ABSTRACT This study investigated the effects of a Self-Regulated Strategy Development (SRSD) intervention on the quality of written explanations for additive problem-solving and reasoning, as well as on mathematical writing strategy use for students with learning difficulties. Participants were three third- and fourth-grade students identified with learning difficulties in mathematics and writing. A special education teacher implemented the individualized intervention across 15 lessons, during which she explicitly taught PRISM✓, a mathematical writing strategy, to help students plan, organize, and compose structured written explanations of their additive problem-solving and reasoning. A multiple-probe design across students was used to examine the effects of the intervention. The results indicated that, compared to the baseline, two of the three students produced higher-quality responses to describe their additive problem-solving and reasoning, including precise vocabulary and using more steps of the strategy during the intervention phase. The other student, who demonstrated significant writing difficulties, made immediate improvements in mathematical writing quality when a speech-to-text device was introduced. While the effects of the intervention were maintained four weeks after the intervention, students’ mathematical writing quality was lower in the generalization probes. The findings highlight the importance of combining explicit strategy instruction, self-regulation, visual representation, and mathematics vocabulary support to strengthen students’ written mathematical reasoning.

ABSTRACT Mathematics education has long been debated, with evidence from Pakistan highlighting poor student performance. However, key factors influencing mathematics achievement remain underexplored. This paper presents findings from a large-scale nationwide study examining predictors of student performance in mathematics. The study assessed the pedagogical quality of elementary science and mathematics teachers and their students’ learning outcomes. It considered factors ranging from school systems to familial influences affecting science and mathematics learning. Using a cross-sectional survey, the study evaluated students’ mathematics achievement and teachers’ classroom practices through reliable assessments and observations. The sample comprised 303 teachers and 15,343 students, selected via multistage cluster random sampling across Pakistan. Multiple linear regression identified significant predictors of student performance, including school system, teacher qualification, pedagogical practices, instructional time, language of instruction, grade level, student age, and parental qualification. The findings have implications for policy, practice, and research.

ABSTRACT In this paper, I present on research that I have done with Riley, a Black male mathematics pre-service teacher who was also a participant in a teacher residency program centered on anti-racist and justice-oriented pedagogy. Empirically, this paper captures an exploration into the educative capacity that Black Language (BL) possesses given one mathematics teacher’s use of it. The research question asks In what ways does Black Language manifest in one Black male pre-service teacher’s mathematics pedagogy, and what pedagogical needs does it serve? In my findings I assert that Riley uses language in at least three definitive ways: for pedagogical purposes related to checking for understanding and formative assessment; to shape and cultivate a joyful learning environment (to build community); and to shift students’ onto-epistemological orientations about, and in service to, the mathematics content. I then discuss how BL may serve the needs of a variety of youth. This paper helps to rethink what teacher educators offer as appropriate, mathematical, or standard to the students we teach and the educators that we prepare.

ABSTRACT This study examined the relationships between recommended mathematics coursework for secondary mathematics teacher preparation, internal program measures, prior academic performance, and the Praxis-II testing requirement for initial teacher certification used in several states. Using structural equation modeling and path analysis, the research aimed to understand these relationships and their policy implications. Conducted over six years and holding the program measures and design constant for five cohorts, the study found strong support for specialized content knowledge courses, particularly for secondary mathematics teacher candidates who were not well-prepared in high school. Additionally, the findings suggest that the Praxis-II exam might not be necessary for all teacher candidates in mathematics, especially those who were well-prepared in high school and engaged in advanced mathematics coursework for teachers while meeting rigorous program requirements for teacher licensing. The study argues for reconsidering programmatic design in light of these findings while providing program faculty suggestions for program improvements. State Departments of Education and policy makers may consider the research methodology, validity of internal measures, and testing requirements for Praxis-II for future discussions.

ABSTRACT The importance of constructing mathematical arguments and critiquing the reasoning of others has been emphasized as a key component for deep mathematical understanding. As a result, acknowledging proof as an essential tool to comprehend mathematics at all grade levels has been suggested by many researchers as well as reform initiatives. To do so, both teachers and prospective teachers should be able to predict how students reason mathematically, identify significant student reasoning instances and decide how to respond productively to those instances. The participants consisted of eleven prospective teachers who enrolled in a teacher education program at a public university in Turkey. All participants enrolled in a two-credit mathematics education course about teaching reasoning and proving in the middle grades taught by the author. The results of this study demonstrated that the participating prospective teachers were able to predict student reasoning productively. However, the results regarding to the participants’ levels of identifying significant student reasoning instances were less successful. This study also documented that majority of the participants listed guiding questions. Although the elective course was not structured toward promoting participants’ noticing skills, all these results could suggest that the course might have influenced the participants’ prediction, identifying, and responding skills.

