The goal of this research was to investigate the relationship between real analysis content and high school mathematics teaching so that we can ultimately better prepare our teachers to teach high school mathematics. Specifically, I investigated the following research questions: (1) What connections between real analysis and high school…

Implementation of the Common Core Mathematical Standards and Practices (CCSS) has emphasized the importance of instruction that develops both procedural knowledge and conceptual understanding. Novice teachers have experienced the implementation of the CCSS during their PreK-12 experience, as well as within their teacher preparation program. It may…

Although geometric shape content should be mastered by early high school, many pre-service teachers (PSTs), particularly those in elementary and special education, have limited yet deeply engrained shape concepts. This poses challenges for how to teach shape concepts in content courses for PSTs. Thus, this study tested an approach atypical for a…

This paper details an exploratory study of ten elementary preservice teachers (PSTs) involvement in the problem-solving process in a mathematics methods course. The dynamic, messy and nonlinear nature of this process was demonstrated by discussing PSTs' solution process of an open box construction problem. Effective approaches to solve this…

This study used a pretest-posttest design to explore the scoring by female preservice teachers (n=25) of student responses to a pattern problem. The treatment consisted of a cooperative activity that required the preservice teachers to assign scores to a rubric intended to enhance careful attention to student reasoning expressed in written…

In this study, we examine the connections between real analysis concepts and secondary mathematics content. This is accomplished by conducting a textbook analysis of a commonly used real analysis textbook. Concepts from the real analysis textbook were mapped to the Common Core State Standards-Mathematics (2010) to determine the relationship…

Recommendations for preparing teachers of mathematics have been published by multiple professional organizations in the United States; however, there is limited research on whether student course perceptions affirm the instructor-identified alignment of mathematics content courses for prospective secondary mathematics teachers (PSMTs) to these…

This paper discusses strategies that two high school geometry teachers employed to solve a challenging geometry problem with the aid of dynamic geometry software (The Geometer's Sketchpad (GSP). The teachers were part of a group of teachers who participated in a summer professional institute funded by the National Science Foundation. The paper…

The purpose of this study was to fill a gap in the literature on student learning and use participant feedback to improve the pedagogical effectiveness in mathematics and literacy classrooms. To this end, an anonymous, semi-structured Qualtrics survey was developed and administered to 1,212 recent high school graduates asking about the best way to…

The United States' Common Core Standards for Mathematics give a prominent role for mathematical modeling in the K-12 curriculum. This has implications and creates challenges for teacher preparation programs. We describe one program's attempt to meet these challenges with a course in mathematical modeling for pre-service secondary mathematics…

In this essay, we describe some challenges that mathematics teacher educators may face when teaching content courses for future elementary and middle school teachers. We summarize research that suggests students in content courses may have fixed mindsets, unproductive beliefs, and mathematics anxiety that can interfere with their ability to learn…

Mathematics content for elementary teachers (MCfET) courses generally provide prospective elementary teachers (PTs) with opportunities to engage with mathematical content and consider it from a teacher's perspective, yet little is known about the intended curriculum of such courses. Findings from an analysis of MCfET course activities using the…

Engaging in productive struggle--grappling with challenging problems--is conducive to understanding mathematics. This paper examines five pre-service teachers as they learned to engage English language learners in productive struggle. The context of this descriptive case study was an elementary mathematics methods course in the Northeastern United…

This paper details an exploratory study of 14 elementary prospective teachers (PTs) solving purposefully crafted, two-digit addition problems. The numbers in each problem were chosen to elicit diverse solution strategies. We coded 95 responses based on the ways the PTs completed the calculation (for example, by referring to the number as…

The aim of this study was to examine the pre-service mathematics teachers' technological pedagogical content knowledge and beliefs using computer technology in mathematics instruction, as well as the effects of teacher training programs on these beliefs and knowledge. Participants included 199 pre-service elementary mathematics teachers. Of these,…