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…

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 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 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 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…

As learning trajectories gain traction in mathematics education, we seek to understand the ways in which teachers may use them in interactions with students. This paper reports on one group of elementary teachers' use of their emerging knowledge of a learning trajectory to examine key pedagogical practices. Findings suggest that a learning…

Even when two-digit numbers are irrelevant to the task at hand, adults process them. Do children process numbers automatically, and if so, what kind of information is activated? In a novel dot-number Stroop task, children (Grades 1-5) and adults were shown two different two-digit numbers made up of dots. Participants were asked to select the…

The acquisition of reading skills is known to rely on early phonological abilities, but only a few studies have investigated the independent contribution of the different steps involved in phonological processing. This 1-year longitudinal study, spanning the initial year of reading instruction, aimed at specifying the development of phonological…

The ability to learn temporal patterns in sequenced actions was investigated in elementary-school age children. Temporal learning depends upon a process of integrating timing patterns with action sequences. Children ages 6-13 and young adults performed a serial response time task in which a response and a timing sequence were presented repeatedly…