Measuring student understanding of math concepts in this manner offers insight into the robustness of their knowledge, particularly of the Common Core State Standards for Mathematics.
Sarah K. Bleiler and Denisse R. Thompson
Jeremy F. Strayer, James B. Hart and Sarah K. Bleiler-Baxter
A four-phase process and three principles for building a mathematics learning community use rich discussion of student work.
Yi-Yin Ko, Sean P. Yee, Sarah K. Bleiler-Baxter and Justin D. Boyle
A three-step instructional sequence gives students authority to judge an argument's veracity by developing class-based criteria for proof.
Sarah K. Bleiler-Baxter, Sister Cecilia Anne Wanner O.P. and Jeremy F. Strayer
Explore what it means to balance love for mathematics with love for students.
Sarah K. Bleiler-Baxter, D. Christopher Stephens, Wesley A. Baxter and Angela T. Barlow
Using simplification, relationship mapping, and situation analysis as a framework, we offer vignettes of student discussions about the Theme Park task to highlight their key choices as they model with mathematics.
Sarah K. Bleiler, Wesley A. Baxter, D. Christopher Stephens and Angela T. Barlow
Teachers' insights could inspire further discussion about interpreting the SMPs.
Justin D. Boyle, Sarah K. Bleiler, Sean P. Yee and Yi-Yin (Winnie) Ko
Mathematics teachers are expected to engage their students in critiquing and constructing viable arguments. These classroom expectations are necessary, given that proof is a central mathematical activity. However, mathematics teachers have been provided limited opportunities as learners to construct arguments and critique the reasoning of others, and hence have developed perceptions of proof as an object that must follow a strict format. In this article, we describe a four-part instructional sequence designed to broaden and deepen teachers' perception of the nature of proof. We analyzed participants' reflections on the instructional sequence in order to gain insight into (a) the differences between this instructional sequence and participants' previous proof learning opportunities and (b) the ways this activity was influential in transforming participants' perceptions of proof. Participants' previous learning experiences were focused on memorizing and reproducing textbook or instructor proofs, and our sequence was different because it actively and collaboratively engaged participants in constructing their own arguments, critiquing others' reasoning, and creating criteria for what counts as proof. Participants found these activities transformative as they became more clear about what counts as proof, began to view proof as socially negotiated, and expanded their conception of proof beyond a rigid structure or format.