This research aims to determine the perceptions of middle school pre-service mathematics teachers regarding the concept of "mathematical thinking" through the usage of metaphors. The phenomenology method, which is one of the qualitative research methods, is adopted in this study. Data of the research was obtained by the pre-service…

Many school districts in North Carolina are striving to increase proficiency levels in mathematics. With the implementation of the Common Core State Standards, mathematics standards have changed drastically and students are expected to solve complex multi-step word problems and explain how they solved them. As a result, teachers equally need a…

This paper reports the results of an investigation into the ways pre-service teachers engaged in structured problem solving as part of their first-year mathematics education course. The purpose of this study was to determine the preferred problem solving strategies of pre-service teachers and the types of difficulties they experienced. The written…

"Catalyzing Change in High School Mathematics: Initiating Critical Conversations" identifies and addresses critical challenges in high school mathematics to ensure that each and every student has the mathematical experiences necessary for his or her future personal and professional success. These challenges include: (1) explicitly…

This paper presents strategies identified in Mexican rural school students in seeking structure on equivalence tasks that involve the equal sign and tasks that do not. The results arise from the pilot study of a research project on the structure of numbers and numerical operations -- a key aspect of early algebraic thinking. [For the complete…

In this paper, we address the variety of ways in which students conceive of binary operations and the metaphors they might leverage when working with binary operations in group theory. We use open-ended surveys paired with interviews to qualitatively explore student's conceptions of binary operation. Through this analysis, we identified three…

Mathematic connection is one of the basic abilities someone must have in order to learn mathematic successfully. Mathematic connection helps someone to understand the function of mathematics, improving mathematic concept, determining the correlation among mathematic concepts, and identifying the application of mathematic in the surrounding…

Finite Mathematics has become an enormously rich and productive area of contemporary mathematical biology. Fortunately, educators have developed educational modules based upon many of the models that have used Finite Mathematics in mathematical biology research. A sufficient variety of computer modules that employ graph theory (phylogenetic trees,…

This research sought to understand the perspectives of 28 elementary school mathematics teachers, on equity, social justice, cultural, socioeconomic, and racial issues and their relationship with the teaching and learning of mathematics (statistical concepts) in an online collaborative mathematics course focused on teaching statistics in an equity…

This study investigated Turkish middle school students' proportional reasoning and provided a diagnostic assessment of their strengths and weaknesses on the ratio and proportion concepts. A proportional reasoning test with 22 multiple-choice items was developed from the context of the loglinear cognitive diagnosis model. The test was developed…

The teaching and learning fractions is one of the most problematic areas in primary school mathematics. A large number of studies have engaged paper-and-pencil test to measure students' instrumental understanding about fractions but few have sought to learn about children's fraction sense. This paper reports a study that investigated fraction…

As a part of the larger study, a case study of two seventh grade students, Peter and Willa, was conducted. To examine links between their fractional knowledge and algebraic reasoning, the students were interviewed twice, once for their fractional knowledge and once for their algebraic knowledge in writing linear equations that required explicit…

Preschoolers' patterning skills are predictive of their concurrent and later math knowledge; however, it is unclear if patterning is only a proxy for general intelligence, or how it might support specific math skills. The current study examined the relation between 66 preschool children's patterning skills and their general cognitive abilities,…

In this study, we analysed a mathematician's teaching journals on eigenvalues and eigenvectors in a first-year linear algebra course. The research team employed Tall's ["How humans learn to think mathematically: Exploring the three worlds of mathematics." Cambridge University Press] three-world model of embodied, symbolic and formal as a…

This study explores the dimensionality of mathematical knowledge needed by elementary school teachers. Specifically, we focus on the construct of Mathematical Knowledge for Teaching to investigate whether common mathematical content knowledge (the generic mathematical knowledge that is held by an educated adult), specialized content knowledge (the…