events occurring throughout the classroom (the left, center, and right). During part of the session, the expert and novice teachers were asked to talk aloud about what they were seeing. Later, they were asked questions about classroom events. Overall,

In one study, a chess master, a Class A player (good but not a master), and a novice were given 5 seconds to view a chess board position from the middle of a chess game; see . After 5 seconds the board was covered, and each participant attempted to reconstruct the board position on another board. This procedure was repeated for multiple trials until everyone received a perfect score. On the first trial, the master player correctly placed many more pieces than the Class A player, who in turn placed more than the novice: 16, 8, and 4, respectively.

However, these results occurred only when the chess pieces were arranged in configurations that conformed to meaningful games of chess. When chess pieces were randomized and presented for 5 seconds, the recall of the chess master and Class A player were the same as the novice—they placed from 2 to 3 positions correctly. Data over trials for valid and random middle games are shown in .

solving problem of educational expert

FIGURE 2.3 Recall for numbers and chess pieces. SOURCE: Adapted from Chi (1978).

the expert teachers had very different understandings of the events they were watching than did the novice teachers; see examples in Box 2.2 .

The idea that experts recognize features and patterns that are not noticed by novices is potentially important for improving instruction. When viewing instructional texts, slides, and videotapes, for example, the information noticed by novices can be quite different from what is noticed by experts (e.g., Sabers et al., 1991; Bransford et al., 1988). One dimension of acquiring greater competence appears to be the increased ability to segment the perceptual field (learning how to see). Research on expertise suggests the importance of providing students with learning experiences that specifically enhance their abilities to recognize meaningful patterns of information (e.g., Simon, 1980; Bransford et al., 1989).


We turn now to the question of how experts’ knowledge is organized and how this affects their abilities to understand and represent problems. Their knowledge is not simply a list of facts and formulas that are relevant to their domain; instead, their knowledge is organized around core concepts or “big ideas” that guide their thinking about their domains.

Expert and novice teachers notice very different things when viewing a videotape of a classroom lesson.

Expert 6: On the left monitor, the students’ note taking indicates that they have seen sheets like this and have had presentations like this before; it’s fairly efficient at this point because they’re used to the format they are using.

Expert 7: I don’t understand why the students can’t be finding out this information on their own rather than listening to someone tell them because if you watch the faces of most of them, they start out for about the first 2 or 3 minutes sort of paying attention to what’s going on and then just drift off.

Expert 2: …I haven’t heard a bell, but the students are already at their desks and seem to be doing purposeful activity, and this is about the time that I decide they must be an accelerated group because they came into the room and started something rather than just sitting down and socializing.

Novice 1: …I can’t tell what they are doing. They’re getting ready for class, but I can’t tell what they’re doing.

Novice 3: She’s trying to communicate with them here about something, but I sure couldn’t tell what it was.

Another novice: It’s a lot to watch.

In an example from physics, experts and competent beginners (college students) were asked to describe verbally the approach they would use to solve physics problems. Experts usually mentioned the major principle(s) or law(s) that were applicable to the problem, together with a rationale for why those laws applied to the problem and how one could apply them (Chi et al., 1981). In contrast, competent beginners rarely referred to major principles and laws in physics; instead, they typically described which equations they would use and how those equations would be manipulated (Larkin, 1981, 1983).

Experts’ thinking seems to be organized around big ideas in physics, such as Newton’s second law and how it would apply, while novices tend to

perceive problem solving in physics as memorizing, recalling, and manipulating equations to get answers. When solving problems, experts in physics often pause to draw a simple qualitative diagram—they do not simply attempt to plug numbers into a formula. The diagram is often elaborated as the expert seeks to find a workable solution path (e.g., see Larkin et al., 1980; Larkin and Simon, 1987; Simon and Simon, 1978).

Differences in how physics experts and novices approach problems can also be seen when they are asked to sort problems, written on index cards, according to the approach that could be used to solve them (Chi et al., 1981). Experts’ problem piles are arranged on the basis of the principles that can be applied to solve the problems; novices’ piles are arranged on the basis of the problems’ surface attributes. For example, in the physics subfield of mechanics, an expert’s pile might consist of problems that can be solved by conservation of energy, while a novice’s pile might consist of problems that contain inclined planes; see Figure 2.4 . Responding to the surface characteristics of problems is not very useful, since two problems that share the same objects and look very similar may actually be solved by entirely different approaches.

Some studies of experts and novices in physics have explored the organization of the knowledge structures that are available to these different groups of individuals (Chi et al., 1982); see Figure 2.5 . In representing a schema for an incline plane, the novice’s schema contains primarily surface features of the incline plane. In contrast, the expert’s schema immediately connects the notion of an incline plane with the laws of physics and the conditions under which laws are applicable.

Pause times have also been used to infer the structure of expert knowledge in domains such as chess and physics. Physics experts appear to evoke sets of related equations, with the recall of one equation activating related equations that are retrieved rapidly (Larkin, 1979). Novices, in contrast, retrieve equations more equally spaced in time, suggesting a sequential search in memory. Experts appear to possess an efficient organization of knowledge with meaningful relations among related elements clustered into related units that are governed by underlying concepts and principles; see Box 2.3 . Within this picture of expertise, “knowing more” means having more conceptual chunks in memory, more relations or features defining each chunk, more interrelations among the chunks, and efficient methods for retrieving related chunks and procedures for applying these informational units in problem-solving contexts (Chi et al., 1981).

Differences between how experts and nonexperts organize knowledge has also been demonstrated in such fields as history (Wineburg, 1991). A group of history experts and a group of gifted, high-achieving high school seniors enrolled in an advanced placement course in history were first given a test of facts about the American Revolution. The historians with back-



FIGURE 2.4 An example of sortings of physics problems made by novices and experts. Each picture above represents a diagram that can be drawn from the storyline of a physics problem taken from an introductory physics textbook. The novices and experts in this study were asked to categorize many such problems based on similarity of solution. The two pairs show a marked contrast in the experts’ and novices’ categorization schemes. Novices tend to categorize physics problems as being solved similarly if they “look the same” (that is, share the same surface features), whereas experts categorize according to the major principle that could be applied to solve the problems.

SOURCE: Adapted from Chi et al. (1981).

solving problem of educational expert

FIGURE 2.5 Network representations of incline plane schema of novices and experts.

SOURCE: Chi et al. (1982:58). Used with permission of Lawrence Erlbaum Associates.

In mathematics, experts are more likely than novices to first try to understand problems, rather than simply attempt to plug numbers into formulas. Experts and students in one study (Paige and Simon, 1966) were asked to solve algebra word problems, such as:

The experts quickly realize that the problem as stated is logically impossible. Although some students also come to this realization, others simply apply equations, which results in the answer of a negative length.

A similar example comes from a study of adults and children (Reusser, 1993), who were asked:

There are 26 sheep and 10 goats on a ship. How old is the captain?

Most adults have enough expertise to realize that this problem is unsolvable, but many school children didn’t realize this at all. More than three-quarters of the children in one study attempted to provide a numerical answer to the problems. They asked themselves whether to add, subtract, multiply, or divide, rather than whether the problem made sense. As one fifth-grade child explained, after giving the answer of 36: “Well, you need to add or subtract or multiply in problems like this, and this one seemed to work best if I add” (Bransford and Stein, 1993:196).

grounds in American history knew most of the items. However, many of the historians had specialties that lay elsewhere and they knew only one-third of the facts on the tests. Several of the students outscored several of the historians on the factual test. The study then compared how the historians and students made sense of historical documents; the result revealed dramatic differences on virtually any criterion. The historians excelled in the elaborateness of understandings they developed in their ability to pose alternative explanations for events and in their use of corroborating evidence. This depth of understanding was as true for the Asian specialists and the medievalists as it was for the Americanists.

When the two groups were asked to select one of three pictures that best reflect their understanding of the battle of Lexington, historians and students displayed the greatest differences. Historians carefully navigated back and forth between the corpus of written documents and the three images of the battlefield. For them, the picture selection task was the quint-

essential epistemological exercise, a task that explored the limits of historical knowledge. They knew that no single document or picture could tell the story of history; hence, they thought very hard about their choices. In contrast, the students generally just looked at the pictures and made a selection without regard or qualification. For students, the process was similar to finding the correct answer on a multiple choice test.

In sum, although the students scored very well on facts about history, they were largely unacquainted with modes of inquiry with real historical thinking. They had no systematic way of making sense of contradictory claims. Thrust into a set of historical documents that demanded that they sort out competing claims and formulate a reasoned interpretation, the students, on the whole, were stymied. They lacked the experts’ deep understanding of how to formulate reasoned interpretations of sets of historical documents. Experts in other social sciences also organize their problem solving around big ideas (see, e.g., Voss et al., 1984).

The fact that experts’ knowledge is organized around important ideas or concepts suggests that curricula should also be organized in ways that lead to conceptual understanding. Many approaches to curriculum design make it difficult for students to organize knowledge meaningfully. Often there is only superficial coverage of facts before moving on to the next topic; there is little time to develop important, organizing ideas. History texts sometimes emphasize facts without providing support for understanding (e.g., Beck et al., 1989, 1991). Many ways of teaching science also overemphasize facts (American Association for the Advancement of Science, 1989; National Research Council, 1996).

The Third International Mathematics and Science Survey (TIMSS) (Schmidt et al., 1997) criticized curricula that were “a mile wide and an inch deep” and argued that this is much more of a problem in America than in most other countries. Research on expertise suggests that a superficial coverage of many topics in the domain may be a poor way to help students develop the competencies that will prepare them for future learning and work. The idea of helping students organize their knowledge also suggests that novices might benefit from models of how experts approach problem solving— especially if they then receive coaching in using similar strategies (e.g., Brown et al., 1989; we discuss this more fully in Chapters 3 and 7 ).


Experts have a vast repertoire of knowledge that is relevant to their domain or discipline, but only a subset of that knowledge is relevant to any particular problem. Experts do not have to search through everything they know in order to find what is relevant; such an approach would overwhelm

their working memory (Miller, 1956). For example, the chess masters described above considered only a subset of possible chess moves, but those moves were generally superior to the ones considered by the lesser ranked players. Experts have not only acquired knowledge, but are also good at retrieving the knowledge that is relevant to a particular task. In the language of cognitive scientists, experts’ knowledge is “conditionalized” —it includes a specification of the contexts in which it is useful (Simon, 1980; Glaser, 1992). Knowledge that is not conditionalized is often “inert” because it is not activated, even though it is relevant (Whitehead, 1929).

The concept of conditionalized knowledge has implications for the design of curriculum, instruction, and assessment practices that promote effective learning. Many forms of curricula and instruction do not help students conditionalize their knowledge: “Textbooks are much more explicit in enunciating the laws of mathematics or of nature than in saying anything about when these laws may be useful in solving problems” (Simon, 1980:92). It is left largely to students to generate the condition-action pairs required for solving novel problems.

One way to help students learn about conditions of applicability is to assign word problems that require students to use appropriate concepts and formulas (Lesgold, 1984, 1988; Simon, 1980). If well designed, these problems can help students learn when, where, and why to use the knowledge they are learning. Sometimes, however, students can solve sets of practice problems but fail to conditionalize their knowledge because they know which chapter the problems came from and so automatically use this information to decide which concepts and formulas are relevant. Practice problems that are organized into very structured worksheets can also cause this problem. Sometimes students who have done well on such assignments—and believe that they are learning—are unpleasantly surprised when they take tests in which problems from the entire course are randomly presented so there are no clues about where they appeared in a text (Bransford, 1979).

