https://naeducation.org/…/2017-naedspencer-dissertation-fe…/

An Innovative Introduction to Proofs: Conjecturing and Constructing Deductive Arguments

Researchers have called for increased efforts to conduct design research and intervention-based studies that support students’ learning of mathematics and bridge the gap between theory and practice (e.g., Bishop, 1998; Stylianides & Stylianides, 2013). This study seeks to address this call through investigating Algebra 1 students’ conceptions of proofs while providing instruction designed to support their understanding of the generality and purpose of proofs. In particular, the 14-session design experiment featured tasks that aimed to establish the generality requirement for mathematical statements, motivate the need for deductive arguments, and engage students in proving conjectures using a definition they developed. Using data from semi-structured interviews, session videos, and students’ written work, I trace the development of students’ understanding of proofs and describe activities that seemed to have contributed to this understanding. Additionally, I analyze the interplay between students’ mathematical knowledge and understanding of proofs visible in the proof tasks they completed during the final interview.

Design experiment studies have two main aims: developing a content-specific learning trajectory and producing a series of empirically tested lessons that can be used to improve student learning in classrooms. In particular, my findings will contribute to the field’s understanding of how students come to understand the generality and purpose of proofs and will result in a series of lessons that can be used to introduce proofs in a secondary mathematics course.