Teacher Practice

The ReLaTe-SA project investigates the research question: what language do teachers use to describe and explain routines in algebra classes? The goal of this article is to inform readers about some ways we have learned to describe the discourse that teachers use when solving linear equations.

This study explored how two professional development approaches to reforming math instruction with different mechanisms for fostering change might have valuable synergies when used in tandem to support take-up, i.e., teachers’ acceptance, adoption, and incorporation of ideas into practice.

The researchers conducted a qualitative analysis of the perceptions of school personnel and pre-service teachers about an Algebra I tutoring program for students with learning disabilities. The researchers surveyed and interviewed the participants about the effectiveness of the program for the mathematics learning of the students with LD at the school and as a learning experience for the pre-service teachers.

In this article, we use data from interviews, class observations, and an analysis of instructional videos to describe an elementary mathematics specialists' efforts to incorporate flipped instruction for mathematics in her fifth grade class. We use this case to highlight how a knowledgeable teacher might use flipped instruction to enhance her teaching, and also describe potential challenges.

The National Council of Teachers of Mathematics has consistently emphasized the importance of curricular coherence in mathematics education. However, the predominance of the Internet has led to a lack of consistency in the use and quality of curricular materials. We drew on teachers’ self-report of their use of curriculum materials and conducted a Latent Class Analysis to examine patterns in 56 elementary teachers’ selection, use, and perceptions of materials for teaching mathematics, including the role that teacher expertise may play in these patterns.

We use an online Content Knowledge for Teaching (CKT) assessment that measures PSTs’ CKT in one science area: matter and its interactions. In this study, we analyzed process data from administering the online CKT matter assessment to 822 PSTs from across the US to better understand PSTs’ behaviors and interactions on this computer-based science assessment.

This study investigates the emergence and cultivation of teachers' “epistemic empathy” in response to analyzing videos of student inquiry. We define epistemic empathy as the act of understanding and appreciating someone's cognitive and emotional experience within an epistemic activity—i.e., activity aimed at the construction, communication, and critique of knowledge. Our goals are (1) to conceptually develop the construct and contrast it to more general notions of caring and (2) to empirically examine epistemic empathy in the context of preservice teacher education. We discuss tensions in teachers' expressions of epistemic empathy, and we end with implications for research and practice.

This is a technical report detailing the methods and findings for each of the research studies in the LLAMA project. 

This book aims to advance ongoing debates in the field of mathematics and mathematics education regarding conceptions of argumentation, justification, and proof and the consequences for research and practice when applying particular conceptions of each construct. Through analyses of classroom practice across grade levels using different lenses - particular conceptions of argumentation, justification, and proof - researchers consider the implications of how each conception shapes empirical outcomes. In each section, organized by grade band, authors adopt particular conceptions of argumentation, justification, and proof, and they analyse one data set from each perspective. In addition, each section includes a synthesis chapter from an expert in the field to bring to the fore potential implications, as well as new questions, raised by the analyses. Finally, a culminating section considers the use of each conception across grade bands and data sets.

Several recent studies have focused on helping students understand the limitations of empirical arguments (e.g., Stylianides, G. J. & Stylianides, A. J., 2009, Brown, 2014). One view is that students use empirical argumentation because they hold empirical proof schemes—they are convinced a general claim is true by checking a few cases (Harel & Sowder, 1998). Some researchers have sought to unseat students’ empirical proof schemes by developing students’ skepticism, their uncertainty about the truth of a general claim in the face of confirming (but not exhaustive) evidence (e.g., Brown, 2014; Stylianides, G. J. & Stylianides, A. J., 2009). With sufficient skepticism, students would seek more secure, non-empirical arguments to convince themselves that a general claim is true. We take a different perspective, seeking to develop students’ awareness of domain appropriateness (DA), whether the argument type is appropriate to the domain of the claim. In particular, DA entails understanding that an empirical check of a proper subset of cases in a claim’s domain does not (i) guarantee the claim is true and does not (ii) provide an argument that is acceptable in the mathematical or classroom community, although checking all cases does both (i) and (ii). DA is distinct from skepticism; it is not concerned with students’ confidence about the truth of a general claim. We studied how ten 8th graders developed DA through classroom experiences that were part of a broader project focused on developing viable argumentation.