Journal of Mathematics Teacher Education

Goodchild, Simon; Apkarian, Naneh; Rasmussen, Chris; Katz, Brian

doi: 10.1007/s10857-020-09456-2pmid: N/A

This paper reports a study of university students’ experiences of learning mathematics in an introductory differential equations course that takes an inquiry approach to learning and teaching. The students are on a trajectory leading toward a bachelor’s degree in mathematics to be followed by a year-long teacher education credential program. The analysis of students’ end of course presentations and written portfolios is framed with community of practice theory, complemented with analytic categories from community of inquiry, including notions of inquiry stance and critical alignment. Our social theorization of university mathematics education adds a complementary perspective to the more conventional cognitive and discursive analyses and is necessitated by the very nature of inquiry approaches to education. The analysis of students’ presentations and writing leads to exploring their development of the notion of critical stance, which the students are seen to take toward the mathematics, their learning, and approaches to teaching mathematics. We find that the notion of critical stance can be distilled into three components: awareness, self-evaluation, and agency.

Ulusoy, Fadime; Çakıroğlu, Erdinç

doi: 10.1007/s10857-020-09457-1pmid: N/A

This paper explores the nature of prospective teachers’ noticing of students’ understanding as they analyze and discuss middle school students’ understandings of trapezoids in micro-case videos in the context of geometry. In this exploratory study, the data were obtained from eight prospective middle school mathematics teachers through individual video analysis, reflection papers, and group discussions. The results indicated that the use of purposeful micro-case video designs based on prospective teachers’ background knowledge of quadrilaterals allowed them to be productive in video analyses and discussions. In individual video analyses, prospective teachers attended to various mathematical elements to identify students’ responses but did not always use them to make interpretations of each student’s understanding of trapezoid. In the group discussions of the micro-case videos, in contrast, prospective teachers could provide alternative interpretations of students’ understanding by identifying links between the mathematical elements in students’ responses and the characteristics of students’ understandings. In the group discussions, they provided more detailed and specific instructional actions to support each student’s understanding of trapezoid than their individual video analyses. This study suggests practical implications for teacher education programs on how to use video cases (e.g., firstly, working individually and then having group discussions about the videos) to explore prospective teachers’ professional noticing skills. Considering prospective teachers’ background knowledge of related mathematical contents, this study can also inspire future studies on how to design effective videos about students’ mathematical understanding.

Beilstein, Shereen Oca; Henricks, Genevieve M.; Jay, Victoria; Perry, Michelle; Bates, Meg Schleppenbach; Moran, Cheryl G.; Cimpian, Joseph Robinson

doi: 10.1007/s10857-020-09459-zpmid: N/A

This study compares web usage data with interviews from 41 participants, who are members of an online professional development site called the Everyday Mathematics Virtual Learning Community (VLC), to explore how elementary school teachers learn from classroom video. Web usage data reveal that the commentary surrounding video posted to the VLC is sparse and surface level, possibly indicating a lack of serious attention to the videos. Interview data, however, indicate that participants felt they learned from this resource. Participants reported that the videos provided them with the opportunity to view and reflect on model lessons, plan curricula, and consider student thinking, among other learning outcomes. Participants also identified key factors that prevented them from posting comments to the site to convey their learning. These results can be used to understand not only how teachers perceive their own learning from classroom video, but also to redesign online professional development experiences to promote expression of that learning.

Myers, Kayla D.; Auslander, Susan Swars; Smith, Stephanie Z.; Smith, Marvin E.

doi: 10.1007/s10857-020-09460-6pmid: N/A

This case study explored Prospective Elementary Mathematics Specialists’ (PEMSs) pedagogical practices during a K-5 Mathematics Endorsement (K-5 ME) program, specifically focusing on the authentic residency with mentor sessions. Participants included nine PEMSs, with qualitative and quantitative data collected via individual interviews, professional portfolios, and observations of classroom practices. Upon completion of the K-5 ME program, all participants were implementing instructional practices learned about in the program in substantial ways. Participants were honing their skills for orchestrating effective discourse, and the application of those skills became more meaningful as they saw the impact it was having on student learning. This implementation and documentation program coursework was rigorous as PEMSs worked to develop themselves as mathematics teachers and teacher leaders. The collaborative support during the authentic residency and mentor sessions seem to have been significant for PEMSs in supporting implementation of newly learned instructional practices. Ultimately, PEMSs completed the program feeling more prepared as elementary mathematics teachers and teacher leaders.