by Pam Meader
About 10 years ago, various documents such as the NCTM Standards and recommendations of the National Research Council were urging more math communications. I decided that I was going to incorporate some writing into my math classes. I wasn’t sure how to start, so I tried a variety of approaches in all my math classes. However, new research has recently been published that lends clarity to the type of writing that occurs in math classes and its benefits.
With a grant from the National Science Foundation, a task force was convened to investigate mathematical writing in elementary school and the implications for math stakeholders. The researchers began their work in October 2015 and released their findings in a report entitled “Types of and purposes for elementary mathematical writing: Taskforce recommendations.” While this research related to elementary school students, I found many of the suggestions relevant to what I was trying to do in my adult education math classes. What the task force discovered was that mathematical writing was important, but that its purposes were not so clearly defined. I had discovered that I, too, had many purposes for incorporating writing, so I could relate to that finding. Some of my purposes included determining if the student understood a particular math concept, how the student was feeling about math, what discoveries or frustrations they were encountering, and where they saw the math they were learning connecting to their daily lives.
Through their research, the task force found two primary goals of introducing writing in the math classroom. One was to have students reason mathematically, and the other was to have students communicate ideas with mathematics. To illustrate reasoning and to be able to communicate mathematically, the task force suggested four types of writing: Exploratory, Informative/Explanatory, Argumentative, and Mathematically Creative. Of the four types of writing, I found most of my students’ writing fell into the first 3 recommendations (exploratory, informative/explanatory, and argumentative). Exploratory writing is when a student tries to make sense of a problem, situation, or their own idea. In my classes, that type of writing occurred more often in non-journal exploratory activities where I would ask my students to explain what happened or make conjectures. Most of my students’ journal writing illustrated informative/explanatory writing where students describe or explain a mathematical concept such as explaining what area and perimeter have in common and how they are different. Argumentative writing is when a student can construct an argument or critique an argument. That type of writing clearly illustrates the Common Core’s Mathematical Practice 3, Construct viable arguments and critique the reasoning of others. I found I used argumentative more with test questions where the student had to determine if a particular assumption was correct and then defend or critique the situation. An example would be: “All squares are rectangles. Do you agree or disagree with this statement?”
The last type of writing, mathematically creative, is defined by the task force as the ability to “think creatively and document their mathematical ideas that extend beyond the expected or intended outcome of a task, situation, or problem.” Part of thinking creatively is to think flexibly and to make connections within and beyond mathematics. At first, I thought my journals would be too structured to allow for this, but that wasn’t the case. Within the journals tasks, my algebra students were able to connect and make abstractions to the math concepts they were writing about. For example, in explaining how the number line was constructed to include both positive and negative values, one student wrote that the number line was like playing the piano where the right hand were the positive values and the left hand were the negative values.
The task force also considered that 1) writing will develop as a student moves through various levels; 2) that the audience can influence student’s mathematical writing; and 3) that mathematical writing can take on many forms. I can attest to the first and third suggestions with my journey in using math journals. My lower level students’ writing might be to just fill in simple statements like Today I struggled with ________, while my higher level algebra classes had to respond to a journal prompt, give an example, discuss where the math connected to their lives or other disciplines, and provide a reflection of their learning. The third suggestion of writing taking on many forms I also utilized with journals that included pictures or diagrams to explain their reasoning.
The one area the task force didn’t address—but which I have found very important with adult learners—are their feelings about math and how they persevered through their struggles. The reflections in my students’ journals told me much about them: when the light came on, when it went off, what strategies they were now using to solve problems, and where they were feeling more or less confident about mathematics. Many adults come to our classes so afraid of math and failure that the reflection piece can be therapeutic for them. I had one student confess to me that it took her 10 years to have the courage to take a math class but through journaling she became very excited about math and the connections she made. To this day, she emails me new math websites she has encountered.
In closing, I would urge you to try incorporating math journals as part of your teaching routine. The quote I leave you with is from a 19 year old student I had in my class a few years back. She hated math and did not want to be in a math classroom, but writing in a journal helped her with math. She said, “I think the most successful part of this course, for me, are the journals. Numbers and formulas tend to float about rather haphazardly in my mind. The act of binding mathematical concepts and numerical processes with words brings me to a far greater level of understanding and clarity. Once I have written about something it becomes very easy to visualize and helps me to see connections between various areas of mathematics. Writing makes it whole for me, so to speak.”
 Casa, T.M., Firmender, J.M., Cahill, J., Cardetti, F., Choppin, J.M., Cohen, J., Zawodniak, R. (2016). Types of and purposes for elementary mathematical writing: Taskforce recommendations. Retrieved from http://mathwriting.education.uconn.edu
Pam Meader, a former high school math teacher, has taught math in adult education for over 25 years. She is a math consultant for the SABES PD Center for Mathematics and Adult Numeracy professional development initiative for Massachusetts. Most recently, she helped co-develop Adults Reaching Algebra Readiness (AR)2 with Donna Curry. She is a national trainer for LINCS and ANI (Adult Numeracy Instruction). Pam enjoys sharing techniques for teaching math conceptually from Basic Math through Algebra and has co-authored the Hands On Math series for Walch Publishing in Portland, Maine.