Generalisation is a skill that enables learners to acquire knowledge in general, and mathematical knowledge in particular. It is a core aspect of algebraic thinking and, in particular, of functional thinking, as a type of algebraic thinking. Introducing primary school children to functional thinking fosters their ability to generalise, explain and…

The purpose of this study is to investigate a mathematically gifted student's self-regulation behaviours while constructing and consolidating mathematical knowledge. However, the objective is to determine which self-regulation strategies influence this student's mathematical abstraction process. The case study method was used in the research. As…

The study investigated the reported regressive performances of students in spatial reasoning concepts with a view to promote early spatial reasoning of lower primary school pupils across ability levels and sex. Non-equivalent experimental research design was employed. A hundred and five (105) pupils in four intact classes were exposed to six weeks…

Gap reasoning is an inappropriate strategy for comparing fractions. In this article, Patrick Sullivan and Joann Barnett look at the persistence of this misconception amongst students and the insights teachers can draw about students' reasoning.

Introduction: In the educational context, information and communication technologies imply a paradigm shift in learning-teaching processes both in the renewal of knowledge and practices and in evaluating knowledge appropriation. In this sense, in the present paper we analyze the incidence of the implementation of didactic strategies, problem-based…

Test results from the Program for International Student Assessment (PISA) reveal that Shanghai students performed less well in solving interactive problems (those that require uncovering necessary information) than in solving analytical problems (those having all information disclosed at the outset). Accordingly, this study investigates…

Secondary school pupils underachieve in tests in which reasoning abilities are required. Brain-based training of working memory (WM) may improve reasoning abilities. In this study, we use a brain-based training programme based on historical content to enhance reasoning abilities in history courses. In the first experiment, a combined intervention…

Legal reasoning is a type of problem solving, and is situated within thinking skills, one of the six threshold learning outcomes established under the auspices of the Australian Learning and Teaching Council's Bachelor of Laws Learning and Teaching Academic Standards Statement. The threshold learning outcomes define what law graduates are…

This study aims to examine the enhancement of mathematical reasoning ability through reflective learning. This study used quasi-experimental method with nonequivalent pretest and posttest control group design. The subject of this study were students of Mathematics Education Program in one of private universities in Palembang, South Sumatera,…

The Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010) identifies the strategic use of appropriate tools as one of the mathematical practices and emphasizes the use of pictures and diagrams as reasoning tools. Starting with the early elementary grades, CCSSM discusses students' solving of problems "by drawing." In later…

Many under-prepared university students do not know how to study (Martin and Arendale 1993) because they have not yet developed the abstract reasoning skills that allow them to learn new ideas simply by reading a text or listening to a lecture. This article draws from selected findings from a PhD study currently being undertaken at a university in…

The question of whether skills in achieving understanding and retention of information at high levels of abstraction can be taught is addressed by analyzing some of the mental processes involved, and briefly reviewing a number of attempts that have been made to induce these processes. (Author)

Described are how students (n=2,000) reduce the complexity of multivariable problems. Tendencies toward "functional reduction" in common reasoning are shown to range from a simple reduction in the number of variables considered, to a more elaborate procedure where all variables are taken into account, but in a simplified way involving…

Examines U.S. and Chinese 6th grade students' mathematical thinking and reasoning involved in solving six process-constrained and six process-open problems. Concludes that the Chinese sample had a significantly higher mean score than the U.S. sample on the process-constrained tasks, but the sample of U.S. students had a significantly higher mean…

Investigates different approaches of students from different cultures to problems and problem-solving strategies. Suggests ways to encourage students to use algebraic strategies. Provides some action research ideas for teachers to try in their classrooms. Contains 11 references. (ASK)