This research integrates context-based learning and modelling. It presents a teaching-learning sequence (TLS) about the dissolution of gases in liquids using carbonated drinks as the context. The impact of the TLS is analysed in a longitudinal short-term study involving two groups of learners aged 13-14 years old (n=53). The results led us to…

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…

The paper presents and analyses a sequence of events that preceded an insight solution to a challenging problem in the context of numerical sequences. A three­week long solution process by a pair of ninth­-grade students is analysed by means of the theory of shifts of attention. The goal for this article is to reveal the potential of this theory…

Sarah Black wanted to remedy Year 9's lack of knowledge about nineteenth-century politics. With just five lessons to work with, she decided to devise a sequence on Gladstone and Disraeli, shaping the sequence with an enquiry question that invited argument about change and continuity. Black analyses the status and function of different layers of…

"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…

Research and educational policies have alerted teachers to the importance of multiliteracies. Communication in society today is characterised by rapidly changing and emergent forms of meaning-making in a context of increased cultural and linguistic diversity. This paper responds to these imperatives, releasing key findings of a critical…