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# News from Mathnasium of Highlands Ranch

### Why It’s Important for Students to Explain Their Mathematical Thinking

Aug 2, 2017 Often, students are most concerned with finding the right answer to a math problem. Unfortunately, this merely shows that the student can solve the problem, but does not demonstrate that they understand the concept behind the problem.

As students progress in their math education, it becomes imperative that they truly understand the concepts to be successful.

Therefore, students need to be able to explain their mathematical thinking—reflecting on how and why they used specific steps to solve a problem.

Explaining the mathematical thinking enables students to:

Understand Their Process

Being able to explain how to solve a problem demonstrates a deep understanding of the concept and process. When students can explain the steps they took to solve a problem, they not only understand how to get the right answer but understand why they perform certain steps to get the answer. Being able to verbalize the process also increases a student’s math fluency—or ability to speak the language of math while strengthening or building new neurological pathways. The students understand both how to solve a problem and why they perform certain steps in the process of solving a problem. This increases the student’s academic potential in later years because they are building and articulating mathematical concepts and language.

Catch Their Mistakes

During the process of explaining the answer, students may sometimes catch mistakes they made when solving the problem. This gives students the ability to explain the mistake and why it was wrong. Students learn most from catching their mistakes and avoiding the same mistake on future problems. If they are perfect all the time, students aren’t truly learning anything new since they already know how to solve the problems. However, when students recognize their own mistakes, they can use their mistakes to inform their learning.

Generalize the Steps for the Next Problem

A major component of math is recognizing patterns. Through explaining their math thinking, students will begin to identify those patterns. With the deep understanding that explaining the problem creates, the student can generalize the patterns in the process to solve similar and more complex problems.

Mathnasium recognizes how important it is for students to be able to explain their mathematical thinking. The Mathnasium curriculum requires students to explain concepts in their own words or why they know an answer to be true. Additionally, instructors will ask students how they solved a problem to encourage students to understand their own learning and/or learn from their mistakes.