This study aimed to apply the novel use of a conceptual interview and flowchart to support teachers in easily identifying areas of development in writing using the developmental/cognitive model of writing (Flower & Hayes, 1980). This study involved two phases. The first phase involved the creation of a conceptual interview and flowchart based…

Classical mechanics challenges students to use their intuitions and experiences as a basis for understanding, in effect to approach learning as "a refinement of everyday thinking'' (Einstein, 1936). Moving on to quantum mechanics (QM), students, like physicists, need to adjust this approach, in particular with respect to the roles that…

The purpose of this study is to explore community college students' reasoning patterns and argumentation within the context of natural selection. Written assessments and interviews were administered to 2-year college students. Participants were given the Lawson Classroom Test of Scientific Argumentation (LCTSR), a Test of Scientific Argumentation…

Multi-digit subtraction is difficult for students to learn. The purpose of this study is to explore how second-grade students communicate their understanding of double-digit subtraction through the use of manipulatives/tools. This qualitative study reports on six case studies of second-grade students where clinical interviews were the main source…

In this research, I set out to elucidate the relationships that might exist between students' conceptual understanding upon which they draw in their proof activity. I explore these relationships using data from individual interviews with three students from a junior-level Modern Algebra course. Each phase of analysis was iterative, consisting of…

Basic multiplication fact fluency is an expected outcome of most third grade classrooms throughout the United States. Students need to know their multiplication facts. This statement does not seem to be under question; it is more about how will students learn their multiplication facts. The purpose of this study was to investigate the use of…

It is widely accepted by the field of mathematics education that proof and reasoning should be integrated into students' mathematical experiences across all grades and across a breadth of content areas. However, studies have shown that both secondary students and teachers have encountered difficulties with learning and teaching geometry proofs. By…

Place-value is an essential concept that is foundational for understanding our number system and for developing procedures for multidigit operations, but there has been limited research into the place-value understanding of students with learning disabilities. This research is a two-part mixed-methods study that links basic research to…

Students' development of conceptual understandings is a central goal of mathematics education (CCSS-Mathematics, 2010). Such a challenging, yet ambiguous, goal cannot be achieved without empowering teachers with the knowledge and tools critical for their ability to adequately convey the content, and assess and interpret students' performance. This…

This case study examined competence in two third-grade classrooms where teachers centered children's mathematical thinking in instructional decision-making. Offering a synthesis of sociocultural characterizations of competence, and drawing from a variety of data sources including classroom video, student work and assessments, and teacher…

The difficulty in observing, recording, and examining internal representations has been well documented (Goldin & Shteingold, 2001). However, the important role that these internal representations play in the learning and understanding of mathematical concepts has been noted (Yackel, 2000). This study sought to develop a framework for…

As widespread as Science, Technology, Engineering, and Math (STEM) initiatives and reforms are today in education, a rudimentary problem with these endeavors is being overlooked. In general, education programs and school districts are failing to ensure that elementary teachers who provide children's early academic experiences have the appropriate…

This case study investigated students' conceptual knowledge of limits in calculus by implementing semi-structured interviews. The constructivist learning principles of Piaget and Inhelder as well as theories of understanding by Skemp guided the study. In Phase I, a pilot study was conducted with 15 students from a Calculus III class. By using…

There has been continuing pressure to incorporate algebraic thinking into K-12 education. Elementary teachers will be expected to incorporate and successfully execute algebra related lessons. This dissertation study examines pre-service elementary teachers' conceptions and content knowledge regarding literal symbols and their usage. A written…

In this study I attempt to shed light on the experiences of the teacher researcher and university students who explored social justice issues in an art education course. The primary purpose of this study is to provide insights in teaching practice and students' learning processes when the course is designed to examine systems of oppression through…