A historical review of mathematics textbooks suggests a canonical method to solving equations that teachers often see as "the" way to solve equations. In this paper, we examine data from a nationally-distributed sample of 524 secondary mathematics teachers who responded to scenario-based survey items that represent the instructional…

This research focuses on the retention of students' algebraic understandings 1 year following a 3-year early algebra intervention. Participants included 1,455 Grade 6 students who had taken part in a cluster randomized trial in Grades 3-5. The results show that, as was the case at the end of Grades 3, 4, and 5, treatment students significantly…

This article explores a conceptual relationship between learner choice and mathematical sense-making. It argues that when learners can exercise choice in their mathematical activities, mathematical sense-making can be enhanced. The literature around mathematical modelling suggests a link between sense-making and learner choice. A three-tiered…

This article describes two heuristic strategies for problem solving: the "use of false assumption" strategy and the "use of double false assumption" strategy. Both of these strategies have their roots deep in history. In this article, we define these two strategies and illustrate their use in a problem developed by Frances…

Math outcomes for students with disabilities, in particular students with emotional disturbance (ED), are bleak, warranting intervention strategies that have research to support their utility. The purpose of this meta-analysis was to examine the literature of math interventions used with students with ED to improve math outcome variables. Our…

Classroom instructional quality is seen as crucial to student learning. Of particular interest is the interpretation and enactment of the intended mathematics curriculum in Singapore schools by experienced mathematics teachers towards quality learning outcomes. This paper discusses the findings from the study which investigate the instructional…

There is an educational expectation that children's natural drawing will develop into proficient mathematical representations and formal diagrams, yet there is little research available to guide the assessment and development of children's mathematical drawing skills. The aim of this paper is to explore how Year 2 children (approx. 7 years) chose…

Mathematics-specific learning difficulties and disabilities (MLD) have received increasing attention in scholarly research. In this study, we place MLD research in its wider context of risk societies by discussing the manufacturing of MLD as "a risk." This framing of MLD builds on a certain idea of "hope" in how research could…

This inquiry examined the pedagogical practices in mathematics of elementary teachers (N = 27) who had been identified as experienced and successful and were working in an urban school district with underserved student populations. Also investigated were relationships between their instructional practices and other elements of proficient teaching…

Increasing numbers of students with disabilities (SWD) receive remote or online instruction in secondary mathematics. Unprecedented shifts in teaching modalities during the COVID-19 pandemic highlighted the need for effective remote instruction. The present study surveyed 31 general and special education teachers to identify features of remote…

This work studies mathematics word problems' use in a classroom of recent immigrants, or newcomers, to a United States public elementary school. I study how word problems foster the recontextualization of mathematical concepts in a lived reality experienced by newcomer students in their new cultural and educational setting. In this study's setting…

This study aimed to analyze views of mathematics student-teachers on teaching practice in classroom contexts by subsuming following the new didactic triangle, which was used as a conceptual framework: (1) Teaching Process, (2) Learning Process, and (3) Thinking Process. A participative research design was employed for the research methodology. The…

We present the evolving fraction conceptions of two elementary school children with mathematics learning disabilities (MLD). We use qualitative analyses to capture the mathematical knowledge and experiences of each child and show how teaching was used to support advancement of their fractional reasoning. Results illustrate two viable pathways of…

In light of rising college student debt, many states now offer multiple options for students to earn college credit while still in high school. Concurrent enrollment programs, which allow qualified high school teachers to teach college credit-bearing classes in the high school, are one such option. Because concurrent enrollment classes teach…

This research study explored teachers' self-reported uptake as well as observed instructional change after participating in a year-long professional development (PD) program focused on supporting the learning and teaching of transformations-based geometry. Analyses illuminate the degree and nature of the pedagogical shifts made by teachers who…