The purpose of this study is to examine how pre-service elementary teachers generalize a non-linear figural pattern task and justify their generalizations. More specifically, this study focuses on strategies and reasoning types employed by pre-service elementary teachers throughout generalization and justification processes. Data were collected…

Cognitive processes are procedures for using existing knowledge to combine it with new knowledge and make decisions based on that knowledge. This study aims to identify the cognitive structure of students during information processing based on the level of algebraic reasoning ability. This type of research is qualitative with exploratory methods.…

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…

Generalisation is a key feature of learning algebra, requiring all four proficiency strands of the Australian Curriculum: Mathematics (AC:M): Understanding, Fluency, Problem Solving and Reasoning. From a review of the literature, we propose a learning progression for algebraic generalisation consisting of five levels. Our learning progression is…

Due to their abstract nature, representation of mathematical concepts through different registers favors their understanding. In the case of ''sequences and regularities'', it becomes propitious the exploration of different registers of representation in the institution of topics, such as term, order, formation law, and generating expression.…

Information and Communication Technology (ICT) education has been actively implemented around the world recently. ICT curriculum in schools is intended to improve students' programming-oriented thinking rather than to train them as programmers. The core of ICT education is 'computational thinking'. Computational thinking is taking an approach to…

The present study explores reasoning and argumentation in Greek mathematics and physics texts in specific topics related to the notion of periodicity. In our study, argumentation is taken as the sequence of the modes of reasoning (MsoR) that an author develops in a text when organizing and presenting new knowledge. Inductive content analysis was…

Students often struggle with concepts from abstract algebra. Typical classes incorporate few ways to make the concepts concrete. Using a set of woven paper artifacts, this paper proposes a way to visualize and explore concepts (symmetries, groups, permutations, subgroups, etc.). The set of artifacts used to illustrate these concepts is derived…

A discussion focusing on the abstractness of analysis in phonology, debated since the 1960s, describes the issue, reviews the literature on the subject, cites specific natural language examples, and examines the extent to which the issue has been resolved. An underlying representation is said to be abstract if it is different from the derived one,…

Although mathematics deals with generalizations relating abstract ideas, very little attention has been given in the mathematics education literature to the role of abstraction and generalization in the development of mathematical knowledge. In this paper, the meanings of "abstraction" and "generalization" are first explored by…

Three experiments using university students explored what constitutes an event and what determines its boundaries. Results supported the hypothesis that sequences of stimuli repeating in different contexts are cut out to become cognitive entities ("things" with a beginning and an end) in their own right. Results suggest that the…

This study investigated the effects of K. J. Klauer's (1989) inductive reasoning training program of teaching children. Effects of training and the range of transfer of the training were assessed. The subjects were 34 third-grade Dutch children of average ability, matched on age, sex, and IQ. Children from the training condition (N=17) received…

This volume of the 27th International Group for the Psychology of Mathematics Education Conference includes the following research reports: (1) Improving Decimal Number Conception by Transfer from Fractions to Decimals (Irita Peled and Juhaina Awawdy Shahbari); (2) The Development of Student Teachers' Efficacy Beliefs in Mathematics during…