What does problem solving in math mean, and how to develop these skills in students? Problem solving involves tasks that are challenging and make students think. In teaching through problem solving, learning takes place while trying to solve problems with specific concepts and skills. Therefore, teachers need to provide safe learning spaces that foster a growth mindset in math in order for students to take risks to solve problems. In addition, providing students with problem solving steps in math builds success in solving problems.
By providing rich mathematical tasks and engaging puzzles, students improve their number sense and mindset about mathematics. Click Here to get this Freebie of 71 Math Number Puzzles delivered to your inbox to use with your students.
Students who feel successful in math class are happier and more engaged in learning. Check out The Bonus Guide for Creating a Growth Mindset Classroom and Students Who Love Math for ideas, lessons, and mindset surveys for students to use in your classroom to cultivate a positive classroom community in mathematics. You can also sign up for other freebies from me Here at Easternshoremathteacher.com.
Have you ever given students a word problem or rich task, and they froze? They have no idea how to tackle the problem, even if it is a concept they are successful with. This is because they need problem solving strategies. I started to incorporate more problem solving tasks into my teaching in addition to making the 4 steps for problem solving a school-wide initiative and saw results.
What is Problem Solving in Math?
When educators use the term problem solving, they are referring to mathematical tasks that are challenging and require students to think. Such tasks or problems can promote students’ conceptual understanding, foster their ability to reason and communicate mathematically, and capture their interests and curiosity (Hiebert & Wearne, 1993; Marcus & Fey, 2003; NCTM, 1991; van de Walle, 2003).
How Should Problem Solving For Math Be Taught?
Problem solving should not be done in isolation. In the past, we would teach the concepts and procedures and then assign one-step “story” problems designed to provide practice on the content. Next, we would teach problem solving as a collection of strategies such as “draw a picture” or “guess and check.” Eventually, students would be given problems to apply the skills and strategies. Instead, we need to make problem solving an integral part of mathematics learning.
In teaching through problem solving, learning takes place while trying to solve problems with specific concepts and skills. As students solve problems, they can use any strategy. Then, they justify their solutions with their classmates and learn new ways to solve problems.
Students do not need every task to involve problem solving. Sometimes the goal is to just learn a skill or strategy.
Criteria for Problem Solving Math
Lappan and Phillips (1998) developed a set of criteria for a good problem that they used to develop their middle school mathematics curriculum (Connected Mathematics). The problem:
- has important, useful mathematics embedded in it.
- requires higher-level thinking and problem solving.
- contributes to the conceptual development of students.
- creates an opportunity for the teacher to assess what his or her students are learning and where they are experiencing difficulty.
- can be approached by students in multiple ways using different solution strategies.
- has various solutions or allows different decisions or positions to be taken and defended.
- encourages student engagement and discourse.
- connects to other important mathematical ideas.
- promotes the skillful use of mathematics.
- provides an opportunity to practice important skills.
Of course, not every problem will include all of the above. However, the first four are essential. Sometimes, you will choose a problem because your students need an opportunity to practice a certain skill.
The real value of these criteria is that they provide teachers with guidelines for making decisions about how to make problem solving a central aspect of their instruction. Read more at NCTM.
Problem Solving Teaching Methods
Teaching students these 4 steps for solving problems allows them to have a process for unpacking difficult problems.
As you teach, model the process of using these 4 steps to solve problems. Then, encourage students to use these steps as they solve problems. Click here for Posters, Bookmarks, and Labels to use in your classroom to promote the use of the problem solving steps in math.
How Problem Solving Skills Develop
Problem solving skills are developed over time and are improved with effective teaching practices. In addition, teachers need to select rich tasks that focus on the math concepts the teacher wants their students to explore.
Problem Solving 4 Steps
Understand the Problem
Read & Think
- Circle the needed information and underline the question.
- Write an answer STEM sentence. There are_____ pages left to read.
Plan Out How to Solve the Problem
Make a Plan
- Use a strategy. (Draw a Picture, Work Backwards, Look for a Pattern, Create a Table, Bar Model)
- Use math tools.
