The study reported here addresses pre-service and in-service teachers' attitudes toward mathematical-geometrical definitions. The goal of the study is to investigate whether understanding the role of definitions as classification and identification criteria will guarantee that participants: (1) accept that there may be more than one equivalent…

The purpose of this action research project was to investigate the impact of a mastery-based grading system on the mindsets of high school students. The mixed methods data collection for this project took place over the course of two years. The students were part of a high achieving and mostly high socio-economic status community. I collected…

Children's understanding of fractions, including their symbols, concepts, and arithmetic procedures, is an important facet of both developmental research on mathematics cognition and mathematics education. Research on infants', children's, and adults' fraction and ratio reasoning allows us to test a range of proposals about the development of…

Using a multisite cluster-randomized controlled trial design, we evaluated the effect of the first year of a three-year teacher professional development called Cognitively Guided Instruction (CGI) on third -fifth grade students' mathematics achievement. Teachers in the intervention condition participated in nine days of professional development…

In this dissertation I seek to examine and expose the world of teaching, and particularly the world of teaching mathematics in public middle schools and high schools in New York City. These schools are administered by the New York City Department of Education which each year is responsible for the education of over one million students. In this…

This paper describes a task that was used, in a broader study on mathematical giftedness and mindsets, as part of a process to identify mathematical giftedness in primary school students (see Parish, 2019). A discussion of the task, together with an analysis of student responses, offers insights that could be used by classroom teachers for both…

In this position paper, we review the practice of differentiation -- a universal concept aimed to support diverse students in our classrooms. In exposing the wide-ranging practices of differentiated instruction, and critiques of current implementation, we argue that differentiation in the mathematics classroom needs to be reframed in terms of a…

This paper contributes to the Symposium: "Research methods involving children's drawings in mathematical contexts" by providing insight into young children's attitudes towards mathematics through the use of drawings. Children in Years 2 and 3 (n=25) participated in this study which aimed to identify a range of attitudes towards…

Professional noticing of student thinking is considered a useful construct to investigate instructional decisions and activity made by teachers to support learning. This paper highlights the findings from one component of a multi-university (United States & Australia) research project focused on improving pre-service secondary mathematics…

This working group continues to develop a research program on the practice of launching mathematical tasks and its resulting impact on learners. Our research agenda contains two strands of inquiry exploring (1) theory and framework building concerning effective launches and (2) empirical examination of the link between launching and opportunities…

Historically underused methodologies in mathematics teacher education such as narrative inquiry, self-study, and autoethnography (i.e., self-based methodologies) are becoming a more frequent choice of mathematics teacher educators (MTEs). This has opened new challenges for MTEs as they try to disseminate their findings in mathematics education…

The implementation of high-stakes testing has radically altered mathematics instruction in elementary classrooms. A curriculum that is heavily focused on developing successful test takers has fostered a weakness in our students' ability to solve complex problems. The purpose of this record of study was to examine the impact of a problem-solving…

The purpose of this mixed methods study was to determine how teachers use questioning techniques in their mathematics classrooms and if teacher questioning techniques correlate with student achievement in mathematics. As pacing and rigor increase and students learning styles vary, schools are challenged with finding new ways to make connections…

The purpose of this study was to explore students' mathematical practices while working on modeling problems using 3 interactive computer simulations. Three fifth grade students' interactions with computer-based modeling simulation were examined to identify how children defined and prioritized and coordinated variables and parameters in…

The goal of this paper is to isolate the preparatory effects of problem-generation from solution generation in problem-posing contexts, and their underlying mechanisms on learning from instruction. Using a randomized-controlled design, students were assigned to one of two conditions: (a) problem-posing with solution generation, where they…