The concept of conditionalized knowledge also has important implications for assessment practices that provide feedback about learning. Many types of tests fail to help teachers and students assess the degree to which the students’ knowledge is conditionalized. For example, students might be asked whether the formula that quantifies the relationship between mass and energy is E=MC, E=MC 2 , or E=MC 3 . A correct answer requires no knowledge of the conditions under which it is appropriate to use the formula. Similarly, students in a literature class might be asked to explain the meaning of familiar proverbs, such as “he who hesitates is lost” or “too many cooks spoil the broth.” The ability to explain the meaning of each proverb provides no guarantee that students will know the conditions under which either proverb is useful. Such knowledge is important because, when viewed solely as propositions, proverbs often contradict one another. To use them

effectively, people need to know when and why it is appropriate to apply the maxim “too many cooks spoil the broth” versus “many hands make light work” or “he who hesitates is lost” versus “haste makes waste” (see Bransford and Stein, 1993).


People’s abilities to retrieve relevant knowledge can vary from being “effortful” to “relatively effortless” (fluent) to “automatic” (Schneider and Shiffrin, 1977). Automatic and fluent retrieval are important characteristics of expertise.

Fluent retrieval does not mean that experts always perform a task faster than novices. Because experts attempt to understand problems rather than to jump immediately to solution strategies, they sometimes take more time than novices (e.g., Getzels and Csikszentmihalyi, 1976). But within the overall process of problem solving there are a number of subprocesses that, for experts, vary from fluent to automatic. Fluency is important because effortless processing places fewer demands on conscious attention. Since the amount of information a person can attend to at any one time is limited (Miller, 1956), ease of processing some aspects of a task gives a person more capacity to attend to other aspects of the task (LaBerge and Samuels, 1974; Schneider and Shiffrin, 1985; Anderson, 1981, 1982; Lesgold et al., 1988).

Learning to drive a car provides a good example of fluency and automaticity. When first learning, novices cannot drive and simultaneously carry on a conversation. With experience, it becomes easy to do so. Similarly, novice readers whose ability to decode words is not yet fluent are unable to devote attention to the task of understanding what they are reading (LaBerge and Samuels, 1974). Issues of fluency are very important for understanding learning and instruction. Many instructional environments stop short of helping all students develop the fluency needed to successfully perform cognitive tasks (Beck et al., 1989; Case, 1978; Hasselbring et al., 1987; LaBerge and Samuels, 1974).

An important aspect of learning is to become fluent at recognizing problem types in particular domains—such as problems involving Newton’s second law or concepts of rate and functions—so that appropriate solutions can be easily retrieved from memory. The use of instructional procedures that speed pattern recognition are promising in this regard (e.g., Simon, 1980).


Expertise in a particular domain does not guarantee that one is good at helping others learn it. In fact, expertise can sometimes hurt teaching because many experts forget what is easy and what is difficult for students.

Recognizing this fact, some groups who design educational materials pair content area experts with “accomplished novices” whose area of expertise lies elsewhere: their task is to continually challenge the experts until the experts’ ideas for instruction begin to make sense to them (Cognition and Technology Group at Vanderbilt, 1997).

The content knowledge necessary for expertise in a discipline needs to be differentiated from the pedagogical content knowledge that underlies effective teaching (Redish, 1996; Shulman, 1986, 1987). The latter includes information about typical difficulties that students encounter as they attempt to learn about a set of topics; typical paths students must traverse in order to achieve understanding; and sets of potential strategies for helping students overcome the difficulties that they encounter. Shulman (1986, 1987) argues that pedagogical content knowledge is not equivalent to knowledge of a content domain plus a generic set of teaching strategies; instead, teaching strategies differ across disciplines. Expert teachers know the kinds of difficulties that students are likely to face; they know how to tap into students’ existing knowledge in order to make new information meaningful; and they know how to assess their students’ progress. Expert teachers have acquired pedagogical content knowledge as well as content knowledge; see Box 2.4 . In the absence of pedagogical content knowledge, teachers often rely on textbook publishers for decisions about how to best organize subjects for students. They are therefore forced to rely on the “prescriptions of absentee curriculum developers” (Brophy, 1983), who know nothing about the particular students in each teacher’s classroom. Pedagogical content knowledge is an extremely important part of what teachers need to learn to be more effective. (This topic is discussed more fully in Chapter 7 .)


An important question for educators is whether some ways of organizing knowledge are better at helping people remain flexible and adaptive to new situations than others. For example, contrast two types of Japanese sushi experts (Hatano and Inagaki, 1986): one excels at following a fixed recipe; the other has “adaptive expertise” and is able to prepare sushi quite creatively. These appear to be examples of two very different types of expertise, one that is relatively routinized and one that is flexible and more adaptable to external demands: experts have been characterized as being “merely skilled” versus “highly competent” or more colorfully as “artisans” versus “virtuosos” (Miller, 1978). These differences apparently exist across a wide range of jobs.

One analysis looked at these differences in terms of information systems design (Miller, 1978). Information systems designers typically work with clients who specify what they want. The goal of the designer is to construct systems that allow people to efficiently store and access relevant informa

Two new English teachers, Jake and Steven, with similar subject-matter backgrounds from elite private universities, set out to teach in high school (Grossman, 1990).

In his teaching, Jake spent 7 weeks leading his students through a word-by-word focusing on notions of “linguistic reflexivity,” and issues of modernism. His assignments included in-depth analyses of soliloquies, memorization of long passages, and a final paper on the importance of language in . Jake’s model for this instruction was his own undergraduate coursework; there was little transformation of his knowledge, except to parcel it out in chunks that fit into the 50-minute containers of the school day. Jake’s image for how students would respond was his own responses as a student who loved Shakespeare and delighted in close textual analysis. Consequently, when students responded in less than enthusiastic ways, Jake was ill-equipped to understand their confusion: “The biggest problem I have with teaching by far is trying to get into the mind-set of a ninth grader…”

Steven began his unit on without ever mentioning the name of the play. To help his students grasp the initial outline of the themes and issues of the play, he asked them to imagine that their parents had recently divorced and that their mothers had taken up with a new man. This new man had replaced their father at work, and “there’s some talk that he had something to do with the ousting of your dad” (Grossman, 1990:24). Steven then asked students to think about the circumstances that might drive them so mad that they would contemplate murdering another human being. Only then, after students had contemplated these issues and done some writing on them, did Steven introduce the play they would be reading.

tion (usually through computers). Artisan experts seek to identify the functions that their clients want automated; they tend to accept the problem and its limits as stated by the clients. They approach new problems as opportunities to use their existing expertise to do familiar tasks more efficiently. It is important to emphasize that artisans’ skills are often extensive and should not be underestimated. In contrast, however, the virtuoso experts treat the client’s statement of the problem with respect, but consider it “a point for departure and exploration” (Miller, 1978). They view assignments as opportunities to explore and expand their current levels of expertise. Miller also observes that, in his experience, virtuosos exhibit their positive characteristics despite their training, which is usually restricted solely to technical skills.

The concept of adaptive expertise has also been explored in a study of history experts (Wineburg, 1998). Two history experts and a group of future teachers were asked to read and interpret a set of documents about Abraham Lincoln and his view of slavery. This is a complex issue that, for Lincoln, involved conflicts between enacted law (the Constitution), natural law (as encoded in the Declaration of Independence), and divine law (assumptions about basic rights). One of the historians was an expert on Lincoln; the second historian’s expertise lay elsewhere. The Lincoln expert brought detailed content knowledge to the documents and easily interpreted them; the other historian was familiar with some of the broad themes in the documents but quickly became confused in the details. In fact, at the beginning of the task, the second historian reacted no differently than a group of future high school teachers who were faced with the same task (Wineburg and Fournier, 1994): attempting to harmonize discrepant information about Lincoln’s position, they both appealed to an array of present social forms and institutions—such as speech writers, press conferences, and “spin doctors” —to explain why things seemed discrepant. Unlike the future teachers, however, the second historian did not stop with his initial analysis. He instead adopted a working hypothesis that assumed that the apparent contradictions might be rooted less in Lincoln’s duplicity than in his own ignorance of the nineteenth century. The expert stepped back from his own initial interpretation and searched for a deeper understanding of the issues. As he read texts from this perspective, his understanding deepened, and he learned from the experience. After considerable work, the second historian was able to piece together an interpretive structure that brought him by the task’s end to where his more knowledgeable colleague had begun. The future history teachers, in contrast, never moved beyond their initial interpretations of events.

An important characteristic exhibited by the history expert involves what is known as “metacognition” —the ability to monitor one’s current level of understanding and decide when it is not adequate. The concept of metacognition was originally introduced in the context of studying young children (e.g., Brown, 1980; Flavell, 1985, 1991). For example, young children often erroneously believe that they can remember information and hence fail to use effective strategies, such as rehearsal. The ability to recognize the limits of one’s current knowledge, then take steps to remedy the situation, is extremely important for learners at all ages. The history expert who was not a specialist in Lincoln was metacognitive in the sense that he successfully recognized the insufficiency of his initial attempts to explain Lincoln’s position. As a consequence, he adopted the working hypothesis that he needed to learn more about the context of Lincoln’s times before coming to a reasoned conclusion.

Beliefs about what it means to be an expert can affect the degree to which people explicitly search for what they don’t know and take steps to improve the situation. In a study of researchers and veteran teachers, a common assumption was that “an expert is someone who knows all the answers” (Cognition and Technology Group at Vanderbilt, 1997). This assumption had been implicit rather than explicit and had never been questioned and discussed. But when the researchers and teachers discussed this concept, they discovered that it placed severe constraints on new learning because the tendency was to worry about looking competent rather than publicly acknowledging the need for help in certain areas (see Dweck, 1989, for similar findings with students). The researchers and the teachers found it useful to replace their previous model of “answer-filled experts” with the model of “accomplished novices.” Accomplished novices are skilled in many areas and proud of their accomplishments, but they realize that what they know is minuscule compared to all that is potentially knowable. This model helps free people to continue to learn even though they may have spent 10 to 20 years as an “expert” in their field.

The concept of adaptive expertise (Hatano and Inagaki, 1986) provides an important model of successful learning. Adaptive experts are able to approach new situations flexibly and to learn throughout their lifetimes. They not only use what they have learned, they are metacognitive and continually question their current levels of expertise and attempt to move beyond them. They don’t simply attempt to do the same things more efficiently; they attempt to do things better. A major challenge for theories of learning is to understand how particular kinds of learning experiences develop adaptive expertise or “virtuosos.”

Experts’ abilities to reason and solve problems depend on well-organized knowledge that affects what they notice and how they represent problems. Experts are not simply “general problem solvers” who have learned a set of strategies that operate across all domains. The fact that experts are more likely than novices to recognize meaningful patterns of information applies in all domains, whether chess, electronics, mathematics, or classroom teaching. In deGroot’s (1965) words, a “given” problem situation is not really a given. Because of their ability to see patterns of meaningful information, experts begin problem solving at “a higher place” (deGroot, 1965). An emphasis on the patterns perceived by experts suggests that pattern recognition is an important strategy for helping students develop confidence and competence. These patterns provide triggering conditions for accessing knowledge that is relevant to a task.

Studies in areas such as physics, mathematics, and history also demon-

strata that experts first seek to develop an understanding of problems, and this often involves thinking in terms of core concepts or big ideas, such as Newton’s second law in physics. Novices’ knowledge is much less likely to be organized around big ideas; they are more likely to approach problems by searching for correct formulas and pat answers that fit their everyday intuitions.

