This study aims to examine the changes in students' mental constructions of function transformation based on the designed activities, classroom discussions, exercises (ACE) teaching cycle in the light of the action, process, object, schema (APOS) theoretical framework. The study was conducted by seven volunteer students who were enrolled in…

The purpose of this article is to present and discuss two recommended sequences of learning the areas of polygons, starting from the area of a rectangle. Exploring the algebraic derivations of the two sequences reveals that both are valid teaching progressions for introducing the area formula for various polygons. Further, it is suggested that…

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.…

Southern Cross University (SCU) educators and local teachers have developed a five-lesson instructional sequence built around fluke identification as a way of resolving the question: How fast do humpback whales travel up the east coast of Australia?

This article describes part of a study in which researchers designed lesson sequences based around using a string number line to help teachers support children's development of relative thinking and understanding of linear scale. In the first year of the study, eight teachers of Years 3-5 participated in four one-day professional development…

The findings discussed here are a small part of a larger study entitled, "Encouraging Persistence Maintaining Challenge". The paper reports five teachers' observations of the implementation of a task which was new to them. The teachers were asked to identify aspects of the task which they perceived as challenging for the Year 6 students.…

Find out how to use photographic images to support the conceptual development of proportional thinking. This paper provides insight into a sequenced activity that promotes student engagement and makes links to familiar and unfamiliar contexts.

Mastery learning techniques were improved through mathematics instruction based on a validated learning hierarchy, presenting tasks in a sequence consistent with the requirements of the hierarchy, and requiring learners to demonstrate achievement before being allowed to proceed. (Author/GDC)

Research conducted at the Institute of General and Pedagogical Psychology of Moscow, and based on the premise that the development of thought processes is a direct product of the social environment, is described. As a corollary to this premise, Piaget's view that the development of the thinking process occurs in orderly fashion is questioned.…

Proposes that ability is a concept central to the current practices of mathematics teaching. Argues that the widespread view that mathematics learning is an ordered progression through a hierarchy of knowledge and skills subjects students to "ability stereotyping" and serves as a gross global model. (TW)