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The Common Core State Standards

Art of Problem Solving courses are not designed to align to the Common Core State Standards ( CCSS ). However, we have many students who have easily replaced CCSS-aligned classes using our coursework. Our curriculum covers all of the Common Core Practices. Each of our classes also covers most or all of the Standards covered in the corresponding class from a CCSS-aligned school (and a good deal more!).

We've compiled some information below to help students and their schools choose the best possible education plan.

• What Is The Common Core?

Differences Between AoPS and the CCSS

Common core coverage, what is the common core.

The Common Core State Standards are a collection of Standards for Mathematical Practice combined with a collection of Standards for Mathematical Content. You can find the Common Core here .

Standards for Mathematical Practice

The Standards for Mathematical Practice ( Practices ) are eight general pedagogical goals suggested for all mathematical education:

• Make sense of problems and persevere in solving them.
• Reason abstractly and quantitatively.
• Construct viable arguments and critique the reasoning of others.
• Model with Mathematics.
• Use appropriate tools strategically.
• Attend to precision.
• Look for and make use of structure.
• Look for and express regularity in repeated reasoning.
• Make sense of problems and persevere in solving them : AoPS does not believe that math is memorizing Trick A to solve Problem A and Trick B for Problem B. Problem solving is about understanding the problem, weighing the possible approaches, and deciding which is the best strategy for solving it. Sometimes the path is not apparent, and sometimes what at first seemed like a promising start needs to be rethought. A good problem solver has the tenacity to work through these obstacles.
• Reason abstractly and quantitatively and Model with Mathematics : Part of problem solving is the ability to translate the problem description into mathematical symbols. At the same time, it is important for students to not treat equations as a series of symbols to be manipulated but understand what their equations mean in the context of the mathematical concepts and the problem. To understand problems deeply, a mathematician needs to be able to follow paths of context and abstraction simultaneously.
• Construct viable arguments and critique the reasoning of others , Use appropriate tools strategically and Attend to precision : Many traditional schools only discuss proofs in Geometry class, and only in simplistic terms. AoPS integrates proof-writing—having the students construct rigorous logical arguments and communicate their ideas clearly—starting from our Prealgebra courses. Each week in our subject series courses, students have one or more free response writing problems. Student responses are human-graded and receive feedback on their solution, including their ability to communicate mathematically. Students learn to construct and analyze mathematical arguments in our classroom as well, where we make the students do all the work .
• Look for and make use of structure and Look for and express regularity in repeated reasoning : Recognizing patterns is an important problem solving strategy. AoPS students learn by studying relevant problems and generalizing their ideas into the underlying principles. This requires dissecting each problem into its constituent pieces and their connective structures. This also requires finding common principles inside different problems and finding ways to extract those principles and use them on the current problem or on problems down the road.

Standards for Mathematical Content

Traditional schools and the Common Core are generally concerned with getting students through the typical four-year high school curriculum, in a large part to prepare them for college-level Calculus. Art of Problem Solving serves high-performing students who learn at a faster pace and can handle more complex cognitive tasks. These students are not stretched by the traditional curriculum, so they do not grow to their full potential. They need more intellectual stimulation.

One way AoPS addresses this is by including advanced topics in Algebra and Geometry that do not appear on the Common Core State Standards. The AoPS curriculum also includes courses in discrete math, namely counting and number theory, which also are not part of the Common Core or standard high school curricula. For example, our Introductory and Intermediate Counting & Probability and Number Theory courses do not contain many Standards because much of their material lies outside the Common Core. This omission in the CCSS is unfortunate since discrete math is a key part of college-level math and the mathematics of programming, and students who have a background in these fields will have a significant advantage in those majors and in the real world. These might be the most applicable skills our students learn in their high school careers.

Furthermore, counting and number theory are accessible fields where students can further their mathematical reasoning and proof techniques. The traditional curriculum generally teaches students many tools to apply to specific straightforward problems, again in large part because the school is in a rush to provide the student all the prerequisites to enroll in Calculus. But this is not what mathematics is about. Our philosophy is to teach students problem solving which, in contrast, is about taking the tools they have and applying them to solve complex problems. Real life will throw students many problems they have not specifically been trained to solve, and the students with stronger problem solving skills will be better positioned to tackle these problems. Learning discrete math, in addition to expanding the students' horizons, gives them the opportunity to develop problem solving skills before moving onto more complex topics.

The other major difference between the Common Core State Standards and the Art of Problem Solving curriculum is the treatment of Statistics. AoPS currently does not have a Statistics course. Several AoPS courses cover standards regarding probability, specifically using problems where student calculate probabilities to illustrate interesting applications of counting techniques and geometric probability. Many Common Core standards regarding interpreting data and justifying conclusions are not covered by AoPS courses at this time. If a student is using an AoPS course to skip a class in a traditional school, she may need to spend a couple of days in the school library reading through the statistics chapter of her local textbook.

• The Common Core grades 6-8 contain numerous standards involving 3-dimensional shapes. The Geometry component in AoPS Prealgebra 2 is closer to a traditional Euclidean plane geometry course, where students apply geometric properties to solve problems. AoPS discusses 3-dimensional geometry first in its Beast Academy 5A curriculum and then defers until Introduction to Geometry , where students can extend their mastery of 2-dimensional geometry to reason about 3-dimensional configurations. We reach the depth expected in the CCSS in our 5A explorations and then wait on the material until students have the tools to solve more complex problems instead of learning extra forumulas earlier.
• The Common Core uses geometric transformations—dilation, reflection, rotation, and translation—to define congruence and similarity. In contrast, AoPS uses an informal definition of congruence and similarity that utilizes the students' intuition, saving transformations for later in the Introduction to Geometry course. AoPS also discusses geometric transformations in Precalculus using the tools of complex numbers and vectors.
• Also, AoPS and the Common Core emphasize different aspects of the Expressions & Equations domains in grades 6-8. The Common Core uses the coordinate plane to connect concepts in ratios, expressions, and geometry that deal with linear equations and their graphs. AoPS does not cover the graphs of linear equations until the high school-level Introduction to Algebra A course. Similarly, the grade 8 Functions domain and standards regarding systems of linear equations are taught in Algebra, where we can provide a more rigorous treatment. Instead, the Common Core high school cluster A.SSE (Algebra: Seeing Structure in Expressions) is pushed forward into AoPS Prealgebra as it is an important problem solving skill when manipulating algebraic expressions.

The following tables describe which AoPS courses cover the various Common Core content standards. You can find similar information for our courses in each Course Syllabus .

