The aim of this study is to determine the 7th grade students' achievements in mathematical patterns presented by figures, tables, number sequences, and word problems. This research is a situation determination study where quantitative methodology is used. The sample of the study consisted of 47 female and 50 male students, totally 97 students from…

Justification and argumentation have been identified as important mathematical practices; however, little work has been done to understand the knowledge and pedagogy teachers need to support students in these ambitious practices. Data for this research was drawn from the "Justification and Argumentation: Growing Understanding in Algebraic…

Students in the United States continue to struggle with fraction mastery despite the fact that understanding fractions is essential for further progress in mathematics (NAEP, 2008). This research project investigated the potential of using high-press mathematical discourse (Kazemi & Stipek, 2008) to investigate fourth graders' emerging…

Interest in understanding mathematics teaching and learning phenomena, and to develop new and effective methodologies to teach Differential Calculus and Linear Algebra led me to look for ways to dialogue between APOS Theory and other mathematics education theories. This enterprise has facilitated a better understanding of them. Bridges between…

The Cognitive Tutor Algebra I (CTAI) curriculum, which includes both textbook and online components, has been shown to boost student learning by about 0.2 standard deviations in a randomized effectiveness trial. Students who were assigned to the experimental condition varied substantially in how, and how much, the used the online component of…

"Saxon Math" is a core curriculum for students in grades K-12 that uses an incremental approach to instruction and assessment. This approach limits the amount of new math content delivered to students each day and allows time for daily practice. New concepts are introduced gradually and integrated with previously introduced content so…

The topic of function transformations is a difficult mathematical topic for school and college students. This article examines how students conceive function transformations after working with GeoGebra, when this conceiving relates to the algebraic representation. The research participants were 19 ninth grade high achieving students who learned,…

Traditionally, "z" is assumed to be a complex number and the roots are usually determined by using de Moivre's theorem adapted for fractional indices. The roots are represented in the Argand plane by points that lie equally pitched around a circle of unit radius. The "n"-th roots of unity always include the real number 1, and…

This qualitative research aimed to explore the integration of the components of pedagogical content knowledge (PCK) in teaching Linear Equation with one unknown. For the purpose of the study, a single local case study with multiple participants was used. The selection of the participants was made based on various criteria: having more than 5 years…

Making sense of mathematical concepts and solving mathematical problems may demand different forms of reasoning. These could be either domain-based, such as algebraic, geometric or statistical reasoning, while others are more general such as inductive/deductive reasoning. This article aims at giving visibility to a particular form of reasoning…

Recent studies of the transition from school to university mathematics have identified a number of epistemological gaps, including the need to change from an emphasis on equality to that of inequality. Another crucial epistemological change during this transition involves the movement from the pointwise and global perspectives of functions usually…

The very nature of algebra concerns the generalization of patterns (Lee 1996). Patterning activities that are geometric in nature can serve as powerful contexts that engage students in algebraic thinking and visually support them in constructing a variety of generalizations and justifications (e.g., Healy and Hoyles 1999; Lannin 2005). In this…

This experiment tested if a modified version of arithmetic practice facilitates understanding of math equivalence. Children within 2nd-grade classrooms (N = 166) were randomly assigned to practice single-digit addition facts using 1 of 2 workbooks. In the control workbook, problems were presented in the traditional "operations = answer"…

An empirical study has been carried out to evaluate the potential of word order matching and static comparison as explanatory models of reversal error. Data was collected from 214 undergraduate students who translated a set of additive and multiplicative comparisons expressed in Spanish into algebraic language. In these multiplicative comparisons…

A challenge for teachers is to incorporate the Standards for Mathematical Practice (CCSSI 2010) throughout their teaching of mathematics so that the Common Core Standards do not revert back to a purely content-driven curriculum. One way to achieve this is through the use of mathematically rich, investigative tasks. These tasks encourage students…