I've always been an English-Language Arts kinda guy. Math was never my forte. When I learned that my new job would involve helping schools make the transition to the Common Core Standards for Math as well as English, I was nervous. How would I get up to speed on the math standards?
As I learned about the math standards, I saw connections to what I loved about the ELA standards and my anxiety diminished. The CCSS for math contain both grade level content standards that explain "the what" - what students should know and be able to do - and Standards for Mathematical Practice (SMPs) that explain "the how" - how students should learn and engage with one another in math class.
The SMPs apply to every grade level and are grounded in "important 'processes and proficiencies' that are highly valued in the field of math." Many of the things that I love about the ELA standards, such as the priority placed on evidence-based reasoning and the importance of explaining one's thinking, are present in the SMPs as well.
Make the Writing-Math Connection
When a school leader recently approached me about ways to incorporate a focus on Writing to Inform and Explain (CCSS ELA Writing Anchor Standard 2) in math class, I thought of the SMPs as a great way to make the connection. SMP 6 (attend to precision in communicating with others) is the standard that is the most natural fit for Writing to Inform and Explain, and also a great place to begin when introducing writing in math.
Excerpt from SMP 6 -- Attend to Precision:
"In the elementary grades, students give carefully formulated explanations to each other… Mathematically proficient students try to use clear definitions in discussion with others and in their own reasoning… by referring specifically to each important mathematical element, describing the relationships among them, and connecting their words clearly to those representations."
SMP 6 also states the importance of precision in terms of specifying units of measure, labeling the axes of a graph, and stating the meaning of mathematical symbols. To be clear, SMP 6 refers as much to oral explanations in small group discussions as it does to written explanations. Though the CCSS math standards don’t emphasize writing, taking the additional step of having students write out explanations after discussing them is a great way to reinforce and assess what the SMP requires.
Connection to Writing to Inform and Explain in ELA
The ELA grade level standards for Writing to Inform and Explain also focus on precise language, clear definitions, and making the relationship among ideas explicit. Compared to the explanations students write in Reading or Writing class, written explanations in math are more of a combination of words and visual representations.
If departmentalized, math teachers should connect with their ELA counterparts to see what students already know about writing to explain, so both teachers can highlight the similarities and differences of writing explanations in ELA and math. If writing to explain is new to ELA teachers as well, this book from Jeffrey Wilhelm is a great place for middle and high school teachers to start.
Getting Started with Writing Explanations in Math
Here is a process I recommend for getting started with writing explanations in math, adapted from my own work coaching teachers. It is most powerful when used by a team of teachers who plan together.
Unpacking the Standard
1. Begin with the language of SMP 6 itself. First, read the "Commentary and Elaborations" document for SMP 6 (available for grades K-5 and 6-8) developed by Illustrative Mathematics. (You might be interested in checking out the recently published Teaching Channel video series sponsored by Illustrative Mathematics.) This document includes the language of the SMP, and helpful annotations and elaborations that explain what the standard looks like at different grade levels. As you read the standard, underline words and phrases you think are particularly important, and then discuss with a colleague what you underlined and why.
2. Next, make a simple T-Chart with elements of SMP 6 that students can do now, and things that are new or are a challenge for students.
Seeing the Standard in Practice
3. After you have an idea of what the standard asks of students, watch videos of students explaining their thinking to get a better idea of how it looks in an actual classroom. Inside Mathematics has a series of several videos of SMP 6 in action at different grade levels. Use insights from these videos to refine your list from Step 2.
4. Now, brainstorm what a good written explanation in math should contain. Return to your T-Chart from Step 2 and determine how these elements would show up in student writing, keeping in mind it may be a combination of words, graphs, equations, and drawings. These "look fors," based on SMP 6 and developed for a school district in Michigan, are a great starting place. Make a list of the characteristics of an effective written explanation in math for your grade level and create an anchor chart. Then identify characteristic(s) you want to target first.
5. Examine your unit plan for an upcoming unit, and determine content standards that would be a good fit for SMP 6 and writing explanations. Craft an objective targeting a specific characteristic (Step 4) you want to address. Then work as a team to create or adapt existing models of a good math explanation highlighting this characteristic. Share these models with students by doing a think aloud as you write your explanation, to help them see the connection between writing and thinking. Once students get comfortable writing explanations, have them examine examples written by their peers. Make a math explanation rubric as a class and post it so everyone can see!
Assessing Student Explanations
If students are going to be expected to explain their thinking, it helps to have a rigorous task that asks them to do so. The team at Mathematics Assessment Project has gathered a number of assessments that align with SMP 6. Requiring a written explanation of the steps or procedure students took in completing one of these assessments is yet another way to incorporate Writing to Explain in your instruction.
Time to Write!
Asking students to write out an explanation of how they solved a problem can give you unique insight into student thinking that goes much further than “show your work” ever will. After students can write explanations, switch the focus to making arguments about which approach to solving a problem is most effective (SMP 3). It pairs nicely with Writing Anchor Standard 1, but that’s a topic for another blog.