When students are tasked with writing about their process for determining a solution, they make their thinking visible. Teachers can gain key insights into the depth of student understanding, and they can use that knowledge to deliver specific, actionable feedback and additional instruction as necessary.
Many math standards and assessments now ask that students explain their reasoning when it comes to solving math problems. Common Core math standards, for instance, state that students should be able to “construct viable arguments and critique the reasoning of others.”
The National Council of Teachers of Mathematics (NCTM) states that math instruction should enable all students to:
In “Principles and Standards for School Mathematics,” NCTM writes that:
“Through communication, ideas become objects of reflection, refinement, discussion, and amendment. When students are challenged to communicate the results of their thinking to others orally or in writing, they learn to be clear, convincing, and precise in their use of mathematical language.”
Writing is a metacognitive task. As such, the process of writing can help students work through complex concepts. Math education expert Marilyn Burns notes that when students write in math class,
“It requires students to organize, clarify, and reflect on their ideas… Writing in math class isn’t meant to produce a product suitable for publication, but rather to provide a way for students to reflect on their own learning and to explore, extend, and cement their ideas.”
When students defend their mathematical solutions in writing, they provide clear evidence of their understanding. Writing forces them to slow down and explain a solution in their own words. As William Zinsser states in Writing to Learn, “Writing is how we think our way into a subject and make it our own.”
Math teachers shouldn’t worry about the intricacies of grammar when they review writing. Rather, you should encourage students to demonstrate their understanding of a subject. If students can explain how they obtained an answer, they can likely replicate that work. When teachers review writing about math, they can see whether students fully grasp a concept – or whether they’re just regurgitating formulas.
While written answers make an appearance every so often in traditional math classes, it usually happens with an abstract question – “Train A goes west at 50 km/h and train B goes east at 40 km/h. Both trains depart at the same time, 1000 km apart. When will they cross?”
When it comes to writing in math, you can do more to engage your students. You can help them make real-world connections to math.
Dr. Mona Kiani, a ThinkCERCA School Success Manager, was teaching an 8th-grade class in 2017 when she posed an essential question to her students:
“How do the financial costs and benefits of different opportunities after high school compare?”
Mona’s class read a ThinkCERCA text leveled for 8th grade, which told them about Javier, a student evaluating three degree options and their impact of cost versus pay over time. Mona’s class calculated the economic benefits of each degree, and wrote arguments for which degree Javier should pursue.
Then, Mona extended the lesson. She asked her students to evaluate their choices for life after high school. Every student calculated the benefits and drawbacks of certain options – like attending a community college for two years and then transferring to a state university; going straight to a four-year college; going straight into the workforce.
“Students were immediately excited about the task – understanding finances and how to budget most effectively is inherently interesting to most middle and high school students,” Mona says.
“Students asked thoughtful questions about post-high school life, like what age people retire, what loans are, and what the drawbacks of getting credit cards are. They refined their internet research skills, hopped on the phone to get car insurance quotes, consulted with their parents about budgeting for food, talked to their advisors about dorms versus apartments, and some even swore they’d stop asking their parents for fashion items after creating a budget and seeing how expensive life can be.”
Through the writing activity, students were able to build strong personal connections to the concepts they learned about in math class. They not only learned how to evaluate career options – they understood the real-world importance of their math instruction as well.
What does literacy in math look like? This video shows how one elementary school makes writing and discussion a core element of math class.