## "Writing About Mathematics" Versus "Mathematical Writing"

*write about mathematics*, which prioritize the learning of literacy over mathematics. Examples of this type of writing include asking students to write about the lives of mathematicians or the math autobiography Ms. Park assigned.

*mathematical writing*—that seems to reflect the National Commission on Writing's (2003) position that "at its best, writing is learning" (p. 51). At its heart, mathematical writing forefronts mathematical reasoning over literacy skills. This writing involves text; it can also include symbols (like the equal sign), numerals, operations, and such visual representations as pictures, charts, or tables unique to the discipline of mathematics.

## 1. Exploratory Writing: Making Sense of It

*exploratory writing*—writing that helps students make sense of a problem or situation and sort through their own thoughts about mathematical concepts. Such writing can be initiated by the student at any time. It may be used more frequently when beginning a mathematical task as a way to brainstorm a problem's possible solution(s), ask questions, or work out confusions. The organic nature of this writing means that it's unlikely any two students' papers will look alike. Figure 1 shows a sample of a student's exploratory writing. This student wrote notes to herself at the top of the paper before answering the question about visual representations of fractions.

#### Figure 1. A 4th Grader's Exploratory Writing

## 2. Informative/Explanatory Writing: Clarifying to Others

*informative/explanatory writing*, which positions students to describe and explain mathematical ideas. This kind of writing is a good opportunity for teachers to remind students that they should be clear in their writing and to guide students so their written messages are mathematically accurate.

#### Figure 2. A Kindergartener's Informative/Explanatory Writing

## 3. Argumentative Writing: Making Your Case

*argumentative writing*in which learners "construct viable arguments and critique the arguments of others" (National Governors Association Center for Best Practices & Council of Chief State School Officers, 2010, p. 6). It's likely that a few of these students would have written that "I just know it," and would need to be reminded that they should clearly state their position and back it with evidence. In addition to justifying their own positions, students read, analyze, and evaluate the mathematical arguments of others, taking the opportunity to either strengthen a peer's argument or disagree with it while providing their own evidence or counterexamples. For instance, Figure 3 shows a student's argument to support his claim that one measuring tool is more effective than others for a specific task.

#### Figure 3. A 2nd Grader's Argumentative Writing

## 4. Mathematically Creative Writing: Thinking Beyond Boundaries

*mathematically creative writing*, in which students think creatively and document mathematical ideas that extend beyond the intended outcome or process of solving a problem. This includes students generating original ideas, posing novel problems or questions, and displaying flexibility and fluency in ideas. Writing down outside-the-box ideas in this manner is something mathematicians do regularly.

## Key Questions to Help You Make Instructional Choices

## Should all students write mathematically?

## How much time will guiding students to do this take?

## Does it matter who the audience is?

## What forms can mathematical writing take?

*mathematical writing*(emphasizing mathematical reasoning) and

*writing about math*(focusing on literacy). Keep in mind that the form writing takes is secondary to the types and purposes of the mathematical writing.

## An Underused Tool

*Authors' Note:*This material is based on work supported by the National Science Foundation under Grant No. 1545908,

*Task Force on Conceptualizing Elementary Mathematical Writing: Implications for Mathematics Education Stakeholders*. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.