Number and Quantity Intro Alg A Intro Alg B Intro NT Intro CP Intro Geo Interm Alg Precalc
The Real Number System: Extend The Properties Of Exponents To Rational Exponents, Use Properties Of Rational And Irrational Numbers
RN.1 RN.1
RN.2 RN.2
Quantities: Reason Quantitatively And Use Units To Solve Problems
Q .1 Q .1
Q .2 Q .2
The Complex Number System: Perform Arithmetic Operations With Complex Numbers, Represent Complex Numbers And Their Operations On The Complex Plane, Use Complex Numbers In Polynomial Identities And Equations
CN.1 CN.1
CN.2 CN.2
CN.4
CN.5
CN.6
CN.7 CN.7 CN.7 CN.7
CN.8 CN.8 CN.8 CN.8
CN.9 CN.9 CN.9 CN.9
Represent And Model With Vector Quantities, Perform Operations On Vectors, Perform Operations On Matrices And Use Matrices In Applications
VM.1
VM.2
VM.3
VM.4
VM.4.a
VM.4.b
VM.4.c
VM.5
VM.5.a
VM.5.b
VM.6
VM.7
VM.8
VM.9
VM.10
VM.11
VM.12
Algebra Intro Alg A Intro Alg B Intro NT Intro CP Intro Geo Interm Alg Precalc
The Real Number System: Interpret The Structure Of Expressions, Write Expressions In Equivalent Forms To Solve Problems
SSE.1 SSE.1
SSE.1.a SSE.1.a
SSE.1.b SSE.1.b SSE.1.b
SSE.2 SSE.2
SSE.3 SSE.3
SSE.3.a SSE.3.a SSE.3.a SSE.3.a
SSE.3.b SSE.3.b SSE.3.b
SSE.3.c SSE.3.c
SSE.4
Arithmetic With Polynomials And Rational Expressions: Perform Arithmetic Operations On Polynomials, Understand The Relationship Between Zeros And Factors Of Polynomials, Use Polynomial Identities To Solve Problems, Rewrite Rational Expressions
APR.1 APR.1 APR.1 APR.1
APR.2 APR.2
APR.3 APR.3
APR.4 APR.4
APR.5 APR.5 APR.5
APR.6
APR.7
Creating Equations: Create Equations That Describe Numbers Or Relationships
CED.1 CED.1
CED.2
CED.4 CED.4
Understand Solving Equations As A Process Of Reasoning And Explain The Reasoning, Solve Equations And Inequalities In One Variable, Solve Systems Of Equations, Represent And Solve Equations And Inequalities Graphically
REI.1 REI.1
REI.2 REI.2 REI.2
REI.3 REI.3
REI.4 REI.4
REI.4.a REI.4.a REI.4.a
REI.4.b REI.4.b
REI.5
REI.6 REI.6
REI.7 REI.7
REI.8
REI.9
REI.10
REI.11
REI.12 REI.12
Functions Intro Alg A Intro Alg B Intro NT Intro CP Intro Geo Interm Alg Precalc
The Real Number System: Understand The Concept Of A Function And Use Function Notation, Interpret Functions That Arise In Applications In Terms Of The Context, Analyze Functions Using Different Representations
IF.1 IF.1 IF.1
IF.2 IF.2
IF.3 IF.3
IF.4 IF.4 IF.4 IF.4
IF.5 IF.5 IF.5 IF.5
IF.6
IF.7 IF.7 IF.7 IF.7
IF.7.a IF.7.a IF.7.a
IF.7.b IF.7.b IF.7.b
IF.7.c
IF.7.d
IF.7.e IF.7.e
IF.8 IF.8 IF.8
IF.8.a IF.8.a
IF.8.b
IF.9 IF.9 IF.9
Building Functions: Build A Function That Models A Relationship Between Two Quantities, Build New Functions From Existing Functions
BF.1 BF.1
BF.1.a BF.1.a
BF.1.b BF.1.b BF.1.b
BF.1.c BF.1.c BF.1.c BF.1.c
BF.2
BF.3 BF.3
BF.4 BF.4
BF.4.a BF.4.a BF.4.a BF.4.a
BF.4.b BF.4.b
BF.4.c BF.4.c
BF.4.d
BF.5
Linear, Quadratic, And Exponential Models: Construct And Compare Linear, Quadratic, And Exponential Models And Solve Problems, Interpret Expressions For Functions In Terms Of The Situation They Model
LE.1
LE.1.a
LE.1.b
LE.1.c
LE.2
LE.3
LE.4
LE.5 LE.5 LE.5
Extend The Domain Of Trigonometric Functions Using The Unit Circle, Model Periodic Phenomena With Trigonometric Functions, Prove And Apply Trigonometric Identities
TF.1
TF.2
TF.3
TF.4
TF.5 TF.5
TF.6 TF.6
TF.7
TF.8 TF.8
TF.9 TF.9
Geometry Intro Alg A Intro Alg B Intro NT Intro CP Intro Geo Interm Alg Precalc
The Real Number System: Experiment With Transformations In The Plane, Understand Congruence In Terms Of Rigid Motions, Prove Geometric Theorems, Make Geometric Constructions
CO.2
CO.3
CO.4
CO.5
CO.6
Similarity, Right Triangles, And Trigonometry: Understand Similarity In Terms Of Similarity Transformations, Prove Theorems Involving Similarity, Define Trigonometric Ratios And Solve Problems Involving Right Triangles, Apply Trigonometry To General Triangles
SRT.7
SRT.8
SRT.9
SRT.10
SRT.11
Expressing Geometric Properties With Equations: Translate Between The Geometric Description And The Equation For A Conic Section, Use Coordinates To Prove Simple Geometric Theorems Algebraically
GPE.1
GPE.2
GPE.3
GPE.5 GPE.5
GPE.6 GPE.6
Apply Geometric Concepts In Modeling Situations
MG.2 MG.2
Statistics and Probability Intro Alg A Intro Alg B Intro NT Intro CP Intro Geo Interm Alg Precalc
Conditional Probability And The Rules Of Probability: Understand Independence And Conditional Probability And Use Them To Interpret Data, Use The Rules Of Probability To Compute Probabilities Of Compound Events In A Uniform Probability Model
CP.2
CP.9
Calculate Expected Values And Use Them To Solve Problems, Use Probability To Evaluate Outcomes Of Decisions
MD.2
MD.5.a
MD.6

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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.

Published Date

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.

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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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Problem-Solving in Elementary School

Elementary students practice problem-solving and self-questioning techniques to improve reading and social and emotional learning skills.

In a school district in New Jersey, beginning in kindergarten each child is seen as a future problem solver with creative ideas that can help the world. Vince Caputo, superintendent of the Metuchen School District, explained that what drew him to the position was “a shared value for whole child education.”

Caputo’s first hire as superintendent was Rick Cohen, who works as both the district’s K–12 director of curriculum and principal of Moss Elementary School . Cohen is committed to integrating social and emotional learning (SEL) into academic curriculum and instruction by linking cognitive processes and guided self-talk.

Cohen’s first focus was kindergarten students. “I recommended Moss teachers teach just one problem-solving process to our 6-year-olds across all academic content areas and challenge students to use the same process for social problem-solving,” he explained.

Moss Elementary classrooms use a specific process to develop problem-solving skills focused on tending to social and interpersonal relationships. The process also concentrates on building reading skills—specifically, decoding and comprehension.

Stop, Look, and Think.  Students define the problem. As they read, they look at the pictures and text for clues, searching for information and asking, “What is important and what is not?” Social problem-solving aspect: Students look for signs of feelings in others’ faces, postures, and tone of voice.

Gather Information . Next, students explore what feelings they’re having and what feelings others may be having. As they read, they look at the beginning sound of a word and ask, “What else sounds like this?” Social problem-solving aspect: Students reflect on questions such as, “What word or words describe the feeling you see or hear in others? What word describes your feeling? How do you know, and how sure are you?”

Brainstorming . Then students seek different solutions. As they read, they wonder, “Does it sound right? Does it make sense? How else could it sound to make more sense? What other sounds do those letters make?” Social problem-solving aspect: Students reflect on questions such as, “How can you solve the problem or make the situation better? What else can you think of? What else can you try? What other ideas do you have?”

Pick the Best One.  Next, students evaluate the solution. While reading, they scan for smaller words they know within larger, more difficult words. They read the difficult words the way they think they sound while asking, “Will it make sense to other people?” Social problem-solving aspect: Students reflect on prompts such as, “Pick the solution that you think will be best to solve the problem. Ask yourself, ‘What will happen if I do this—for me, and for others involved?’”

Go . In the next step, students make a plan and act. They do this by rereading the text. Social problem-solving aspect: Students are asked to try out what they will say and how they will say it. They’re asked to pick a good time to do this, when they’re willing to try it.

Check . Finally, students reflect and revise. After they have read, they ponder what exactly was challenging about what they read and, based on this, decide what to do next. Social problem-solving aspect: Students reflect on questions such as, “How did it work out? Did you solve the problem? How did others feel about what happened? What did you learn? What would you do if the same thing happened again?”

You can watch the Moss Elementary Problem Solvers video and see aspects of this process in action.

The Process of Self-Questioning

Moss Elementary students and other students in the district are also taught structured self-questioning. Cohen notes, “We realized that many of our elementary students would struggle to generalize the same steps and thinking skills they previously used to figure out an unknown word in a text or resolve social conflicts to think through complex inquiries and research projects.” The solution? Teach students how to self-question, knowing they can also apply this effective strategy across contexts. The self-questioning process students use looks like this:

Stop and Think. “What’s the question?”

Gather Information. “How do I gather information? What are different sides of the issue?”

Brainstorm and Choose. “How do I select, organize, and choose the information? What are some ways to solve the problem? What’s the best choice?”

Plan and Try. “What does the plan look like? When and how can it happen? Who needs to be involved?”

Check & Revise. “How can I present the information? What did I do well? How can I improve?”

The Benefits

Since using the problem-solving and self-questioning processes, the students at Moss Elementary have had growth in their scores for the last two years on the fifth-grade English language arts PARCC tests . However, as Cohen shares, “More important than preparing our students for the tests on state standards, there is evidence that we are also preparing them for the tests of life.”

Center for Teaching

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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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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5 Steps to Teaching Students a Problem-Solving Routine

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By Jeff Heyck-Williams, the director of curriculum and instruction for Two Rivers Public Charter School

When I visited a 5th grade class recently, the students were tackling the following problem:

If there are nine people in a room and every person shakes hands exactly once with each of the other people, how many handshakes will there be? How can you prove your answer is correct using a model or numerical explanation?

There were students on the rug modeling people with Unifix cubes. There were kids at one table vigorously shaking each other’s hand. There were kids at another table writing out a diagram with numbers. At yet another table, students were working on creating a numeric expression. What was common across this class was that all of the students were productively grappling around the problem.

On a different day, I was out at recess with a group of kindergartners who got into an argument over a vigorous game of tag. Several kids were arguing about who should be “it.” Many of them insisted that they hadn’t been tagged. They all agreed that they had a problem. With the assistance of the teacher, they walked through a process of identifying what they knew about the problem and how best to solve it. They grappled with this very real problem to come to a solution that all could agree upon.

Then just last week, I had the pleasure of watching a culminating showcase of learning for our 8th graders. They presented to their families about their project exploring the role that genetics plays in our society. Tackling the problem of how we should or should not regulate gene research and editing in the human population, students explored both the history and scientific concerns about genetics and the ethics of gene editing. Each student developed arguments about how we as a country should proceed in the burgeoning field of human genetics, which they took to Capitol Hill to share with legislators. Through the process, students read complex text to build their knowledge, identified the underlying issues and questions, and developed unique solutions to this very real problem.

