As social distancing guidelines are relaxed and/or removed in school settings, we hear a lot of buzz about “getting back to normal” and “making up for lost time”. Through all the difficulties of distance learning, there have been some bright spots. Teachers and students were challenged to find alternate strategies for making connections and collaborating and doing mathematics. And many parents got a glimpse into how we teach and learn mathematics. We can capitalize on the many lessons learned from the past year and a half as we build on students’ strengths and resiliency and use this knowledge to rejuvenate our classroom practices.
In preparing for the upcoming school year, it is a great opportunity to create a “new normal” for the teaching and learning of mathematics. Make a plan to refresh your instructional practices with strategies and tools that help our youngest learners experience deep mathematical learning. In this post, we describe three actions to refresh and rejuvenate your instructional practices using rich math tasks.
Principles to Actions (NCTM 2014, p.17), reminds us that “effective teaching of mathematics engages students in solving and discussing tasks that promote mathematical reasoning and problem solving and allow multiple entry points and varied solutions strategies.” To facilitate students’ development in mathematics and build on their prior learning experiences, we can rejuvenate our instructional practices by implementing rich math tasks to help: engage students in doing-math tasks; support the needs of diverse learners; and build shared understanding of big mathematical ideas.
Engage students in doing-math tasks
Consider the following questions:
- What is your “game plan” for engaging your students in mathematical experiences that allow them to “do the math”? How will you actively engage your students in deep problem-based mathematics? How will you encourage early childhood learners to reason about mathematics? How will you help students use and connect multiple representations? How will you implement tasks that allow your students to engage in rich discussions and justify their thinking?
“Doing-math tasks require your students to explore, yet also to self-monitor, their thinking as they mentally retrieve prior instructional experiences while working through a task.” Use doing-math tasks as a tool to help students learn and understand mathematics concepts. By engaging in deep, problem-based mathematics regularly, students are given the opportunity to use reasoning and problem-solving skills as they engage in grade-level mathematics activities. Doing-math tasks allow students to use sense-making, connect prior understanding, use and connect representations, explain their thinking, and use a variety of strategies to solve math tasks while engaging in rich discussions with their peers. Doing-math tasks promote the use of multiple solution paths and are characterized by a high-cognitive demand or high level of mathematical rigor. If students exhibit a struggle, the multi-faceted components of the task allow the teacher to use just-in-time scaffolding to help students re-engage with the task without lowering the cognitive demand of the task.
Use rich tasks as a tool to support the needs of diverse learners
Compared to procedural tasks, rich tasks offer more opportunities for teachers to better serve their students. As Aguirre et al. (2013) write: “Equity demands that responsive accommodations be made as needed to promote equitable access, attainment, and advancement in mathematics education for each student” (p. 9). When teachers facilitate rich tasks, they include more time for students to process, think, collaborate, and reason, as well as provide more opportunities for students to make choices about the manipulatives they use, the representations they create, and the way they share their ideas. For example, in a measurement task, students could select their own measurement units. Providing choice promotes student agency and individualizes the task. More generally, the complexity of rich tasks allows teachers to make different decisions about think time or offer time for learners to share ideas with partners first before sharing with the class. This could potentially provide students with access to multiple strategies before engaging in the task.
Building shared understanding of big mathematical ideas
Rich, higher level tasks require students to work collaboratively to problem solve, share their strategies, listen to other students’ ideas, and offer feedback to help develop mathematical understanding. As we return to face-to-face instruction, with students physically in the same classroom, with access to shared mathematical tools and with greater ability to share and discuss, the use of rich mathematical tasks provides incredible opportunities for students. By nature, rich tasks allow students to have multiple entry points and personal, varied solution strategies, all of which serve as opportunities to have meaningful mathematical discussions. Through analyzing and comparing strategies and thinking, students can build shared understanding of big mathematical ideas.
As we return to schools, let us create learning environments that draw from the successes and struggles that we have just experienced. To help each and every student experience deep mathematical learning, facilitate students’ development in mathematics, and build on students’ prior learning experiences, let’s implement rich mathematical tasks now to ensure we engage students in doing-math tasks, support the needs of diverse learners, and build shared understanding of big mathematical ideas!
Aguirre, J. M., Mayfield-Ingram, K., & Martin, D. B. (2013). The Impact of Identity in K-8 Mathematics Learning and Teaching: Rethinking Equity-Based Practices. National Council of Teachers of Mathematics.
Kobett, B. M., Fennell, F., Karp, K. S., Andrews, D., Knighten, L., & Shih, J. (2021). Classroom-Ready Rich Math Tasks, Grades K-1: Engaging Students in Doing Math. Corwin.
Principles to Actions: Ensuring Mathematical Success for All. (2014). National Council of Teachers of Mathematics.