Developing mathematical practices through reflection cycles

Reflective Apprenticeship for Teaching and Learning Mathematical Proof

“…As a result of this turn, there is now rich empirical evidence (e.g., Freeman et al, 2014) for much earlier educational theories that focused on the ideas of learning by doing, or experiential learning (e.g., Dewey, 1933;Kolb, 1984). A key component of experiential learning is reflection: the act of processing an experience, action, or practice to gain further insight into the experience to better inform and guide future actions (Reinholz, 2016). Reflection is seen as a fundamental component of teacher education, to help teachers develop reflective practice (e.g., Averill, Drake, Anderson, & Anthony, 2016;Reinholz, 2017;Sherin, Jacobs, & Philipp, 2011).…”

Analysis of Effect of Answering Reflection Prompts in a Computer Organization Class

“…Namely, some students saw reflection as only improving conceptual understanding and not contributing to their typical approach to studying, which focused on practicing their problem-solving skills. Future studies should explore the use of reflection prompts specifically focused on helping students enhance their problem-solving skills similar to those used by Meneske et al [14], Reinholz [13] and Han [15].…”

“…Overall, the quantitative analyses in mathematics [13], engineering [14] and chemistry [15] confirm that guided reflection prompts that ask students "why" and "how" can enhance performance on exams. This finding provides further support for the qualitative studies in CS education that report that students better engage with a reflection activity if they are given guided prompts [10] [12] that ask students to explain why they chose a particular answer [11].…”

“…Given the lack of empirical studies on the impact of reflection on exam performance, we reviewed quantitative studies in the STEM literature to find evidence that links answering reflection prompts to enhanced student performance on exams. Reinholz [13] compared test scores for experimental and control groups of students in different sections of a calculus course to determine if students who participated in peer assisted reflection had higher scores than the students who did not. Reflection prompts included: "Explain why, not just what".…”

“…This paper aims to measure the impact of reflection on students' exam performance in a Computer Organization course. We adopted a similar approach to that used by Reinhold [13], Han et al [14], and Meneske et al [15] that separated students by course section. We use the prompts from Pear and Larzon's study [12] and do a quantitative analysis of the difference in performance on exams between students who wrote reflections immediately before exams and students who did not.…”