Curricula that emphasize breadth of knowledge may prevent effective organization of knowledge because there is not enough time to learn anything in depth. Instruction that enables students to see models of how experts organize and solve problems may be helpful. However, as discussed in more detail in later chapters, the level of complexity of the models must be tailored to the learners’ current levels of knowledge and skills.

While experts possess a vast repertoire of knowledge, only a subset of it is relevant to any particular problem. Experts do not conduct an exhaustive search of everything they know; this would overwhelm their working memory (Miller, 1956). Instead, information that is relevant to a task tends to be selectively retrieved (e.g., Ericsson and Staszewski, 1989; deGroot, 1965).

The issue of retrieving relevant information provides clues about the nature of usable knowledge. Knowledge must be “conditionalized” in order to be retrieved when it is needed; otherwise, it remains inert (Whitehead, 1929). Many designs for curriculum instruction and assessment practices fail to emphasize the importance of conditionalized knowledge. For example, texts often present facts and formulas with little attention to helping students learn the conditions under which they are most useful. Many assessments measure only propositional (factual) knowledge and never ask whether students know when, where, and why to use that knowledge.

Another important characteristic of expertise is the ability to retrieve relevant knowledge in a manner that is relatively “effortless.” This fluent retrieval does not mean that experts always accomplish tasks in less time than novices; often they take more time in order to fully understand a problem. But their ability to retrieve information effortlessly is extremely important because fluency places fewer demands on conscious attention, which is limited in capacity (Schneider and Shiffrin, 1977, 1985). Effortful retrieval, by contrast, places many demands on a learner’s attention: attentional effort is being expended on remembering instead of learning. Instruction that focuses solely on accuracy does not necessarily help students develop fluency (e.g., Beck et al., 1989; Hasselbring et al., 1987; LaBerge and Samuels, 1974).

Expertise in an area does not guarantee that one can effectively teach others about that area. Expert teachers know the kinds of difficulties that students are likely to face, and they know how to tap into their students’ existing knowledge in order to make new information meaningful plus assess their students’ progress. In Shulman’s (1986, 1987) terms, expert teach-

ers have acquired pedagogical content knowledge and not just content knowledge. (This concept is explored more fully in Chapter 7 .)

The concept of adaptive expertise raises the question of whether some ways of organizing knowledge lead to greater flexibility in problem solving than others (Hatano and Inagaki, 1986; Spiro et al., 1991). Differences between the “merely skilled” (artisans) and the “highly competent” (virtuosos) can be seen in fields as disparate as sushi making and information design. Virtuosos not only apply expertise to a given problem, they also consider whether the problem as presented is the best way to begin.

The ability to monitor one’s approach to problem solving—to be metacognitive—is an important aspect of the expert’s competence. Experts step back from their first, oversimplistic interpretation of a problem or situation and question their own knowledge that is relevant. People’s mental models of what it means to be an expert can affect the degree to which they learn throughout their lifetimes. A model that assumes that experts know all the answers is very different from a model of the accomplished novice, who is proud of his or her achievements and yet also realizes that there is much more to learn.

We close this chapter with two important cautionary notes. First, the six principles of expertise need to be considered simultaneously, as parts of an overall system. We divided our discussion into six points in order to facilitate explanation, but each point interacts with the others; this interrelationship has important educational implications. For example, the idea of promoting fluent access to knowledge (principle 4) must be approached with an eye toward helping students develop an understanding of the subject matter (principle 2), learn when, where and why to use information (principle 3), and learn to recognize meaningful patterns of information (principle 1). Furthermore, all these need to be approached from the perspective of helping students develop adaptive expertise (principle 6), which includes helping them become metacognitive about their learning so that they can assess their own progress and continually identify and pursue new learning goals. An example in mathematics is getting students to recognize when a proof is needed. Metacognition can help students develop personally relevant pedagogical content knowledge, analogous to the pedagogical content knowledge available to effective teachers (principle 5). In short, students need to develop the ability to teach themselves.

The second cautionary note is that although the study of experts provides important information about learning and instruction, it can be misleading if applied inappropriately. For example, it would be a mistake simply to expose novices to expert models and assume that the novices will learn effectively; what they will learn depends on how much they know already. Discussions in the next chapters ( 3 and 4 ) show that effective instruction begins with the knowledge and skills that learners bring to the learning task.

First released in the Spring of 1999, How People Learn has been expanded to show how the theories and insights from the original book can translate into actions and practice, now making a real connection between classroom activities and learning behavior. This edition includes far-reaching suggestions for research that could increase the impact that classroom teaching has on actual learning.

Like the original edition, this book offers exciting new research about the mind and the brain that provides answers to a number of compelling questions. When do infants begin to learn? How do experts learn and how is this different from non-experts? What can teachers and schools do-with curricula, classroom settings, and teaching methods—to help children learn most effectively? New evidence from many branches of science has significantly added to our understanding of what it means to know, from the neural processes that occur during learning to the influence of culture on what people see and absorb.

How People Learn examines these findings and their implications for what we teach, how we teach it, and how we assess what our children learn. The book uses exemplary teaching to illustrate how approaches based on what we now know result in in-depth learning. This new knowledge calls into question concepts and practices firmly entrenched in our current education system.

Topics include:

  • How learning actually changes the physical structure of the brain.
  • How existing knowledge affects what people notice and how they learn.
  • What the thought processes of experts tell us about how to teach.
  • The amazing learning potential of infants.
  • The relationship of classroom learning and everyday settings of community and workplace.
  • Learning needs and opportunities for teachers.
  • A realistic look at the role of technology in education.


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The benefits of decision-based learning

By Fraser Scott 2019-03-25T09:30:00+00:00

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Fraser Scott explains what this approach could mean for your classroom

All too often, teachers hear, ‘I couldn’t do the question because I didn’t know which equation to use!’ The student may have the procedural knowledge – the ‘how to’ – to answer the question. They may also have the underlying conceptual knowledge – the ‘why’. However, their conditional knowledge is missing – the student does not know the circumstances to use their conceptual or procedural knowledge.

An image showing a decision flowchart, with a notebook to the leftand pens to the right

Source: Redrawn from DOI: 10.1021/acs.jchemed.8b00754 (© 2019 American Chemical Society)

Rooted in cognitive psychology, decision-based learning helps students problem solve with a decision tree

Experts navigate their conditional knowledge like a map when they are solving problems. They often do this tacitly, making it challenging for students to emulate. However, in decision-based learning (DBL), conditional knowledge is attended to in an explicit, rather than implicit, learning activity. Students follow a decision tree, based on experts’ problem-solving strategies, for particular types of problems.

DBL is rooted in cognitive psychology. Students proceed through a problem one decision at a time, so working memory is not overloaded. DBL also helps students internalise knowledge in their long-term memory as it is already arranged in a conceptual framework.

Tough decisions made easy

New research by Rebecca Sansom and colleagues from Brigham Young University, US, investigates DBL within a chemistry context. The researchers asked an expert to complete typical problem-solving questions on heat and enthalpy while thinking out loud. The research team constructed a DBL model for the topic using the conditional knowledge the expert described during the exercise.

They incorporated their DBL model for heat and enthalpy into the teaching programme of around 200 first year undergraduate students studying general chemistry, with a similar number used as a control group. The DBL model was not just used when attempting problems, but was embedded into the conceptual and procedural learning of the topic.

Those students who engaged with the DBL model significantly outperformed the control group on problem-solving questions related to heat and enthalpy. Importantly, 38% of students stated that, in addition to helping them make the correct decisions, the DBL approach helped them understand the problem better. For many students the DBL model helped them to feel less overwhelmed, stressed or confused.

Teaching tips

One of teaching’s great difficulties is attending to the things we do automatically, like using conditional knowledge. It is easy to overlook conditional knowledge during instruction, or to deal with it in an unorganised fashion. It should be straightforward to adopt a DBL approach to help with this. After all, we most likely already do it when modelling our solutions to students. So, why not go a little further and write out this decision framework. The benefits are multiple:

  • It makes our preferred problem-solving strategies explicit, and easier for students to engage with.
  • Giving students rapid feedback on their problem-solving strategies may take less time if both student and teacher are using a common framework of reference.
  • As students become more familiar with the DBL model, it will become automatic, freeing up their working memory to tend to other aspects of a problem.
  • DBL can provide a route to promote engagement outside of class. Without it, students may quickly give up on solving problems where they do not have direct teacher intervention.

R L Sansom, E Suh and K J Plummer, J. Chem. Educ. , 2019, DOI: 10.1021/acs.jchemed.8b00754

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  • Evidence-based teaching
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Expert Problem Solving

Evidence from school and district leaders, alternative formats available from:.

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Table of contents

List of Tables



1. Introduction

2. The School Administrators' World from a Problem-Solving Perspective

Toward a Comprehensive Model of Expert Processes

3. Principals' Individual Problem-Solving Processes

4. Superintendents' Individual Problem-Solving Processes

5. Processes Used by Expert and Typical Principals to Solves Problems in Groups

6. Processes Used by Expert Superintendents to Solves Problems in Groups

Key Processes

7. Problem Interpretation: How Administrators Classify and Manage Their Problems

8. The Nature and Role of Values in Administrators' Problem-Solving Processes

9. Cognitive Flexibility and Inflexibility in Principals' Problem Solving

The Relationship Between Thought and Action

10. Problem-Solving Expertise as an Explanation for Variations to Instructional Leadership

11. Total Quality Leadership: Expert Thinking plus Transformational Practice

From Answers to Questions

12. Improving the Problem-Solving Expertise of School Administrators

13. Concluding Thoughts


This book presents a series of related empirical studies about the thinking and problem solving processes of expert educational leaders. It describes the nature of expert thinking and provides substantial explanations for the cognitive processes associated with expert thinking. Differences in the thinking and problem solving of male and female; novice and experienced; elementary, secondary, district administrators are all explored. In addition, the book provides a glimpse of the school administrator's world from a problem solving perspective and clarifies the kinds of experiences that give rise to expert thinking.

Kenneth Leithwood is Professor of Educational Administration and Head of the Centre for Leadership Development at The Ontario Institute for Studies in Education. He is the author of Developing Expert Leadership for Future Schools (with P. Begley and B. Cousins); Understanding School System Administration (with D. Musella); Cognitive Perspectives on Educational Leadership (with P. Hallinger and J. Murphy); and Improving Principal Effectiveness: The Principal Profile . Rosanne Steinbach is Senior Research Officer at The Ontario Institute for Studies in Education.

"This book represents something quite rare in the field of educational administration, a sustained program of research testing a particular model of leadership. The model is rooted in cognitive/constructivist notions of learning and leadership. The research is among the most respected in educational administration today, and this volume represents the first occasion when all of it has been pulled together in a single book. "The topic of expertise and school leadership is one of the most important in educational administration today. Leithwood and Steinbach offer hope to those who feel leadership cannot be learned. New perspectives on leadership make for stimulating reading for those of us steeped in traditional sociological notions of school leadership. " — Daniel L. Duke, University of Virginia "The authors discuss points that are on the minds both of those who study leadership and school transformation and of practitioners. The descriptions of potential models for understanding the thought processes of expert and typical leaders are both interesting and accessible. This book is exciting because I think about these issues daily in my work. " — Sharon Rallis, Vanderbilt University and The Regional Laboratory for Educational Improvement of the Northeast and Islands
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Problem solving.