Problem-solving is at the heart of each of these scenarios and is an essential set of skills our students need to develop. They need the abilities to think critically and solve challenging problems without a roadmap to solutions. At Two Rivers Public Charter School in the District of Columbia, we have found that one of the most powerful ways to build these skills in students is through the use of a common set of steps for problem-solving. These steps, when used regularly, become a flexible cognitive routine for students to apply to problems across the curriculum and their lives.

The Problem-Solving Routine

At Two Rivers, we use a fairly simple routine for problem-solving that has five basic steps. The power of this structure is that it becomes a routine that students are able to use regularly across multiple contexts. The first three steps are implemented before problem-solving. Students use one step during problem-solving. Finally, they finish with a reflective step after problem-solving.

Problem Solving from Two Rivers Public Charter School on Vimeo .

Before Problem-Solving: The KWI

The three steps before problem-solving: We call them the K-W-I.

The “K” stands for “know” and requires students to identify what they already know about a problem. The goal in this step of the routine is two-fold. First, the student needs to analyze the problem and identify what is happening within the context of the problem. For example, in the math problem above, students identify that they know there are nine people and each person must shake hands with each other person. Second, the student needs to activate their background knowledge about that context or other similar problems. In the case of the handshake problem, students may recognize that this seems like a situation in which they will need to add or multiply.

The “W” stands for “what” a student needs to find out to solve the problem. At this point in the routine, the student always must identify the core question that is being asked in a problem or task. However, it may also include other questions that help a student access and understand a problem more deeply. For example, in addition to identifying that they need to determine how many handshakes in the math problem, students may also identify that they need to determine how many handshakes each individual person has or how to organize their work to make sure that they count the handshakes correctly.

The “I” stands for “ideas” and refers to ideas that a student brings to the table to solve a problem effectively. In this portion of the routine, students list the strategies that they will use to solve a problem. In the example from the math class, this step involved all of the different ways that students tackled the problem from Unifix cubes to creating mathematical expressions.

This KWI routine before problem-solving sets students up to actively engage in solving problems by ensuring they understand the problem and have some ideas about where to start in solving the problem. Two remaining steps are equally important during and after problem-solving.

During Problem-Solving: The Metacognitive Moment

The step that occurs during problem-solving is a metacognitive moment. We ask students to deliberately pause in their problem-solving and answer the following questions: “Is the path I’m on to solve the problem working?” and “What might I do to either stay on a productive path or readjust my approach to get on a productive path?” At this point in the process, students may hear from other students that have had a breakthrough or they may go back to their KWI to determine if they need to reconsider what they know about the problem. By naming explicitly to students that part of problem-solving is monitoring our thinking and process, we help them become more thoughtful problem-solvers.

After Problem-Solving: Evaluating Solutions

As a final step, after students solve the problem, they evaluate both their solutions and the process that they used to arrive at those solutions. They look back to determine if their solution accurately solved the problem, and when time permits, they also consider if their path to a solution was efficient and how it compares with other students’ solutions.

The power of teaching students to use this routine is that they develop a habit of mind to analyze and tackle problems wherever they find them. This empowers students to be the problem-solvers that we know they can become.

The opinions expressed in Next Gen Learning in Action are strictly those of the author(s) and do not reflect the opinions or endorsement of Editorial Projects in Education, or any of its publications.

New Designs for School 5 Steps to Teaching Students a Problem-Solving Routine

Jeff Heyck-Williams (He, His, Him) Director of the Two Rivers Learning Institute in Washington, DC

We’ve all had the experience of truly purposeful, authentic learning and know how valuable it is. Educators are taking the best of what we know about learning, student support, effective instruction, and interpersonal skill-building to completely reimagine schools so that students experience that kind of purposeful learning all day, every day.

Students can use the 5 steps in this simple routine to solve problems across the curriculum and throughout their lives.

When I visited a fifth-grade class recently, the students were tackling the following problem:

If there are nine people in a room and every person shakes hands exactly once with each of the other people, how many handshakes will there be? How can you prove your answer is correct using a model or numerical explanation?

There were students on the rug modeling people with Unifix cubes. There were kids at one table vigorously shaking each other’s hand. There were kids at another table writing out a diagram with numbers. At yet another table, students were working on creating a numeric expression. What was common across this class was that all of the students were productively grappling around the problem.

On a different day, I was out at recess with a group of kindergarteners who got into an argument over a vigorous game of tag. Several kids were arguing about who should be “it.” Many of them insisted that they hadn’t been tagged. They all agreed that they had a problem. With the assistance of the teacher they walked through a process of identifying what they knew about the problem and how best to solve it. They grappled with this very real problem to come to a solution that all could agree upon.

Then just last week, I had the pleasure of watching a culminating showcase of learning for our 8th graders. They presented to their families about their project exploring the role that genetics plays in our society. Tackling the problem of how we should or should not regulate gene research and editing in the human population, students explored both the history and scientific concerns about genetics and the ethics of gene editing. Each student developed arguments about how we as a country should proceed in the burgeoning field of human genetics which they took to Capitol Hill to share with legislators. Through the process students read complex text to build their knowledge, identified the underlying issues and questions, and developed unique solutions to this very real problem.

Problem-solving is at the heart of each of these scenarios, and an essential set of skills our students need to develop. They need the abilities to think critically and solve challenging problems without a roadmap to solutions. At Two Rivers Public Charter School in Washington, D.C., we have found that one of the most powerful ways to build these skills in students is through the use of a common set of steps for problem-solving. These steps, when used regularly, become a flexible cognitive routine for students to apply to problems across the curriculum and their lives.

The Problem-Solving Routine

At Two Rivers, we use a fairly simple routine for problem solving that has five basic steps. The power of this structure is that it becomes a routine that students are able to use regularly across multiple contexts. The first three steps are implemented before problem-solving. Students use one step during problem-solving. Finally, they finish with a reflective step after problem-solving.

Problem Solving from Two Rivers Public Charter School

Before Problem-Solving: The KWI

The three steps before problem solving: we call them the K-W-I.

The “K” stands for “know” and requires students to identify what they already know about a problem. The goal in this step of the routine is two-fold. First, the student needs to analyze the problem and identify what is happening within the context of the problem. For example, in the math problem above students identify that they know there are nine people and each person must shake hands with each other person. Second, the student needs to activate their background knowledge about that context or other similar problems. In the case of the handshake problem, students may recognize that this seems like a situation in which they will need to add or multiply.

The “W” stands for “what” a student needs to find out to solve the problem. At this point in the routine the student always must identify the core question that is being asked in a problem or task. However, it may also include other questions that help a student access and understand a problem more deeply. For example, in addition to identifying that they need to determine how many handshakes in the math problem, students may also identify that they need to determine how many handshakes each individual person has or how to organize their work to make sure that they count the handshakes correctly.

The “I” stands for “ideas” and refers to ideas that a student brings to the table to solve a problem effectively. In this portion of the routine, students list the strategies that they will use to solve a problem. In the example from the math class, this step involved all of the different ways that students tackled the problem from Unifix cubes to creating mathematical expressions.

This KWI routine before problem solving sets students up to actively engage in solving problems by ensuring they understand the problem and have some ideas about where to start in solving the problem. Two remaining steps are equally important during and after problem solving.

The power of teaching students to use this routine is that they develop a habit of mind to analyze and tackle problems wherever they find them.

During Problem-Solving: The Metacognitive Moment

The step that occurs during problem solving is a metacognitive moment. We ask students to deliberately pause in their problem-solving and answer the following questions: “Is the path I’m on to solve the problem working?” and “What might I do to either stay on a productive path or readjust my approach to get on a productive path?” At this point in the process, students may hear from other students that have had a breakthrough or they may go back to their KWI to determine if they need to reconsider what they know about the problem. By naming explicitly to students that part of problem-solving is monitoring our thinking and process, we help them become more thoughtful problem solvers.

After Problem-Solving: Evaluating Solutions

As a final step, after students solve the problem, they evaluate both their solutions and the process that they used to arrive at those solutions. They look back to determine if their solution accurately solved the problem, and when time permits they also consider if their path to a solution was efficient and how it compares to other students’ solutions.

The power of teaching students to use this routine is that they develop a habit of mind to analyze and tackle problems wherever they find them. This empowers students to be the problem solvers that we know they can become.

Jeff Heyck-Williams (He, His, Him)

Director of the two rivers learning institute.

Jeff Heyck-Williams is the director of the Two Rivers Learning Institute and a founder of Two Rivers Public Charter School. He has led work around creating school-wide cultures of mathematics, developing assessments of critical thinking and problem-solving, and supporting project-based learning.

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Problem-Solving

creative writing
children's book
activities
classroom tools
language arts and writing
vocabulary

Jabberwocky

Problem-solving is the ability to identify and solve problems by applying appropriate skills systematically.

