Editor’s note: I did a series on writing in math classes over at my Education Week Teacher column but, due to my disorganizational skills, I overlooked this contribution. The authors have graciously given me permission to publish it here. I’ll add it to The Best Resources For Writing In Math Class
Laura Bolton, Ben Avila, and Kelly Mahoney are teachers in the Central Unified School District in Fresno, California. Laura is at Saroyan Elementary School, has been teaching for 15 years, and has taught math using Cognitively Guided Instruction for the last 11 years. Ben is at Teague Elementary School, has been teaching for 15 years, and has taught math using Cognitively Guided Instruction for the last 11 years. Kelly is at River Bluff Elementary School, has been teaching for 12 years, and has taught math using Cognitively Guided Instruction for the last 10 years. They are members of the Instructional Leadership Corps, a collaboration among the California Teachers Association, the Stanford Center for Opportunity Policy in Education, and the National Board Resource Center at Stanford.
Writing has become an essential part of a 21st century math class. It is no longer enough for students to merely solve twenty problems on a worksheet and regurgitate answers. Students need to explain their thinking and justify their answers. According to Common Core Mathematical Practice Standard Three students must construct viable arguments and critique the reasoning of others.
“They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is.” (p. 6, CCCSS, 2014)
Writing can take on many purposes and forms. Writing for mathematics can promote a deeper understanding of concepts and procedures. By explaining their thinking students are more apt to make connections and solidify their thinking. Explaining their thinking to others is a good way to sort through their understandings and misconceptions.
“Students might demonstrate deep conceptual understanding of core mathematics concepts by solving short conceptual problems, applying mathematics in new situations, and speaking and writing about their understanding. Students who lack understanding of a topic may rely on procedures too heavily.” (Overview of the Frameworks, p.11, 2015)
The new standards ask students to apply mathematics to everyday life and situations. Students can write to explain how their strategy works in a real world context. They can explain why their solution strategy is the best and most efficient path to an answer. Or explain why their answer given a multitude of possible answers would be the best choice in a given scenario.
Writing in mathematics classrooms is also a good form of assessment. By having the students write you can get to know what students are thinking. Teachers may know if a student got the correct or incorrect answer, but that doesn’t always tell you the full picture. By having students write their explanation for their answers you can better formatively assess their understanding and tailor lessons to your students’ strengths and weaknesses.
At the kindergarten and first grade level, writing in mathematics will and should look different than in second grade and above. Young children can begin writing in math with simple drawings with labels. Labels could be words and/or pictures. Sentence frames and math word banks can help young students with basic descriptions of their solution strategies. Annotation apps such as Seesaw and Explain Everything can help kinder and first grade students record explanations of their thinking in greater detail before their writing skills have fully developed.
Some ideas to get your students writing in math class could be:
- Describe how to solve a problem
- Explain why an answer or solution is reasonable
- Write a journal entry about what they learned in class or what was difficult or easy
- Explain whether or not they agree with a given solution or statement and explain why
- Examine errors in other students’ work and explain what could be done to correct the mistake
- Describe how two solution strategies are alike or different
Students at all grade levels can and should write during math class. Younger students can benefit from learning to label their work and writing sentences to clarify their answers and strategies. The written rehearsal of strategies helps older students consolidate their thinking and strategies, pushes them to think reflectively about their own and their classmates’ explanations or strategies, and can provide teachers with a means of assessing a student’s understanding and misconceptions.
California Department of Education. California Common Core State Standards: Mathematics. Edited by CDE Press. Sacramento, CA, 2014. http://www.cde.ca.gov/re/cc/.
Instructional Quality Commission. Mathematics Framework for California Public Schools: Kindergarten through Grade Twelve. California Department of Education. Sacramento, CA, 2015. http://www.cde.ca.gov/ci/ma/cf/mathfwchapters.asp.