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November 21, 2018
By Rachel Awkward, Lower School CSE Coordinator
Last year, I applied for and received an MMFS Parents Association grant to use for professional development in math instruction. Using this generous funding, I was able to attend two continuing professional studies courses at Bank Street College: “Language Matters! Supporting Mathematical Discourse in the Classroom” (instructor: Amy Withers), and “Early Number, Addition, and Subtraction” (instructor: Eliza Chung).
The focus of the “Language Matters!” course was to demonstrate the importance of discourse in math instruction to support students’ understanding of mathematical concepts and overall critical thinking skills. Discourse refers to the process of students having conversations and sharing ideas, including ones where they agree and disagree. As teachers, we have an important role of providing the structure for these conversations, as well as encouraging students to share their ideas, and identifying connections among ideas. Teachers can promote mathematical discourse by using mathematical routines and rich mathematical tasks. One of the mathematical routines that stood out to me was the “Noticing Routine: See/Wonder.” In this routine, the math teacher displays an image or object and asks students: “What do you notice?” and “What do you wonder?” These open-ended questions allow for no wrong answers, and encourage students to think critically and share their thinking, rather than racing to find an answer. The instructor also emphasized the importance of having students engage in rich mathematical tasks, rather than rote procedures. She shared the example of the following word problem to demonstrate how to “open up” closed-ended problems:
Tickets to a baseball game are $20 for an adult and $15 for a student. A school buys tickets for 45 adults and 600 students. How much money will the school spend for the tickets? (Engage NY 5th Grade, Module 2: Multi-Digit Multiplication)
|Opening up the closed problem:
A school has a budget of $1000 for baseball game tickets. Tickets for adults cost $20 and for students cost $15. What combination(s) of tickets could you buy? Remember that at least one adult must go as a chaperone for every 10 students.
Traditionally, math instruction emphasizes one correct answer, but there is so much learning that occurs through the process, rather than just the result. The goal of including both mathematical routines and mathematical tasks is to foster critical thinking and to deepen a student’s understanding of mathematical concepts through discourse.
Similarly, the “Early Number, Addition, and Subtraction” course emphasized process. One of the major struggles students encounter in the earlier phases of math instruction is adding and subtracting when there is a need to regroup. Over the past few years of teaching math at MMFS, this has been a challenge for many of my students, and I have also heard other faculty members express the same. Given this struggle, I was both shocked and inspired to hear that Eliza Chung, the instructor, shared that students should learn regrouping when they are learning third grade level math skills. Just because students struggle with the regrouping algorithm, does not mean they have to be limited in their exposure and practice with adding and subtracting larger numbers. Eliza shared a few techniques to introduce to students to support their addition and subtraction fluency, and modeled how to have a conversation with students about solving addition and subtraction problems using these strategies. During this conversation, each student would share which strategy he/she/they selected to solve the problem. There was no right or wrong way, but rather an opportunity for students to deepen their understanding of what actually occurs when adding and subtracting. It also strengthens their number sense.
I am incredibly grateful to the Parents Association for providing the funding to attend these two courses. I will be integrating all that I learned into my math instruction throughout this school year!