Superpowers for Math Lessons: Writing

Researchers in mathematics education have long hypothesized that requiring students to write about mathematics is extremely powerful.  Writing-to-learn can add to a student’s understanding, deepen their ability to justify their answers, and improve metacognition.  But with mounting pressures of high stakes testing and pacing guides, often teachers find it difficult to add more things to daily lessons without leaving something valuable out.   According to a study published this year, teachers don’t have to choose. Writing is a superpower when teaching fractions!

Sharlene Kiuhara and her team wanted to know if the writing-to-learn hypothesis worked when teaching fractions to  4^th-6^th grade students who either had learning disabilities in mathematics or scored at or below the 35^th percentile on standardized tests for mathematics (Kiuhara, Rouse, Dai, Witzel, Morphy, & Unker, 2019).  Using a randomized, pre- and post-test design, which is the strongest evidence I’ve seen to date, they found that students who learned fractions while learning how to write arguments out-performed their peers in the control group.  They observed the largest improvement in the performance of students who were enrolled in special education.

The results show argumentative writing can be used as a learning activity for improving students’ fraction learning, as well as the quality of their mathematical reasoning.

Kiuhara, et al. 2019, p. 1

Their paper, published in the Journal of Educational Psychology, was flush with details not only about how they measured the students’ improvements, but how the teachers changed the way they taught.  But before going into the details, let’s take a step back to consider different ways that writing can be incorporated in the math classroom.  Here are some I’ve used:

• Math journals and journal prompts – A daily activity that allows students to write (and draw figures) about what they are learning, what questions they still have, and how they feel about the learning process. I treat these as a scientific journal as students make discoveries.
• 3-minute papers – I’ve used these as an “exit ticket” for my classes to quickly assess if my lessons are effective or if there are questions or concerns that my quiet students may have.
• Math reports – When working with lengthy, real-world problems or problems that have many solution paths, I’ve asked students to prepare a full report explaining their solution and solutions they’ve seen other students or groups propose.

ARGUMENTATIVE WRITING IN MATH

The purposes of writing in mathematics can vary from expository writing (explaining what is observed), to reflective writing (allowing for self-regulation or opportunities to think about the learning process), to argumentative writing (justifying the correctness of a solution and the solution process).  Kosovo has published many papers on Mathematical Argumentative Writing, which he distinguishes from persuasive writing.  In the latter, you’re trying to persuade someone to agree with your idea (Kosko, 2016; Kosko, 2014; Kosko & Zimmerman, 2019).  However, argumentative writing is more akin to mathematical proof.  You’re making the case that something is true (some might argue that “truth” is something that is socially accepted as true – but let’s not get too distracted with theoretical stuff here!). In any case, Kosko has completed some fascinating work in K-3 classrooms, demonstrating the strength of teaching writing with children.

Kiuhara and her team worked with 10 teachers, randomly assigning five of them to complete a 2-day professional development program on teaching argumentative writing.  The other five reviewed the mathematics core content based on the district’s pacing guide.  The teachers who learned about argumentative writing, taught their students to use R²C² model (I hope you just chuckled like I did – why couldn’t it be R2-D2?!?). Anyway, here’s how you use it for writing a mathematical argument:

• RESTATE: What do I need to explain, describe, justify or compare? In my writing, did I use precise math words and transition words?
• REASONS: What is my reasoning or evidence for my answer?  In my writing, did I use precise math words and transition words?
• COUNTER CLAIM: Was there another possible answer? Why was my reasoning better? In my writing, did I use precise math words and transition words?
• CONCLUSION: How can I wrap up my ideas? In my writing, did I use precise math words and transition words?

Problem Solving? Just use the FACT!

Before asking students to write argumentatively, teachers used a strategy filled with reflective questioning to help with metacognition and employed a graphic organizer called FACT to teach the children problem solving.  Here’s how Kiuhara and her team explained FACT on page 9 of their paper: 

• F – Figure out my plan: What is my task? Do I understand the problem? What do I need to know? What tools do I need?
• A – Act on it: What are the math procedures? What reasons, evidence, and support will I use? What words will I choose? How will I interpret my results?
• C – Compare my reasoning with a peer: What is similar or different? What are my reasons? Does it make sense? Can I make improvements?
• T- Tie it up in an argumentative paragraph: Did I provide reasons, evidence, and support? Did I present the counterclaim? Did I choose good tools and words for solving the problem?

The teachers used these tools with their students to teach them to compare the magnitude of two fractions.  When the researchers compared the pre-tests to the post-tests, they found that students learning from teachers who used argumentative writing in their lessons had greater gains on the fractions tests, the quality of mathematical reasoning, the number of rhetorical elements (e.g. statement and claim, counterclaim, reasons, etc.), and total word count.  These were statistically significant differences, showing that argumentative writing is a tool that is more efficient than traditional lessons about fractions. 

Argumentative writing improves performance on tests while improving mathematical reasoning, especially with struggling students. 

So, I think I’ll spend tomorrow making sure the teacher’s guide to Newton’s Nemesis has plenty of writing prompts that not only reinforce mathematical mindset but can also be used to initiate argumentative writing.  After all, shouldn’t all comic books have superpowers in them??

References

• Kiuhara, S. A., Gillespie Rouse, A., Dai, T., Witzel, B. S., Morphy, P., & Unker, B. (2019, July 18). Constructing Written Arguments to Develop Fraction Knowledge. Journal of Educational Psychology. http://dx.doi.org/10.1037/edu0000391
• Kosko, K. W., & Zimmerman, B. S. (2019). Emergence of argument in children’s mathematical writing. Journal of Early Childhood Literacy, 19(1), 82-106.  
•  Kosko, K. W. (2016). Making use of what’s given: Children’s detailing in mathematical argumentative writing. Journal of Mathematical Behavior, 41, 68–86.  https://doi.org/10.1016/j.jmathb.2015.11.002  
• Kosko, K. W. . (2014). What Students Say About Their Mathematical Thinking When They Listen. School Science & Mathematics, 114(5), 214–223. https://doi.org/10.1111/ssm.12070