Language plays a key role in statistics and, by extension, in statistics education. Enculturating students into the practice of statistics requires preparing them to communicate results of data analysis. Statistical argumentation is one way of providing structure to facilitate discourse in the statistics classroom. In this study, a teaching…

Mathematics education practitioners and researchers have long debated best pedagogical practices for introducing new concepts. Our design-based research project evaluated a heuristic framework, whereby students first develop acontextual sensorimotor schemes and only then extend these schemes to incorporate both concrete narratives (grounding) and…

In teaching proportion, the teachers usually give the students a formal formula, such as cross-multiplication, without providing them the meaning of proportionality. Thus, the students just apply it in order to solve proportional problems. However, it does not connote that they understand what proportionality means. In this paper, the authors…

In this work we investigated the problem solving behaviors of 3 high school students as each solved four common non-routine problems with the goal to trace performance constancy across different subject areas and problem types. Additionally, we aimed to identify possible factors that influenced children's choices of heuristics in different problem…

For this article, the development of 1 teacher's pedagogical content knowledge (Shulman, 1986) was tracked longitudinally across 2 years as she taught a new instructional unit in middle school mathematics. Growth in pedagogical content knowledge is characterized as the interanimation of 2 Discourses (Gee, 1999). One Discourse refers to…

After a year of instruction, 70 kindergarten children were individually interviewed as they solved basic, multistep, and nonroutine word problems. Thirty-two used a valid strategy for all 9 problems, and 44 correctly answered 7 or more problems. Modeling provided a unifying framework for thinking about problem solving. (Author/MDH)

Reports on conceptual understanding and solution strategies for percent problems of (n=31) students representing 2 ability levels from grades 5, 7, 9, and 11. Strategies evolved from intuitive to formal and increased in diversity with increasing age. Appendix includes concept and computation interview questions. (Contains 15 references.) (MKR)