In this paper, we examine the interactions of mathematical abilities when 6 high achieving Swedish upper-secondary students attempt unfamiliar non-routine mathematical problems. Analyses indicated a repeating cycle in which students typically exploited abilities relating to the ways they orientated themselves with respect to a problem, recalled…

How can a cognitively demanding real-world task such as the Seven Billion People problem promote productive struggle "and" help shape students' mathematical dispositions? Driving home from school one evening, Jaclyn Murawska heard a commentator on the radio announce three statements: (1) experts had determined that the world population…

This paper explores an innovative assessment framework for measuring children's formal and informal mathematical knowledge. Many existing standardized measures, such as the Early Grade Mathematics Assessment, measure children's performance in early primary grade skills that have been identified by researchers and policy makers as foundational and…

Many students around the world are exposed to a rote teaching style in mathematics that emphasizes memorization of procedures. Students are frequently presented with standard types of equations in their textbooks, in which the equal sign is immediately preceding the answer (a + b = c). This exposure can lead to many misconceptions, such as…

The purpose of this quantitative correlational study was to assess to what extent math anxiety and math attitudes predicted math self-efficacy among community college students enrolled in one of two developmental mathematics courses at a metropolitan community college in the Southwest United States. Self-efficacy, math attitudes, math anxiety and…

Research on community college students tends to focus on their deficits and failures rather than assets and achievements. This narrative study focuses on African-American community college students and their remedial math achievements. Research questions addressed participants' descriptions of their mathematics identity (Anderson, 2007; Bishop,…

The Dijkstra's algorithm is an algorithm that determines the shortest paths needed to go from a starting node to any node in a graph. In this article, the process and results of an activity that included route formation among the provinces in the Aegean region using Dijkstra's algorithm are shared. The activity was designed based on a mathematical…

In recent years, there has been a growing interest in studying the knowledge that mathematics teachers require in order for their teaching to be effective. However, only a few studies have focused on the design and application of instruments that are capable of exploring different aspects of teachers' didactic-mathematical knowledge about specific…

Given two vectors u and v, their cross product u × v is a vector perpendicular to u and v. The motivation for this property, however, is never addressed. Here we show that the existence of the cross and dot products and the perpendicularity property follow from the concept of linear combination, which does not involve products of vectors. For our…

This work is part of a larger project that seeks to understand how students blend (integrate) chemistry and mathematics as they work through chemical kinetics problems. Here we focus on four students from our larger sample: two students that demonstrated more instances of blending chemistry and mathematics in their interviews ("high-frequency…

This paper illustrates how the academic literacy in mathematics framework (Moschkovich, J Math Behav 40:43-62, 2015) can be used to uncover the multiple layers of work bilingual learners accomplish during mathematical discussions. Using this framework allows researchers to examine students' joint mathematical activity in terms of mathematical…

Many students enter community college underprepared in math and must take multiple semesters of developmental (remedial) classes. Far too few of these students ever enroll in -- let alone pass -- an introductory college-level math course, but without those credits, they cannot graduate. Among the many reforms practitioners are undertaking to try…

This paper explores a deep transformation in mathematical epistemology and its consequences for teaching and learning. With the advent of non-Euclidean geometries, direct, iconic correspondences between physical space and the deductive structures of mathematical inquiry were broken. For non-Euclidean ideas even to become "thinkable" the…

Previous research of math anxiety (MA) was largely concerned with the population of high school students. Although there are findings on the existence of MA at early primary school age, a very small number of questionnaires or scales, which have been validated in several cultures and can be used in research with children of this age, have been…

The purpose of this study is to explore preservice teachers' (PTs') ability to implement multiple strategies using standard algorithms and alternative strategies and to investigate their conceptual knowledge of decimal operations. There were 37 PTs who participated in this study, all of whom attended a mathematics course in the K-8 Teacher…