Incorporating writing into math helps students understand their thinking.
If you’d asked me not too long ago about the challenges of teaching pre-algebra to adolescents, I would have talked about procedural questions such as “What is the square root of 121?” or “What is the formula for volume of a sphere?” Today my response is very different because what counts as math in the middle grades is also shaped by notions of academic language within and across content areas.
Beyond the Numbers
More than strictly procedural fluency and factual recall, students today solve language-rich, complex, real-world application problems. For example, a problem from a unit on the laws of exponents today might read something like: “A shipping box is in the shape of a cube. Each side measures 3c^2d^2 inches. Express the volume of the cube as a monomial.”
In short, adolescent learners need to not only know the exponent laws, they also need to apply prior knowledge about volume as they interpret and process a multi-step word problem.
Finally, and perhaps at the center of CCSS math reform, learners need to articulate on paper the thinking behind their solutions—step by step. Common Core math pushes students to think deeply and apply what they know and what they are learning. Freewriting on paper can help take adolescent learners there.
Sometimes students reject writing when it comes to solving mathematical problems. However, exploratory writing—thinking aloud on paper—can provide access to higher-level questions, word problems. Or, to paraphrase a quote by British novelist E. M. Forester, “I’ll know what I am thinking when I see what I say.” Discipline-specific exploratory writing allows problem solvers to tease out their reasoning and work behind each step of a solution with words.
Stop and Jot
One technique that I use is called “Stop and Jot.” The Stop and Jot strategy is a brief moment when everybody pauses and writes about what we’ve been learning. I tell my students that they don’t need to worry about correct grammar, spelling, or punctuation—they simply need to write their thoughts about the day’s math activities: what they understood or what they are still trying to figure out. The idea is for students to see what they and their classmates are thinking.
For example, when a September lesson centered on the laws of exponents, the Stop and Jot prompt went like this: “Describe what law of exponents would help solve this problem. What do you already know about this question?”
To guide them, I provide the following instructions: “Write between 3–5 sentences about the day’s problems. You can write about your understanding or you can extend a problem. You can write a question you have or you can explain how you solved the problem. Write silently and independently. We’ll share our thinking on paper with desk mates.”
Here’s what three students wrote about the shipping box container:
- “The question is asking me to multiply, so I use power to a power law.”
- “I know it is multiplication because in the volume formula you multiply; I know the volume of that shape is length x width x height.”
- “I am not sure how to write the exponent law using those numbers.”
Talking About Math
The great thing about Stop and Jot is that we can choose to freewrite as often or as little as we need. Students only need a journal, a pen or pencil, and a quiet place where they can write and then share with peers. Having my math students see what they think on paper has made them confident about doing math and talking about math!