1. General Introduction
1.10. Overview of dissertation: Studies about the role of peer feedback provision in
geometry proofs
Based on the issues discussed in the earlier sections, it seems that despite the possible usefulness of PF provision for preservice mathematics teachers’ validation skills and comprehension of complex geometric tasks (i.e., constructions and proofs), PF is still not widely used in preservice mathematics teachers’ instruction. Furthermore, the possibility to train PF skills is still not investigated with preservice mathematics teachers. Although individual characteristics were frequently emphasized in feedback models and frameworks as influential factors, some of these individual characteristics (e.g., domain knowledge, beliefs about PF provision, PF providers’ perceptions of their PF, and epistemic emotions) are often not addressed explicitly in many PF studies. This dissertation attempts to address these issues in two empirical studies. In Study 1, we focused on training PF provision skills taking into account providers’ domain knowledge, and changes in their beliefs about PF provision representing two important PF providers’ individual characteristics in the MI2PA framework. PF characteristics investigated in this study was PF content. In study 2, the PF composition processes (distinguished in the MI2PA framework) was closely explored using eye-tracking methodology, and the relationships between PF content with other PF providers’ individual characteristics were investigated including epistemic emotions, beliefs about PF provision, and perceptions of their PF. The impact of peer solution quality representing a major recipients’ individual characteristic (i.e., domain knowledge) was investigated in this study. Figure 2 illustrates the elements of the MI2PA framework that were investigated in the current project. The first empirical study (Chapter 2) focused on training PF skills of geometric construction tasks, the role of domain knowledge, and beliefs about PF provision of preservice
mathematics teachers. The second empirical study (Chapter 3) concerned the PF composition process by investigating cognitive processing during PF provision on different qualities of peer solutions to a geometry proof, and the role of preservice mathematics teachers’ beliefs about PF provision, their perceptions of their PF, and their epistemic emotions. To address the main research aim in detail, more specific research questions were developed to be investigated in each study. Next, an overview of the chapters of this dissertation is provided.
Chapter 2 presents a study of training PF skills of 43 preservice mathematics teachers on geometric construction tasks. A quasiexperimental field study with a mixed design was conducted. All participants received PF training focused on Hattie and Timperley’s (2007) feedback model, and they practiced providing PF on fictional peer solutions to geometric construction tasks over several sessions. Before the PF training, participants’ PF skills, their basic geometric knowledge, and their beliefs about PF provision were measured. Performance on the basic geometric knowledge test was used to group the preservice mathematics teachers into three domain knowledge groups (low, medium and high). Participants’ PF skills and their beliefs about PF provision were measured again after the PF practice sessions. The following research questions were investigated:
RQ 1. What is the impact of a structured PF provision training on preservice mathematics teachers’ PF provision skills, and will students with different levels of domain knowledge benefit differentially from the training?
RQ 2. Will preservice mathematics teachers’ beliefs about PF provision change after the training, and will domain knowledge play a role in that change?
Chapter 3 presents a study investigating preservice mathematics teachers’ cognitive processing of peer solutions to a geometry proof during PF provision while taking into account their beliefs about PF provision, their perceptions of their PF, and their epistemic emotions. This study adopted an experimental between-subject design. The quality of fictional peer solution to a geometry proof was manipulated (near-correct vs. erroneous). Participants were required to provide oral PF to a fictional peer. Eye-tracking was used to monitor the participants’ eye-movements while providing PF on the fictional peer solution to a geometry proof. After PF provision, the participants’ proof comprehension, their basic geometric knowledge and their beliefs about PF provision, perceptions of their PF, and epistemic
emotions were measured. Fifty-three preservice mathematics teachers participated, and the following research questions were examined:
RQ 1. How does reading cognitive processing while providing PF (measured by proportional total dwell time) differ depending on the quality of a peer solution (near-correct vs. erroneous) to a geometry proof?
RQ 2. What is the impact of the peer solution quality (near-correct vs. erroneous) to a geometry proof on the PF providers’ comprehension of the proof?
RQ 3. What is the impact of the peer solution quality (near-correct vs. erroneous) to a geometry proof on the content of the provided PF?
RQ 4. What are the relationships between the PF providers’ proportional total dwell time on the peer solution, PF providers’ proof comprehension, and content of the provided PF?
RQ 5. What is the impact of the quality of the peer solution (near-correct vs. erroneous) to a geometry proof on the experience of the epistemic emotions curiosity and confusion?
RQ 6. What are the relationships between the PF providers’ epistemic emotions, proportional total dwell time on the peer solution, proof comprehension, beliefs about PF provision, perceptions of their PF, and the content of their PF?
In the remainder of this dissertation, the two studies will be reported in more detail, followed by a general discussion in Chapter 4, in which general conclusions from both studies
will be discussed. Finally, methodological limitations, research and practical implications, and directions for future research will be outlined.