Exploring the underlying mechanisms of a sixth grade student’s first steps towards the deductive proof scheme

Dilberoğlu, Merve
This study used an individual teaching experiment methodology to investigate a sixth-grade student’s first steps towards the deductive proof scheme. The study consisted of two major parts. The first part aimed to explore the processes by which an individual student may (1) come to understand a deductive argument as an instance of mathematical proof for the first time (Learning Goal 1). The second part aimed to (2) develop the main idea of this first instance proof as a transferrable main idea to the tasks of proving conjectures analogous to the first one proved and then explore (3) how the student’s developed understandings enabled or constrained her attempts to prove other similar and novel theorems. The main focus of the second part was on definitional reasoning as a crucial way of thinking associated with the development of the deductive proof scheme (Learning Goal 2). The study used constructs from DNR-Based Instruction in Mathematics and Learning Through Activity (LTA) theoretical frameworks complementarily to achieve its purposes. The study’s instructional approach to the first learning goal successfully explicated the mechanisms behind the student’s understanding of the first instance proof of the study. Its approach to the second learning goal, on the other hand, did not result in the intended definitional reasoning yet informed empirically-based hypotheses regarding its development. The study concluded with a second elaboration of how the DNR and LTA constructs can be used together to provide a theoretical foundation for the learning and teaching of proof.
Citation Formats
M. Dilberoğlu, “Exploring the underlying mechanisms of a sixth grade student’s first steps towards the deductive proof scheme,” Ph.D. - Doctoral Program, Middle East Technical University, 2023.