How rich math tasks help to build community and culture, provide rich assessment data, and support your students in seeing themselves as mathematicians.
Let’s think about our typical planning process for our mathematics lessons. We may: 1) find a task aligned to a standard, 2) make copies, 3) gather and prepare classroom materials, 4) prepare formative assessment questions, and 5) consider how we will group our students. The intention behind the planning decisions have long-lasting impact for the students in our classrooms and can have vastly different implications for the culture of our classroom. Much of this culture depends on the richness of the mathematics task we choose. Flipping through a book or skimming a resource to find a task that meets a learning goal is important, but not all tasks ignite curiosity, spark mathematics joy, and help students think critically about the world. Traditional tasks may address a targeted mathematical idea, but when working alone, it is more difficult for students to remain engaged in doing mathematics. Planning for rich tasks can help create a positive learning community and a classroom culture of learning together, provide valuable assessment data about what students know, and offer authentic opportunities for students to see themselves and their classmates as mathematicians!
Let’s reflect on the following three shifts to move from traditional math tasks toward classroom-ready rich math tasks!
- Create a classroom culture of learning together
Instead of having students work individually, let’s have them collaborate and work together to solve a problem that interests them.
How do rich math tasks help to build a positive learning community and support your effort to create a classroom culture of learning? With many rich math tasks, students can work together embodying the adage “two heads are better than one.” Students’ collaboration helps them see each other as resources with important ideas and strategies to try. However, please be mindful that just pairing students or creating small groups does not automatically ensure that all students will engage or that groups will work together effectively. As with all skills, students need to be taught how to participate in groups. Rich math tasks help support this effective group work in your classroom by providing students with specific ways to work with classmates and engage with the mathematics. Providing structured opportunities for this collaboration also helps to build critical social skills and allows students to develop relationships with one another.
Example: A teacher purposefully selects a groupworthy task, Estimating Collections, to provide structured opportunities for every student to participate in the lesson on understanding rounding (Kobett et al., 2021). During this task, students are randomly assigned roles that dictate how they should interact with their group and the mathematics – providing opportunities for both individual think time and time for students to share their thinking with their group. Each of these purposefully designed participation structures allows every student’s voice to be heard during the lesson and allows individual ideas to be shared so that students can see the value in each other’s thinking and ideas. The roles also support each student’s meaningful engagement with the mathematics in the task.
- Use assessment data gathered from rich tasks
Replace a paper/pencil assessment with a rich mathematics task.
How do you get to know the strengths of your students (Kobett & Karp, 2020)? At the beginning of the school year or the beginning of a new unit of instruction, traditional “paper and pencil” pre-assessments might be selected to collect this student data. This approach, especially when timed, can create or increase a child’s text anxiety and runs the risk of children associating mathematics with the anxiety of testing while only providing teachers with information about the answers a child produces. Rich math tasks reimagine this traditional approach and affords opportunities to engineer a low stress mathematics environment where teachers can listen to authentic student thinking while students are working, creating rich formative assessment data moments.
Example: As students are working together in their groupworthy task above, a teacher can circulate around the room observing how students are working, listening in on their conversations and even interviewing groups to elucidate individual thinking (Kobett, Fennell, & Wray, 2016). Taking notes and keeping track of the different ways students are thinking about estimation and rounding serve as this essential assessment data.
- Provide opportunities for students to see themselves as mathematicians
Rather than modeling how to solve a problem, implement tasks with engaging contexts so students can see how the mathematics relates to their lives.
How can we authentically engage students in the mathematics? When students are asked to passively listen to a teacher and re-create a step-by-step procedure for solving a problem, they may disengage. This makes it difficult for them to connect the mathematics to their world. Rich tasks invite authentic engagement, demanding students to think, create, and solve in ways that build on intuition and understanding of the ideas. Showcase the brilliance of your students by engaging them in a meaningful rich task that honors their thinking, backgrounds, and communities.
Additionally, students can continue to develop their creativity by using different tools by representing their thinking, strategies, and solutions in multiple ways and seeing themselves as mathematicians! Such opportunities allow students to engage in the work of mathematicians by designing and carrying out a plan, representing and communicating their strategies to the class, and feeling the gratification of solving authentic mathematics problems.
Example: The Estimating Collections task provides students with different amounts of everyday objects (e.g., paper clips, beads, and blocks) in the same size bags so that they can use their own experiences and reasoning to estimate the number of objects in the bags. They then use the number line to help them understand how to round numbers to the tens and hundreds places and explore why rounding is a useful strategy. Teachers can easily adapt this task to use objects from their own classrooms or have students bring in objects from home to connect the mathematics they are learning in school to their personal lives.
Reflect on how you might adapt a task that you just taught or will teach.
Consider the following questions before you teach the task. Does the mathematics task:
- Provide opportunities for students to collaboratively work together to solve problems?
- Allow you to collect valuable formative assessment data?
- Showcase students as capable mathematicians?
Let’s use our preparation time strategically by selecting a classroom-ready rich math task that promotes a classroom community and positive learning culture, opportunities to collect rich assessment data, and allows students to see themselves as brilliant mathematicians!
Kobett, B. M., Fennell, F., Karp, K. S., Harrison, D., Swartz, B. A. (2021). Classroom-Ready Rich Math Tasks, Grades 2-3: Engaging Students in Doing Math. Corwin.
Kobett, B. M. & Karp, K. S. (2020). Strengths-Based Teaching and Learning in Mathematics: Five Teaching Turnarounds for Grades K-6. Corwin.