  • Richard E. Mayer Richard E. Mayer University of California, Santa Barbara
  • Published online: 30 October 2019

Problem solving refers to cognitive processing directed at achieving a goal when the problem solver does not initially know a solution method. A problem exists when someone has a goal but does not know how to achieve it. Problems can be classified as routine or non-routine, and as well-defined or ill-defined. The major cognitive processes in problem solving are representing, planning, executing, and monitoring. The major kinds of knowledge required for problem solving are facts, concepts, procedures, strategies, and beliefs. The theoretical approaches that have developed over the history of research on problem are associationism, Gestalt, and information processing. Each of these approaches involves fundamental issues in problem solving such as the nature of transfer, insight, and goal-directed heuristics, respectively. Some current research topics in problem solving include decision making, intelligence and creativity, teaching of thinking skills, expert problem solving, analogical reasoning, mathematical and scientific thinking, everyday thinking, and the cognitive neuroscience of problem solving. Common theme concerns the domain specificity of problem solving and a focus on problem solving in authentic contexts.

  • problem solving
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  • analogical reasoning
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Teaching problem solving: Let students get ‘stuck’ and ‘unstuck’

Subscribe to the center for universal education bulletin, kate mills and km kate mills literacy interventionist - red bank primary school helyn kim helyn kim former brookings expert @helyn_kim.

October 31, 2017

This is the second in a six-part  blog series  on  teaching 21st century skills , including  problem solving ,  metacognition , critical thinking , and collaboration , in classrooms.

In the real world, students encounter problems that are complex, not well defined, and lack a clear solution and approach. They need to be able to identify and apply different strategies to solve these problems. However, problem solving skills do not necessarily develop naturally; they need to be explicitly taught in a way that can be transferred across multiple settings and contexts.

Here’s what Kate Mills, who taught 4 th grade for 10 years at Knollwood School in New Jersey and is now a Literacy Interventionist at Red Bank Primary School, has to say about creating a classroom culture of problem solvers:

Helping my students grow to be people who will be successful outside of the classroom is equally as important as teaching the curriculum. From the first day of school, I intentionally choose language and activities that help to create a classroom culture of problem solvers. I want to produce students who are able to think about achieving a particular goal and manage their mental processes . This is known as metacognition , and research shows that metacognitive skills help students become better problem solvers.

I begin by “normalizing trouble” in the classroom. Peter H. Johnston teaches the importance of normalizing struggle , of naming it, acknowledging it, and calling it what it is: a sign that we’re growing. The goal is for the students to accept challenge and failure as a chance to grow and do better.

I look for every chance to share problems and highlight how the students— not the teachers— worked through those problems. There is, of course, coaching along the way. For example, a science class that is arguing over whose turn it is to build a vehicle will most likely need a teacher to help them find a way to the balance the work in an equitable way. Afterwards, I make it a point to turn it back to the class and say, “Do you see how you …” By naming what it is they did to solve the problem , students can be more independent and productive as they apply and adapt their thinking when engaging in future complex tasks.

After a few weeks, most of the class understands that the teachers aren’t there to solve problems for the students, but to support them in solving the problems themselves. With that important part of our classroom culture established, we can move to focusing on the strategies that students might need.

Here’s one way I do this in the classroom:

I show the broken escalator video to the class. Since my students are fourth graders, they think it’s hilarious and immediately start exclaiming, “Just get off! Walk!”

When the video is over, I say, “Many of us, probably all of us, are like the man in the video yelling for help when we get stuck. When we get stuck, we stop and immediately say ‘Help!’ instead of embracing the challenge and trying new ways to work through it.” I often introduce this lesson during math class, but it can apply to any area of our lives, and I can refer to the experience and conversation we had during any part of our day.

Research shows that just because students know the strategies does not mean they will engage in the appropriate strategies. Therefore, I try to provide opportunities where students can explicitly practice learning how, when, and why to use which strategies effectively  so that they can become self-directed learners.

For example, I give students a math problem that will make many of them feel “stuck”. I will say, “Your job is to get yourselves stuck—or to allow yourselves to get stuck on this problem—and then work through it, being mindful of how you’re getting yourselves unstuck.” As students work, I check-in to help them name their process: “How did you get yourself unstuck?” or “What was your first step? What are you doing now? What might you try next?” As students talk about their process, I’ll add to a list of strategies that students are using and, if they are struggling, help students name a specific process. For instance, if a student says he wrote the information from the math problem down and points to a chart, I will say: “Oh that’s interesting. You pulled the important information from the problem out and organized it into a chart.” In this way, I am giving him the language to match what he did, so that he now has a strategy he could use in other times of struggle.

The charts grow with us over time and are something that we refer to when students are stuck or struggling. They become a resource for students and a way for them to talk about their process when they are reflecting on and monitoring what did or did not work.

For me, as a teacher, it is important that I create a classroom environment in which students are problem solvers. This helps tie struggles to strategies so that the students will not only see value in working harder but in working smarter by trying new and different strategies and revising their process. In doing so, they will more successful the next time around.

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Teaching problem solving.

Print Version

Tips and Techniques

Expert vs. novice problem solvers, communicate.

  • Have students  identify specific problems, difficulties, or confusions . Don’t waste time working through problems that students already understand.
  • If students are unable to articulate their concerns, determine where they are having trouble by  asking them to identify the specific concepts or principles associated with the problem.
  • In a one-on-one tutoring session, ask the student to  work his/her problem out loud . This slows down the thinking process, making it more accurate and allowing you to access understanding.
  • When working with larger groups you can ask students to provide a written “two-column solution.” Have students write up their solution to a problem by putting all their calculations in one column and all of their reasoning (in complete sentences) in the other column. This helps them to think critically about their own problem solving and helps you to more easily identify where they may be having problems. Two-Column Solution (Math) Two-Column Solution (Physics)

Encourage Independence

  • Model the problem solving process rather than just giving students the answer. As you work through the problem, consider how a novice might struggle with the concepts and make your thinking clear
  • Have students work through problems on their own. Ask directing questions or give helpful suggestions, but  provide only minimal assistance and only when needed to overcome obstacles.
  • Don’t fear  group work ! Students can frequently help each other, and talking about a problem helps them think more critically about the steps needed to solve the problem. Additionally, group work helps students realize that problems often have multiple solution strategies, some that might be more effective than others

Be sensitive

  • Frequently, when working problems, students are unsure of themselves. This lack of confidence may hamper their learning. It is important to recognize this when students come to us for help, and to give each student some feeling of mastery. Do this by providing  positive reinforcement to let students know when they have mastered a new concept or skill.

Encourage Thoroughness and Patience

  • Try to communicate that  the process is more important than the answer so that the student learns that it is OK to not have an instant solution. This is learned through your acceptance of his/her pace of doing things, through your refusal to let anxiety pressure you into giving the right answer, and through your example of problem solving through a step-by step process.

Experts (teachers) in a particular field are often so fluent in solving problems from that field that they can find it difficult to articulate the problem solving principles and strategies they use to novices (students) in their field because these principles and strategies are second nature to the expert. To teach students problem solving skills,  a teacher should be aware of principles and strategies of good problem solving in his or her discipline .

The mathematician George Polya captured the problem solving principles and strategies he used in his discipline in the book  How to Solve It: A New Aspect of Mathematical Method (Princeton University Press, 1957). The book includes  a summary of Polya’s problem solving heuristic as well as advice on the teaching of problem solving.

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Expert Problem Solving: Evidence from School and District Leaders (SUNY Series, Educational Leadership)

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Kenneth A. Leithwood

Expert Problem Solving: Evidence from School and District Leaders (SUNY Series, Educational Leadership)

  • ISBN-10 0791421074
  • ISBN-13 978-0791421079
  • Publisher State University of New York Press
  • Publication date December 23, 1994
  • Language English
  • Dimensions 6.5 x 1 x 9.25 inches
  • Print length 366 pages
  • See all details

Editorial Reviews

"The authors discuss points that are on the minds both of those who study leadership and school transformation and of practitioners. The descriptions of potential models for understanding the thought processes of expert and typical leaders are both interesting and accessible. This book is exciting because I think about these issues daily in my work." -- Sharon Rallis, Vanderbilt University and The Regional Laboratory for Educational Improvement of the Northeast and Islands

About the Author

Kenneth Leithwood is Professor of Educational Administration and Head of the Centre for Leadership Development at The Ontario Institute for Studies in Education. He is the author of Developing Expert Leadership for Future Schools (with P. Begley and B. Cousins); Understanding School System Administration (with D. Musella); Cognitive Perspectives on Educational Leadership (with P. Hallinger and J. Murphy); and Improving Principal Effectiveness: The Principal Profile.

Rosanne Steinbach is Senior Research Officer at The Ontario Institute for Studies in Education.

Product details

  • Publisher ‏ : ‎ State University of New York Press (December 23, 1994)
  • Language ‏ : ‎ English
  • Hardcover ‏ : ‎ 366 pages
  • ISBN-10 ‏ : ‎ 0791421074
  • ISBN-13 ‏ : ‎ 978-0791421079
  • Item Weight ‏ : ‎ 8 ounces
  • Dimensions ‏ : ‎ 6.5 x 1 x 9.25 inches

About the author

Kenneth a. leithwood.

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solving problem of educational expert

Exploring the Differences Between Experts and Novices on Inquiry-Based Learning Cases

  • Published: 29 November 2021
  • Volume 5 , pages 97–105, ( 2021 )

Cite this article

solving problem of educational expert

  • Andrew A. Tawfik   ORCID: 1 ,
  • Jessica D. Gatewood 1 ,
  • Jaclyn J. Gish-Lieberman 1 &
  • Charles W. Keene 2  

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Theorists suggest that problem-solving is an important element to engender higher order learning outcomes. According to case-based reasoning (CBR) theory, learners in inquiry-based learning (IBL) are able to engage in deep learning and retain cases over time, which better prepares them for domain practice. Although various studies have explored the experiences of learners as they engage in IBL , few studies have quantified how experts and novices weigh variables within a case and the degree to which they differ. In this study, experts and novices weighed an array of indices (labels) on a series of IBL) cases. Novices’ questions were also analyzed. Using the structural-function-behavior (SBF) framework, the study found differences on basic understanding (structure) and systems thinking (function); however, no differences on casual reasoning (behavior). Implications for case-based reasoning retrieval and reuse are discussed, as well as IBL.

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Don’t Just Tell Students to Solve Problems. Teach Them How.

The positive impact of an innovative uc san diego problem-solving educational curriculum continues to grow.

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Problem solving is a critical skill for technical education and technical careers of all types. But what are best practices for teaching problem solving to high school and college students? 

The University of California San Diego Jacobs School of Engineering is on the forefront of efforts to improve how problem solving is taught. This UC San Diego approach puts hands-on problem-identification and problem-solving techniques front and center. Over 1,500 students across the San Diego region have already benefited over the last three years from this program. In the 2023-2024 academic year, approximately 1,000 upper-level high school students will be taking the problem solving course in four different school districts in the San Diego region. Based on the positive results with college students, as well as high school juniors and seniors in the San Diego region, the project is getting attention from educators across the state of California, and around the nation and the world.


In Summer 2023, th e 27 community college students who took the unique problem-solving course developed at the UC San Diego Jacobs School of Engineering thrived, according to Alex Phan PhD, the Executive Director of Student Success at the UC San Diego Jacobs School of Engineering. Phan oversees the project. 

Over the course of three weeks, these students from Southwestern College and San Diego City College poured their enthusiasm into problem solving through hands-on team engineering challenges. The students brimmed with positive energy as they worked together. 

What was noticeably absent from this laboratory classroom: frustration.

