This study investigates sixth-grade Turkish students' pattern-generalization approaches among arithmetical generalization, algebraic generalization, and naïve induction. A qualitative case study design was employed. The data was collected from four sixth-grade students through the Pattern Questionnaire (PQ) and individual interviews based on the…

Our study aims to determine how Habermas' construct of rationality can serve to identify and interpret the difficulties experienced by university students in the mathematical problem-solving process. To this end, a problem which required modelling and solving a differential equation was used. The problem-solving processes of university students…

Language is often depicted as the sine qua non of mathematical thinking, a view buttressed by findings of language-of-training effects among bilinguals. These findings, however, have been limited to studies of arithmetic. Nothing is known about the potential influence of language on the ability to learn rules about the relations among variables…

The study of linear relationships is foundational for mathematics teaching and learning. However, students' abilities to connect different representations of linear relationships have proven to be challenging. In response, a computer-based instructional sequence was designed to support students' understanding of the connections among…

In this report, the theoretical background and procedures for a study of concept learning are discussed. Several definitions of the term "concept" are analyzed, and the relations among concepts, chains of concepts, and hierarchies of concepts are explored. Conceptual learning is discussed from several points of view, and axiom systems for the…

In this volume, the results of a study of concept learning are presented. (The background for the study, and descriptions of the treatments--rote reception, rote discovery, conceptual reception, and conceptual discovery--are provided in Part 1.) Several hypotheses concerning the effectiveness of these treatments in learning concepts and on the…

Technology in secondary schools has become of increasing interest as the power of the microchip has developed. For the students of Mathematics, computers and handheld graphic calculators need to be accessible to all. They are relevant to the needs of the students' courses and to support and develop their Mathematical learning (Smith, 1997).…