# James Morris School

## A Peek Into the Classroom: Mathematical Problem Solving

As part of an ongoing effort to help parents and guardians understand the expectations of today's student, I would like to take you on a virtual tour of a vital component of your child(ren)'s education: mathematical problem solving.

Below is the type of a word problem that our students have begun to explore regularly in the classroom the past few years. This particular example addresses fifth-grade math standards:

For many, school taught us to immediately identify (highlight, underline, circle) the numbers in the problem.

However, this approach often finds students focusing on extraneous or misleading information, while also detracting from the vital step of reading for understanding.

Instead, we ask students to read the problem a few times to be sure that they COMPREHEND what is being presented and to identify what exactly is being asked. This may include students writing their own statement that summarizes what they need to do:

Initially, many students want to jump right to solving the problem. However, this approach has been shown again and again to often result in misreading or misunderstanding what is being asked. It is important that students THINK and PLAN, especially as the problems become more challenging and what is being asked expands in both quantity and depth.

Our teachers encourage and expect students to identify possible STRATEGIES that can be used to solve the problem - developing awareness of effective strategies, and knowing when each is most appropriate. As you read the problem at the top, ask yourself: What strategy/approach would I use to solve this problem? What resources would be useful in solving this problem? A protractor? Ruler? Stopwatch? Graph paper? Compass? Counting blocks? We want our students to consider the wide array of resources and tools available to them, both in the classroom and in the real world, and to seek them out independently and purposefully.

Here is one fifth-grader's response to this problem. This response meets grade-level expectations:

Things worth noting in this student's response include

• It is clear that the student comprehends the problem, as evidenced by her written statement at the top.
• This student clearly understands the importance of neatness and labeling, both of which make it easy for both the student and reader to follow along with the thought process and the steps taken toward a solution.
• The student included "connections" - additional mathematical statements that show links between the content in this problem and other content (i.e. the concept of parallel and cardinal directions).
• The student's use of a key demonstrates the understanding of when and how to use such a feature, as well as the use of representative variables - skills that go beyond math class.

Here is another student's response:

The response above also meets 5th-grade expectations. Note that this student's "answer" is different from the first student's. Both, however, are possible successful solutions to the problem presented. Below is a third student's response:

In this and each of the previous examples, the student left little doubt of his understanding of what was asked and how it could be solved.

Before submitting their work, students are expected to REVIEW their solution. This does not mean to simply "check your answer" by looking it over. Rather, it means trying the problem again, ideally using a different strategy. Making the effort to do this may find the student not just meeting but EXCEEDING grade-level expectations: providing alternate strategies and/or solutions, connecting the given situation to other mathematical learning, demonstrating accurate understanding and usage of key math terminology and concepts - thinking like a mathematician and sharing that understanding with others.

This image above illustrates one of many ways to approach a problem, whether it be in the classroom at any level of one's education or in the real world. In fact, we often share with our students how we adults go through this mental process many times throughout the day, such as adjusting our route due to a traffic jam or planning for a quick and efficient trip through the supermarket. While only a small percentage our students will find themselves in a career in which success is defined by repeatedly finding one specific correct answer, all of them will need to navigate through an increasingly complex world as efficiently and effectively as they can. For this reason, we are constantly striving to promote teaching and learning that emphasizes depth of understanding and real-world application.

Thank you,

KC