"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…

How should a wide variety of educational activities be sequenced to maximize student learning? Although some experimental studies have addressed this question, educational data mining methods may be able to evaluate a wider range of possibilities and better handle many simultaneous sequencing constraints. We introduce Sequencing Constraint…

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 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…

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.

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 case study focuses on generalist primary (elementary) school teachers teaching music in an Australian school. With the onus for teaching music moving away from the specialist music teacher to the generalist classroom teacher, this case study adds to a growing body of literature focusing on generalist primary school teachers and music…

Complex systems are an important topic in science education today, but they are usually difficult for secondary-level students to learn. Although graphic simulations have many advantages in teaching complex systems, scaffolding is a critical factor for effective learning. This dissertation study was conducted around two complementary research…

This article reports on 2 studies that attempted to replicate the findings of a study by Szmalec, Loncke, Page, and Duyck (2011) on Hebb repetition learning in dyslexic individuals, from which these authors concluded that dyslexics suffer from a deficit in long-term learning of serial order information. In 2 experiments, 1 on adolescents (N = 59)…

This report describes the implementation of arts-based instruction during in-school and out-of-school times. Specifically, it summarizes the results of four components of the inventory: (a) sequential fine arts instruction during school, (b) community arts experiences during school, (c) out-of-school time arts opportunities on campus, and (d)…

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.

The aspirational model resulted from the authors' secondary analysis of the Mother/Child (M/C) test block from the 2008 National Assessment of Educational Progress restricted data that examined the responses of the national sample of 8th-grade students (n = 1648). This test block presented no artmaking task and consisted of the same 13 questions…

The representation of numerical and non-numerical ordered sequences was investigated in children from preschool to grade 3. The child's conception of how sequence items map onto a spatial scale was tested using the Number-to-Position task (Siegler & Opfer, 2003) and new variants of the task designed to probe the representation of the alphabet…

This report summarizes recommendations from NCTM, NRC, CCSSM, NMAP, and IES to guide early numeracy instruction for elementary age students in general and special education classroom settings. We highlight common threads among general and special education research recommendations and provide a numeracy intervention curriculum model connecting…