This study explores the notion of deep learning as constructed in the discourses of practicing mathematics teachers. Analyses of data from written texts show that the teachers tend to conceptualise deep learning in terms of two broad categories: students' deep learning and the work of teaching for deep learning. In both categories, students'…

This study examined the effects of two training methods (interest-based and traditional) used to improve math word problem performance of middle school students with and without learning disabilities, as measured by the Herr Scale of Mathematical Word Problem Solving Situations. Students were randomly assigned to one of the two treatment groups:…

Spearman concluded that performance on any test of mental ability could be explained by several cognitive factors organized hierarchically as one general factor and several subordinate specific factors (Spearman, 1904, 1927). The general factor accounted for the significant amount of inter-correlation between all ability tests for any one…

This study was conducted during the first semester of 2016, from March 21st to June 30th, with 104 students, in eight educational centers or "polos," in the states of Minas Gerais and São Paulo. Previously, these mathematics teacher education students had no opportunity to study in higher education in Brazil. They were enrolled in a…

Students who are adept in modeling with mathematics have the capability to use mathematics in situations that arise in everyday life. The German Tank problem described in this article created the expectation that student reasoning was rooted in logical deductions (NCTM 2000). By engaging in this problem, students grappled with challenging…

Effective collaboration between student peers is not spontaneous. A system that can measure collaboration in real-time may be useful, as it could alert an instructor to pairs that need help in collaborating effectively. We tested whether superficial measures of speech and user interface actions would suffice for measuring collaboration. Pairs of…

Intuitive conceptions in mathematics guide the interpretation of mathematical concepts. We investigated if they bias teachers' conceptions of student arithmetic word problem solving strategies, which should be part of their pedagogical content knowledge (PCK). In individual interviews, teachers and non-teaching adults were asked to describe…

In this article, the authors describe how a theoretical framework--the modeling cycle of Bliss, Fowler, and Galluzzo (2014)--came to life in their classroom as students struggled with an open-ended modeling task. The authors share their high school students' work--warts and all. They explain how they used their students' ideas and errors to help…

The purpose of this study was to evaluate the effect of a multicomponent mathematics intervention (modified schema-based instruction, video anchors, and goal setting with self-graphing) on mathematical problem-solving skills of secondary students with intellectual and developmental disabilities. Three participants were taught to solve percent of…

In the era of multi-tiered system of support approach to learning, identifying mathematical interventions that have been found to be effective for students who are struggling academically is imperative. Given the divide between instructional approaches in general and special education mathematical teaching approaches, it is important to bridge the…

In recent years, researchers have become more interested in quadratic equations. This study explores the conceptions high school students have concerning quadratic equations with one unknown, while using concept definition and images as theoretical framework. The data was gathered through semi-structured interviews with 14 eleventh grade high…

The current study aimed to investigate the relation between conditional reasoning, which is a common type of logical reasoning, and children's mathematical problem solving. A sample of 124 fourth graders was tested for their conditional reasoning skills and their mathematical problem solving skills, as well as a list of control variables (e.g.,…

The vision of mathematics learning advocated by the National Council of Teachers of Mathematics (NCTM) for twenty-five years (1989, 1991, 2000, 2014) positions students as active learners, constructing their knowledge of mathematics through exploration, discussion, and reflection. World-class standards put into place by states and provinces over…

Mathematics teacher education aims to improve teachers' use of mathematical knowledge to support teaching and learning, an aspect of pedagogical content knowledge (PCK). In this study, we interviewed teachers to understand how they used mathematics to make sense of student solutions to proportional reasoning problems. The larger purpose was to…

Ratio and proportional relationships, along with the interrelated topics of fractions, decimals, and percent provide a critical foundation for algebra (National Mathematics Advisory Panel, 2008). Solving even simple proportion problems is challenging for many children and adolescents. A small number of studies have examined the efficacy of…