This article discusses large-scale assessment of change in student achievement and takes the study by Hickendorff, Heiser, Van Putten, and Verhelst (2009) as an example. This study compared the achievement of students in the Netherlands in 1997 and 2004 on written division problems. Based on this comparison, they claim that there is a performance…

The present study concerns redundant data problems, defined as problems in which irrelevant data is provided. This type of problem provides a misleading context [Pascual-Leone, J. (1987). Organismic process for neo-Piagetian theories: A dialectical causal account of cognitive development. "International Journal of Psychology," 22, 531-570] similar…

This article describes how a crystal ball known as "The Flash Mind Reader" is played. "The Flash Mind Reader" is a mathematics game in which the player is invited to select any-two digit number and then subtract the sum of these two digits from the original number. A chart is provided in which the (adjusted) number they…

Working memory is the cognitive ability to hold a discrete amount of information in mind in an accessible state for utilization in mental tasks. This cognitive ability is impaired in many clinical populations. There have been a number of theoretical shifts in the way that working memory is conceptualized and assessed in the experimental…

The purpose of this study was to examine the effects of a schema-based instructional strategy that emphasizes prealgebraic conceptualization of multiplicative relations on solving arithmetic word problems with elementary students with learning disabilities or problems (LP). Introducing symbolic representation and algebraic thinking in earlier…

This article focuses on spontaneous and progressive knowledge building in ''the arithmetic of the child.'' The aim is to investigate variations in the behavior patterns of eight pupils attending a school for the intellectually disabled. The study is based on the epistemology of radical constructivism and the methodology of multiple clinical…

This manual is collection of examinations. The first part contains 150 examination papers, the questions for which have been selected mainly from the English, French, and German collections of problems. These papers may be divided into three groups. The first 50 papers are confined to the simple rules, fractions, and weights and measures; the next…

Visuospatial working memory and its involvement in arithmetic were examined in two groups of 7- to 11-year-olds: one comprising children described by teachers as displaying symptoms of nonverbal learning difficulties (N = 21), the other a control group without learning disabilities (N = 21). The two groups were matched for verbal abilities, age,…

Errors in written multi-digit computation were investigated in children with math difficulties. Third- and fourth-grade children (n = 291) with coexisting math and reading difficulties, math difficulties, reading difficulties, or no learning difficulties were compared. A second analysis compared those with severe math learning difficulties, low…

Two intervention studies are described. Both were designed to study the effects of teaching children about the inverse relation between addition and subtraction. The interventions were successful with 8-year-old children in Study 1 and to a limited extent with 5-year-old children in Study 2. In Study 1 teaching children about inversion increased…

In the Netherlands, national assessments at the end of primary school (Grade 6) show a decline of achievement on problems of complex or written arithmetic over the last two decades. The present study aims at contributing to an explanation of the large achievement decrease on complex division, by investigating the strategies students used in…

This paper describes six tricks on different mathematical concepts for mathematics classrooms. The mathematical concepts emphasized in these activities include arithmetic, modular arithmetic, limit cycles, graph theory, pairings, combinatorics, cyclic groups, induction, and sequences. (ASK)

Previous research (e.g., De Bock, 2002) has shown that--due to the extensive attention paid to proportional reasoning in elementary and secondary mathematics education--many students tend to overrely on proportional methods in diverse domains of mathematics (e.g., geometry, probability). We investigated the development of misapplication of…

Synthetic division is viewed as a change of basis for polynomials written under the Newton form. Then, the transition matrices obtained from a sequence of changes of basis are used to factorize the inverse of a bidiagonal matrix or a block bidiagonal matrix.