This study explored a diagnostic assessment method that emphasized the cognitive process of algebra learning. The study utilized a design and a theory-driven model to examine the content knowledge. Using the theory driven model, the thinking skills of algebra learning was also examined. A Bayesian network model was applied to represent the theory…

This study explores how preservice teachers (PSTs) transfer the intended specialized content knowledge (SCK) to elementary classrooms. Focusing on the case of the associative property of multiplication, we compared three PSTs' SCK during enacted lessons in fourth grade classrooms with their own learning in professional development (PD) settings.…

The correct use of visual perspective is one of the main reasons that virtual reality environments and realistic works of art look lifelike. Geometric construction techniques used by artists to achieve an accurate perspective effect were developed during the Renaissance. With the rise of computer graphics, translating the geometric ideas of 600…

The Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010) propose a new vision for the mathematics classroom with updated content standards and Standards for Mathematical Practice (SMP). These practices are founded on NCTM processes (Problem Solving, Reasoning and Proof, Communication, Representation, and Connections) and abilities…

The test of understanding of vectors (TUV) is a multiple-choice test that was recently developed to assess student understanding of vector concepts required in introductory physics courses at the university level. In this study, the TUV was administered to 889 first-year students at the University of Zagreb. The Rasch model was used to evaluate…

This study used modified schema-based instruction (MSBI) to teach mathematical word problem solving to three students with ASD in fifth and sixth grade. Following explicit strategy instruction, the participants learned to use an 8-step task analysis and a graphic organizer to solve and discriminate between math word problems requiring algebraic…

This quantitative study compares the course grades earned by adult learners enrolled in college algebra amid different delivery formats to determine if one option is more viable than the other at a southeastern community college in the United States. Presented as a Dissertation in Practice (DiP), three manuscripts are incorporated in this study.…

This work is an exploration of upper elementary students' sense making around four conventional representations of function: equations with algebraic notation, Cartesian graphs, function tables, and natural language. The cornerstone to the empirical work is a task called the Function Puzzle, where students are given 16 cards representing four…

In this study I explore the construction of algebraic structure sense through engaging students in task sequences designed to elicit the development of competencies related to this understanding. The primary task-design principle employed in this study is strategic variation, in which certain components of items within task sequences vary while…

My dissertation evaluates two efforts to improve undergraduate economics education---the College Fed Challenge (CFC) competition and requiring intermediate algebra as a prerequisite for taking introductory economics courses. Using survey data of undergraduate students who participated in the CFC competition and a control group of students who did…

Most community college students in the U.S. must complete at least one developmental class, such as elementary algebra, before they can enroll in a college-level mathematics course. Increasingly common in such courses is the use of a web-based activity and testing system (WATS). This report presents initial results of a mixed-methods study of…

This study investigated the use of the interactive white board (IWB) and the impact the technology had on mathematics teaching practices for algebra teachers. The study used the Technological Pedagogical Content Knowledge (TPACK) model as the conceptual framework for the investigation, collection, and analysis of data. Teachers were interviewed to…

We investigated teachers' responses to a common set of varied-potential instances of student mathematical thinking to better understand how a teacher can shape meaningful mathematical discourse. Teacher responses were coded using a scheme that both disentangles and coordinates the teacher move, who it is directed to, and the degree to which…

A theoretical model of metacognition in complex modeling activities has been developed based on existing frameworks, by synthesizing the reconceptualization of metacognition at multiple levels by looking at the three sources that trigger metacognition. Using the theoretical model as a framework, this multiple-case study explores students'…

In our study, 32 German and Swiss 8th/9th-grade classes of lower-secondary school worked with their teacher on the same proving problem. The sample belongs to the Swiss-German study "Quality of Instruction, Learning Behavior and Mathematical Understanding". Our data analyses relate to the teachers' approaches to generating a specific…