In this paper, the aim is to make a theoretical contribution by focusing on the origin, characteristics, and potential values of the concepts of instrumental and relational understanding. Five characteristics are identified to make it easier to operationalise the concepts and use them as an analytical framework. There is also a focus on how the…

How do learners make sense of what they are learning? In this article, I present a new framework of sense-making based on research investigating the benefits and boundaries of generative learning activities (GLAs). The generative sense-making framework distinguishes among three primary sense-making modes--explaining, visualizing, and…

Scholarly inquiry into teaching and learning in higher education has long been undertaken through a wide array of theoretical and methodological approaches. This article offers a novel theoretical framework for reconceptualizing and analyzing teaching and learning processes as textual acts. Drawing on Roland Barthes's concept of the writerly text,…

This article explores teaching practices described in NCTM's Principles to Actions: Ensuring Mathematical Success for All. Student thinking, a learning cycle, and procedural fluency are discussed in this article, which is the second installment in the series. [For the first installment in this series see "Promoting a Conceptual Understanding…

This paper introduces Rewritten Scripture and scriptural rewriting as a creative process that, when mirrored in a teaching exercise, may serve as an effective practice in teaching sacred texts. Observing changes made between scripture and its rewriting may allow readers to identify different contexts among these texts. Furthermore, the act of…

Meaningful learning of formal mathematics in regular classrooms remains a problem in mathematics education. Research shows that instructional approaches in which students work collaboratively on tasks that are tailored to problem solving and reflection can improve students' learning in experimental classrooms. However, these sequences involve…

Group and team tasks are the culminating outputs of student learning in team and collaborative learning environments. How they are conceived and designed, therefore, can directly determine the success of the pedagogical strategy. A key design issue for creating effective tasks is how best to focus student knowledge, observation, and analysis…

Latvian Education Foundation presents methods and tools to reach comprehension and develop creative thinking. The Web page www.goerudio.com contains wordings of conceptions and patterns under training standards, as well as appropriate models/examples created by students and teachers, which interprets mentioned conceptions and patterns by use of…

As facilitator, the author noted some trepidation in the room as the eight secondary principals from Eugene (Oregon.) School District 4J quietly discussed questions that surfaced through their hopes and fears exercise. Could the practice of visiting classrooms together help them to better lead instruction in their buildings? Would this process…

Problem solving skills and abilities are critical in life and more specifically in the engineering field. Unfortunately, significant numbers of South African students who are accessing higher education lack problem solving skills and this results in poor academic performance jeopardizing their progress especially from first to second year. On the…

The article describes qualitative variation in micro processes of learning, focusing the dynamic interplay between conceptions, expressions and meanings of expressions in students' learning in higher education. The intentional-expressive approach employed is an alternative approach to the function of language use in learning processes. In the…

This article describes five representations and the connections between and among them. It also describes how to use multiple representations to support students' mathematical understanding.

Most students in most schools today study subject matter. They and their teachers conceive of the educational task as committing to memory large numbers of facts, formulas, and figures. A far more sophisticated perspective emphasizes teaching disciplines and disciplinary thinking. The goal of this approach is to instill in students the disposition…

A discussion of the connectionist approach to language looks at the nature of language, language processing, and language acquisition. Language processing is seen as a means of satisfying the linguistic constraints of comprehension and production, and is also viewed as a process that operates with other aspects of cognition and involves mutually…

In the renewed "Primary Framework for Mathematics" for England, great emphasis is given to calculation and its prerequisites (DfES, 2006). Expectations are increased for calculations and the recall of number facts, with mental calculation owning a higher profile, while progression in written calculation is clarified. The greater focus on…