Problem-solving is a process—an ongoing activity in which we take what we know to discover what we don't know. It involves overcoming obstacles by generating hypo-theses, testing those predictions, and arriving at satisfactory solutions.

Problem-solving involves three basic functions:

Seeking information

Generating new knowledge

Making decisions

Problem-solving is, and should be, a very real part of the curriculum. It presupposes that students can take on some of the responsibility for their own learning and can take personal action to solve problems, resolve conflicts, discuss alternatives, and focus on thinking as a vital element of the curriculum. It provides students with opportunities to use their newly acquired knowledge in meaningful, real-life activities and assists them in working at higher levels of thinking (see Levels of Questions ).

Here is a five-stage model that most students can easily memorize and put into action and which has direct applications to many areas of the curriculum as well as everyday life:

Expert Opinion

Here are some techniques that will help students understand the nature of a problem and the conditions that surround it:

• List all related relevant facts.
• Make a list of all the given information.
• Restate the problem in their own words.
• List the conditions that surround a problem.
• Describe related known problems.

It's Elementary

For younger students, illustrations are helpful in organizing data, manipulating information, and outlining the limits of a problem and its possible solution(s). Students can use drawings to help them look at a problem from many different perspectives.

Understand the problem. It's important that students understand the nature of a problem and its related goals. Encourage students to frame a problem in their own words.

Describe any barriers. Students need to be aware of any barriers or constraints that may be preventing them from achieving their goal. In short, what is creating the problem? Encouraging students to verbalize these impediments is always an important step.

Identify various solutions. After the nature and parameters of a problem are understood, students will need to select one or more appropriate strategies to help resolve the problem. Students need to understand that they have many strategies available to them and that no single strategy will work for all problems. Here are some problem-solving possibilities:

Create visual images. Many problem-solvers find it useful to create “mind pictures” of a problem and its potential solutions prior to working on the problem. Mental imaging allows the problem-solvers to map out many dimensions of a problem and “see” it clearly.

Guesstimate. Give students opportunities to engage in some trial-and-error approaches to problem-solving. It should be understood, however, that this is not a singular approach to problem-solving but rather an attempt to gather some preliminary data.

Create a table. A table is an orderly arrangement of data. When students have opportunities to design and create tables of information, they begin to understand that they can group and organize most data relative to a problem.

Use manipulatives. By moving objects around on a table or desk, students can develop patterns and organize elements of a problem into recognizable and visually satisfying components.

Work backward. It's frequently helpful for students to take the data presented at the end of a problem and use a series of computations to arrive at the data presented at the beginning of the problem.

Look for a pattern. Looking for patterns is an important problem-solving strategy because many problems are similar and fall into predictable patterns. A pattern, by definition, is a regular, systematic repetition and may be numerical, visual, or behavioral.

Create a systematic list. Recording information in list form is a process used quite frequently to map out a plan of attack for defining and solving problems. Encourage students to record their ideas in lists to determine regularities, patterns, or similarities between problem elements.

Try out a solution. When working through a strategy or combination of strategies, it will be important for students to …

Keep accurate and up-to-date records of their thoughts, proceedings, and procedures. Recording the data collected, the predictions made, and the strategies used is an important part of the problem solving process.

Try to work through a selected strategy or combination of strategies until it becomes evident that it's not working, it needs to be modified, or it is yielding inappropriate data. As students become more proficient problem-solvers, they should feel comfortable rejecting potential strategies at any time during their quest for solutions.

Monitor with great care the steps undertaken as part of a solution. Although it might be a natural tendency for students to “rush” through a strategy to arrive at a quick answer, encourage them to carefully assess and monitor their progress.

Feel comfortable putting a problem aside for a period of time and tackling it at a later time. For example, scientists rarely come up with a solution the first time they approach a problem. Students should also feel comfortable letting a problem rest for a while and returning to it later.

Evaluate the results. It's vitally important that students have multiple opportunities to assess their own problem-solving skills and the solutions they generate from using those skills. Frequently, students are overly dependent upon teachers to evaluate their performance in the classroom. The process of self-assessment is not easy, however. It involves risk-taking, self-assurance, and a certain level of independence. But it can be effectively promoted by asking students questions such as “How do you feel about your progress so far?” “Are you satisfied with the results you obtained?” and “Why do you believe this is an appropriate response to the problem?”

TeacherVision Editorial Staff

The TeacherVision editorial team is comprised of teachers, experts, and content professionals dedicated to bringing you the most accurate and relevant information in the teaching space.

• Collaborative Problem Solving® »

Collaborative Problem Solving® (CPS)

At Think:Kids, we recognize that kids with challenging behavior don’t lack the will  to behave well. They lack the  skills  to behave well.

Our Collaborative Problem Solving (CPS) approach is proven to reduce challenging behavior, teach kids the skills they lack, and build relationships with the adults in their lives.

Anyone can learn Collaborative Problem Solving, and we’re here to help.

What is Collaborative Problem Solving?

Kids with challenging behavior are tragically misunderstood and mistreated. Rewards and punishments don’t work and often make things worse. Thankfully, there’s another way. But it requires a big shift in mindset.

Helping kids with challenging behavior requires understanding why they struggle in the first place. But what if everything we thought was true about challenging behavior was actually wrong? Our Collaborative Problem Solving approach recognizes what research has pointed to for years – that kids with challenging behavior are already trying hard. They don’t lack the will to behave well. They lack the skills to behave well.

Kids do well if they can.

CPS helps adults shift to a more accurate and compassionate mindset and embrace the truth that kids do well if they can – rather than the more common belief that kids would do well if they simply wanted to.

Flowing from this simple but powerful philosophy, CPS focuses on building skills like flexibility, frustration tolerance and problem solving, rather than simply motivating kids to behave better. The process begins with identifying triggers to a child’s challenging behavior and the specific skills they need help developing.  The next step involves partnering with the child to build those skills and develop lasting solutions to problems that work for everyone.

The CPS approach was developed at Massachusetts General Hospital a top-ranked Department of Psychiatry in the United States.  It is proven to reduce challenging behavior, teach kids the skills they lack, and build relationships with the adults in their lives. If you’re looking for a more accurate, compassionate, and effective approach, you’ve come to the right place. Fortunately, anyone can learn CPS. Let’s get started!

Attend a cps training.

60% of children exhibited improved behavior

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Extracurriculars

Why Teaching Problem-Solving Skills is Essential for Student Success

Teaching the art of problem-solving is crucial for preparing students to thrive in an increasingly complex and interconnected world. Beyond the ability to find solutions, problem-solving fosters critical thinking, creativity, and resilience: qualities essential for academic success and lifelong learning.

This article explores the importance of problem-solving skills, critical strategies for nurturing them in students, and practical approaches educators and parents can employ.

By equipping students with these skills, we empower them to tackle challenges confidently, innovate effectively, and contribute meaningfully to their communities and future careers .

Why Teaching Problem-Solving Skills is Important

Problem-solving is a crucial skill that empowers students to tackle challenges with confidence and creativity . In an educational context, problem-solving is not just about finding solutions; it involves critical thinking, analysis, and application of knowledge. Students who excel in problem-solving can understand complex problems, break them down into manageable parts, and develop effective strategies to solve them. This skill is applicable across all subjects, from math and science to language arts and social studies, fostering a more profound understanding and retention of material .

Beyond academics, problem-solving is a cornerstone of success in life. Successful people across various fields possess strong problem-solving abilities. They can navigate obstacles, innovate solutions, and adapt to changing circumstances. In engineering and business management careers, problem solvers are highly valued for their ability to find efficient and creative solutions to complex issues.

Educators prepare students for future challenges and opportunities by teaching problem-solving in schools. They learn to think critically , work collaboratively, and persist in facing difficulties, all essential lifelong learning and achievement skills. Thus, nurturing problem-solving skills in students enhances their academic performance and equips them for success in their future careers and personal lives.

Aspects of Problem Solving

Developing problem-solving skills is crucial for preparing students to navigate the complexities of the modern world. Critical thinking, project-based learning, and volunteering enhance academic learning and empower students to address real-world challenges effectively. By focusing on these aspects, students can develop the skills they need to innovate, collaborate, and positively impact their communities.

Critical Thinking

Critical thinking is a fundamental skill for problem-solving as it involves analysing and evaluating information to make reasoned judgments and decisions. It enables students to approach problems systematically, consider multiple perspectives, and identify underlying issues.

Critical thinking allows students to:

• Analyse information : Students can assess the relevance and reliability of information to determine its impact on problem-solving. For example, in a science project, critical thinking helps students evaluate experimental results to draw valid conclusions.
• Develop solutions : Students can choose the most effective solution by critically evaluating different approaches. In a group project, critical thinking enables students to compare and refine ideas to solve a problem creatively.

Project-Based Learning

Project-based learning (PBL) is an instructional approach where students learn by actively engaging in real-world and personally meaningful projects. It allows students to explore complex problems and develop essential skills such as collaboration and communication.

Here is how project-based learning helps students develop problem-solving skills.

