A key aspect of young children's development of algebraic reasoning is the process of visualising and identifying structures to both abstract and generalise. There has been a growing body of research focused on how students form generalisations, this article adds to the existing body of research by examining how young culturally diverse students…

Due to their abstract nature, representation of mathematical concepts through different registers favors their understanding. In the case of ''sequences and regularities'', it becomes propitious the exploration of different registers of representation in the institution of topics, such as term, order, formation law, and generating expression.…

Learning trajectories are built upon progressions of mathematical understandings that are typical of the general population of students. As such, they are useful frameworks for exploring how understandings of diverse learners may be similar or different from their peers, which has implications for tailoring instruction. The purpose of this…

Previous research has verified the benefits obtained when learners trace out worked examples with the index finger. Our study conducted two experiments to explore the reasons for this phenomenon and its generalizability. Experiment 1 compared the learning effects among tracing, non-tracing, and cueing methods. The cueing method was included to…

The aim of this research is to characterize profiles of the teaching competence "noticing students' mathematical thinking" in the context of the pattern generalization. Prospective primary teachers were asked to describe and interpret the answers of three primary students to three linear pattern generalization problems. Five profiles for…

Spatial visualisation of geometric patterns and their generalisation have become a recognised pathway to developing students' functional thinking and understanding of variables in algebra. This design-based research project investigated upper primary students' development of explicit generalisation of functional relationships and their…

This paper presents a hypothesised learning trajectory for a Year 3 Indigenous student en route to generalising growing patterns. The trajectory emerged from data collected across a teaching experiment (students n = 18; including a pre-test and three 45-minute mathematics lessons) and clinical interviews (n = 3). A case study of one student is…

The Common Core Standards require demonstration of conceptual knowledge of numbers, operations, and relations between mathematical concepts. Supplemental instruction should explicitly guide students with specific learning disabilities (SLD) in these skills. In this article, we illustrate implementation of the concrete-representational-abstract…

Problem Statement: Rich stimuli received by sensory organs such as vision, hearing, and touch are important elements that affect an individual's perception, identification, classification, and conceptualization of the external world. In primary education, since students perform conceptual abstraction based upon concrete characteristics, when they…

The paper presents findings of primary school children's performance on classification and generalisation tasks to demonstrate the fundamental connection between their verbal thinking processes and problem-solving, on the one hand, and the practical activities of their society and culture, on the other. The results reveal that, although children…

Demonstrates that conservation of amount does not always precede conservation of weight. Subjects were 60 six-year-old children. (BD)

Degree of organization in presenting stimuli, and training through modeling versus guided practice, were studied on a dial-reading concept using 144 third or fifth graders. (ST)

Results show that children with flexible styles obtained higher performances on school learning measures than children who used consistent styles. Study results suggest feasibility of identifying children who tend to use a consistent conceptual style for the purposes of prescribing instructional methods and materials. (Author/PC)

Kindergarten and first grade children were trained to choose the middle-sized stimulus in either a single stimulus set or in each of two nonoverlapping stimulus sets. Findings were reported in terms of the assumption that cognitive processes are important in the intermediate-sized transposition paradigm. (Author/DB)