Though research on effective instruction in math word problem solving is prominent at the middle and secondary levels, much less work has been done in elementary grades. In this article, we review the research on varied problem-solving instructional interventions at the third-grade level for students across ability levels. Third grade was chosen…

Documenting how students with learning disabilities (LD) initially conceive of fractional quantities, and how their understandings may align with or differ from students with mathematics difficulties, is necessary to guide development of assessments and interventions that attach to unique ways of thinking or inherent difficulties these students…

Adopting a multitiered design-based research perspective, this study examines pre-service secondary mathematics teachers' developing conceptions about (a) the nature of mathematical modeling in simulations of "real life" problem solving, and (b) pedagogical principles and strategies needed to teach mathematics through modeling. Unlike…

We studied the acquisition of the ordinal meaning of number words and examined its development relative to the acquisition of the cardinal meaning. Three groups of 3-, 4-, and 5-year-old children were tested in two tasks requiring the use of number words in both cardinal and ordinal contexts. Understanding of the counting principles was also…

We compared the materialization of knowledge integration processes in class discussions that followed troubleshooting (TS) and problem-solving (PS) tasks and examined the impact of these tasks on students' conceptual understanding. The study was conducted in two sixth-grade classes taught by the same teacher, in six lessons that constituted a…

While some students are enjoying days at the park or at the beach, forty middle school students are in a classroom solving challenging mathematics problems. The second Math Camp for middle school students was offered in 2013 at a western university for students from local school districts. For three days, these students met from 10 a.m. to 3 p.m.…

This article reports on a small-scale investigation of how teachers organise goal-oriented learning in Swedish preschools. The revised Swedish curriculum (National Agency for Education 2011) highlights the need for children to develop their mathematics skills through activities that integrate play and learning. This study investigates how…

The distinction between procedural and conceptual learning has long been a topic of discussion in mathematics education and the idea of compression into thinkable concepts that enable the individual make links between them (Tall, 2007). In addition to, the compression to thinkable concept was to be thinking mechanism arising naturally and…

In this article, fourth-grade teacher Tabetha Finchum describes how a program called Arizona Master Teacher of Mathematics (AZ-MTM), a Noyce grant funded through the National Science Foundation, helped boost her confidence and broaden her understanding of the philosophies, curricula, and instructional decisions being implemented by other teachers.…

This paper compares the performance of students at a high-performing U.S. public school (n = 64) on the advanced placement (AP) chemistry exam to their performance on the ChemQuery assessment system. The AP chemistry exam was chosen because, as the National Research Council acknowledges, it is the "perceived standard of excellence and school…

This special issue of "Journal of Research in Science Teaching" reflects conclusions and recommendations in the "Discipline-Based Education Research" (DBER) report and makes a substantial contribution to advancing the field. Research on undergraduate science learning is currently a loose affiliation of related fields. The…

Adults are prone to treating percents, one representational format of rational numbers, as novel cases of natural number. This suggests that percent values are not differentiated from natural numbers; a conceptual shift from the natural numbers to the rational numbers has not yet occurred. This is most surprising, considering people are inundated…

Compared with introductory physics, relatively little is known about the development of expertise in advanced physics courses, especially in the case of quantum mechanics. Here, we describe a framework for understanding the patterns of student reasoning difficulties and how students develop expertise in quantum mechanics. The framework posits that…

Despite few limitations, GeoGebra as a dynamic geometry software stood as a powerful instrument in helping university math majors understand, explore, and gain experiences in visualizing the limits of functions and the ?-d formalism. During the process of visualizing a theorem, the order mattered in the sequence of constituents. Students made use…

Threshold concepts are transformative, integrative, and provocative; understanding these difficult concepts allows students to be capable of solving advanced problems. This investigation and evaluation of a metacognitive curricular approach explore variation in students' and teachers' discernment of structural complexity of concepts and its…