Content Knowledge: The Performance Task and Discourse

Designing Coherent Instruction in the area of Learning ActivitiesWhen I think of math, what used to come to mind was boring, solitary, repetitive exercises involving memorizing times tables or algorithms. Throughout this program I have learned that the most effective math instruction is creative, engaging, and social. According to Ernst & Ryan (2014), math discourse, or the ways students talk about math, shapes the way they think about it (p. 196). Having students engage in listening, responding, and expressing their thinking process helps them to develop critical thinking habits while at the same time creating that safe and supportive environment where students can try and use different methods. Math discourse not only fundamentally shapes student learning around mathematics but can positively impact classroom environment.


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Click here for a presentation of the Performance Task findings

As part of a partner project in my Elementary Math Methods course, I worked with a fellow third grade teacher in my cohort to design, implement and evaluate a performance task based on the CCSS for Numbers & Operations in fractions. The process of creating an assessment was a learning process of its own. By seeking feedback on the task from my partner’s experiences, other teachers in my PLC and cohort, and my field supervisors, we were able to design a rigorous but relatable assessment centered around sharing and splitting pizzas. One struggle during the early stages of the performance task was choosing clear and concise language understandable or accessible to all students. For example, the word ‘toppings’ in describing pizzas with items other than cheese on them was confusing to my partner’s English Language Learners. To mitigate that confusion, I added images and a key to the performance task clearly labeling the pepperoni and vegetarian pizzas as having ‘toppings’.

Instead of administering the task as strictly an assessment or test I used it to instruct my students in basic elements of math discourse. At the beginning of the lesson we reviewed vocabulary from our recent fractions unit and I introduced sentence frames similar to transition words we use in English Language Arts. These sentence starters allowed students to explain their thinking in a clear way to their partners. Once the students practiced explaining their thinking using “First I…then I…finally I…” I provided several open-ended questions for students to ask one another such as, “How did you solve that?” and “Can you explain how you…”. By using open-ended questioning in math, teachers can “draw out student thinking instead of funneling it” as well as allowing students “to become more aware of their own thinking, often catching mistakes in the process.” (pg. 201). Students then worked with a partner on the performance task and were expected to use the vocabulary and discourse language to explain the process to each other, a teacher, and the class.

“First I cut the pizzas into thirds and fourths. Then I filled in the number line. Finally I colored each number line in the amount they ate. It was clear that Mrs. Douma ate more.” – 3rd grade student

In the past I have used informal discussion moves such as turn and talk or had students provide comments, questions and compliments at the end of a presentation but this was the first explicit lesson I had taught introducing discourse structures to my students. My field supervisor noted that oftentimes we expect our students to know how and what to talk about without truly modeling the academic structures we want them to use.

“2/2=1 Dubble the Numerator 4/2=2” – 3rd grade student, IEP

The most striking result of this activity though was student engagement. While I anticipated that my already advanced students would thrive on the challenge of both the task and the chance to present explanations to their peers, it was my English Language Learners and struggling students that blossomed during the learning activity. As I checked in with various pairs I would ask those students “How did you solve that?” and their eyes would light up as they walked me through the steps, usually with the help and support of their partners. At the conclusion of the lesson I called pairs to share their answers to various questions and it was those students, who normally I resort to cold calling to share, that raised their hands with already practiced explanations to share with the class. We continued the sharing portion the following Monday and students were able to ask questions and give compliments or feedback after a pair shared their answers. The dialogue that resulted from that experience not only continued but deepened the math discourse as students were able to share different methods of solving the same problem.

Looking back on the activity, it was difficult but insightful into the strategies and progress of my students’ understanding of fractions. Many students struggled using number lines accurately to represent fractions and also comparing benchmark fractions. In a way the performance task served its purpose in helping me to formatively assess my student’s learning in fractions – I realized what essential learnings I needed to reteach and review with students. I also know that a number of students could not finish the performance task in the 20 minutes that I gave them to work on it. As I continue to gain experience as an educator, a facilitator, and assessment designer I hope to not only be able to incorporate discourse structures into formative assessments of my students but to continue inviting my students to collaborate as well as we grow together in this learning community.


Ernst, K. & Ryan, S. (2014). Success From the Start: Your First Years Teaching Elementary Mathematics.






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