# "Eyes on Progressive Education" Blog

*A Green Acres School journal that chronicles progressive education in action, the research that supports and informs our practice, and ways in which we live out our mission each and every day.*

## Why Are We Writing in Math Class?

Marylouise, Middle School Math Teacher

Math is not just about numbers — it’s also about expressing your problem-solving process through writing. Students often ask me, “Why are we writing in math? This is not a language arts class!” I explain that writing can demonstrate your understanding of a concept because you are explaining your thought process to others — instead of just computing answers. When you are explaining how you derived an answer, you are using higher-order thinking. So, writing is an important skill in math, too, because it helps you remember, understand, apply, and evaluate the math concepts you’re learning.

Our present math program, EnVision Math, supports the idea that writing is more than just a way to document information; it is a way to deepen students’ learning and a tool for helping students gain new perspectives. David Pugalee (*Writing to Develop Mathematical Understanding*, 2005), who researched the relationship between language and mathematical learning, asserts that writing supports mathematical reasoning and problem solving, and it helps students internalize the characteristics of effective communication. In the EnVision Math curriculum, there are three types of mathematical questions: exploratory, informative/explanatory, and argumentative.

Exploratory writing allows students to make sense of a problem and sort through their own thoughts about mathematical concepts. Generally, teachers will begin a unit with this type of question as an introduction or to better grasp students’ background knowledge. Exploratory writing exercises also demonstrate to all participants that there are a variety of answers which broadens students’ understanding that a math problem can be viewed or solved in a variety of ways. A current 5th grade student’s answer of an exploratory question about decimals was, “In everyday life, you use decimals with money, swimming meets, and measurement. Decimals allow you to be more precise.”

In our math program, informative/explanatory is another questioning format. These answers require students to write descriptions of mathematical concepts, representations, and definitions. These types of problems invite students to write about mathematical connections and comparisons. These questions provide opportunities for students to apply their understanding to the real world and to reinforce math vocabulary. Often informative/explanatory answers demonstrate how math concepts build upon one another. An example of an informative/explanatory prompt is to write about the similarities and differences between a square and a rectangle. For example, a student’s written response was, “A square and rectangle always has four right angles. The opposite sides of a rectangle and square are parallel but a square’s sides are of equal length. A rectangle has two short sides and two long sides.”

The final type of writing exercise used in math instruction is an argumentative question in which learners construct viable arguments. These types of questions have students justify their own positions and back it with evidence. These questions provide opportunities for students to hear, analyze, and evaluate others’ mathematical arguments. An example of a 5th grade question is, “Why do larger denominators create smaller fractions?”

Learning how to write what you’re thinking is challenging, but important. Writing exercises in math classrooms set the stage for active problem solving, invention and discovery, increased reading, and improved content learning. Writing prompts give students the chance to express new knowledge and skills in their own words, organize their thinking about the content, share their ideas, experience a creative side of mathematics, and learn to value the act of writing. At the same time, teachers get a tool that can motivate and engage students, assess students’ understanding, and demonstrate interdisciplinary collaborations.

**Mrs. Sara Kendall Huneke**in Middle School on Monday November, 19, 2018

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