“In school, we often tell students to brainstorm, but they don’t often know where to start. This curriculum gives students direct strategies for brainstorming, for identifying problems, for solving problems,” sai d Jennifer Ogo, a teacher from Kearny High School who taught the problem-solving course in summer 2023 at UC San Diego. Ogo was part of group of educators who took the course themselves last summer.

The curriculum has been created, refined and administered over the last three years through a collaboration between the UC San Diego Jacobs School of Engineering and the UC San Diego Division of Extended Studies. The project kicked off in 2020 with a generous gift from a local philanthropist.

Not getting stuck

One of the overarching goals of this project is to teach both problem-identification and problem-solving skills that help students avoid getting stuck during the learning process. Stuck feelings lead to frustration – and when it’s a Science, Technology, Engineering and Math (STEM) project, that frustration can lead students to feel they don’t belong in a STEM major or a STEM career. Instead, the UC San Diego curriculum is designed to give students the tools that lead to reactions like “this class is hard, but I know I can do this!” –  as Ogo, a celebrated high school biomedical sciences and technology teacher, put it. 

Three years into the curriculum development effort, the light-hearted energy of the students combined with their intense focus points to success. On the last day of the class, Mourad Mjahed PhD, Director of the MESA Program at Southwestern College’s School of Mathematics, Science and Engineering came to UC San Diego to see the final project presentations made by his 22 MESA students.

“Industry is looking for students who have learned from their failures and who have worked outside of their comfort zones,” said Mjahed. The UC San Diego problem-solving curriculum, Mjahed noted, is an opportunity for students to build the skills and the confidence to learn from their failures and to work outside their comfort zone. “And from there, they see pathways to real careers,” he said. 

What does it mean to explicitly teach problem solving? 

This approach to teaching problem solving includes a significant focus on learning to identify the problem that actually needs to be solved, in order to avoid solving the wrong problem. The curriculum is organized so that each day is a complete experience. It begins with the teacher introducing the problem-identification or problem-solving strategy of the day. The teacher then presents case studies of that particular strategy in action. Next, the students get introduced to the day’s challenge project. Working in teams, the students compete to win the challenge while integrating the day’s technique. Finally, the class reconvenes to reflect. They discuss what worked and didn't work with their designs as well as how they could have used the day’s problem-identification or problem-solving technique more effectively. 

The challenges are designed to be engaging – and over three years, they have been refined to be even more engaging. But the student engagement is about much more than being entertained. Many of the students recognize early on that the problem-identification and problem-solving skills they are learning can be applied not just in the classroom, but in other classes and in life in general. 

Gabriel from Southwestern College is one of the students who saw benefits outside the classroom almost immediately. In addition to taking the UC San Diego problem-solving course, Gabriel was concurrently enrolled in an online computer science programming class. He said he immediately started applying the UC San Diego problem-identification and troubleshooting strategies to his coding assignments. 

Gabriel noted that he was given a coding-specific troubleshooting strategy in the computer science course, but the more general problem-identification strategies from the UC San Diego class had been extremely helpful. It’s critical to “find the right problem so you can get the right solution. The strategies here,” he said, “they work everywhere.”

Phan echoed this sentiment. “We believe this curriculum can prepare students for the technical workforce. It can prepare students to be impactful for any career path.”

The goal is to be able to offer the course in community colleges for course credit that transfers to the UC, and to possibly offer a version of the course to incoming students at UC San Diego. 

As the team continues to work towards integrating the curriculum in both standardized high school courses such as physics, and incorporating the content as a part of the general education curriculum at UC San Diego, the project is expected to impact thousands more students across San Diego annually. 

Portrait of the Problem-Solving Curriculum

On a sunny Wednesday in July 2023, an experiential-learning classroom was full of San Diego community college students. They were about half-way through the three-week problem-solving course at UC San Diego, held in the campus’ EnVision Arts and Engineering Maker Studio. On this day, the students were challenged to build a contraption that would propel at least six ping pong balls along a kite string spanning the laboratory. The only propulsive force they could rely on was the air shooting out of a party balloon.

A team of three students from Southwestern College – Valeria, Melissa and Alondra – took an early lead in the classroom competition. They were the first to use a plastic bag instead of disposable cups to hold the ping pong balls. Using a bag, their design got more than half-way to the finish line – better than any other team at the time – but there was more work to do. 

As the trio considered what design changes to make next, they returned to the problem-solving theme of the day: unintended consequences. Earlier in the day, all the students had been challenged to consider unintended consequences and ask questions like: When you design to reduce friction, what happens? Do new problems emerge? Did other things improve that you hadn’t anticipated? 

Other groups soon followed Valeria, Melissa and Alondra’s lead and began iterating on their own plastic-bag solutions to the day’s challenge. New unintended consequences popped up everywhere. Switching from cups to a bag, for example, reduced friction but sometimes increased wind drag. 

Over the course of several iterations, Valeria, Melissa and Alondra made their bag smaller, blew their balloon up bigger, and switched to a different kind of tape to get a better connection with the plastic straw that slid along the kite string, carrying the ping pong balls. 

One of the groups on the other side of the room watched the emergence of the plastic-bag solution with great interest. 

“We tried everything, then we saw a team using a bag,” said Alexander, a student from City College. His team adopted the plastic-bag strategy as well, and iterated on it like everyone else. They also chose to blow up their balloon with a hand pump after the balloon was already attached to the bag filled with ping pong balls – which was unique. 

“I don’t want to be trying to put the balloon in place when it's about to explode,” Alexander explained. 

Asked about whether the structured problem solving approaches were useful, Alexander’s teammate Brianna, who is a Southwestern College student, talked about how the problem-solving tools have helped her get over mental blocks. “Sometimes we make the most ridiculous things work,” she said. “It’s a pretty fun class for sure.” 

Yoshadara, a City College student who is the third member of this team, described some of the problem solving techniques this way: “It’s about letting yourself be a little absurd.”

Alexander jumped back into the conversation. “The value is in the abstraction. As students, we learn to look at the problem solving that worked and then abstract out the problem solving strategy that can then be applied to other challenges. That’s what mathematicians do all the time,” he said, adding that he is already thinking about how he can apply the process of looking at unintended consequences to improve both how he plays chess and how he goes about solving math problems.

Looking ahead, the goal is to empower as many students as possible in the San Diego area and  beyond to learn to problem solve more enjoyably. It’s a concrete way to give students tools that could encourage them to thrive in the growing number of technical careers that require sharp problem-solving skills, whether or not they require a four-year degree. 

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Denise Cummins Ph.D.

How to Solve Problems Like an Expert

It's not so much what you know as how easily you can retrieve what you know..

Posted September 7, 2013

You have a problem when your current situation differs from your desired goal. You want to be rich, but your checking account balance is circling the drain. You want to date that gorgeous person, but you get tongue-tied whenever you even think about it. You are running late for work, and your car won’t start. In each case, what you want and what you have are decidedly different.

Problem solving is nothing more and nothing less searching for means to reduce the differences between your goal state and your current state. Yes, that’s right: All problem solving, at bottom, is search. When there is a clear procedure that will take you from the one to the other, we call that a well-defined problem. Making scrambled eggs is a well-defined problem. For the first, you simply follow a recipe, and voila, you’ve got breakfast.

If there is no clear procedure, we call that an ill-defined problem. Unfortunately, most of life’s important problems are ill defined. How do you make enough money to save for retirement , how do you avoid war, or how do you get that girl or guy to go out with you? These are all ill-defined problems because they don’t have clear goal states (how much is “enough” for retirement?) or they don’t have clear solution paths (how do you attract the interest of someone you find attractive?).

In 1945, the brilliant mathematician, George Pólya (1887–1985) wrote the quintessential text for solving problems, aptly titled How to Solve It. Here is how he summarized the problem-solving process.

1. First, make sure you understand the problem. You do this by developing a representation of the essential aspects of the problem. You do that by searching your knowledge base for information that seems to you to be solution-relevant.

2. After understanding, then make a plan for solving the problem. This will also usually involve searching one’s knowledge base for solutions that are appropriate for the problem as represented.

3. Carry out the plan by executing your solutions.

4. Look back on your work and ask “how could it be better?”

That is how it should be done. But most people make one huge mistake that derails the entire process, making it far less likely that they will succeed. What is that mistake?

They skip the first step.

Regardless of the domain, inexperienced problem-solvers tend to jump right to the solution stage of problem solving, with typically disastrous consequences. They often use a trial-and-error strategy in which the first solution that comes to mind is put into play. Because they didn’t take the time to fully understand the problem, their solution attempts fail when foreseeable glitches arise.

In contrast, experts tend to spend more time developing a full understanding of the problem, comparing what they currently know about the problem with what they need to know in order to get a complete picture of the situation. Because they spend more time in the problem representation stage, they are more likely to derive successful solutions, and to spend less time overall in generating a successful solution.

Here are three tips for executing step one like an expert.

1. Organize knowledge correctly. Often, novices have all the knowledge they need to solve the problem at hand. They just can’t get to it because their knowledge is organized in ways that make it difficult to see the connection between the current problem and what they already know.

Experts organize their knowledge in problem schemas that include relevant information about a type of problem and the procedures for solving problems of that type. This means that when experts think about problems, relevant information is automatically activated in memory , along with relevant solution procedures. In contrast, when novices think about a problem, their knowledge is too general and too scattered throughout memory, making problem-solving a tedious trial-and-error search. For example, a novice salesperson will focus on the general goal of “make the sale”, and will apply sales techniques in willy-nilly or fixed fashion to reach that goal. An experienced salesperson will focus on the specific goal of understanding what the customer needs and wants, and in developing a trust relationship with the customer. As a result, the experienced salesperson spends less time “working” the customer or showing them things in which they have no interest.

solving problem of educational expert

2. Ask the right questions. If you’ve ever done a Google search, you know that the quality of the search results depends entirely on the quality of the keywords you use. Garbage in, garbage out. This in a nutshell, is the key to developing a strong understanding of a problem—asking the right questions.

Experts are more likely to ask the right questions because their domain-specific knowledge is organized more efficiently. Continuing with the previous example, an expert salesperson’s schema is organized around understanding customer wants and needs. As a result, he or she will spend more time asking specific questions about those needs and wants, and then tailoring subsequent choices to match the answers given. Sometimes the customer isn’t aware that there are product features that may be attractive to them. For example, they may focus on price yet be unaware that a higher priced item carries a better warranty. Because the salesperson has taken the time to impress upon the customer that their needs and wants matter, a relationship of trust is established that makes it easier for the salesperson to introduce these relevant features without putting the customer off. In contrast, novice salespeople will often deluge the customer with more product features than they can possibly remember and process, or will try hard-sell techniques that create an atmosphere of distrust .

3. Work forward from known to unknown. Because of the way expert knowledge is organized, experts solve problems by working forward from the information given (or information obtained) to arrive at a viable solution. Novices, on the other hand, tend to work backwards because they are focused more at arriving at a quick solution that at ensuring that they fully understand the problem. As a result, the typically have incomplete problem-solving schemas that are full of irrelevant information. This slows down the problem-solving process, and makes it less likely that a viable solution will be reached—or remembered!

For three more tips on how to be a better problem solver, see this article Dr. Art Markman.

References: Pólya, George (1957). How to Solve It. Garden City, NY: Doubleday.

Dr. Denise Cummins is a Fellow of the Association for Psychological Science, and the author of Good Thinking: Seven Powerful Ideas That Influence the Way We Think (2012, Cambridge University Press).

Denise Cummins Ph.D.

