The improvement of mathematics teaching and learning is a complicated undertaking. It relies on teacher understanding of math curriculum in addition to awareness of how children acquire mathematics concepts. It also depends on teachers' abilities to translate these understandings into learning tasks and instructional routines, as well as the…

Our study was enacted in university mathematics education classes in the USA with preservice teachers (PSTs). This research focused on PSTs' interview responses that were used to assess their understanding of balance when challenged with tasks involving virtual manipulatives. Siegler's rules were used in analyzing PSTs' responses to…

Students with learning disabilities are most typically characterized as struggling readers (i.e., 80-90% of students are identified on the basis of reading failure; LD OnLine, 2008 Lerner, 1989; Lyon, Fletcher, Shaywitz, Torgesen, Wood, et al., 2001); however, as many as 50% of students with learning disabilities have IEP goals in the area of…

This paper analyses pre-service secondary mathematics teachers' responses to a hypothetical situation concerning a student's struggle to determine the area of an irregular hexagon. The analysis focuses on individuals' Knowledge at the Mathematical Horizon, as it relates to philosophical notions of inner and outer horizons. Specifically, the paper…

While previous work in the domain of proportional reasoning has primarily focused on the coordination of integer quantities, this study investigates how students coordinate fractional quantities. Fine-grained analysis of two seventh graders' responses to a set of systematically designed proportional tasks, shows how their knowledge of…

This study used a multiple probe across participants design to examine the effects of concrete-representational-abstract sequence of instruction on solving equations using inverse operations with high school students with mild intellectual disability. Results demonstrated a functional relation between the Abstract sequence of instruction and…

We explored transformations that teachers made to modify geometry proof problems into investigation problems and analyzed how these transformations differ in teachers who use a dynamic geometry environment (DGE) in their classes and those who do not. We devised a framework for the analysis of problem transformations and types of teacher-generated…

Although official curriculum documents make cursory mention of the need for problem posing in school mathematics, problem posing rarely becomes part of the implemented or assessed curriculum. This paper provides examples of how problem posing can be made an integral part of mathematics teacher education programs. It is argued that such programs…

Effort to determine teachers' effects on students has been continuously made with national data. However, paucity of research has been conducted on how teachers' instructional strategies impact on student learning with national data, although instructional theories suggest a direct relationship between instructional strategies and learning…

Middle school students' mathematical understanding benefits from connecting mathematics to other content areas in the curriculum. This month's activity explores the issue of the scarcity of freshwater, a natural resource (activity sheets are included). This activity concentrates on the critical areas mentioned in the Common Core State…

The aim of this study was to analyse the role of verbal and visuo-spatial working memory (WM) and language skills (vocabulary, listening comprehension) in predicting preschool and kindergarten-aged children's ability to solve mathematical word problems presented orally. The participants were 116 Finnish-speaking children aged 4-7?years. The…

In this article, the authors illustrates techniques for integrating diverse learners in shared mathematical contexts while providing differentiated support or challenge, as necessary. The techniques described were developed for a curriculum project entitled Learning Mathematics through Representations (LMR). A premise of LMR is that students'…

Decision making during instruction that is responsive to children's mathematical thinking is examined reflexively by the researcher in the context of teaching second graders. Focus is on exploring how the research base on learning informs teaching decisions that are oriented to building on children's sound conceptions. The development of four…

Statistics learners often bypass the critical step of understanding a problem before executing solutions. Worked-out examples that identify problem information (e.g., data type, number of groups, purpose of analysis) key to determining a solution (e.g., "t" test, chi-square, correlation) can address this concern. The authors examined the…

This report focuses on key elements of teaching occurring during intensive, one-to-one instruction with 3rd- and 4th-graders. The study involves six cases in all, each consisting of video records of up to eight lessons, each of 30-45 minutes' duration, resulting in the analysis of about 33 hours of video data. A resulting framework of four stages…