• Apply knowledge : Students apply academic concepts to real-world problems by working on projects. For instance, in designing a community garden, students use math to plan the layout and science to understand plant growth.
• Develop skills : PBL fosters problem-solving by challenging students to address authentic problems. For example, in a history project, students might analyse primary sources to understand the causes of historical events and propose solutions to prevent similar conflicts.

Volunteering

Volunteering allows students to contribute to their communities while developing empathy, leadership , and problem-solving skills. It provides practical experiences that enhance learning and help students understand and address community needs.

Volunteering is important because it allows students to:

• Identify needs : Students can identify community needs and consider solutions by working in diverse settings. For example, volunteering at a food bank can inspire students to address food insecurity by organising donation drives.
• Collaborate : Volunteering encourages teamwork and collaboration to solve problems. Students learn to coordinate tasks and resources to achieve common goals when organising a charity event.

The Problem-Solving Process

Problem-solving involves a systematic approach to understanding, analysing, and solving problems. Here are the critical steps in the problem-solving process:

• Identify the problem : The first step is clearly defining and understanding the problem. This involves identifying the specific issue or challenge that needs to be addressed.
• Define goals : Once the problem is identified, it's essential to establish clear and measurable goals. This helps focus efforts and guide the problem-solving process.
• Explore possible solutions : The next step is brainstorming and exploring various solutions. This involves generating ideas and considering different approaches to solving the problem.
• Evaluate options : After generating potential solutions, evaluate each option based on its feasibility, effectiveness, and possible outcomes.
• Choose the best solution : Select the most appropriate solution that best meets the defined goals and addresses the root cause of the problem.
• Implement the solution : Once a solution is chosen, it must be implemented. This step involves planning the implementation process and taking necessary actions to execute the solution.
• Monitor progress : After implementing the solution, monitor its progress and evaluate its effectiveness. This step helps ensure that the problem is being resolved as expected.
• Reflect and adjust : Reflect on the problem-solving process, identify any lessons learned, and make adjustments if necessary. This continuous improvement cycle helps refine solutions and develop better problem-solving skills.

How to Become a General Problem Solver

Parents play a crucial role in nurturing their children's problem-solving skills. Here are some ways parents can help their children become effective problem solvers.

• Encourage critical thinking : Encourage children to ask questions, analyse information, and consider different perspectives. Engage them in discussions that challenge their thinking and promote reasoning.
• Support independence : Allow children to tackle challenges on their own. Offer guidance and encouragement without immediately providing solutions. This helps build confidence and resilience.
• Provide opportunities for problem-solving : Create opportunities for children to solve real-life problems, such as planning a family event, organising their room, or resolving conflicts with siblings or friends.
• Foster creativity : Encourage creative thinking and brainstorming. Provide materials and activities that stimulate imagination and innovation.
• Model problem-solving behaviours : Demonstrate problem-solving skills in your own life and involve children in decision-making processes. Show them how to approach challenges calmly and methodically.

How Online Schooling Encourages Problem-Solving

Online schooling encourages problem-solving skills by requiring students to navigate digital platforms, manage their time effectively , and troubleshoot technical issues independently.

Students often engage in interactive assignments and projects that promote critical thinking and creativity. They learn to adapt to different learning environments and collaborate virtually, fostering innovative solutions.

Online schooling also encourages self-directed learning , where students must identify and address their own learning gaps. This enhances problem-solving abilities and prepares them for the complexities of the digital age.

Developing Problem-Solving Skills for Kids | Strategies & Tips

We've made teaching problem-solving skills for kids a whole lot easier! Keep reading and comment below with any other tips you have for your classroom!

Problem-Solving Skills for Kids: The Real Deal

Picture this: You've carefully created an assignment for your class. The step-by-step instructions are crystal clear. During class time, you walk through all the directions, and the response is awesome. Your students are ready! It's finally time for them to start working individually and then... 8 hands shoot up with questions. You hear one student mumble in the distance, "Wait, I don't get this" followed by the dreaded, "What are we supposed to be doing again?"

When I was a new computer science teacher, I would have this exact situation happen. As a result, I would end up scrambling to help each individual student with their problems until half the class period was eaten up. I assumed that in order for my students to learn best, I needed to be there to help answer questions immediately so they could move forward and complete the assignment.

Here's what I wish I had known when I started teaching coding to elementary students - the process of grappling with an assignment's content can be more important than completing the assignment's product. That said, not every student knows how to grapple, or struggle, in order to get to the "aha!" moment and solve a problem independently. The good news is, the ability to creatively solve problems is not a fixed skill. It can be learned by students, nurtured by teachers, and practiced by everyone!

Your students are absolutely capable of navigating and solving problems on their own. Here are some strategies, tips, and resources that can help:

Problem-Solving Skills for Kids: Student Strategies

These are strategies your students can use during independent work time to become creative problem solvers.

1. Go Step-By-Step Through The Problem-Solving Sequence

Post problem-solving anchor charts and references on your classroom wall or pin them to your Google Classroom - anything to make them accessible to students. When they ask for help, invite them to reference the charts first.

2. Revisit Past Problems

If a student gets stuck, they should ask themself, "Have I ever seen a problem like this before? If so, how did I solve it?" Chances are, your students have tackled something similar already and can recycle the same strategies they used before to solve the problem this time around.

3. Document What Doesn’t Work

Sometimes finding the answer to a problem requires the process of elimination. Have your students attempt to solve a problem at least two different ways before reaching out to you for help. Even better, encourage them write down their "Not-The-Answers" so you can see their thought process when you do step in to support. Cool thing is, you likely won't need to! By attempting to solve a problem in multiple different ways, students will often come across the answer on their own.

4. "3 Before Me"

Let's say your students have gone through the Problem Solving Process, revisited past problems, and documented what doesn't work. Now, they know it's time to ask someone for help. Great! But before you jump into save the day, practice "3 Before Me". This means students need to ask 3 other classmates their question before asking the teacher. By doing this, students practice helpful 21st century skills like collaboration and communication, and can usually find the info they're looking for on the way.

Problem-Solving Skills for Kids: Teacher Tips

These are tips that you, the teacher, can use to support students in developing creative problem-solving skills for kids.

When a student asks for help, it can be tempting to give them the answer they're looking for so you can both move on. But what this actually does is prevent the student from developing the skills needed to solve the problem on their own. Instead of giving answers, try using open-ended questions and prompts. Here are some examples:

2. Encourage Grappling

Grappling  is everything a student might do when faced with a problem that does not have a clear solution. As explained in this article from Edutopia , this doesn't just mean perseverance! Grappling is more than that - it includes critical thinking, asking questions, observing evidence, asking more questions, forming hypotheses, and constructing a deep understanding of an issue.

There are lots of ways to provide opportunities for grappling. Anything that includes the Engineering Design Process is a good one! Examples include:

• Engineering or Art Projects
• Design-thinking challenges
• Computer science projects
• Science experiments

3. Emphasize Process Over Product

For elementary students, reflecting on the process of solving a problem helps them develop a growth mindset . Getting an answer "wrong" doesn't need to be a bad thing! What matters most are the steps they took to get there and how they might change their approach next time. As a teacher, you can support students in learning this reflection process.

4. Model The Strategies Yourself!

As creative problem-solving skills for kids are being learned, there will likely be moments where they are frustrated or unsure. Here are some easy ways you can model what creative problem-solving looks and sounds like.

• Ask clarifying questions if you don't understand something
• Talk through multiple possible outcomes for different situations
• Verbalize how you’re feeling when you find a problem

Practicing these strategies with your students will help create a learning environment where grappling, failing, and growing is celebrated!

Problem-Solving Skill for Kids

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Teaching Problem-Solving Skills

Many instructors design opportunities for students to solve “problems”. But are their students solving true problems or merely participating in practice exercises? The former stresses critical thinking and decision­ making skills whereas the latter requires only the application of previously learned procedures.

Problem solving is often broadly defined as "the ability to understand the environment, identify complex problems, review related information to develop, evaluate strategies and implement solutions to build the desired outcome" (Fissore, C. et al, 2021). True problem solving is the process of applying a method – not known in advance – to a problem that is subject to a specific set of conditions and that the problem solver has not seen before, in order to obtain a satisfactory solution.

Below you will find some basic principles for teaching problem solving and one model to implement in your classroom teaching.

Principles for teaching problem solving

• Model a useful problem-solving method . Problem solving can be difficult and sometimes tedious. Show students how to be patient and persistent, and how to follow a structured method, such as Woods’ model described below. Articulate your method as you use it so students see the connections.
• Teach within a specific context . Teach problem-solving skills in the context in which they will be used by students (e.g., mole fraction calculations in a chemistry course). Use real-life problems in explanations, examples, and exams. Do not teach problem solving as an independent, abstract skill.
• Help students understand the problem . In order to solve problems, students need to define the end goal. This step is crucial to successful learning of problem-solving skills. If you succeed at helping students answer the questions “what?” and “why?”, finding the answer to “how?” will be easier.
• Take enough time . When planning a lecture/tutorial, budget enough time for: understanding the problem and defining the goal (both individually and as a class); dealing with questions from you and your students; making, finding, and fixing mistakes; and solving entire problems in a single session.
• Ask questions and make suggestions . Ask students to predict “what would happen if …” or explain why something happened. This will help them to develop analytical and deductive thinking skills. Also, ask questions and make suggestions about strategies to encourage students to reflect on the problem-solving strategies that they use.
• Link errors to misconceptions . Use errors as evidence of misconceptions, not carelessness or random guessing. Make an effort to isolate the misconception and correct it, then teach students to do this by themselves. We can all learn from mistakes.