Denise Dellarosa Cummins, Ph.D. , is the author of Good Thinking, The Historical Foundations of Cognitive Science , and Evolution of Mind.

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Veteran educator finds support in College of Education Coaching Academy

Dottie Adams hopes the experience continues for teacher leaders around the state.

One would assume a veteran educator of 23 years would know all the tricks in the book. Dottie Adams shares that the Coaching Academy offered more than one new technique to engage with fellow colleagues, interact with teaching interns and practice problem solving in her school. After eight years of teaching in Columbia, Adams has been a coaching educator for seven interns. Each of these interns represented a variety of degree programs and focus areas in the classroom.

“One of the hurdles to the coaching teacher experience is understanding all of the programs that the interns are housed in,” says Adams. “Every year, my intern may be in my classroom a different time period with different achievement goals, so learning how to support each of them could be challenging.”

While Adams’ early motivation for participating in the Coaching Academy was to better support her students, she found a larger highlight of the program was the support she received for her own work in her classroom and with her colleagues.

“I’m always someone who wants to make the education profession better,” says Adams. “Right now, we have to keep people in the classroom, and one of the ways we can do that is by being honest about what future educators are going to face on a daily basis. I also really love to learn from fellow educators.”

Some of the strategies the Coaching Academy offered were techniques for supportive and productive conversations and how to build capacity with current interns. Adams shared that the academy created a space for this work that is not always available during a typical teacher workday. She also shared that the time commitment for this work was accessible to an educator’s schedule. The academy’s first meeting at Dreher High School sealed the deal for Adams.

“I saw educators that I knew, and we were surrounded by master teachers,” says Adams. “It was great to be in a room across grade levels and age brackets and hear their stories. It was reassuring and validating that we were all committed to growing in this process.”

One of the messages Adams is passionate about sharing with her interns revolves around understanding how to prevent burnout. Adams had a previous experience where an intern was spending a great deal of time creating entertaining and engaging lesson plans for every day of the week. While Adams was proud of the student’s effort, she wanted the student to understand that this level of effort was not sustainable.

“I let the student know that if you try to teach at this level for 180 days, you’re going to last about two and a half years,” says Adams. “I know they wanted to do their best, but I wanted to have real conversations that can be hard about how to take care of yourself. When educators get burnt out and leave the profession, they can’t help the kids.”

Adams has also had to have hard conversations in the opposite direction with interns as well. Sometimes the internship can help students figure out for themselves if teaching is the profession they are truly passionate about. After participating in the Coaching Academy, Adams is more empowered to be direct with her interns to help when they are struggling. She also now knows how to better connect the interns with the available resources at the college.

“I think early on in my coaching experience, it was hard to know how the whole system functioned,” says Adams. “Previously, I may have felt like my job was at the school, and I could do my best with the intern in that environment; now I know more of the community surrounding each of these students. I think the biggest blessing is those added connection points.”

Adams is excited for the future of the Coaching Academy. She’s joined a group of educators from the first cohort to help imagine how the program could continue.

“I flourish when I am around people,” says Adams. “I’m an external processor, so being able to talk things out with fellow educators is helpful for me. I really believe this work is improving education.”

Adams says the focus of the group’s continued work is about building internal capacity at schools and recognizing the work of teacher leaders through coaching.

“Teaching is coaching,” says Adams. “We do this work with students all day every day, but sometimes we forget about coaching each other.”

Some of the work in which Adams is engaging centers on creating safe spaces for her teaching team to support one another. She shares that vulnerability with her fellow educators is the key.

“I always feel like I have to fix the problems that arise,” says Adams. “The Coaching Academy taught me that it was okay for me to not fix problems, but to lead people to solve them for themselves. It taught me to create comfortable, safe spaces in my school where teachers could be real and feel empowered to tackle things in our own ways. Teaching must be collaborative. The people you work with help you survive.”

Adams says that the College of Education made the connection that supporting teachers is the difference maker in education. She says that teachers must put aside their perfectionist tendencies and let themselves be coached, so that they can continue to pour into the next generation. She’s acutely aware that when veteran teachers leave the classroom, a wealth of institutional knowledge is lost.

“The Coaching Academy validates the people in schools who are instructional leaders, pedagogical leaders, and innovators,” says Adams. “It seems simple, but it’s amazing what appreciation can do.”

Challenge the conventional. Create the exceptional. No Limits.

A business journal from the Wharton School of the University of Pennsylvania

For New Ideas, Think Inside (This) Box

June 25, 2024 • 7 min read.

In this Nano Tool for Leaders, Penn's David Resnick offers tips on how to set helpful constraints that will unlock your creativity.

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Nano Tools for Leaders®   —  a collaboration between  Wharton Executive Education  and  Wharton’s Center for Leadership and Change Management  — are fast, effective tools that you can learn and start using in less than 15 minutes, with the potential to significantly impact your success and the engagement and productivity of the people you lead.

Harness constraints and analogies to unlock new solutions to old problems.

Traditional brainstorming,  as coined by Alex Osborne in the 1950s, asks participants to consider any and all ideas that might solve a problem. While blue-sky, no-limits thinking has several benefits, the drawback is that leaders often, paradoxically, get stuck. They encounter challenges like the “curse of the blank page,” not knowing where to start because they can start anywhere. They may also face the “ Einstellung effect ,” a phenomenon whereby the easy recollection of familiar solutions can block their ability to think of new ones.

This has led some to (erroneously) believe that generating solutions is best left to people who are naturally creative. The good news is that there are tools that can help one become much better at generating new ideas. The even better news is that using these tools does not involve extensive training or attending workshops. In fact, one tool developed at Penn Medicine’s Center for Health Care Transformation and Innovation is a simple  card game , and the “secret sauce” it teaches is how to leverage constraints and analogies. The  Accelerators in Innovation  game has teams of players use accelerator cards to create new kinds of solutions with questions such as “How would you solve postpartum depression if you operated like IKEA?” and “How might you tackle long emergency room wait times if you were Warren Buffet?” The solutions are then applied to problems presented on challenge cards while trying to avoid monkey wrenches from their opponents. After rapid-fire pitches, the judge determines each round’s winner.

Action Steps

1. make sure you are solving a problem..

Don’t solve for how to implement a solution. A classic example involved a design team brought in to figure out how to increase access to incubators. The issue is that the solution was already baked in (increase access to incubators). The team spent some time reframing the problem to focus on the true issue: ensuring that newborns are kept at a safe temperature, especially when delivery occurs in places with little or no access to electricity. Reframing to focus on the actual problem opened the team to entirely different solutions.

2. Leverage analogies.

Having to pull ideas out of thin air can be difficult and stressful. Analogies force us to consider other options or perspectives we may never have thought of, or thought of and dismissed. They cause us to ask ourselves “What is good about this other solution and how might it be applied to solving the problem I’m facing?” Examples include:

Think about successful companies and how their strengths could be applied to your problem. For example, IKEA is phenomenal at clearly explaining to people with limited background knowledge and literacy how to do something. So how might IKEA go about explaining post-op care to knee replacement patients?

Similarly, try using personas. Mary Poppins is renowned for making an unpleasant experience a delightful one. Mr. Rogers is known for his commitment to leveraging the kindness of neighbors. Darth Vader’s approach to getting things done is a ruthless level punishment for those who fail. Regardless of whom you choose, you can use the strengths or philosophies of these characters to inspire ideas. How might Mary Poppins improve adherence to physical therapy regimens? How might Darth Vader?

3. Leverage constraints.

Constraints are, unintuitively, another great way to force new thinking. Some options are:

How might you solve a problem if you were forced to delete a crucial (but perhaps onerous or costly) step of the process? Great examples are “How might tollbooths collect fees without a human there to do it?” (FastPass) or “How might people get their rental car if there was no line to wait in?” (Hertz Gold).

Design for extremes

How might you solve the problem if you had to solve for extreme use cases or extreme targets? For example, what would it take to screen 100 percent of eligible patients for colon cancer? How might you reduce civilian traffic fatalities to zero?

Real-world issues

Apply real-world constraints that have thrown a monkey wrench in your plans for past ideas. For example, how might you create a new marketing campaign that must be successful for consumers who do not speak English? How might you build a new product to launch on time even if multiple team members take a sabbatical or parental leave?

Focus on solving for how to make your solution delightful to users. This isn’t about making something silly or fun. It’s about surprising your users in a manner that unexpectedly accomplishes something for them.

4. Push for volume.

An additional benefit to Penn Medicine’s  Accelerators  card game is that it encourages multiple rounds to hear multiple ideas. When thinking of solutions, push for volume in your initial rounds. You’ll soon “use up” the ideas that come to mind easily and be forced to consider more creative or audacious alternatives.

5. Don’t take yourself too seriously.

Another key component of generating ideas while playing a game is that it allows for laughter and a sense of play. This mindset can foster creativity and an atmosphere of psychological safety for sharing ideas.

How One Leader Uses It

Rebecca Trotta, PhD, director of the Center for Nursing Excellence at Penn, leveraged this tool in developing a new program to support older adults after hospitalization. Her challenge was to build a service that could provide intensive at-home support. Despite an existing evidence-based protocol, there was concern that patient acceptance of this support would be low. Many folks are simply exhausted after being in the hospital and don’t want someone in their home. Using the constraint of solving for “delight,” Trotta and her team came up with the idea of delivering home meals to these patients and their caregivers.

While it might appear as a frivolous and seemingly useless expense, it turned out that after spending days (and sometimes weeks) in the hospital, patients came home to fridges that were empty or full of spoiled food. Providing them with a meal ensured they had adequate nutrition. More importantly, though, the meals showed a sense of caring and thoughtfulness that went well beyond patients’ expectations. It built a strong sense of trust that paid dividends in drastically increasing the acceptance of home services compared to baseline.

Contributor to this Nano Tool

David Resnick, MPH, MSEd, Senior Innovation Manager at Penn Medicine’s Center for Health Care Transformation and Innovation.  Accelerators in Health Care  card game co-created with Michael Begley, MA, Senior Experience Consultant at EPAM Systems, and Visiting Professor and Assistant Program Director of Masters of UX at Thomas Jefferson University.

Knowledge in Action: Related Executive Education Programs

  • Effective Decision Making: Thinking Critically and Rationally
  • The Neuroscience of Business: Innovations in Leadership and Strategic Decisions
  • Mastering Innovation: Strategy, Process, and Tools
  • Business Model Innovation in the Age of AI

Additional Resources

Access all Wharton Executive Education Nano Tools

Download this Nano Tool as a PDF

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Numeracy in schools doesn’t add up. here’s how experts would solve the problem, by robyn grace, save articles for later.

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All Australian children would be tested for numeracy knowledge in the first two years of school under a plan to halt underachievement in maths.

Education experts are stepping up pressure on the government to adopt a universal screening tool – similar to the grade 1 phonics test – to more quickly identify and assist children at risk of falling behind.

Education experts say universal numeracy screening could halt Australia’s “catch-up crisis”.

Education experts say universal numeracy screening could halt Australia’s “catch-up crisis”. Credit: Getty Images

In a report out on Thursday, Kelly Norris from think tank the Centre for Independent Studies says current student assessments do not meet adequate standards for universal screening.

She said the lack of a robust, consistent and evidence-based safety net had triggered a national “catch-up crisis”.

“Many children who perform poorly in maths in the first few years at school go on to suffer a failure cycle that is very difficult for schools to reverse,” she said.

