Introducing new concepts to learners in an order of increasing complexity appears to be beneficial for learning, but typically introduction of concepts does not always adhere to this principle. We examined whether introducing new algebra concepts in a contrasted manner or in an order of increasing complexity instead of a different more typical…

Mairead Hourigan and Aisling Leavy describe a range of teaching and learning activities focusing on the identification and classification of 2-dimensional shapes. The activities described are useful in highlighting students' misconceptions regarding non-traditioanl and non-prototypical shapes.

"That was the day I decided I was bad at math." Countless times, preservice and in-service teachers make statements such as this after sharing vivid memories of learning multiplication facts. Timed tests; public competitive games, such as Around the World; and visible displays of who has and has not mastered groups of facts still…

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.…

In this paper, we describe our learning progressions approach to early algebra research that involves the coordination of a curricular framework, an instructional sequence, written assessments, and levels of sophistication describing the development of students' thinking. We focus in particular on what we have learning through this approach about…

The purpose of this study was to examine the effects of grade-aligned math instruction on math skill acquisition of four middle schools with moderate intellectual disability. Teachers were trained to follow a task analysis to teach grade-aligned math to middle school students using adapted math problem stories and graphic organizers. The teacher…

The researcher examined the effects of two alternative instructional methods, Programmed Learning Sequenced (PLS) and Interactive Whiteboard (IWB), on the mathematics achievement and attitude of eighth graders. The relationship between specific Dunn & Dunn learning-style elements and the posttest scores after instruction with the PLS and IWB…

The premise underlying this article is that identifying and using the "five practices model" can make discussions of cognitively challenging tasks more manageable for teachers. By giving teachers a roadmap that they can follow before and during whole-class discussions, these practices have the potential for helping teachers more effectively…