Woods’ problem-solving model

Define the problem.

• The system . Have students identify the system under study (e.g., a metal bridge subject to certain forces) by interpreting the information provided in the problem statement. Drawing a diagram is a great way to do this.
• Known(s) and concepts . List what is known about the problem, and identify the knowledge needed to understand (and eventually) solve it.
• Unknown(s) . Once you have a list of knowns, identifying the unknown(s) becomes simpler. One unknown is generally the answer to the problem, but there may be other unknowns. Be sure that students understand what they are expected to find.
• Units and symbols . One key aspect in problem solving is teaching students how to select, interpret, and use units and symbols. Emphasize the use of units whenever applicable. Develop a habit of using appropriate units and symbols yourself at all times.
• Constraints . All problems have some stated or implied constraints. Teach students to look for the words "only", "must", "neglect", or "assume" to help identify the constraints.
• Criteria for success . Help students consider, from the beginning, what a logical type of answer would be. What characteristics will it possess? For example, a quantitative problem will require an answer in some form of numerical units (e.g., \$/kg product, square cm, etc.) while an optimization problem requires an answer in the form of either a numerical maximum or minimum.

• “Let it simmer”.  Use this stage to ponder the problem. Ideally, students will develop a mental image of the problem at hand during this stage.
• Identify specific pieces of knowledge . Students need to determine by themselves the required background knowledge from illustrations, examples and problems covered in the course.
• Collect information . Encourage students to collect pertinent information such as conversion factors, constants, and tables needed to solve the problem.

Plan a solution

• Consider possible strategies . Often, the type of solution will be determined by the type of problem. Some common problem-solving strategies are: compute; simplify; use an equation; make a model, diagram, table, or chart; or work backwards.
• Choose the best strategy . Help students to choose the best strategy by reminding them again what they are required to find or calculate.

Carry out the plan

• Be patient . Most problems are not solved quickly or on the first attempt. In other cases, executing the solution may be the easiest step.
• Be persistent . If a plan does not work immediately, do not let students get discouraged. Encourage them to try a different strategy and keep trying.

Encourage students to reflect. Once a solution has been reached, students should ask themselves the following questions:

• Does the answer make sense?
• Does it fit with the criteria established in step 1?
• Did I answer the question(s)?
• What did I learn by doing this?
• Could I have done the problem another way?

If you would like support applying these tips to your own teaching, CTE staff members are here to help.  View the  CTE Support  page to find the most relevant staff member to contact.

• Fissore, C., Marchisio, M., Roman, F., & Sacchet, M. (2021). Development of problem solving skills with Maple in higher education. In: Corless, R.M., Gerhard, J., Kotsireas, I.S. (eds) Maple in Mathematics Education and Research. MC 2020. Communications in Computer and Information Science, vol 1414. Springer, Cham. https://doi.org/10.1007/978-3-030-81698-8_15
• Foshay, R., & Kirkley, J. (1998). Principles for Teaching Problem Solving. TRO Learning Inc., Edina MN.  (PDF) Principles for Teaching Problem Solving (researchgate.net)
• Hayes, J.R. (1989). The Complete Problem Solver. 2nd Edition. Hillsdale, NJ: Lawrence Erlbaum Associates.
• Woods, D.R., Wright, J.D., Hoffman, T.W., Swartman, R.K., Doig, I.D. (1975). Teaching Problem solving Skills.
• Engineering Education. Vol 1, No. 1. p. 238. Washington, DC: The American Society for Engineering Education.

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Strategies to develop problem-solving skills in students.

• November 14, 2023

Students need the freedom to brainstorm, develop solutions and make mistakes — this is truly the only way to prepare them for life outside the classroom. When students are immersed in a learning environment that only offers them step-by-step guides and encourages them to focus solely on memorisation, they are not gaining the skills necessary to help them navigate in the complex, interconnected environment of the real world.

Choosing a school that emphasises the importance of future-focussed skills will ensure your child has the abilities they need to survive and thrive anywhere in the world. What are future-focussed skills? Students who are prepared for the future need to possess highly developed communication skills, self-management skills, research skills, thinking skills, social skills and problem-solving skills. In this blog, I would like to focus on problem-solving skills.

What Are Problem-Solving Skills?

The Forage defines problem-solving skills as those that allow an individual to identify a problem, come up with solutions, analyse the options and collaborate to find the best solution for the issue.

Importance of Problem-Solving in the Classroom Setting

Learning how to solve problems effectively and positively is a crucial part of child development. When children are allowed to solve problems in a classroom setting, they can test those skills in a safe and nurturing environment. Generally, when they face age-appropriate issues, they can begin building those skills in a healthy and positive manner.

Without exposure to challenging situations and scenarios, children will not be equipped with the foundational problem-solving skills needed to tackle complex issues in the real world. Experts predict that problem-solving skills will eventually be more sought after in job applicants than hard skills related to that specific profession. Students must be given opportunities in school to resolve conflicts, address complex problems and come up with their own solutions in order to develop these skills.

Benefits of Problem-Solving Skills for Students

Learning how to solve problems offers students many advantages, such as:

When students have a well-developed set of problem-solving skills, they are often better critical and analytical thinkers as well. They are able to effectively use these 21st-century skills when completing their coursework, allowing them to become more successful in all academic areas. By prioritising problem-solving strategies in the classroom, teachers often find that academic performance improves.

Developing Confidence

Giving students the freedom to solve problems and create their own solutions is essentially permitting them to make their own choices. This sense of independence — and the natural resilience that comes with it — allows students to become confident learners who aren’t intimidated by new or challenging situations. Ultimately, this prepares them to take on more complex challenges in the future, both on a professional and social level.

Preparing Students for Real-World Challenges

The challenges we are facing today are only growing more complex, and by the time students have graduated, they are going to be facing issues that we may not even have imagined. By arming them with real-world problem-solving experience, they will not feel intimidated or stifled by those challenges; they will be excited and ready to address them. They will know how to discuss their ideas with others, respect various perspectives and collaborate to develop a solution that best benefits everyone involved.

The Best Problem-Solving Strategies for Students

No single approach or strategy will instil a set of problem-solving skills in students.  Every child is different, so educators should rely on a variety of strategies to develop this core competency in their students.  It is best if these skills are developed naturally.

These are some of the best strategies to support students problem-solving skills:

Project-Based Learning

By providing students with project-based learning experiences and allowing plenty of time for discussion, educators can watch students put their problem-solving skills into action inside their classrooms. This strategy is one of the most effective ways to fine-tune problem-solving skills in students.  During project-based learning, teachers may take notes on how the students approach a problem and then offer feedback to students for future development. Teachers can address their observations of interactions during project-based learning at the group level or they can work with students on an individual basis to help them become more effective problem-solvers.

Encourage Discussion and Collaboration in the Classroom Setting

Another strategy to encourage the development of problem-solving skills in students is to allow for plenty of discussion and collaboration in the classroom setting.  When students interact with one another, they are naturally developing problem solving skills.  Rather than the teacher delivering information and requiring the students to passively receive information, students can share thoughts and ideas with one another.  Getting students to generate their own discussion and communication requires thinking skills.

Utilising an Inquiry-Based approach to Learning

Students should be presented with situations in which their curiosity is sparked and they are motivated to inquire further. Teachers should ask open-ended questions and encourage students to develop responses which require problem-solving. By providing students with complex questions for which a variety of answers may be correct, teachers get students to consider different perspectives and deal with potential disagreement, which requires problem-solving skills to resolve.

Model Appropriate Problem-Solving Skills

One of the simplest ways to instil effective problem-solving skills in students is to model appropriate and respectful strategies and behaviour when resolving a conflict or addressing an issue. Teachers can showcase their problem-solving skills by:

• Identifying a problem when they come across one for the class to see
• Brainstorming possible solutions with students
• Collaborating with students to decide on the best solution
• Testing that solution and examining the results with the students
• Adapting as necessary to improve results or achieve the desired goal

Prioritise Student Agency in Learning

Recent research shows that self-directed learning is one of the most effective ways to nurture 21st-century competency development in young learners. Learning experiences that encourage student agency often require problem-solving skills.  When creativity and innovation are needed, students often encounter unexpected problems along the way that must be solved. Through self-directed learning, students experience challenges in a natural situation and can fine-tune their problem-solving skills along the way.  Self-directed learning provides them with a foundation in problem-solving that they can build upon in the future, allowing them to eventually develop more advanced and impactful problem-solving skills for real life.