Almost half of Australia’s 15-year-olds are failing to achieve national standards in maths, and the nation is more than four years behind Singapore, the world’s top-performing jurisdiction, the latest Programme for International Student Assessment (PISA) results show .

Meanwhile, an average of 33 per cent of students are below expectations in NAPLAN testing, including almost one in 10 who don’t achieve the expected outcomes for numeracy at their year level.

Norris said students who struggled with maths could be discovered in their first weeks at school, but were often not identified until their first NAPLAN tests in grade three.

She said about 400,000 Australian students a year –10 per cent – needed extra support or were below the international benchmark in maths. Only about 20 per cent of those who fall behind catch up.

In Screening that Counts: Why Australia needs universal early numeracy screening, Norris said school systems throughout the country were carrying out inefficient and haphazard early assessments of maths skills.

She said early maths screening should be carried out twice yearly and focus on robust models of “number sense”, which encompasses numbers (including saying, reading, and writing them); number relations (comparing and understanding them in terms of “more” and “less”); and number operations (understanding addition and subtraction).

Ultimately, Norris envisages screening being carried out in every year of schooling, as maths concepts progress through multiplication, algebra and more complicated concepts.

Calls for a universal numeracy screening test were first made by a national advisory panel in 2017. More recently, an expert panel informing the next National School Reform Agreement recommended adopting a nationally consistent numeracy screening check by the end of 2028.

“Sadly, over the course of these six years, little change in practice and supporting policy has been implemented,” Norris said in the report. “As a result, current tools available to Australian schools are not designed for, or well suited to, universal screening procedures.”

Mathematics achievement has implications for life beyond formal schooling.

“Adults with poor numeracy have lower rates of employment, income, higher rates of homelessness and poorer health outcomes,” Norris said.

“It is estimated that around one in five adults do not have the numeracy levels required to successfully complete daily tasks such as reading a petrol gauge or managing a household budget.”

Norris said early identification of struggling students and providing high-quality help made it possible to alter patterns of underachievement. But teachers needed the tools to do so in efficient and accurate ways.

“We know a great deal now about what predicts early numeracy success and what predicts, by extension, numeracy failure,” she said.

“It’s time to start getting some of these reliable tools into the hands of teachers so they can actually be intervening and offering the support that children need as early as possible.”

Grattan Institute education program director Jordana Hunter said numeracy performance had flatlined in the past decade and improving primary school outcomes was key to lifting achievement for older students.

Hunter, who served on the National School Reform Agreement expert panel, said that without robust universal screening of early numeracy skills, it was too easy to miss children who needed intervention.

“If we don’t adopt universal screening, we will continue to take a ‘hit or miss’ approach to identifying students who need extra help,” she said.

Dr Katherin Cartwright, Mathematical Association of NSW president and a former primary school teacher, agreed there needed to be a greater focus on early intervention.

But she said there were many factors at play, including lack of access to free preschool, students’ backgrounds and even their sense of belonging at school.

“I don’t think there is a lack in systems, schools and teachers working to support students in developing proficiency in numeracy, but there is a lack of consistency Australia-wide and access to national data for our younger students,” she said.

Federal Education Minister Jason Clare said he had “made it clear” that the next National School Reform Agreement must tie funding to reforms that “help children catch up, keep up and finish school”.

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Peter Dutton has promised to solve our energy problems – but his nuclear policy still leaves Australians in the dark

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Professor, School of Economics, The University of Queensland

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John Quiggin is a former Member of the Climate Change Authority

University of Queensland provides funding as a member of The Conversation AU.

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In 1971 on a family holiday, my father drove us to look at a huge concrete slab at Jervis Bay, on the South Coast of New South Wales. Still visible today, it was the foundation for what would have been Australia’s first nuclear power plant.

The project had just been cancelled by then-prime minister Billy McMahon who had recently replaced John Gorton. A Treasury analysis showed coal-fired power was much cheaper .

That long-ago episode is still relevant to Australia’s policy choices. Today, Opposition leader Peter Dutton revealed seven sites across Australia where the Coalition, if elected, would build nuclear power stations. Unsurprisingly, the plan has already run into opposition from state politicians, both Labor and the LNP.

The announcement answers a few basic questions about the Coalition’s nuclear plans. For example, Dutton said the plants would be Commonwealth-owned, and built at the site of decommissioned coal plants. But central issues remain unaddressed. Exactly what kind of reactors will be built? Who will build them? And how much they will cost?

As the Jervis Bay experience shows, nuclear energy can be a hard sell in Australia. Times have obviously changed since the 1970s, but significant political and economic barriers remain – and the problem of cost is still unsolved.

What the Coalition has revealed

The seven sites for nuclear power plants mooted by the Coalition are:

  • Tarong and Callide in Queensland
  • Liddell and Mount Piper in NSW
  • Port Augusta in South Australia
  • Loy Yang in Victoria
  • Muja in Western Australia.

At a press conference in Sydney, Dutton said:

We know the government has [a] renewables only policy which is not fit for purpose. No other country in the world can keep the lights on 24/7 with the renewables only policy. We want to utilise existing assets that we have got […] new poles and wires that are used at the moment on the coal-fired power station sites can be utilised to distribute the energy generated from the latest generation nuclear reactors.

Under the Coalition plan, the federal government would own and pay for the plants. In this respect, Dutton is following the precedent set by the Snowy Scheme – and more recently, by the National Broadband Network.

This is a welcome acknowledgement of the reality that, whatever technology we adopt, private investment is likely insufficient to manage the transition away from coal and gas in the electricity sector – let alone the massive electrification in other sectors needed to meet Australia’s 2050 emissions targets.

Dutton says he remains committed to the 2050 target for now, despite flagging the Coalition will abandon Australia’s 2030 emissions goal.

The Coalition says it will develop two “establishment projects” using either small modular reactors or larger plants. It claims the small reactors will start producing electricity by 2035, and the larger plants by 2037.

These timeframes are at odds with analysis by the CSIRO, which recently found reactors could not be operational in Australia until 2040 at the earliest.

The same report found construction of a large-scale nuclear power facility would cost at least A$8.6 billion, and possibly up to $17 billion. It said the electricity produced would be about 50% more costly than renewable energy.

On Wednesday, Dutton refused to provide a price tag for the Coalition policy. But he claimed it would be a “fraction” of Labor’s renewable energy policy.

wind turbines

Lessons from Jervis Bay

Dutton this week ruled out Jervis Bay as a nuclear reactor location, should the Coalition win the next federal election. But the 1970s experience still holds valuable lessons.

The Jervis Bay territory was ruled directly by the federal government – circumventing any potential state opposition. The Coalition faces a different battle with regards to its proposed sites.

Queensland LNP Leader David Crisafulli on Wednesday said he did not support Dutton’s plan for a nuclear power station in Central Queensland, and has previously ruled out lifting a state ban on nuclear power if elected in October.

NSW Labor Premier Chris Minns says building a nuclear reactor in the Hunter Valley is impossible under existing laws, and would disrupt the renewable energy transition.

Dutton pledged to work with state premiers to resolve such issues, and suggested financial incentives would be offered.

man in dark suit

It’s unclear whether existing coal plant owners, including state-owned generators, will be willing to sell the sites to the federal government. However, Dutton said on Wednesday that, according to legal advice, the government could compulsorily acquire the sites if needed.

When Jervis Bay was on the table as a nuclear site, there was no question the federal government would build, own and operate it. The idea that something as crucial as a nuclear power plant might be entrusted to a state government, let alone a foreign corporation, was never entertained.

The national government was at the postwar height of its power and confidence. It employed the best and brightest, and was expanding the scope and scale of its activity. The Snowy Mountains Scheme, a massive engineering endeavour built under the Commonwealth’s defence power, was nearing completion.

Dutton says the government will own the proposed nuclear plants, but form partnerships with nuclear companies to build and operate them. But which companies?

Internationally, about 60 nuclear plants are under construction, mostly in Asia. The vast majority are Chinese and Russian designs , built by Chinese and Russian firms. Presumably, for national security reasons, that is not an option for Australia.

The only real contenders for large modern projects in Australia are South Korea’s KEPCO, and Electricity de France (EDF).

KEPCO built four plants at Barakah, in the United Arab Emirates, between 2009 and 2024. But no new orders for KEPCO plants outside South Korea have been announced since 2009.

EDF is building a reactor at Flamanville in France and two at Hinkley Point in the United Kingdom. The projects have suffered massive delays and cost overruns . The UK government is also struggling to organise finance for an additional EDF reactor proposed at the existing Sizewell plant.

hydro infrastructure in mountain landscape

And what about the so-called small modular reactors suggested by Dutton? This term is applied to two types of technology.

First, there are reactors of less than 100 megawatt capacity, which would be built in a factory and shipped to the required site where they would be installed as individual modules.

The most promising contender was the NuScale Voygr design, however its pilot project has been abandoned . Similarly, Rolls Royce has spiked its plans for a factory in Wales that would have progressed technology used in small modular reactors.

The term is also applied to cut-down versions of existing large-scale designs: reactors of 300 to 500 megawatt capacity compared to the traditional 1,000 to 1,500 megawatts. These are “modular” only in the sense that most parts are built in factories and assembled onsite.

The government of Ontario in Canada has announced plans for four such reactors to be built by GE-Hitachi, but no final commitment has been made.

Meanwhile, the climate crisis continues

As the next federal election rolls closer, Dutton will come under pressure to reveal crucial details underpinning the Coalition’s nuclear plan – most importantly, how much it will cost.

Nothing announced by Dutton today changes the fact that nuclear energy is, according to reams of expert analysis, economically unfeasible in Australia. This is as true today as it was in the 1970s.

Meanwhile, the climate crisis continues to worsen. Solar panels, wind turbines and energy storage must be rolled out as rapidly as possible – and we must not allow Dutton’s policy detour to distract from the task.

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Problem and Solution

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A problem is a situation, condition, or issue that creates difficulty or presents an obstacle to achieving a desired goal or outcome. Problems can be identified in various contexts, including personal, professional, social, and technical environments. They require resolution to improve circumstances, processes, or performance. A solution is a method, process, or action taken to resolve a problem or address an issue.

Writing a short problem statement can help clearly define the issue at hand. For instance, a business problem solving proposal outlines the steps and strategies needed to tackle specific business challenges. In academic settings, a thesis problem statement articulates the research problem and its significance. Crafting a comprehensive problem statement is essential for setting the stage for finding effective solutions. Addressing a communication problem involves identifying barriers to effective communication and implementing strategies to overcome them.

What is Problem and Solution?

A problem and solution refers to a framework used to identify an issue and propose a way to address or resolve it. This approach involves clearly defining the problem, analyzing its causes and effects, and then developing and implementing strategies or actions to solve it. This method is commonly used in various fields such as business, education, engineering, and everyday life to systematically tackle challenges and improve outcomes.

Examples of Problem and Solution

  • Traffic congestion: Build more public transportation options.
  • Air pollution: Implement stricter emissions regulations for factories.
  • Water scarcity: Develop advanced water recycling systems.
  • Deforestation: Promote reforestation and sustainable logging practices.
  • Obesity: Increase public awareness about healthy eating and exercise.
  • Homelessness: Provide affordable housing and job training programs.
  • Cybersecurity threats: Enhance encryption and cybersecurity protocols.
  • Plastic waste: Promote the use of biodegradable materials and recycling.
  • Climate change: Increase the use of renewable energy sources.
  • Unemployment: Offer job retraining and education programs.
  • Poor education quality: Invest in teacher training and educational resources.
  • Food insecurity: Create community gardens and food banks.
  • Income inequality: Implement progressive tax policies and social programs.
  • Lack of healthcare access: Expand healthcare coverage and services.
  • Energy consumption: Develop and promote energy-efficient technologies.
  • Animal extinction: Enforce wildlife protection laws and conservation efforts.
  • Ocean pollution: Regulate and reduce plastic disposal and cleanup efforts.
  • Mental health issues: Increase mental health resources and support services.
  • Traffic accidents: Improve road infrastructure and enforce traffic laws.
  • Noise pollution: Implement noise control measures and urban planning strategies.

