Access to advanced study in mathematics, in general, and to calculus, in particular, depends in part on the conceptual architecture of these knowledge domains. In this paper, we outline an alternative conceptual architecture for elementary calculus. Our general strategy is to separate basic concepts from the particular advanced techniques used in…

In this study, the authors assessed the contribution of engagement (on-task behavior) to the mathematics problem-solving performance of seventh-grade students after accounting for prior mathematics achievement. A subsample of seventh-grade students in four mathematics classrooms (one high-, two average-, and one low-achieving) from a larger…

This article describes activities in which students deepen their relational understanding of the equals sign through exploring inequalities in a competitive dice game, built around the familiar fairy-tale "The Three Little Pigs" and "The Big Bad Wolf." The activity can be adapted to different abilities by choosing more or less…

This article explores links between student experiences with technology-rich mathematics instruction and the ISTE Standards for Students. Research methods applied constructivist grounded theory to analyze data from student interviews against the ISTE Standards for Students to identify which elements of the design of this learning environment…

Understanding of base 10 and place value are important foundational math concepts that are associated with higher use of decomposition strategies and higher accuracy on addition problems (Laski, Ermakova, & Vasilyeva, 2014; Fuson, 1990; Fuson & Briars, 1990; National Research Council, 2001). The current study examined base-10 knowledge,…

Researchers have linked teachers' use of mathematical tasks and questions to students' achievement in mathematics, and also have documented that the types of tasks and questions posed might change throughout the year in grades that include high-stakes tests of student achievement. This qualitative research study explored 3 elementary school…

In order to address concerns with the underrepresentation of spatial thinking in K-12 curricula, (National Research Council, 2006), Valentine and Kopcha (in press) designed and implemented a learning environment integrating cases as alternative perspective (Jonassen, 2011) in the context of eighth-grade mathematics. The design aimed to provide…

In this study, the authors assessed the contribution of engagement (on-task behavior) to the mathematics problem-solving performance of seventh-grade students after accounting for prior mathematics achievement. A subsample of seventh-grade students in four mathematics classrooms (one high-, two average-, and one low-achieving) from a larger…

This study explored the effectiveness of a unique math intervention program in a local school district in Orange County, California in terms of academic achievement and student perceptions about their math abilities as a result of their experiences in the program. As the predominate instructional approach, the program provided students with…

This study examined the efficacy of a kindergarten mathematics intervention program, ROOTS, focused on developing whole-number understanding in the areas of counting and cardinality and operations and algebraic thinking for students at risk in mathematics. The study utilized a randomized block design with students within classrooms randomly…

This paper reports on the findings from individual interviews and focus group discussions involving six teachers implementing the Singapore Mathematics Curriculum (SMC) in the Foundation Phase (Grade R to Grade 3) in a school in South Africa. The interviews presented an opportunity to explore teachers' experiences with their attempts to use the…

For many students, coming to learn mathematics is as much about the pedagogical relay through which concepts are conveyed as it is about the mathematics per se. This relay comprises social, cultural and linguistic norms as well as the mathematical discourse. In this study, I outline the practices of one remote school and how the teaching practices…

Reasoning and constructing mathematical explanations for an audience have become increasingly important activities in elementary classrooms with the implementation of reform-oriented curriculum and standards. Mobile learning tools and applications, such as screencasts, allow students to generate multimedia presentations of their solution…

A test project at the University of Puerto Rico in Mayagüez used GeoGebra applets to promote the concept of multirepresentational fluency among high school mathematics preservice teachers. For this study, this fluency was defined as simultaneous awareness of all representations associated with a mathematical concept, as measured by the ability to…

Children can learn mathematics and sciences effectively even before being exposed to formal school curriculum if basic Mathematics and Sciences concepts are communicated to them early using activity oriented (Hands-on) method of teaching. Mathematics and Science are practical and activity oriented and can best be learnt through inquiry (Okebukola…