21st-Century Skill Development at OWIS Singapore

Problem-solving has been identified as one of the core competencies that young learners must develop to be prepared to meet the dynamic needs of a global environment.  At OWIS Singapore, we have implemented an inquiry-driven, skills-based curriculum that allows students to organically develop critical future-ready skills — including problem-solving.  Our hands-on approach to education enables students to collaborate, explore, innovate, face-challenges, make mistakes and adapt as necessary.  As such, they learn problem-solving skills in an authentic manner.

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I Can Problem Solve

Get info and pricing on the provider’s website.

I Can Problem Solve provides a lesson-based approach to SEL. It includes programming for grades Pre-K-5 and demonstrates evidence of effectiveness at grade 1. Translated materials for the preschool & kindergarten levels as well as the parent program are available in Spanish.

• SEL lessons
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• Self-report tools for monitoring implementation
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Evidence of effectiveness

Results from a randomized control trial (RCT) conducted in the 1997-1998 school year (published in 2002) supported the effectiveness of I Can Problem Solve for early elementary school students. This evaluation included 578 grade 1 students enrolled in multiple rural schools in the US West region (87% white; sample was largely middle class). Students who participated in the program had greater growth in teacher-reported self-regulation (i.e., decreases in impulsivity, hyperactivity, aggressive, disruptive behaviors) and in student-reported school bonding (i.e., engagement and student-teacher relationship quality) compared to students in the control group (9 months after baseline, analyses controlled for outcome pretest).

• Not Specified
• Reduced emotional distress
• Improved identity development and agency
• Reduced problem behaviors
• Improved school climate
• Improved school connectedness
• Improved social behaviors
• Improved teaching practices
• Improved other SEL skills and attitudes

How does I Can Problem Solve support SEL implementation across multiple settings?

“The I Can Problem Solve (ICPS) program teaches students to recognize that when there is a problem, there is a process they can call upon to solve it. With support materials across settings, the ICPS problem solving approach creates consistent communication between adults and youth by engaging students as active participants, not passive recipients. ”

• Accepted by CASEL

Kumpfer, K. L., Alvarado, R., Tait, C., & Turner, C. (2002). Effectiveness of school-based family and children’s skills training for substance abuse prevention among 6-8-year-old rural children.  Psychology of Addictive Behaviors, 16 (4S), S65-S71.

• Other references

Boyle, D., & Hassett-Walker, C. (2008). Reducing Overt and Relational Aggression Among Young Children: The Results from a Two-Year Outcome Study.  Journal of School Violence, 7 (1), 27-42.

Feis, C. L., & Simons, C. (1985). Training Preschool Children in Interpersonal Cognitive Problem-Solving Skills: A Replication. Prevention in Human Services, 3 (4), 59-70.

Gaete, J., Nejaz, L., Otegui, M., & Perry, R. (2019). Mental Health Prevention in Preschool Children: study protocol for a feasibility and acceptability randomised controlled trial of a culturally adapted version of I Can Problem Solve (ICPS) program in Chile. Poster presented at the annual meeting of the Society for Prevention Research, San Francisco, CA.  Trials, 20,  158.

Shure, M. B., & Spivack, G. (1982). Interpersonal problem-solving in young children: A cognitive approach to prevention. American  Journal of Community Psychology, 10 (3), 341-356.

Shure, M. B., & Spivack, G. (1980). Interpersonal problem solving as a mediator of behavioral adjustment in preschool and kindergarten children.  Journal of Applied Developmental Psychology, 1 (1), 29-44.

Shure, M. B., & Spivack, G. (1979). Interpersonal cognitive problem solving and primary prevention: Programming for preschool and kindergarten children.  Journal of Clinical Child Psychology, 8 (2), 89-94.

Become an Insider

Bob Kuhn, Biotechnology Teacher at Fulton County School’s Innovation Academy, helps students study bee colonies.

Students Collect Data from Apiaries for Project-Based Learning

Adam Stone writes on technology trends from Annapolis, Md., with a focus on government IT, military and first-responder technologies.

Nationwide, pollinators are in trouble. After years of steady decline, 2022 to 2023 marked a 37 percent loss of managed bee colonies in the United States, according to the nonprofit Bee Informed Partnership .

At Fulton County Schools’ Innovation Academy in Georgia, high school biotechnology teacher Bob Kuhn helps students in grades 10 through 12 to understand the bee situation. Students are charged with tagging and tracking bees as members of an after-school biotechnology research group called the DNA Club.

They work with “an apiary here on campus that has three hives, and at a city farm about three miles away that also has an apiary, the city of Alpharetta’s Old Rucker Farm,” Kuhn says.

As a project-based, career pathway high school, FCS students use hands-on science, technology, engineering and math projects to master certain subjects. It’s one of several bee-related science projects nationwide that rely on technology to help students build STEM skills as they conduct fieldwork.

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Students Embrace a Range of Technologies for Their STEM Projects

For the FCS project, Kuhn takes advantage of readily available radio-frequency identification technology . This is the same technology Amazon uses to keep track of products in its warehouses.

“We are using a miniature RFID tag that you can physically glue to the back of the bee. It’s so small you have to use tweezers to place it,” he says. “We collect bees from the hive, then the students attach the tags with super glue on the back of their bodies and put them back into the hive.”

With the trackers in place, “we can measure how much time they’re spending outside of the hive on trips and how much time they’re spending inside the hive, when they’re not making trips,” he says. “There’s a lot of data that can be collected.”

RELATED: Modern data management platforms track student attainment.

All of that data is uploaded into a Microsoft Excel file, and students are learning to code with Python to make that data available for analysis. That information will paint a picture of bee behaviors — how far they have to go for food, for example — which helps students understand the impact of homebuilding, artificial landscapes and other effects of suburban development.

In Pennsylvania’s California Area School District , Superintendent Laura Jacob has fostered a similar effort. The district has four beehives on campus, managed by an after-school club.

“I grew up on a farm, and I know the critical need for bees in our food ecosystem, so I wanted to teach kids the benefits of bees,” Jacob says. “We go up to the beehives, we take care of the bees, and we also harvest the honey. We make lip balm and candles out of the wax.”

Caring for the bees also supports STEM learning for K–12 students. “I’m a strong proponent of technology in education. I wanted kids to see how they can be involved in agriculture and technology at the same time,” Jacob says.

To that end, the school is using Raspberry Pi devices, with a connected Raspberry Pi camera running a Linux system through which the kids learn Python. “We put the camera right at the entrance of the beehive and collect visual data,” she says.

“We programmed it to take a picture every minute or two minutes and send those to an Amazon Web Services cloud-based system. The kids also use existing Python code to teach an artificial intelligence algorithm. It is free AI code that we adapted to our photos,” she says. Students also use their Chromebooks to interact with the data, all of which helps them understand the health of the colony.

DISCOVER: Mobile labs bring STEM to more students .

STEM Projects Help Students Solve Real-World Problems

Hands-on field projects can be an important part of a STEM curriculum.

With field projects, young people “are using technology in ways that align with the world of work, creating authentic, meaningful learning opportunities,” says Tara Nattrass, managing director of innovation strategy at ISTE+ASCD.

In the California Area School District project, students are “learning Big Data collection out in the field, computer technology skills and programming, where we take somebody’s code and adapt it to our specific needs,” Jacob says.

“There’s also the science of bees, understanding bees and understanding the challenges that our bees are experiencing because of climate change, herbicides and pesticides,” she says.

The percentage of surveyed students who said their STEM knowledge increased because of their after-school experience

FCS’s Kuhn points to several key lessons. “Students are doing authentic open-ended research, where they’re collecting data and then asking questions about that data to see what kind of trends and patterns they can spot, and how they can gain more information about the bees’ behavior,” he says. Overall, “we’re applying things to the real world, trying to figure out solutions to real problems.”

Beekeeping Connects Students to Larger STEM Goals

Beekeeping projects can work in support of a school’s overall STEM goals and strategies .

For Jacob, whose school is within an agricultural community, bees are just one way to connect STEM to agrarian concerns. “We have a lot of animals on campus for teaching and learning. We have goats, chickens and fish, we have dogs for dog therapy, and we apply many of the STEM components in working with the animals,” Jacob says.

For other schools looking to take STEM tech into the field in support of mastery-based and project-based learning, a few best practices apply.

Tara Nattrass Managing Director of Innovation Strategy, ISTE+ASCD

For bees, in particular, “there’s a little bit of expertise needed,” Kuhn says. “The tagging is kind of complicated. You have to develop protocols for how you handle the bees and make sure you’re not hurting them. It is a technically advanced project.”

It’s equally important, ISTE+ASCD’s Nattrass suggests, to give students the tools and encourage them to use the technology in ways that align with real-world experience.

“Students should have opportunities to use technology as designers and creators, mirroring the ways in which technology is seamlessly integrated across industries,” she says.

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Inspiring Collaborative Thinking and Problem Solving

Help me give my students the opportunity to work collaboratively using the Building Thinking Classroom model. The Doodle Boards will help us save money on whiteboard markers and allow students to show their work.