Types of Problem and Solution

Types of Problem and Solution

1. Technical Problems

  • Description : Issues related to technology , software , or hardware.
  • Solutions : Debugging code, replacing faulty hardware, updating software, optimizing network configurations.

2. Operational Problems

  • Description : Challenges in day-to-day operations and processes.
  • Solutions : Streamlining processes, improving logistics, automating tasks, implementing new operational strategies.

3. Strategic Problems

  • Description : Issues affecting the long-term direction and success of an organization.
  • Solutions : Conducting market research, revising strategic plans, aligning organizational objectives, adopting new business models.

4. Financial Problems

  • Description : Challenges related to the management of finances.
  • Solutions : Creating a detailed budget, improving financial planning, cutting unnecessary costs, finding new revenue streams.

5. Human Resource Problems

  • Description : Issues involving the workforce and employee management.
  • Solutions : Enhancing employee engagement, offering competitive benefits, providing training and development, improving recruitment strategies.

6. Customer Service Problems

  • Description : Challenges in delivering satisfactory customer service.
  • Solutions : Implementing better customer service protocols, training staff, using customer feedback to improve services, adopting customer relationship management (CRM) systems.

7. Marketing Problems

  • Description : Issues related to marketing and advertising strategies.
  • Solutions : Developing targeted marketing campaigns, using data analytics, enhancing digital marketing efforts, rebranding.

8. Legal Problems

  • Description : Issues involving legal compliance and regulations.
  • Solutions : Ensuring compliance with laws, consulting with legal experts, protecting intellectual property, revising contracts.

9. Environmental Problems

  • Description : Challenges related to environmental impact and sustainability.
  • Solutions : Implementing sustainable practices, reducing waste, using renewable resources, enhancing environmental policies.

Problem and Solution in Research

1. identifying the research problem.

  • Description : The research problem is a specific issue, difficulty, contradiction, or gap in knowledge that a researcher aims to address.
  • Example : Lack of effective treatment for a certain disease, unclear mechanisms behind a social phenomenon, or inefficiencies in a technological process.

2. Formulating the Research Problem

  • Description : Clearly defining and articulating the problem in a way that guides the research objectives and questions.
  • Example : “What are the underlying factors contributing to the low recovery rate of patients with XYZ disease?”

3. Literature Review

  • Description : Conducting a comprehensive review of existing research and theories related to the problem to understand the current state of knowledge.
  • Example : Reviewing past studies, articles, and reports on XYZ disease to identify what has been discovered and what gaps remain.

4. Developing Research Questions

  • Description : Formulating specific questions that the research aims to answer, derived from the research problem.
  • Example : “What treatments have been most effective in improving recovery rates for XYZ disease?” or “How do socioeconomic factors influence recovery rates?”

5. Choosing the Research Methodology

  • Description : Selecting appropriate methods and techniques to gather and analyze data that will address the research questions.
  • Example : Deciding between qualitative methods (like interviews and focus groups) or quantitative methods (like surveys and experiments).

6. Data Collection

  • Description : Gathering data using the chosen methods to obtain information relevant to the research problem.
  • Example : Conducting surveys among patients, collecting medical records, or performing laboratory experiments.

7. Data Analysis

  • Description : Analyzing the collected data to identify patterns, relationships, and insights that address the research questions.
  • Example : Using statistical analysis to determine the effectiveness of different treatments or thematic analysis to identify common themes in interview responses.

8. Presenting the Solution

  • Description : Proposing solutions or recommendations based on the findings of the research.
  • Example : Recommending a new treatment protocol based on the data showing its higher effectiveness or suggesting policy changes to address identified socioeconomic barriers.

9. Evaluating the Solution

  • Description : Assessing the proposed solutions for feasibility, effectiveness, and potential impact.
  • Example : Conducting pilot studies to test the new treatment protocol or evaluating the practicality of suggested policy changes.

10. Disseminating the Findings

  • Description : Sharing the research findings and proposed solutions with the wider community through publications, presentations, and reports.
  • Example : Publishing in academic journals, presenting at conferences, or preparing reports for policymakers and practitioners.

Problem and Solution Synonyms

Issue, Challenge, Difficulty, Obstacle, Hurdle, Complication, Concern, Dilemma, Predicament, Quandary
Answer, Resolution, Fix, Remedy, Cure, Key, Explanation, Approach, Strategy, Plan

Uses of Problem and Solution

  • Critical Thinking and Analysis : The problem and solution framework helps develop critical thinking and analytical skills. By systematically identifying a problem, analyzing its causes, and brainstorming possible solutions, individuals enhance their ability to think logically and solve complex issues.
  • Education and Learning : Teachers and educators use the problem and solution approach to enhance learning experiences. It encourages students to engage with material actively, apply knowledge to real-world scenarios, and develop problem-solving skills essential for academic and personal success.
  • Business and Management : In business, identifying problems and devising solutions is crucial for maintaining competitiveness and efficiency. Managers use this framework to address operational issues, improve processes, resolve conflicts, and innovate products and services.
  • Engineering and Technology : Engineers and technologists rely on the problem and solution framework to design and develop new products, systems, and technologies. They identify technical challenges, analyze requirements, and create solutions that meet specific needs and constraints.
  • Healthcare and Medicine : Healthcare professionals use the problem and solution approach to diagnose and treat medical conditions. By identifying symptoms (problems), they can determine the underlying causes and develop appropriate treatment plans (solutions).
  • Policy Making and Public Administration : Policymakers use this framework to address societal issues such as poverty, education, and public health. By understanding the root causes of problems, they can create and implement policies aimed at providing effective solutions.
  • Environmental Management : Environmental scientists and managers use the problem and solution approach to address issues like pollution, climate change, and resource depletion. Identifying environmental problems allows them to develop and implement strategies to mitigate negative impacts and promote sustainability.
  • Project Management : Project managers use this framework to identify potential risks and issues that could affect project success. They develop risk mitigation plans and solutions to ensure projects are completed on time, within budget, and to the desired quality standards.

What are common problem-solving methods?

Common methods include brainstorming, root cause analysis, trial and error, and the scientific method.

What is root cause analysis?

Root cause analysis identifies the fundamental cause of a problem to address it effectively.

How does brainstorming help in problem-solving?

Brainstorming generates diverse ideas and solutions through collaborative thinking.

What is the scientific method’s role in problem-solving?

The scientific method uses systematic observation, measurement, and experimentation to identify solutions.

How do you prioritize problems?

Prioritize problems based on their urgency, impact, and feasibility of solutions.

What is a problem statement?

A problem statement clearly defines the issue, its context, and its impact.

How can you evaluate potential solutions?

Evaluate solutions by considering their effectiveness, feasibility, and potential consequences.

What is the role of creativity in problem-solving?

Creativity introduces novel and innovative approaches to finding solutions.

How can collaboration aid in solving problems?

Collaboration brings diverse perspectives and expertise, enhancing solution development.

What are the steps in the problem-solving process?

Steps include identifying the problem, analyzing it, generating solutions, implementing solutions, and evaluating outcomes.


Text prompt

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10 Examples of Public speaking

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Ohio public schools have problems a lawsuit can't solve. It's time to refocus.

I believe in the importance of good public schools, but they shouldn’t be immune to the consequences of their failures..

New Albany resident Philip Derrow is a retired business owner. He was a two-term member of the New Albany-Plain Local Board of Education . He is a frequent Columbus Dispatch contributor.

K-12 education is too often failing in its most elementary role, and neither the cost of that failure nor its solution will ultimately be measured in money.

Two recent stories with markedly different angles on the challenges facing primary and secondary education are more closely related than they might appear. 

In “ Divided Upper Arlington school board joins lawsuit to end universal vouchers in Ohio ” the board chose to take a partisan position on Ohio’s school voucher program. Then, “ Study shows Ohio students losing ground in math post pandemic ” highlighted the failure of Ohio schools to make up for the educational losses caused by their response to the pandemic. 

Universal vouchers in Upper Arlington: Divided Upper Arlington school board joins lawsuit to end universal vouchers in Ohio

What’s the connection? Let’s start with the basics.

Prioritizing education

I have long argued that the primary role of K-12 education is to successfully impart foundational knowledge to students in literacy, math, the natural sciences, history, civics and the arts. Schools have only 12 short years to convey the basic knowledge acquired from over ten thousand years of human civilization. Teachers and staff more than have their hands full just doing that.

Schools that cannot fulfill that role shouldn’t spend a penny on much of anything else. 

If only that were true. Ohioans spend tens of billions of dollars on K-12 education while tens of thousands of Ohio kids will leave high school woefully ignorant of that foundational knowledge.

The money each district spends is even less connected to the academic outcomes they achieve.  Columbus City Schools  spends just under $20,000 per student each year, while  Upper Arlington  spends just under $17,000. My home district of  New Albany-Plain Local Schools  spends just under $13,000.

Which one produces the best results for kids and the best value for taxpayers? Look up these schools on  Ohio’s school report card  and see for yourself. 

Fights over public education remain

Nationally, the problem is even worse as the U.S. falls further and further behind our international peers , trading partners and competitors. 

The fight over vouchers for private schools, while often framed as being elitist, racist or religious in nature, is instead ultimately about parents’ growing dissatisfaction with the academic performance and/or political partisanship of their public schools. 

Voucher arguments: Ohio lawmakers want 'apples to apples' comparison between public and private schools

Of course, money is always given as a big reason for the fight. Public schools rightly complain about losing funding, and parents of kids in private schools rightly complain about having to pay for school twice — once in taxes and a second time in private tuition.

I learned early in my business career that if an employee quit or a customer changed suppliers because of money, money was rarely the actual reason. If I hadn’t given them lots of other reasons to leave, they would have given me lots of other chances to resolve any actual complaints over pay or price. 

Public schools serve as microcosm of community

The same is true for most parents seeking educational options for their children. Public schools have always been a microcosm of their communities.

When Randi Weingarten, the head of the nation’s second-largest teacher’s union in the U.S.,  wrote about public schools that “They are the manifestation of our civic values and ideals…," she ignores the fact that our nation is sharply divided about what those values and ideals are or should be, and that her members have no business trying to be the arbiters of them.

Public schools could — and should be — a respite for kids from those conflicts. But rather than focus on the primary role of imparting foundational knowledge, far too many teachers and administrators have chosen to take one-sided and highly partisan positions on virtually every issue. 

Parents and voters have rightly responded with their choice of schools for their kids and their choice of elected representatives who’ve put the voucher programs in place to support them. 

Working to improve public schools; Children's education matters

I believe in the importance of good public schools, but they shouldn’t be immune to the consequences of their failures. They should keep students and the money that follows them because they’re a better choice, not by suing to prevent parents from having it.

There is, however, a significant accountability gap in the current voucher programs.

If private schools are going to get hundreds of millions of public funding, as they are likely to do under these programs, their students should be held to the same standards and testing requirements.

Ohio  House Bill 407  is a good start for such accountability.  

Public schools need to refocus on their primary academic role, stop trying to replace parents and learn from parents’ choices instead. 

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