For learning math, non-symbolic quantity skills, symbolic skills and the mapping between number symbols and non-symbolic quantities are all important precursors. Little is known, however, about the interrelated development of these skills. The current study focuses on numerical development by: (a) investigating the structure of non-symbolic,…

Bilingual education programs implicitly assume that the acquired knowledge is represented in a language-independent way. This assumption, however, stands in strong contrast to research findings showing that information may be represented in a way closely tied to the specific language of instruction and learning. The present study aims to examine…

Developmental dyscalculia (DD) is a learning difficulty specific to mathematics learning. The prevalence of DD may be equivalent to that of dyslexia, posing an important challenge for effective educational provision. Nevertheless, there is no agreed definition of DD and there are controversies surrounding cutoff decisions, specificity and gender…

We confronted 151, 5th and 6th elementary grade pupils with a quantitative problem in a mathematics or religion class, to examine the influence of the context on pupils' understanding and solution of such problems inside and outside the mathematics class. Pupils were first asked to solve a problem about fair sharing either during a mathematics or…

This study investigated students' activating positive affective experiences in mathematics lessons, their antecedents, their cognitive and motivational consequences, as well as their effect on achievement. The participants were 682 Grade 8 and 9 students from 37 classes from Germany and Switzerland who participated in a video study of lessons on…

Considerable evidence indicates that student motivation and use of learning strategies are related. There is insufficient understanding, however, about their reciprocal effects--whether motivation affects strategy use, the converse, or whether the effects are bidirectional--and which components of motivation and strategies are involved. A two-wave…

This study investigated how metacognition appears as a socially shared phenomenon within collaborative mathematical word-problem solving processes of dyads of high-achieving pupils. Four dyads solved problems of different difficulty levels. The pupils were 10 years old. The problem-solving activities were videotaped and transcribed in terms of…

The theoretical framework of conceptual change has gained growing influence for analysing learning difficulties. The article pleads for combining conceptual change approaches in the learning sciences with established categories from mathematics education research, such as "Grundvorstellungen" and epistemological obstacles. These didactic…

Most mathematical problems can be solved using different methods. We tested the effectiveness of presenting more than one solution method by means of worked-out examples. In Experiment 1, a 2x3-factorial design was implemented ("multiple solutions": multiple/uniform; "instructional support": none/self-explanations/instructional explanations).…

This paper focuses on the role of evaluation in mathematics in 749 elementary school children. The macroevaluative skills and calibration scores of high versus low mathematical problem solvers were contrasted as measures of metacognition. No relevant calibration differences were found for gender. In addition, the performances of children with…

The study examined the effects of gender and ethnicity on mathematics achievement on a national test and on dispositions (attitudes, perceived parental expectations, effort, and help) towards the study of mathematics of a representative sample of Jewish and Arab eighth graders in Israel. The results indicated a large ethnic gap in achievement in…

An experiment is reported that investigated the development of students' understanding of the numerical value of fractions. A total of 200 students ranging in age from 10 to 16 years were tested using a questionnaire that required them to decide on the smallest/biggest fraction, to order a set of given fractions and to justify their responses.…

This paper introduces a study aimed at ascertaining students' beliefs about mathematics and mathematical learning, as well as developing those beliefs and related variables by changing the classroom learning environment. Eighty-six fifth graders were involved, divided in two groups: one in the innovative learning environment (N=46) and the other…

Place-based mathematics education (PBME) has the potential to engage students with the mathematics inherent in the local land, culture, and community. However, research has identified daunting barriers to this pedagogy, especially in abstract mathematics courses such as algebra and beyond. In this study, 15 graduates of a doctoral program in rural…

"Going Further" presents a roadmap to the works of the ACCLAIM (Appalachian Collaborative Center for Learning, Assessment, and Instruction in Mathematics) Research Initiative, the research effort of one the Centers for Learning and Teaching (CLTs) created with a grant (2001-2005) from the National Science Foundation. The Center began with a broad…