Currently, there are more theories of learning in use in mathematics education research than ever before. Although this is a positive sign for the field, it also has brought with it a set of challenges. In this article, the author identifies some of these challenges and considers how mathematics education researchers might think about, and work with, the multiple theories available.

The goal of this study is to uncover the successes and challenges that preservice teachers are likely to experience as they unpack lesson-level mathematical learning goals (i.e., identify the subconcepts and subskills that feed into target learning goals). Unpacking learning goals is a form of specialized mathematical knowledge for teaching, an essential starting point for studying and improving one’s teaching.

Using case study analysis and a cognitive theoretical orientation, the authors examine elements of knowledge for teaching needed by a mathematician to orchestrate whole-class discussions in an undergraduate mathematics classroom. Examples of classroom teaching and interview data demonstrate that, despite having extensive teaching experience and possessing strong content knowledge, some instructors may still face challenges when trying to provide analytic scaffolding to move whole-class discussions toward a lesson’s mathematical goals.

The Journal for Research in Mathematics Education (JRME) is seeking innovative ways to promote and support research that has the potential to encourage and sustain conversations at the intersection between research and practice. As such, the journal plans to pilot special issues of JRME that will address topics of key importance that are considered to be at the boundary of research and practice. The special issue will be accessible to all NCTM members online and become an NCTM publication upon completion.