Discussions about school mathematics often address the importance of reasoning and proving for building students' understanding of mathematics. However, there is little research examining how teachers enact tasks designed to engage students in justifying and proving in the classroom. This article presents results of a study investigating the processes and outcomes of implementing proof-related tasks in the classroom. Data collection consisted of observations of 7 middle school classrooms during implementation of proof-related tasks—tasks providing opportunities for students to produce generalizations, conjectures, or proofs—in the Connected Mathematics Project (CMP) curriculum by teachers experienced in using the materials. The findings suggest that students' experiences with such tasks are insufficient for developing an understanding of what constitutes valid mathematical justification.
Enacting Proof-Related Tasks in Middle School Mathematics: Challenges and Opportunities
Kristen N. Bieda
The Whole Is the Sum of Its Parts
Kristen N. Bieda
Scenarios of students using manipulatives to explore and justify mathematical ideas show how they are poised to generate effective proofs.
Informing Practice: Examples as Tools for Constructing Justifications
research matters for teachers
Kristen N. Bieda and Jerilynn Lepak
Research explores how to help students build from, instead of building with, examples when justifying mathematical ideas.
Investigating Problem-Solving Perseverance Using Lesson Study
Kristen N. Bieda and Craig Huhn
Middle and high school mathematics teachers share what they learned about supporting students by conducting a series of three lesson studies.
Justification as an Equity Practice
Kristen N. Bieda and Megan Staples
This article highlights the role of students' engagement in mathematical justification in supporting classrooms that provide equitable access to mathematics and develop students' agency for doing mathematics.
Proof: Examples and Beyond
Eric J. Knuth, Jeffrey M. Choppin, and Kristen N. Bieda
Asking middle school students to verify the math they do requires them to think about proof. By doing so, students construct arguments in the middle school and are more ready for proof in high school.
Mentor-Guided Lesson Study as a Tool to Support Learning in Field Experiences*
Kristen N. Bieda, Jillian Cavanna, and Xueying Ji
Field experience can be a rich site for intern teachers to develop the knowledge and skills they need for effective teaching. Lesson study has been shown to be a powerful form of professional development that enhances practicing teachers' mathematical knowledge for teaching through collaborative inquiry with their peers. In this article, we discuss the use of mentor-guided lesson study to support mentor and intern collaboration in the field and share what we have learned about its potential to support interns' attention to student thinking. We will also share insights from the field for those interested in implementing this activity in teacher preparation coursework.