Despite curriculum expectations, many students, including a disproportionate number of girls, do not 'just know' (retrieve) single-digit addition facts by Year 3. The current study employed structured interviews to explore which strategies Year 3/4 students (n = 166) used when solving more difficult addition combinations. Results revealed that…

Teaching and learning Calculus concepts and procedures, particularly the definite integral concept, is a challenge for teachers and students in their academic careers. In this research, we supplement the analysis made by different authors, applying the theoretical and methodological tools of the Onto-Semiotic Approach to mathematical knowledge and…

Central elements of adaptive expertise in arithmetic problem solving are flexibility, using multiple strategies, and adaptivity, selecting the optimal strategy. Research shows that the strategies children actually use do not fully reflect the strategies they know: there is hidden potential. In the current study a sample of 147 third graders from…

Algebraic thinking and strategy flexibility are essential to advanced mathematical thinking. Early algebra instruction uses 'missing-operand' problems (e.g., x - 7 = 2) solvable via two typical strategies: (1) direct retrieval of arithmetic facts (e.g., 9 - 7 = 2) and (2) performance of the inverse operation (e.g., 2 + 7 = 9). The current study…

We investigated how the updating function supports the integration process in solving arithmetic word problems. In Experiment 1, we measured reading time, that is, translation and integration times, when undergraduate and graduate students (n = 78) were asked to solve 2 types of problems: those containing only necessary information and those…

"Primary Mathematics" is a magazine for primary grades teachers. It contains activities which can be used, or adapted for use, with children over a wide ability range. It also contains articles on the teaching and learning of mathematics. The material in this book was selected from 18 issues of "Primary Mathematics" published…

Intended for use in conjunction with guidance and instruction from a teacher or tutor, this guide provides an overview of the philosophy of quality as well as some tools used in business and industry today. Each of four sections consists of a teacher explanation of the topics followed by student worksheets with annotated teacher keys. The first…

Mathematics in the primary schools is discussed. This bulletin puts forth some suggestions to assist individual teachers in reaching their own decisions about changes and developments in the curriculum. The bulletin is divided into nine chapters. Two factors described in Chapter 1 and 2 support views expressed in the introduction. First, the…