Mathematical literacy and numeracy are critical for students during school and post-graduation, however, many U.S. students do not develop the mathematical skillset needed for college or the workplace, despite curricular importance placed on solving problems encountered in mathematics classrooms and spaces. Part of this skillset for critical…

Strategies mathematics teachers use can unintentionally have an adverse impact on student anxiety in the classroom. The purpose of the Action Research study was to investigate and strengthen strategies that mathematics teachers use to reduce student anxiety. Participants and data collected in Cycle 1 consisted of interviews and a focus group with…

Although there have been calls for secondary mathematics education in the U.S. to incorporate problem-solving and creativity, the lion's share of instruction is designed to train students to accurately use procedures or understand concepts made by mathematicians in the past (National Research Council, 1999; Watson, 2008). This disconnect…

Researchers and instructors have only recently embraced the role of errors as vehicles for learning in the algebra classroom. Studying a mixture of correct and incorrect worked examples has been shown to be beneficial relative to correct worked examples alone. This study examines the effectiveness of having students generate, or anticipate, errors…

Word problems are an integral part of any secondary mathematics curriculum and one purpose has been to prepare students for the real-world--for everyday events as well as workplace problem-solving. Prior literature suggests that word problems have not met this objective, in part, because the textbook problems do not mirror the kinds of problems…

Many problems related to synthesis with intelligent tutoring may be phrased as program synthesis problems using AI-style search and formal reasoning techniques. The _x000C_first two results in this dissertation focus on problem synthesis as an aspect of intelligent tutoring systems applied to STEM-based education frameworks, specifically high…

Mathematics classrooms have reflected little change over the past century, consisting of the learning of inert, disjoint procedures with few connections between mathematics concepts and students' everyday experiences. However, problem posing, that is, the reformatting of existing problems and the generation of new ones, has been promoted by the…

Quantitative reasoning (P. W. Thompson, 1990, 1994) is a powerful mathematical tool that enables students to engage in rich problem solving across the curriculum. One way to support students' quantitative reasoning is to develop prospective secondary teachers' (PSTs) mathematical knowledge for teaching (MKT; Ball, Thames, & Phelps, 2008)…

Generalization has been identified as a cornerstone of algebraic thinking (e.g., Lee, 1996; Sfard, 1995) and is at the center of a rich conceptualization of K-8 algebra (Kaput, 2008; Smith, 2003). Moreover, mathematics teachers are being encouraged to use figural-pattern generalizing tasks as a basis of student-centered instruction, whereby…

The goal of this thesis was to investigate and enhance our understanding of what occurs while pre-service mathematics teachers engage in a mathematical modeling unit that is broadly based upon mathematical modeling as defined by the Common Core State Standards for Mathematics (National Governors Association Center for Best Practices & Council…

The Common Core State Standards for Mathematics (CCSSM) highlight the importance of students' conceptual understanding, mathematical reasoning, and problem solving in order to prepare students for college and careers. However, the success of this reform effort largely depends on how teachers actually design and implement instruction based on the…

Regulatory Fit Theory research has indicated that the presence of a regulatory fit between an individuals chronic regulatory focus orientation and induced regulatory state can increase motivation, performance, and achievement. The research in support of regulatory fit theory is immense; however, there has been little research that focuses on…

There are three hypotheses for this research: 1. High school mathematics students in urban public schools, who are provided interactive technology resources during normal course work, will experience a multiplier effect of enhanced learning in mathematics. They will have an increase in positive dispositions indicative of their identity development…

The purpose of this study was to determine the metaphors used by students to describe mathematical problem solving. This study focused on identifying how students interpret and perceive mathematical problem solving via conceptual metaphors (Lakoff and Johnson, 2003). These perceptions and interpretations were coded and analyzed qualitatively and…

Engagement and motivation have become increasingly important to mathematics education, particularly as concern about the educational success of students in the US grows. As a way to describe the patterns cognitive, behavioral, and affective engagement of students, Goldin, Epstein, Warner, and Schorr (2011) developed the theoretical concept of…