When we write our thoughts, something powerful happens: we organize our thinking, test our ideas, clarify and restate, and ultimately refine what we understand. Writing forces us to slow down and make sense of the jumble of concepts swirling in our minds. This process isn’t just valuable in language arts, it’s an essential tool in mathematics, too.
How Writing About Mathematical Thinking Builds Deeper Understanding
Mathematics is often viewed as a subject of numbers and procedures, but at its core, it’s about reasoning. When students write about their mathematical thinking, they do more than find answers, they engage in reflection, communication, and reasoning. Here’s how writing deepens their understanding:
- Organizing Thoughts: Writing requires students to carefully structure their reasoning. Instead of jumping straight to an answer, they map out the steps and rationale behind their solution.
- Testing Ideas: As they explain their methods and conclusions, students often catch errors or gaps in their understanding, prompting re-evaluation and deeper insight.
- Clarifying and Restating: Putting math ideas into their own words promotes reasoning and precision. Vague or incomplete thoughts become clearer as students grapple with ways to express them.
- Refining Understanding: Through revision, students refine their explanations, making their thinking sharper and more coherent.
Meaningful Ways to Integrate Writing in Math Class
Integrating writing into math isn’t about adding busy work, it’s about weaving reflection and communication into mathematics tasks. Here are some types of writing that fit seamlessly into your math lessons.
- Explain How: Ask students to describe the steps they took to solve a problem or perform a math task. This helps them clarify and articulate their process and reasoning. Example: Explain how you solved this problem. What steps did you take to get to your answer? or Explain how to add 285 + 347.
- Justify Why: Encourage students to justify their choices including why a method works, why a formula applies, or why an answer makes sense. Example: What operation did you use to solve the problem? Why does that operation make sense for this problem? or Is a square a rectangle? Prove your answer.
- Define or Describe: Have students define key terms or describe mathematical concepts in their own words to reinforce understanding. Example: What is an equivalent fraction? or What is an odd number?
- Compare: Prompt students to compare different approaches to a problem or different solutions to highlight similarities and differences. Example: Compare the traditional algorithm for multiplying two-digit numbers to the area model. How are they alike? How are they different?
- Generalize: Challenge students to identify patterns or principles that extend beyond a specific problem to generalize the big ideas. Example: What do you notice in these equations?
3 x 20 = 60
2 x 40 = 80
4 x 30 = 120
Can you write a rule for multiplying a single-digit number by a multiple of ten?
- Summarize: Students can summarize what they learned in a lesson or unit, reinforcing retention and big-picture thinking. Example: Write a summary of what you learned today about polygons. What are the most important ideas?
Classroom Activities to Encourage Mathematical Writing
Activity 1: Math Journal
Provide students with a dedicated math journal where they routinely respond to prompts related to lessons, reflect on problem-solving strategies, or explain concepts in their own words. This does not have to be the only place in which students write about math, but it holds examples of their writing over time so gives students and teacher a look at progress throughout the school year.
Activity 2: Think-Write-Pair-Share
After being posed an open-ended question, students think about their ideas, briefly write their ideas, then pair up to discuss their approaches before sharing with the class. First putting their thoughts in writing helps clarify those thoughts for partner and class discussions.
Activity 3: Exit Tickets with Writing
At the end of a lesson, ask students to write a short answer to a prompt like:
Is 9 a prime number? Justify your answer.
Explain how to add 23 + 8.
What is a multiple?
How are squares and rectangles alike? How are they different?
Activity 4: Math Concept Posters
Assign small groups to create posters defining and illustrating a math concept using words, pictures, numbers, and/or examples. This is a great way to prompt valuable conversations among students.
Activity 5: Error Analysis Writing
Give students a solved problem with a deliberate error. Have them identify and explain the mistake in writing, justifying why it’s incorrect and how to fix it.
Activity 6: Folded Books
Have students fold a paper into 2, 3, or 4 sections to create a folded book, then have them use words, pictures, numbers, and/or examples to define or describe a math concept in each part. Two-fold books might be created to share ideas about Odd/Even, Add/Subtract, Fraction/Decimal, or Prime/Composite. Three-fold books might focus on Shapes (rectangle, square, triangle), Angles (acute, obtuse, right), or Graphs (bar, circle, line). Four-fold books might explore Coins (penny, nickel, dime, quarter), Operations (add, subtract, multiply, divide), or Quadrilaterals (rectangle, square, trapezoid, rhombus).
The Takeaway
Writing provides an opportunity for meaningful reflection and communication. By integrating writing prompts that ask students to explain, justify, define, compare, generalize, and summarize, we empower them to build stronger, more flexible mathematical understanding. When students write their math thinking, they don’t just learn math, they learn to think mathematically.
