One of the challenges of teaching content courses for prospective elementary teachers (PTs) is engaging PTs in deepening their conceptual understanding of mathematics they feel they already know (Thanheiser, Philipp, Fasteen, Strand, & Mills, 2013). We introduce the Diverge then Converge strategy for orchestrating mathematical discussions that we claim (1) engenders sustained engagement with a central conceptual issue and (2) supports a deeper understanding of the issue by engaging PTs in considering both correct and incorrect reasoning. We describe a recent implementation of the strategy and present an analysis of students’ written responses that are coordinated with the phases of the discussion. We close by considering conditions under which the strategy appears particularly relevant, factors that appear to influence its effectiveness, and questions for future research.
Understanding mathematics teacher noticing has been the focus of a growing body of research, in which student work and classroom videos are often used as artifacts for surfacing teachers’ cognitive processes. However, what teachers notice through reflecting on artifacts of teaching may not be parallel to what they notice in the complex and demanding environment of the classroom. This article used a new technique, side-by-side coaching, to uncover teacher noticing in the moment of instruction. There were 21 instances of noticing aloud during side by side coaching which were analyzed and classified, yielding 6 types of teacher noticing aloud, including instances in which teachers expressed confidence, struggle, and wonder. Implications for coaching and future research on teacher noticing are discussed.
Formative assessment helps teachers make effective instructional decisions to support students to learn mathematics. Yet, many teachers struggle to effectively use formative assessment to support student learning. Therefore, teacher educators must find ways to support teachers to use formative assessment to inform instruction. This case study documents shifts in teachers’ views and reported use of formative assessment that took place as they engaged in professional development (PD). The PD design considered the formative assessment cycle (Otero, 2006; Popham, 2008) and embedded it within a pedagogical framework (Lamberg, 2013, in press) that took into account the process of mathematics planning and teaching while supporting teachers to learn math content. Teachers restructured their definition of student understanding, which influenced how they interpreted student work and made instructional decisions. Teachers’ pre-PD instructional decisions focused on looking for right and wrong answers to determine mastery and focused on pacing decisions. Their post-PD decisions focused on student thinking and adapting teaching to support student thinking and learning. Implications for PD to support teachers to use formative assessment and research are discussed.
Mathematics Teacher Educators (MTEs) help preservice teachers in transitioning from students to teachers of mathematics. They support PSTs in shifting what they notice and envision to align with the collective vision encoded in the AMTE and NCTM standards. This study analyzes drawings and descriptions completed at the beginning and end of a one-year teacher education program—snapshots depicting optimized visions of teaching and learning mathematics. This study analyzed drawings-and-descriptions by cohort and by participants. The findings suggest that the task can be used as formative assessment to inform supports for specific PSTs such as choosing a cooperating teacher or coursework that challenges problematic beliefs. It can also be used as summative assessment to inform revision of coursework for the next cohort.
MTE is a scholarly, peer-reviewed journal for practitioners in mathematics teacher education that is published twice a year. MTE contributes to building a professional knowledge base for mathematics teacher educators that stems from, develops, and strengthens practitioner knowledge. The audience for the journal is broadly defined as anyone who contributes to the preparation and professional development of pre-K–12 pre-service and in-service teachers of mathematics. Mathematics teacher educators include mathematics educators, mathematicians, teacher leaders, school district mathematics experts, and others.
Karen Hollebrands, Editor
Valerie Faulkner, Associate Editor
Jan Yow, Panel Chair
Laura Bofferding, Panel Member
Matt Campbell, Panel Member
Theodore Chao, Panel Member
Zandra de Araujo, Panel Member
Keith Leatham, Panel Member
Beth Kobett, NCTM Board Liaison
Eva Thanheiser, AMTE Board Liaison
Babette Benken, AMTE VP of Publications
David Barnes, NCTM Staff Liaison
Headquarters Journal Staff
David E. Barnes, Associate Executive Director for Research, Learning, and Development
Ken Krehbiel, Executive Director
Eleanore Tapscott, Director of Publications
Aisha Jamil, Sr. Production and Copy Editor (Consultant)
What to Write for MTE
The mission of the online journal Mathematics Teacher Educator (MTE) is to contribute to building a professional knowledge base for mathematics teacher educators that stems from, develops, and strengthens practitioner knowledge. The journal provides a forum for sharing practitioner knowledge related to the preparation and support of teachers of mathematics as well as for verifying and improving that knowledge over time. The journal is thus a tool that uses the personal knowledge that mathematics educators gain from their practice to build a trustworthy knowledge base that can be shared with the profession.
Therefore, all manuscripts should be crafted in a manner that makes the scholarly nature of the work apparent. Toward that end, manuscripts should contain a description of the problem or issue of mathematics teacher education that is addressed, the methods/interventions/tools that were used, the means by which these methods/interventions/tools and their results were studied and documented, and the application of the results to practice (both the authors’ practice and the larger community).
The nature of evidence in a practitioner journal is different from that in a research journal, but evidence is still critically important to ensuring the scholarly nature of the journal. Thus, authors must go beyond simply describing innovations to providing evidence of their effectiveness. Note that effectiveness implies that something is better and not just different as a result of the innovation. In addition, authors should make explicit the specific contribution to our knowledge. Findings should be reported with enough warrants to allow the construction or justification of recommendations for policy and practice.
Manuscripts should be no longer than 25 pages of text or 6,250 words (exclusive of references). For ease of reading by reviewers, all figures and tables should be embedded in the correct locations in the text. All manuscripts should be formatted according to the guidelines of the Publication Manual of the American Psychological Association (6th edition). Manuscripts not conforming to these specifications may be returned without review. Please submit manuscripts using the online manuscript submission and review system.
Because MTE is published online-only, authors are encouraged to take advantage of the possibilities of this medium by including items such as student work, videos, applets, hyperlinks, and other items that enhance the manuscript. Appropriate permission for such items must be submitted before a manuscript will be accepted for publication. In addition, color can be used to the extent that it enhances the submission.
Mathematics Teacher Educator (MTE) is a scholarly, peer-reviewed online journal for practitioners. Two issues of this journal are published each year. NCTM members can add MTE as an additional subscription for $24 for Essential and Premium members, and $12 for Student and Emeritus members.
The primary audience of Mathematics Teacher Educator is practitioners in mathematics teacher education, with practitioner broadly defined as anyone who contributes to the preparation and professional development of pre-K–12 pre-service and in-service teachers of mathematics. Mathematics teacher educators include but are not limited to mathematics educators, mathematicians, teacher leaders, school district mathematics experts, and professional development providers. Learn more about MTE now.