Recognizing, building, describing, extending, and analyzing patterns are key components of algebraic reasoning. Oftentimes pattern-based instruction is used to support the understanding of functions and variables. In this study, elementary preservice teachers (n = 23) were asked to explore, extend, explain, create equations for, and analyze…

The purpose of this study was to explore how elementary preservice teachers (PSTs) responded to students' hypothetical misconceptions about volume measurement. We carried out both pre-assessments and follow-up interviews with 17 PSTs, with tasks focused on both volume content knowledge and hypothetical student responses to volume tasks.…

Empirical studies of angle, angle measure, and radian angle measure have primarily focused on documenting students' and teachers' conceptions. Representations of angle measure have the potential to inform and build on these conceptions. To gain insight into the concept of radian angle measure from a curricular perspective, I investigated the…

The purpose of this research is to promote the construction of mathematical proof from argumentation at the primary level. To show this is a viable instructional strategy at the primary level, we use a teaching experiment methodology and a task related to geometric proof in this research study. To model and analyze the collective argumentation…

The Common Core State Standards for Mathematics ("CCSSM") explicitly states many specific theorems for students to prove across multiple domains (i.e., congruence, similarity, circles, and coordinates) in high school geometry. This study examined five high school geometry textbooks for how they approached proof of 17 theorems stated in…

The purpose of this study is to determine the effects of metacognitive strategies and content-specific feedback on student achievement in high school mathematics. Participants consisted of a convenience sample of students in honors geometry. An analysis of variance with repeated measures was employed to address the research questions. For both the…

International standardized tests are showing an underperformance of students in geometry and spatial ability relative to other content domains. In this research, we examined the relationship between a teacher's judgment of third- and fourth-grade students' geometry and spatial ability (i.e., grades), three spatial ability tasks (Water-Level-Task,…

The Common Core State Standards for Mathematics (CCSSM) is a primary focus of attention for many stakeholders' (e.g., teachers, district mathematics leaders, and curriculum developers) intent on improving mathematics education. This article reports on specific content shifts related to the geometry domain in the middle grades (6-8)…

Body-based activities have the potential to support mathematics learning, but we know little about the impact they have in the classroom. This study compares high school geometry students learning through either body-based or analogous non-body-based activities over the course of a two-week unit on similarity. Pre- and post-tests revealed that…

This paper brings together research on slope from mathematics education and research on line of best fit from statistics education by considering what knowledge of slope students transfer to a novel task involving determining the placement of an informal line of best fit. This study focuses on two students who transitioned from placing inaccurate…

Metaphors are regularly used by mathematics teachers to relate difficult or complex concepts in classrooms. A complex topic of concern in mathematics education, and most STEM-based education classes, is problem solving. This study identified how students and teachers contextualize mathematical problem solving through their choice of metaphors.…

The theory of realistic mathematics education establishes that framing mathematics problems in realistic contexts can provide opportunities for guided reinvention. Using data from a study group, I examine geometry teachers' perspectives regarding realistic contexts during a lesson study cycle. I ask the following. (a) What are the participants'…

This study investigated the ways in which four middle grades teachers developed mathematical knowledge for teaching (MKT) geometry as they implemented dynamic geometry software in their classrooms with the assistance of a coach. Teachers developed various components of MKT by observing coaches teach, by dynamic discourse with students, which is…

Use of mathematics-related literature can engage students' interest and increase their understanding of mathematical concepts. A quasi-experimental study of two second-grade classrooms assessed whether daily inclusion of geometry-related literature in the classroom improved attitudes toward geometry and achievement in geometry. Consistent with the…

Effective competition in a rapidly growing global economy places demands on a society to produce individuals capable of higher-order critical thinking, creative problem solving, connection making, and innovation. We must look to our teacher education programs to help prospective middle grades teachers build the mathematical habits of mind that…