Learning the sequence of number words in English up to 30 is not a simple process. In NSW government schools taking part in "Early Action for Success," over 800 students in each of the first 3 years of school were assessed every 5 weeks over the school year to determine the highest correct oral count they could produce. Rather than…

Ninety-six first grade students in an urban school system were tested in October and May on reading, mathematics, and their understanding of sequences of letters and numbers. A time lag analysis was subsequently conducted. In such analyses, cross-correlations between the first measurement of one variable and the second measurement of another are…

"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 distinction between procedural and conceptual learning has long been a topic of discussion in mathematics education and the idea of compression into thinkable concepts that enable the individual make links between them (Tall, 2007). In addition to, the compression to thinkable concept was to be thinking mechanism arising naturally and…

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…

In this action research, first-graders were challenged to cope with a sequence of modelling tasks involving an analysis of given situations and choices of mathematical tools. In the course of the sequence, they underwent a change in the nature of their problem-solving processes and developed modelling competencies. Moreover, during the task…

This article promotes the use of mathematically appropriate, engaging and challenging tasks to support learning that is worthwhile. The authors share insights from a three-lesson design experiment and the three tasks along with the results from their implementation are explored.