This study examined and compared the intended mathematics curricula according to topic coverage, focus, coherence, and learning progression in grades 1-12 within China and the province of Ontario, Canada. The findings show that the overall topics in the two curricula are similar: Chinese curriculum covers 78 topics out of 79 while the Ontario…

Learning progressions (LPs) have seen a growing interest in recent years due to their potential benefits in the development of formative assessments for classroom use. Using an LP as the backbone of an assessment can yield diagnostic classifications of students that can guide instruction and remediation. In operationalizing an LP, assessment items…

This study reports on an early career Year 2 teacher's reflections of enacting specifically structured resource materials and her practice change when participating in a mathematics professional learning project. A qualitative case study was designed to examine the reflections of a teacher's pre-service and in-service teaching experiences. Data…

The foundation of geometric knowledge and understanding starts in primary school, and in contemporary mathematics education there is an emphasis on identifying learning progressions and trajectories as a way of moving students forward. The van Hiele (1986) theory is well-documented and provides insights into the progression and differences of…

"Patterning" is a cognitive intervention that is unknown to psychologists, but has nevertheless been taught for half a century in nearly all kindergartens and many preschools in English-speaking countries. Patterning is the understanding that a certain rule governs the sequence of items in a series. At the simplest level, if the series…

Understanding related to fraction concepts is a critical prerequisite for advanced study in mathematics such as algebra. Therefore, it is important that elementary students form conceptual and procedural understanding of fractional numbers, allowing for advancement in mathematics. The concrete-representational-abstract (CRA) instructional sequence…

An evaluation of the national curriculum by practitioners suggests that learning materials across school levels still overlap, are irrelevant to student development phases and competencies required, too challenging for students to learn, too broad in terms of topics, and lacking in depth. This evaluation encourages the needs for special studies…

This study investigates the descriptions of support measures in the sequential pedagogical documents (individual education plans or programs and others) of children with special education needs from early childhood education and care to preprimary education. According to the previous research, the role of pedagogical work is largely disregarded in…

Background: The worked example effect in cognitive load theory suggests that providing worked examples first followed by solving similar problems would facilitate students' learning. Using problem solving-worked example sequence is another way of implementing example-based instruction. Although research has demonstrated the superiority of worked…

Current educational discourse holds that effective pedagogy requires engagement through active student participation with subject matter relating to them. The lack of testing of lessons in series is recognized as a potential weakness in the evidence base, not least because standard parallel designs cannot capture serial interaction effects (cf.…

Written argumentation is a complex skill to master. It can be assumed that students can transfer oral argumentation skills into a written format. Still, students from disadvantaged backgrounds for whom this task is highly novel require greater scaffolding to formulate persuasive arguments in writing. Therefore, there is a need for developing sound…

This study examined the effects of two teaching treatments [multiple-representation instruction (MR) and traditional algorithmic instruction (TA)] on students' performance on mathematics problems that integrated fractions, decimals, and percent. Using a 2 × 2 crossover design, the effect of the teaching treatments and their sequences on student…

Design is a key element of both the teaching and learning of engineering and technology. However, the process of engineering design has yielded limited research results. This study explored the iterative design process by searching for sequential design thinking patterns. The researchers collected nine concurrent think-aloud protocols from…

Open-ended learning environments (OELEs) allow students to freely interact with the content and to discover important principles and concepts of the learning domain on their own. However, only some students possess the necessary skills for efficient and effective exploration. Guidance in the form of targeted interventions or feedback therefore has…

Reporting on a Grade 4 teaching and learning sequence, we highlight foundational constructs of measurement and data modelling which are fundamental to competence development in both science and mathematics. The sequence involved students generating and representing measures of their teacher's arm-span, with a focus on the invention and refinement…