Repeating patterning proficiency predicts students' later mathematical proficiency. A comparative multi-case design enabled the present study to compare patterning success and strategy use for repeating patterns of 75 Norwegian 6-year-old grade 1 students. We provided the students with duplicate, extend, transfer, and unit isolation activities in…

The purposes of this study were to assess the effects of fractions intervention for students who are at risk for poor outcomes and to examine whether a component that combines self-regulated learning with growth-mindset instruction (SR-GM) provides added value for improving outcomes. At-risk students (N = 84) were randomly assigned to three…

This study examined and compared the intended mathematics curricula according to topic coverage, focus, coherence, and learning progression in grades 1-12 within China and the province of Ontario, Canada. The findings show that the overall topics in the two curricula are similar: Chinese curriculum covers 78 topics out of 79 while the Ontario…

The purposes of this study were to assess the effects of fractions intervention for students who are at-risk for poor outcomes and to examine whether a component that combines self-regulated learning with growth mindset instruction (SR-GM) provides added value for improving outcomes. At-risk students (N = 84) were randomly assigned to 3…

In this study, we explore four, second graders' performances on integer addition problems before and after analyzing contrasting cases involving integers. The students, as part of a larger study, participated in a pretest, small group sessions, one short whole-class lesson on integer addition, and a posttest. Based on their integer mental models…

This article presents results of a research study. Sixty-one first graders' responses to interview questions about negative integer values and order and directed magnitudes were examined to characterize the students' mental models. The models reveal that initially, students overrelied on various combinations of whole-number principles as…

For many students, developing mathematical reasoning can prove to be challenging. Such difficulty may be explained by a deficit in the core understanding of many arithmetical concepts taught in early school years. Multiplicative reasoning is one such concept that produces an essential foundation upon which higher-level mathematical thinking skills…

Reported are early results of a research program that aims to improve children's mathematics learning by developing attitudes and strategies that support processes of interpretation and meaning construction in mathematics. Considerable research shows that many children learn mathematics as symbol manipulation rules, without meaning. Collaborative…

Mathematics is generally regarded as a well-structured discipline by educators and cognitive scientists. This leads to the analysis of the suggestion that practitioners begin investigating possibilities for teaching mathematics as if it were an ill-structured discipline, with more than one interpretation for mathematical statements. The paper is…

Explored is young children's ability to estimate set sizes and use reference points such as 10. Results indicated that many children could accurately place sets somewhat smaller than a reference point but had difficulty placing sets somewhat larger than a reference point. (CW)

Describes environments for concretely enacting multiplication and division. Discusses difficulties occurring when students use one of the concrete environments to model situations involving modified environments. (YP)

In two parallel one-year studies, solution strategies for subtraction number facts and achievement patterns of matched groups of first graders in two different instructional programs were examined. Significant differences between groups were found favoring the strategy approach. (Author/CW)

Investigated was the learning of the mathematical uses of "more,""fewer," and "less" at a very early stage in the development of ideas. (CW)

This report discusses the role of affect in cognitive processing. The importance of affect in processing mathematical information is described in the context of solving arithmetic story problems. Some ideas are offered about the way affective responses to mathematical problem solving situations influence the development, maintenance, and retrieval…

Describes the characteristics of progressive schematization with regard to column multiplication and column division. Contrasts this with column arithmetic based on progressive complexity. Presents a summary of research data concerning column arithmetic. (TW)