I started my teaching career at a large comprehensive high school, teaching math exactly as I had been taught. Each day, I introduced my students to a new type of problem, solved a problem for them, and wrote the procedure in listed steps alongside my solution. Then I assigned them additional problems to solve on their own using the procedure that I provided. My students’ progress was slow with this approach, and I felt like I was struggling to reach them.
After four years of teaching, I switched gears and spent my fifth year teaching physics to 9th graders at a new engineering-themed small school in the Bronx borough of New York City. That year was completely different from my past teaching experience, both in terms of the content I was teaching and the type of instruction I was trying to provide my students. I used an inquiry-based curriculum with project-based assessments in this physics course with mixed success.
I finished the year feeling like the course had gone better than the teacher-centered math courses I had taught during the previous four years, but I wasn’t able to instantaneously change the learning in my classroom as much as I had hoped. Again, I found myself struggling to accurately assess what had gone wrong and how to improve.
Vocabulary Lessons
My principal contacted me over the summer because she was looking for someone to attend a training on teaching English-language learners. Our district’s department of education required someone from each school to attend a weeklong summer professional-development course, and no one else from my school was available or wanted to go. Initially, I felt like the training wouldn’t be applicable to my practice, but I decided to attend mostly to “take one for the team.” But, in fact, it was this PD experience that opened my eyes as to what had gone wrong the previous year and started to provide me with concrete strategies to improve the teaching and learning in my classroom. I learned, specifically, about the central role of language development in learning, even in math classes.
Through this activity and others like it, I started to think about how much vocabulary my students actually needed to learn in my classroom, especially if I was going to talk to them with appropriate mathematical and scientific words as they learned the new content. Regardless of whether my students were ELLs or former ELLs or neither, all the new content they were learning required them to learn new academic language as well, and I needed to teach this language to them. At this point in my career, I made a commitment that going forward, I would make a conscious effort to help my students develop both spoken and written academic language.
I continued to teach a variety of math and science classes for four years after this eye-opening summer training. I experimented with different ways to get my students talking and writing about math and science. I tried grouping my students purposefully, providing different participation structures like “round robins” and “novel ideas only,” and asking my students to write lab reports in science class and essays to identify and explain their mistakes in solving problems in math class. I even had my calculus students read a nonfiction book in literature circles about Newton and Leibniz’s independent discoveries of calculus and required them to keep a journal about their reading and the connections they were making to their own learning in calculus.
It was an exciting time for me as I tried to help improve the teaching and learning in my classroom, and I definitely felt more successful as a teacher. My students’ written work gave me insight into what they understood and what they didn’t in a way I had never experienced when the majority of the assessment in my classroom was summative and focused on correct answers rather than explanations and processes.
Academic-Language Development
After nine years of teaching, I left the classroom to take a position at an amazing nonprofit organization where I planned and facilitated PD for preservice and new math teachers. The Common Core State Standards had just started to be implemented, and they were creating a different culture from the one in which I had learned to teach. Students were now being asked to explain their thinking and the processes they used to solve problems and not just to provide the correct answer.
Additionally, the preservice teachers I was working with were required to complete the edTPA, a performance-based assessment, as a part of their certification process, and I had to learn this assessment in order to support them through the process. Part of the edTPA stresses the development of academic language of students, even in a math classroom. Specifically, it requires preservice teachers to identify one language function essential for students to learn in connection with the math lesson they’re teaching. It suggests “compare/contrast,” “conjecture,” “describe,” “explain,” and “prove” as language functions to be frequently used in a math classroom. As I tried to support the preservice teachers through this process, I began to look around to find examples of how other math teachers in our community were supporting language development in their classrooms.
When I was specifically looking for ways the teachers in our community were supporting their students’ academic-language development, I noticed that it was something that many teachers took seriously and incorporated almost daily. One common method that some teachers utilized came out of work traditionally associated with debate teams. They would ask students to justify their work using a “claim warrant” explanation. For example, while referencing a picture of triangle ABC, a student could say or write, “My claim is that angle A is the biggest angle. My warrant is that it is across from the longest side: BC.”
I also saw teachers adopt the idea of a problem without a question. They’d present students with a diagram or a situation and then ask questions like, “What is this situation about? What quantities do you have? What questions could be asked?” This process takes students away from traditional procedural methods of solving problems and gets them to think about different situations mathematically and to describe mathematical scenarios verbally and in writing.
A group of beginning math teachers that I worked with on an inquiry project gave their students examples of problems that were solved incorrectly and asked them to write about the misconception presented in the solution, using sentence starters like “I believe that ...,” “I can see that ...,” “My evidence for this idea is ...,” or “I think this means ...”
A Window on Understanding
All these methods and others were shared among the teachers in our community and were experimented with in different ways, all in hopes of helping develop students’ mathematical understanding, generally, through the use of writing. These methods provided for a symbiotic relationship between teaching and learning that previously didn’t exist between the two. Through verbal and written strategies, the students gained a deeper understanding of the content.
Meanwhile, students’ writing gave teachers a window into students’ understanding so that they could really address the content learning of their students. It enabled teachers to assess exactly what their students did and did not understand and adjust their teaching accordingly.
This fall, I return to the classroom, where I will be teaching 7th grade math and science. I re-enter the classroom with a wealth of knowledge from my work as a PD coordinator, knowledge I did not have when I started my teaching career. I hope to be able to synthesize all that I learned, both as a teacher myself and as an educator of educators, to develop my students’ mathematical and scientific abilities through writing.
If there’s one thing I learned as a math educator, it’s that while it’s important to have students learn to solve problems and to talk about solutions, it is equally, if not more important, to teach them to write about their strategies and thought processes, or they will always struggle to exhibit their mathematical understandings. And I need to be able to accurately assess exactly where my students are in their content development, so that I can reach them where they are and adjust my teaching accordingly.
I now believe that the key to creating a classroom environment with a true symbiotic relationship between teaching and learning is writing, so next year, my students will be doing a lot of it.