• \$661 still needed

expires Aug 01

• \$661 - Complete this project and be a hero!

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Celebrating Hispanic & Latinx Heritage Month

This project is a part of the Hispanic & Latinx Heritage Month celebration because it supports a Latino teacher or a school where the majority of students are Latino.

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The whiteboards will allow students to work collaboratively in groups and show their work, problem solving, and strategies. The goal is to utilize the whiteboards to effectively implement Building Thinking Classroom principles.

The standing whiteboards allow students to meet in randomly selected groups to collaborate and problem solve in all subjects.

The boards are a great way to have students come together to work out problems, especially math problems. Once the group has completed their work on the board we are able to discuss and/or do gallery walks.

The LCD writing tablets are going to be terrific for showing their work without the expense of Dry Erase Markers.

The items will help make everything we do even more engaging. Our students are special and they have so much to add to the learning of others.

• Menifee, CA
• More than three‑quarters of students from low‑income households
• Mathematics
• Classroom Basics

Ms. Belle will only receive her materials if this project is fully funded by August 1 .

• Quail Valley Elementary School
• Equity Focus

At this school, more than 50% of students are Black, Latino, and/or Native American, and more than 50% come from low-income households. Learn how your donation to this school supports a more equitable education .

This project will reach 32 students.

2 donors have given to this project.

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You can start a project with the same resources being requested here!

Materials Cost Quantity Total
maxtek Magnetic Mobile White Board, 40 x 24 Double Sided Dry Erase Board Rolling Whiteboard, Aluminum Frame Standing Whiteboard on Wheels for Home Office Classroom (40 x 24 Black) • Amazon Business \$94.89 4 \$379.56
16 Pcs LCD Writing Tablet for Kids 12 Inch Doodle Board Bulk Colorful Erasable Drawing Tablet Writing Pad Reusable Electronic Toys Gifts for Girls Boys 8-10 3-10, Blue, Red, Pink • Amazon Business \$54.99 3 \$164.97
 Materials cost \$544.53 Vendor shipping charges FREE Sales tax \$49.82 3rd party payment processing fee \$8.17 Fulfillment labor & materials \$30.00 Total project cost \$632.52 Suggested donation to help DonorsChoose reach more classrooms \$111.62 Total project goal \$744.14 1 Donor -\$75.00 Donations toward project cost Donations to help DonorsChoose reach more classrooms Excluded support for DonorsChoose

Our team works hard to negotiate the best pricing and selections available.

Find opportunities to impact local needs by exploring a map of classroom projects near you.

DonorsChoose is the most trusted classroom funding site for teachers.

As a teacher-founded nonprofit, we're trusted by thousands of teachers and supporters across the country. This classroom request for funding was created by Ms. Belle and reviewed by the DonorsChoose team.

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More From Forbes

The most rigorous math program you've never heard of.

Math-M-Addicts students eagerly dive into complex math problems during class.

In the building of the Speyer Legacy School in New York City, a revolutionary math program is quietly producing some of the city's most gifted young problem solvers and logical thinkers. Founded in 2005 by two former math prodigies, Math-M-Addicts has grown into an elite academy developing the skills and mindset that traditional schooling often lacks.

"We wanted to establish the most advanced math program in New York," explains Ruvim Breydo, co-founder of Math-M-Addicts. "The curriculum focuses not just on mathematical knowledge, but on developing a mastery of problem-solving through a proof-based approach aligned with prestigious competitions like the International Mathematical Olympiad."

From its inception, Math-M-Addicts took an unconventional path. What began as an attempt to attract only the highest caliber high school students soon expanded to offer multiple curriculum levels. "We realized we couldn't find enough kids at the most advanced levels," says Breydo. "So we decided to develop that talent from an earlier age."

The program's approach centers on rigor. At each of the 7 levels, the coursework comprises just a handful of fiendishly difficult proof-based math problems every week. "On average, we expect them to get about 50% of the solutions right," explains instructor Natalia Lukina. "The problems take hours and require grappling with sophisticated mathematical concepts."

But it's about more than just the content. Class sizes are small, with two instructors for every 15-20 students. One instructor leads the session, while the other teacher coordinates the presentation of the homework solutions by students. The teachers also provide customized feedback by meticulously reviewing each student's solutions. "I spend as much time analyzing their thought processes as I do teaching new material," admits instructor Bobby Lee.

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Lee and the Math-M-Addicts faculty embrace an unconventional pedagogy focused on developing logic, creativity, and a tenacious problem-solving mindset over procedures. "We don't dumb it down for them," says Breydo. "We use technical math language and allow students to struggle through the challenges because that's where real learning happens."

Impressive results of Math-M-addicts students in selective math competitions highlight their ... [+] preparation and dedication.

For the Math-M-Addicts team, finding the right teachers is as essential as shaping brilliant students. Prospective instructors go through a rigorous multi-stage vetting process. "We seek passionate mathematical problem solvers first," says program director Sonali Jasuja. "Teaching experience is great, but first and foremost, we need people who deeply understand and enjoy the reasoning behind mathematics."

Even exceptional instructors undergo extensive training by co-teaching for at least a year alongside veteran Math-M-Addicts faculty before taking the lead role. "Our approach is different from how most US teachers learned mathematics," explains instructor Tanya Gross, the director of Girls Adventures in Math (GAIM) competition. "We immerse them in our unique math culture, which focuses on the 'why' instead of the 'how,' empowering a paradigm shift."

That culture extends to the students as well. In addition to the tools and strategies imparted in class, Math-M-Addicts alumni speak of an unshakable confidence and camaraderie that comes from up to several thousands of hours grappling with mathematics at the highest levels alongside peers facing the same challenges.

As Math-M-Addicts ramps up efforts to expand access through online classes and global partnerships, the founders remain devoted to their core mission. "Math education should not obsess with speed and memorization of math concepts," argues Breydo. "This is not what mathematics is about. To unlock human potential, we must refocus on cognitive reasoning and problem-solving skills. We are seeking to raise young people unafraid to tackle any complex challenge they face"

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Sixteen middle schoolers explore preserve, creative problem solving through stem camp program day.

PHOTO PROVIDED Sixteen middle school girls from across the Susquehanna Valley visited the Montour Preserve on Thursday, June 27, for a special CSIU STEM Camp program in this photo by the Middle Susquehanna Riverkeeper Association.

Sixteen middle school girls from across the Susquehanna Valley visited the Montour Preserve on Thursday, June 27, for a special CSIU STEM Camp program.They got to visit various popular areas of the preserve, getting a wide variety of experiences designed to expand their STEM skills while showcasing all the preserve has to offer.

The day began in the fossil pit with a presentation from Middle Susquehanna Riverkeeper board member Doug Fessler and Vernal School Program Supervisor Marissa Crames. The students then spent about a half-hour searching for fossils and taking some home with them afterward.

They were then split into groups for a rotation through three stations. One was a scavenger hunt throughout the Nature Center for interesting facts that were hidden in various signage and other locations in the center, including the new Eels in the Classroom display. This station was led by Crames.

Another rotation included a stream study with Riverkeeper John Zaktansky with help from Fessler, starting with an observational look at how to tell if a stream is healthy or not, a look for macroinvertebrates and other aquatic creatures and chemical testing of a waterway. Students tested the Chillisquaque Creek’s pH and turbidity and discussed how water sampling can lead to data that can identify sources for possible pollution.

The third morning station involved an underwater videography overview with Middle Susquehanna Riverkeeper Association President Michael Kinney. Students learned how to effectively take photos and videos under waterways to find different life, including an overview on how to safely use their phones for such an effort.

After the rotations, the girls tried out electric skateboards they built earlier in the week during a different program day in a scavenger hunt for puzzle pieces using bird calls and vocal patterns. Zaktansky discussed the association’s BirdNet project as another STEM-related creative solution to help monitor stream health during this session.

After lunch, the girls took a hike into the backside of the preserve and then split in two. One group went with Fessler and Crames and looked at various environmental sensors from MWEE weather kits and discussed how they can be used to test for a wide variety of factors. The second group hiked across a forested section with Zaktansky to look for various signs of wildlife, observe browse patterns from deer in the wooded section and did some nature journaling along the way with various observations.

Throughout the day, the girls engaged with association interns Sarah Joy and Theadora Duane, who helped connect them to the lessons and find various nature-related items along the way.

“This is another program that showcases the essential partnership approach we have with the Vernal School effort at the Montour Preserve,” said Zaktansky. “The Central Susquehanna Intermediate Unit (CSIU) working with the Middle Susquehanna Riverkeeper Association, the Montour Area Recreation Commission, Fessler IT Consulting and Get Lost Photography (Kinney) to connect young people with nature and the wide variety of opportunities at the preserve. These programs not only spark creative problem solving through STEM-colored glasses, but also help inspire the next generation of stewards and will bring new families to this vital venue.”

The Middle Susquehanna Riverkeeper Association serves an 11,000-square-mile watershed of the Susquehanna River, including Sullivan, Lycoming, Clinton, Union and Northumberland counties. Read more at www.middlesusquehannariverkeeper.org.

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