The use of artifacts to introduce the distributive law of multiplication over addition in primary school is a diffused approach: it is possible to find pre-constructed learning trajectories in instructional materials. However, it is still unclear how the teacher might support his/her students in transitioning from concrete to symbolic…

In this 3-year longitudinal study, we examined the interplay of children's motivational orientations, spontaneous focusing on numerosity (SFON) and number sequence and arithmetical skills from kindergarten (at age 6) to grade 1 (at age 7). We also examined the direct and indirect contributions of motivation and SFON to the acquisition of…

Children who experience difficulties with learning mathematics should be taught by teachers who focus on the child's best way of learning. Analyses of the mathematical difficulties are necessary for fine-tuning mathematics education to the needs of these children. For this reason, an instrument for Observing and Analyzing children's Mathematical…

While the value of "schematic representations" in problem solving requires no further demonstration, the way in which students should be taught how to construct these representations invariably gives rise to various debates. This study, conducted on 146 grade 4 students in Luxembourg, analyzes the effect of two types of "schematic…

In this paper, we focus on Finnish pre-service elementary teachers' (N = 269) and upper secondary students' (N = 1,434) understanding of division. In the questionnaire, we used the following non-standard division problem: "We know that 498:6 = 83. How could you conclude from this relationship (without using long-division algorithm) what 491:6…

Argues that deaf children lag behind their hearing cohorts in mathematics achievement tests and that this difficulty is a consequence of their lack of covert counting strategies and reliance on memorized verbal facts. Investigates the acquisition of an alternative method by deaf students (N=6). Recommends examining better ways to teach arithmetic…

Presented are findings from a comparative study involving five developing nations and a longitudinal study of these nations concerning the educational transition between lower and upper secondary school. Results of these studies are discussed with reference to the educational policies of the countries involved in the study. (Author/CW)

Presented is a comparison of two major surveys of the teaching and learning of mathematics conducted by the International Association for the Evaluation of Educational Achievement. Surveys indicate that performance levels have declined in computational skills and increased in algebra. (Author/CW)

Investigated was the effect of presenting arithmetic word problems in the students' native language or in English on Nigerian students mathematics skills and strategies. Findings indicated that both private and public school students performed better when the word problems were presented in their native language. (CW)

A class of 32 fourth graders, who studied inverse operations in grades 1-3, was given 3 written tests, each followed by an interview, to see how well they could simplify computations using inverse operations. Most could not evaluate 28 + 75 - 75, for example, without performing all operations. (GW)

Compared project (n=79) and nonproject (n=111) third-grade students on their conceptual development in arithmetic, their personal goals in mathematics, and their beliefs about reasons for success in mathematics. Project students attained more advanced levels of conceptual understanding and held stronger beliefs about the importance of working…