How do we help students develop written skills in mathematics? Being able to verbalize process is an important skill in any subject. In math, we emphasize the importance of showing all work, which is one way for students to document their thought process. Beyond this, a goal of mine has been to help students become more adept at fluently describing the “why” behind their math logic.
I also have a great interest in encouraging my students to help others beyond our school community. In flipping my classes and offloading direct instruction to videos students watch for homework, I have created a large resource of free, publicly available instructional math videos.1 One of the most rewarding parts of this process has been discovering the reach of my voice and lessons; being able to teach students around the world who find and use my videos has been extremely fulfilling. So I asked myself: How can I share this experience with my students?
This year I revised my definition of participation for my AP Calculus classes. Beyond asking students to contribute to class discussion and stay on task, I now include “helping others work through challenges” as part of students’ contributions in class. This, I hypothesized, would bring out a student’s willingness to break down difficult concepts for his or her classmates, thus explaining his or her own logic as well. But I also discovered, along the way, an opportunity for my students to help students beyond the classroom walls.
I believe that students reinforce their learning and gain deeper insight into material by teaching others. To that end, I ask my students to post to Socratic.org throughout the year. This forum encourages students to ask or answer calculus questions (as well as other subjects). Once a month, students are expected to answer a question posed by one of their classmates on Socratic as a formal assignment for class. Students have the option to complete additional response posts and, in doing so, reveal an interest beyond class requirements while displaying their initiative to go above and beyond.
I explain to students that their answers are not meant to be perfect — they are learning! A wonderful feature of Socratic is that all answers are editable, so that somebody from the Socratic community (or myself) is able to correct errors. The edits are reported back to the student, and a revision history is shown so that students can learn from updates.
Screenshot of the revision feature in Socratic. On the top pane, edits are highlighted and marked in line with the post. On the left pane, the original post is displayed. On the right pane, the edited post is displayed.
Each student in my classes has posted four or five answers this academic year. The process of posting answers to Socratic requires students to go beyond simply showing the computation used in arriving at an answer. Responses are getting much stronger, reflecting not only increased student understanding of calculus but also growth in their ability to thoroughly explain and teach a concept.
Students are getting more comfortable with the idea of “writing” in math class. After our first postings, I required that each student conference with me, one-on-one, for about 10 minutes. This conversation allows me to show students how to improve answers. Writing and verbalizing their math explanations is not a skill that we ask of students every day. So it’s important that I help them develop and improve in this area.
Though one-on-one conferencing is a valuable addition to the assignment, meeting with each student in the class takes a fair amount of time. Instead, in the future, I might edit a student’s work directly in Socratic and ask him or her to submit a reflection on my feedback. Further, as students gain more mastery of material, I plan to ask them to “update” their classmates’ answers. By looking back through the update history, I will be able to easily grade students on meaningful contributions and enhancements to their classmates’ original posts.
I’ll continue to improve my process, but there are many clear benefits to integrating this type of teaching into the classroom. First, we’re building a set of resources to study that are specifically tailored to our classwork. We’re also building a record of each student’s progress throughout the year, which will be powerful to look back on and would make a great addition to a student’s ePortfolio. Perhaps most important, though, I believe that having students explain their problem-solving process at this level of detail is critical to helping them build their analytical and verbal math skills — a task that’s often overlooked in mathematics pedagogy. And in doing so, we’re giving students the opportunity to contribute to a free, publicly available resource for other students around the world. I can’t imagine a better way to empower my students and share the importance of generously helping others!
Above is a sample of one of my student’s Socratic posts. In this problem, the student is explaining how to solve a related rates question. As is evident by the student’s post, she thoroughly explains her thought process going into the problem and carefully labels each step in her work, including mental notes and reminders.