Michael Drake

The use of questions within in-the-moment coaching in initial mathematics teacher education: enhancing participation, reflection, and co-construction in rehearsals of practice

ABSTRACT Managing mathematical discussion is known to be challenging for novice teachers. Coaching within student teacher rehearsals of teaching has been shown to develop mathematics teaching practice, but can be time consuming. To examine how coaching using questions could assist novice teachers to promote mathematical thinking and discussions within time-constrained programmes, videos of rehearsals, reflective debriefs, and student teacher surveys were collected across a range of courses over 4 years. Findings included that student teacher roles in rehearsals were enhanced through coaching with questions and co-construction was enabled. Coaching questions exposed effective practice, particularly in relation to orchestrating mathematical discussion, enabling student teachers to reflect, discuss, make decisions, and immediately trial teaching strategies. Questions appeared to lengthen rehearsals but improved their effectiveness through enhancing participation and enabling co-construction of meaning. Findings indicate that questions used in coaching of rehearsals inform and empower novice teachers, essential factors within initial teacher education for equitable and ambitious mathematics teaching.

Revised Bloom's taxonomy and integral calculus: unpacking the knowledge dimension

ABSTRACT In this paper, the knowledge dimension for Revised Blooms taxonomy (RBT) is unpacked for integral calculus. As part of this work, the 11 subtypes of the knowledge dimension are introduced, and through document analysis of chapter 4 of the RBT handbook, these subtypes are defined. Then, by consulting materials frequently used for teaching integral calculus, each subtype is exemplified. The developed dimension may enable or enhance opportunities for dialogue between lecturers, teachers, and researchers about how to develop and align educational objectives, teaching activities, and assessments in integral calculus, or how metacognition and metacognitive knowledge could be used to support teaching and learning.

Exploring students' mathematical performance, metacognitive experiences and skills in relation to fundamental theorem of calculus

ABSTRACT Several studies have explored students’ understanding of the relationships between definite integrals and areas under curve(s). So far, however, there has been less attention to students’ understanding of the Fundamental Theorem of Calculus (FTC). In addition, students’ metacognitive experiences and skills whilst solving FTC questions have not previously been explored. This paper explored students’ mathematical performance, metacognitive experiences and metacognitive skills in relation to FTC questions by interviewing nine university and eight Year 13 students. The findings show that several students had difficulty solving questions related to the FTC and that students’ metacognitive experiences and skills could be further developed.

Learning to Coach in Practice-Based Teacher Education: A Self-Study

Abstract In some forms of practice-based teacher education, one important task for the teacher educator is to undertake in-the-moment coaching during rehearsals of practice. However, being such a coach is a new role for many teacher educators and requires a different skill set to other forms of teacher educator practice. In addition, there is little literature to which teacher educators can turn when seeking to address the problem of enactment in this context. This article seeks to address this gap in the literature. It reports a self-study undertaken by one mathematics teacher educator as he learned to coach pre-service teachers on the fly, while in turn they learned to orchestrate whole-class mathematical discussions. It seeks to illustrate how the process of journaling can support the journey of discovery that is the development of new practice. Through consulting the literature and story-telling, a picture is painted of how the educator addressed early concerns such as “what is a coach supposed to do?” and “what should a coach pause a rehearsal to talk about?” and began to master coaching – work that was never routine, but rather situated, adaptive, and responsive. The stories draw from a personal journal of field notes and reflections from such events as student rehearsals, lesson conferences, team meetings, reading student work, and professional reading. Journal entries from 12 rehearsal cycles over four years were consulted.