ABSTRACT In the United States, calls for improved K-12 learning opportunities in mathematics have shifted focus in school district offices from bureaucratic pursuits to instructional improvement efforts. Yet, district leaders often receive little guidance on how to achieve these goals. Further, although widely recognized that content-specificity matters in instructional improvement efforts, mathematics-based district leadership has received relatively limited attention in the literature. In this qualitative study, we drew on district leaders’ narratives of their work to examine: 1) How do district-level mathematics specialists engage in and make sense of their practice? and 2) What influences the ways they make sense of their practice? Results indicate that the ways in which participants made sense of their leadership practices through their agency, agenda, and positioning was strongly influenced by both personal and systemic factors. Personal factors included the leaders’ personal and professional backgrounds and experiences. Systemic factors included the degree of coherence leaders perceived in the district’s vision of instructional improvement, the clarity of the district leader’s role, and management of staffing resources for improving mathematics instruction. The study concludes with implications for further research and practice.

ABSTRACT This study investigated upper elementary teachers’ framings of their students’ mathematical thinking in written across the three component skills of noticing. Drawing on a situated perspective, the research examines the influences of teachers’ culturalhistorical backgrounds, attitudes, dispositions, interactions with students, and other situated elements of teaching on noticing mathematical thinking. Interviews used a think-aloud method to capture real-time framing as teachers observed children’s thinking on the same problem, using written work from their own and unfamiliar classrooms. Analysis of transcripts involved iterative coding to identify frames and determine their prevalence across noticing skills (attending, interpreting, deciding). Results show teachers used multiple frames beyond focusing on the mathematical thinking present in the work, such as past performance, affective traits, and curricular expectations. The prevalence of these frames appeared primarily in the interpretation and deciding how to respond. Findings highlight the situated nature of noticing, as interpretations were impacted by teachers’ sociohistorical interactions and perceptions. Implications point to explicitly addressing teacher framing in professional development, as deficit views of children’s capabilities can limit productive noticing. Considering teachers’ lenses and co-constructing frameworks can promote growth towards equitable noticing practices that privilege children’s mathematical reasoning. Implications for research and practice are explored and discussed.

ABSTRACT Instructional routines, like Number Talks and Notice and Wonder, engage students in doing and then talking about their mathematical thinking. Number Talk routines are short mathematical discussions where students mentally solve and share the strategies they used to make sense of the problem. In comparison, the Notice and Wonder routine asks students to reflect on a high-interest visual prompt with multiple entry points, share their noticings and wonderings, and then the teacher steers the discussion toward a mathematical question to explore further. But what happens when the Notice and Wonder routine is used in conjunction with a Number Talk? In this descriptive case study, we analyze whether and how this variation of a Number Talk provides a class of third-grade students opportunities to exercise agency. Findings from this study yielded two major themes: 1) agency is built when authority is shared during a mathematical discussion, and 2) Notice and Wonder is an instructional routine that supports sharing authority. We then discuss why this matters and next steps for research and practice.

ABSTRACT This article provides an analysis of a data set coming from a two-phase qualitative study that focused on fostering primary students’ abstraction of interrelations among quadrilaterals (squares, rectangles, parallelograms, rhombuses, trapezoids). The pilot study consisted of work with eight primary students operating at van Hiele level 2 (e.g., understanding quadrilaterals without interrelations). We benefitted from the teaching experiment methodology to develop a task sequence applied in a dynamic geometry environment and a paper-pencil environment to help each participant develop quadrilateral hierarchy at van Hiele level 3 (e.g., understanding quadrilaterals with their interrelations). The main study used a case study approach to investigate two primary students’ progress (Efe and Ayla, age 10). After the pre-interviews, each participant was taught the developed task sequence individually during seven up-to-one-hour teaching sessions, followed by a post-interview. This article only details Efe’s case as he worked on developing the relationship between parallelogram and trapezoid. We analyzed Efe’s data (from the pre-interview, Teaching Session-7, and the post-interview) to describe how the different parts of the task sequence fostered his abstraction of the interrelation between parallelogram and trapezoid as he moved from van Hiele Level 2 to 3. This article provides initial evidence for the classification process.