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The study of pivotal teaching moments (PTMs) offers significant insights into mathematics classroom interactions. PTMs are student-generated instances within a lesson that provide opportunities for teachers to modify planned instruction (Stockero & Van Zoest, 2013). Given the importance of interactions and discourse in students’ mathematical growth and understanding, we examine them in the context of PTM episode triples. PTM episode triples consist of three main elements: (1) a PTM, (2) a teacher response to the PTM, and (3) the immediately ensuing student utterance. Analysis of data from nine elementary mathematics lessons shows that teacher responses that explicitly “pursued students’ thinking” elicited significantly higher cognitive levels of student discourse than teachers who "ignored or dismissed" PTMs or simply "acknowledged [PTMs] but continued as planned." While many researchers have focused on PTM episode “doubles” (combinations of student-generated interruptions and the teacher’s response), no studies to our knowledge have addressed PTM episode “triples” as we have. Implications of these findings prove helpful for identifying concrete ways that educators can increase the cognitive level of student discourse within their classrooms. Further, our integration and modification of existing theory and frameworks for analyzing PTM episode triples—incorporating the relationship between PTMs and teachers’ responses to them, on the one hand, and the cognitive level of the ensuing student utterance, on the other hand—are a unique contribution to the field and provide a method by which researchers and educators can study classroom practice.

Translating a mathematics lesson from curriculum materials into instruction is not straightforward, and launching, or beginning, a lesson such that students will become productively engaged in the target mathematics is nontrivial. The purpose of the study was to investigate preservice teachers’ curricular noticing as they draw upon curriculum materials to design instruction, with a focus on how to launch that lesson. We engaged preservice elementary licensure students at two universities in a four-part process of analyzing mathematics curriculum, planning a lesson, demonstrating their visualization of enactment through animating their lesson launch, and reflecting on the process. Findings indicate that the focal case study pair modified the curricular materials to model mathematical aspects of fractions, adapted the introduction of key academic vocabulary, and introduced materials not mentioned in the curriculum to draw children into the lesson. We discuss implications for preservice teachers’ planning of the lesson launch and their curricular noticing.

This paper explores how problem solving is approached in two 6th grade mathematics textbooks and national elementary mathematics curriculum in Turkey. The curriculum and textbooks’ problem solving approaches are analysed and compared in the light of three approaches of ‘teaching for, about and through problem solving’. Four learning objectives from different content areas (e.g. algebra, data processing) from the curriculum are determined and their treatments in the textbooks are specifically analysed. The analysis showed that the curriculum did not have a prescriptive stance on any one of problem solving approaches. Similarly, the textbooks also did not follow any approach faithfully. ‘Teaching for problem solving’ approach was not employed while ‘teaching through problem solving’ approach was used for only one learning objective in the textbooks. ‘Teaching about problem solving’ approach was encountered in terms of only one problem solving heuristic (table drawing). We discuss the implications of these findings and note some further research areas.

The purpose of this study was to investigate the relationship between prospective teachers’ (PTs) instructional practises and their efficacy beliefs in classroom management and mathematics teaching. A sequential, explanatory mixed-methods design was employed. Results from efficacy surveys, implemented with 54 PTs were linked to a sample of teachers’ instructional practises during the qualitative phase. In this phase, video-recorded lessons were analysed based on tasks, representations, discourse, and classroom management. Findings indicate that PTs with higher levels of mathematics teaching efficacy taught lessons characterised by tasks of higher cognitive demand, extended student explanations, student-to-student discourse, and explicit connections between representations. Classroom management efficacy seems to bear influence on the utilised grouping structures. These findings support explicit attention to PTs’ mathematics teaching and classroom management efficacy throughout teacher preparation and a need for formative feedback to inform development of beliefs about teaching practises.

The Fennema-Sherman Mathematics Attitude Scales (FSMAS) are among the most popular instruments used in studies of attitudes toward mathematics. However, the FSMAS has been mainly used among student populations and rarely used with teachers. In the present study, three scales from the FSMAS—Confidence, Effectance Motivation, and Anxiety—were revised and used with lower-primary (kindergarten to third grade) teachers. This study includes three parts: (1) a pilot study to ensure the modifications made to the FSMAS were appropriate to use with teachers, (2) confirmatory factor analyses to assess the factor structure of the revised FSMAS with 225 lower-primary teachers, and (3) measurement invariance analyses using data from a similar sample of 171 lower-primary teachers to examine whether the revised FSMAS measures each construct in the same way as in the previous sample. The final three-factor model, after removing three problematic items, achieves acceptable model fit, with each construct meeting all conditions for strict measurement invariance. Additionally, repeated measures analyses were performed on data collected from 39 in-service lower-primary teachers who participated in an elementary mathematics specialist program to examine the use of the revised FSMAS in program evaluation. Overall results suggest that researchers and program evaluators may use the revised FSMAS to reliably measure lower-primary teachers’ mathematical attitudes, and it can be a valuable tool for evaluating the effectiveness of professional development programs.

In the evolving field of mathematics education, there is the need to maintain the relationship between what is presented in college level preparation courses and the skills required to teach mathematics in classrooms. This research examines the knowledge demands placed on 73 pre-service primary teachers as they use lesson study to plan and teach data handling in primary classrooms. Pre-service teachers are observed as they plan, teach and re-teach data lessons in classrooms. Problems of practice are identified and categorized using the Ball, Thames and Phelps (2008) subdomains of common content knowledge (CCK), specialized content knowledge (SCK), knowledge of content and students (KCS) and knowledge of content and teaching (KCT). The results provide insights into the specific knowledge demands placed on early career teachers when teaching data and statistics and identifies foci area that can be addressed in teacher preparation programs. The results illustrate that development of understandings in one knowledge subdomain can motivate and impact learning in another subdomain. These interrelationships were found to exist both within and between the domains of content and pedagogical content knowledge.

The objective of the present study was to examine the relationship between mathematics anxiety and the procedural and conceptual knowledge of fractions in prospective teachers. Thirty-two preservice teachers enrolled in an elementary mathematics methods course were administered the Revised Mathematics Anxiety Rating Scale (RMARS, Baloglu, 2002). Procedural and conceptual knowledge of fractions was assessed with a validated paper and pencil test (Saxe, Gearhart, & Nasir, 2001) and with four additional problems created by the researchers. Results indicated that as mathematics anxiety scores increased, scores on the validated measure of procedural knowledge of fractions decreased. The same relationship was found between the RMARS and the validated measure of conceptual knowledge. The findings provide some insight on the cognitive and pedagogical factors associated with mathematics anxiety in the preservice teacher population, underscoring the importance of facilitating their proficiency in both mathematical procedures and concepts.