The ideas of measurement and measurement comparisons (e.g., fractions, ratios, quotients) are introduced to students in elementary school. However, studies report that students of all ages have difficulty comparing two quantities in terms of their relative size. Students often understand fractions such as 3/7 as part-whole relationships or…

Response time is an important research topic in the field of psychometrics. This dissertation tries to explore some response time properties across several item characteristics and examinee characteristics, as well as the interactions between response time and response outcomes, using data from a statewide mathematics assessment in two grades.…

This holistic, mixed-methods action research case study aimed to determine the influence of professional development on participants' mathematical teaching practices and how the changes influenced students' opportunities for discourse. In this two-year study, participants engaged in two professional development phases and implemented new…

This study combined the principles of multimedia message design with an enclosing-rectangle scaffold to facilitate instruction on deriving the area of basic geometric shapes. A pretest/posttest/delayed-posttest design was used to compare the effectiveness of the enclosing-rectangle scaffold with that of conventional dissection/rearrangement…

Pedagogical Content Knowledge (PCK) is a fundamental component for effective teaching and plays a crucial role in teacher education. Even though pre-service teachers are engaged in training to improve their PCK, the literature reveals that most of their difficulties in practicum courses stem from their PCK. The purpose of this research is to…

It is important to understand how students reason in K-12 integrated STEM settings to better prepare teachers to engage their students in integrated STEM tasks. To understand the reasoning that occurs in these settings, we used the lens of collective argumentation, specifically attending to the types of warrants elementary students and their…

In order to learn more about student understanding of the structure of proofs, we generated a novel genre of tasks called "Proof Without Claim" (PWC). Our work can be viewed as an extension of Selden and Selden's (1995) construct of "proof framework"; while Selden and Selden discuss how the structure of a proof can be discerned…

An important consideration in the design and development of numeracy-focused coursework is ensuring that one meets students where they are with respect to both their mathematics background and their existing numeracy practices in relation to public issues. The latter consideration is especially important, given that students already think about…

Proof validation plays a significant role in students' understanding and learning of mathematical proofs. Recent studies have shown that university students were lacking skills in proof validation and were challenged by the implementation of the appropriate acceptance criteria when validating proofs. Drawing on Habermas' construct and rational…

Research indicates that institutions and teachers' pedagogical and content knowledge are essential to student learning and achievement. Nevertheless, teachers' knowledge and practices have been researched primarily in K-12th grades. Therefore, there is a gap in understanding teaching practices in higher education. Moreover, research has forgotten…

Though teacher education programs must document candidates' teaching dispositions, there is a gap in the literature around what faculty may learn by observing students in contexts outside of the k-12 classroom. This case study explores what faculty may learn about teaching dispositions by observing tutors. For our study, three mathematics…

Parental involvement in schooling has been shown to have a positive impact on children's educational outcomes. With changing mathematics curricula and pedagogical approaches as a context, we explore how mathematical dispositions emerge through gendered and classed experiences with mathematics homework. We share the experiences of mothers from…

The increasing use of computerization in the testing industry and the need for items potentially measuring higher-order skills have led educational measurement communities to develop technology-enhanced (TE) items and conduct validity studies on the use of TE items. Parallel to this goal, the purpose of this study was to collect validity evidence…

Tychonov's 1935 solution of the heat equation, exhibiting nontrivial heat fluxes spontaneously appearing along an isolated conducting rod initially held at zero degrees, has intrigued some specialists for almost a century. No doubt those practicing heat engineers who took mathematics seriously were initially relieved to learn that the construction…

The coordinate system is a fundamental tool for many daily activities, yet it is usually taught to children in middle school. Research suggests that children should be exposed to the coordinate system at a younger age, using methods appropriate to their developmental level. This paper presents a set of instructional activities designed to teach…