Do the Problem
Solve the Problem
- Show your work to solve the problem. This could include an equation.
Check Your Work on the Problem
Answer & Check
- Write the answer into the answer stem.
- Does your answer make sense?
- Check your work using a different strategy.
Check out these Printables for Problem Solving Steps in Math.
Teaching Problem Solving Strategies
A problem solving strategy is a plan used to find a solution. Understanding how a variety of problem solving strategies work is important because different problems require you to approach them in different ways to find the best solution. By mastering several problem-solving strategies, you can select the right plan for solving a problem. Here are a few strategies to use with students:
- Draw a Picture
- Work Backwards
- Look for a Pattern
- Create a Table
- Bar Model
Why is Using Problem Solving Steps For Math Important?
Problem solving allows students to develop an understanding of concepts rather than just memorizing a set of procedures to solve a problem. In addition, it fosters collaboration and communication when students explain the processes they used to arrive at a solution. Through problem-solving, students develop a deeper understanding of mathematical concepts, become more engaged, and see the importance of mathematics in their lives.
NCTM Process Standards
In 2011 the Common Core State Standards incorporated the NCTM Process Standards of problem-solving, reasoning and proof, communication, representation, and connections into the Standards for Mathematical Practice. With these process standards, the focus became more on mathematics through problem solving. Students could no longer just develop procedural fluency, they needed to develop conceptual understanding in order to solve new problems and make connections between mathematical ideas.
Engaging Students to Learn in Mathematics Class
Engaging students to learn in math class will help students to love math. Children develop a dislike of math early on and end up resenting it into adult life. Even in the real world, students will likely have to do some form of mathematics in their personal or working life. So how can teachers make math more interesting to engage students in the subject? Read more at 5 Best Strategies for Engaging Students to Learn in Mathematics Class
Teachers can promote number sense by providing rich mathematical tasks and encouraging students to make connections to their own experiences and previous learning.
Sign up on my webpage to get this Freebie of 71 Math Number Puzzles delivered to your inbox to use with your students. Providing opportunities to do math puzzles daily is one way to help students develop their number sense. CLICK Here to sign up for 71 Math Number Puzzles and check out my website.
Promoting a Growth Mindset
Research shows that there is a link between a growth mindset and success. In addition, kids who have a growth mindset about their abilities perform better and are more engaged in the classroom. Students need to be able to preserve and make mistakes when problem solving.
Read more …5 Powerful and Easy Lessons Teaching Students How to Get a Growth Mindset
Here are some Resources to Use to Grow a Growth Mindset
Using Word Problems
Story Problems and word problems are one way to promote problem solving. In addition, they provide great practice in using the 4 steps of solving problems. Then, students are ready for more challenging problems.
For Kindergarten
For First Grade
For Second Grade
- Two Step Word Problems with Addition and Subtraction
- Grade 2 Addition and Subtraction Word Problems
- Word Problems with Subtraction
For Third Grade
For Fourth Grade
Resources for Problem Solving
- 3 Act Tasks
- What’s the Best Proven Way to Teach Word Problems with Two Step Equations?
- 5 Powerful and Easy Lessons Teaching Students How to Get a Growth Mindset
- 5 Powerful Ideas to Help Students Develop a Growth Mindset in Mathematics
Problem Solving Steps For Math
In mathematics, problem solving is one of the most important topics to teach. Learning to problem solve helps students apply mathematics to real-world situations. In addition, it is used for a deeper understanding of mathematical concepts.
By providing rich mathematical tasks and engaging puzzles, students improve their number sense and mindset about mathematics. Click Here to get this Freebie of 71 Math Number Puzzles delivered to your inbox to use with your students.
Check out The Free Ultimate Guide for Creating a Growth Mindset Classroom and Students Who Love Math for ideas, lessons, and mindset surveys to use to cultivate a growth mindset classroom.
Start by modeling using the problem solving steps in math and allowing opportunities for students to use the steps to solve problems. As students become more comfortable with using the steps and have some strategies to use, provide more challenging tasks. Then, students will begin to see the importance of problem solving in math and connecting their learning to real-world situations.
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