Different Types of Subitizing Activity: A Teaching Experiment with Preconservers

Introduction: Subitizing, a quick apprehension of the numerosity of a small set of items, is consistently utilized to support early number understanding. Perceptual subitizing is the innate ability to recognize less than five items without consciously using other mental or mathematical processes. Conceptual subitizing, which requires higher-level abilities, means perceiving the quantities as groups and performing a mental process on them. Research on conceptual and perceptual subitizing indicates some limitations about the activities regarding the children’s early number development. So, MacDonald and Wilkins (2016) developed a framework that explained the types of activities that young children used while subitizing. In this framework, five sets of perceptual subitizing activity were described to explain how young children’s perceptual subitizing activity changed. Besides, two types of conceptual subitizing activities were defined to explain how children’s limited or flexible number understanding related to their subitizing activity. These seven different types of activities characterize the changes in children’s subitizing actions. The study aims to investigate the relationship between children’s number understanding and subitizing activity. Methods: A teaching experiment was conducted with two preschool-aged children to analyze what perceptual and conceptual processes children relied upon when subitizing. The teaching experiment consisted of twenty-six sessions. The interviews were conducted to determine whether children are able to conserve numbers or not, and whether they rely on a variety of different types of subitizing activity or not. After the interviews, 26 teaching sessions were carried out with two preconserver children. Results: In the experimental process, it was observed that the children rely on the color of items, the gap between items, and symmetrical aspects of items when perceptually subitizing. However, they could not manage to transition their subitizing activity from perceptual to conceptual subitizing. The study indicates that children’s subitizing skills were closely related to their number conservation development. Discussion: Based on the findings from this study, for Eren and Beren, subitizing activities were found to be perceptually limited. Specifically, it was found that four types of perceptual subitizing emerged to explain how symmetry, the gap between items, color of items, and canonical patterns promoted strategies that children relied on when constructing number understanding. During the teaching experiment, although these children carried out the activities that required the separating and combining numbers and seeing the relationship between the subgroups and the composite groups, they used perceptual units in this process. The relationship between the number conservation activity and the conceptual subitizing activity requires the coordination of thinking structures related to both ordering and classification. However, it was found that the children could not move from perceptual to the conceptual subitizing. Limitations: As all studies have some limitations, this study has, too. One of the limitations of the study is the sample size/number of participants. But teaching experiments aim to get a deep understanding, studying with a small sample is an obligation. Secondly, this study focused on some compounds of subitizing such as perceptual and conceptual ones. Conclusion: In order to make the transition from perceptual subitizing to conceptual subitizing children should have more experiences with subitizing activities.When designing mathematical games and assessments for young children, being aware of different types of subitizing categories may provide better support children’s number understanding and subitizing.

Development of an instrument to assess early number concept development in four South African languages

A recently published interview-based test, known by its partly German acronym, MARKO-D SA, is introduced in this article by way of a narrative of its development through various cycles of research. The 48-item test, in 4 South African languages, captures number concept development of children in the 6 to 8-year age group. The authors present their argument for the South African versioning and translation of the test for this country, where there is a dearth of suitable assessment instruments for gauging young children’s mathematical concept development. We also present the findings of the research that was conducted to standardise and norm the local version of the test, along with our reasoning about the theoretical strength of the conceptual model that undergirds the test.

Investigating the Dimensionality of Early Numeracy Using the Bifactor Exploratory Structural Equation Modeling Framework

The few studies that have analyzed the factorial structure of early number skills have mainly used confirmatory factor analysis (CFA) and have yielded inconsistent results, since early numeracy is considered to be unidimensional, multidimensional or even underpinned by a general factor. Recently, the bifactor exploratory structural equation modeling (bifactor-ESEM)—which has been proposed as a way to overcome the shortcomings of both the CFA and the exploratory structural equation modeling (ESEM)—proved to be valuable to account for the multidimensionality and the hierarchical nature of several psychological constructs. The present study is the first to investigate the dimensionality of early number skills measurement through the application of the bifactor-ESEM framework. Using data from 644 prekindergarten and kindergarten children (4 to 6 years old), several competing models were contrasted: the one-factor CFA model; the independent cluster model (ICM-CFA); the exploratory structural equation modeling (ESEM); and their bifactor counterpart (bifactor-CFA and bifactor-ESEM, respectively). Results indicated acceptable fit indexes for the one-factor CFA and the ICM-CFA models and excellent fit for the others. Among these, the bifactor-ESEM with one general factor and three specific factors (Counting, Relations, Arithmetic) not only showed the best model fit, but also the best coherent factor loadings structure and full measurement invariance across gender. The bifactor-ESEM appears relevant to help disentangle and account for general and specific factors of early numerical ability. While early numerical ability appears to be mainly underpinned by a general factor whose exact nature still has to be determined, this study highlights that specific latent dimensions with substantive value also exist. Identifying these specific facets is important in order to increase quality of early numerical ability measurement, predictive validity, and for practical implications.

Journeys towards sociomathematical norms in the Foundation Phase

Background: The co-establishment of social and sociomathematical norms in the microculture of South African classrooms and its possible effects on early number learning has largely been unexplored. Social norms are considered to be general classroom norms that are relevant in any teaching and learning space, whilst sociomathematical norms are specific to the mathematical aspects of students’ working.Aim: In the midst of poor numeracy outcomes in South African schools, our interest lies in the connections between the establishment of particular norms and the affordances or constraints for learning that they provided. Part of our interest, in a context where sense-making, co-operative working and mathematical progression beyond one-by-one counting have been described as infrequent in Foundation Phase mathematics learning, was to explore whether it was possible to institute norms related to these aspects.Setting: We report on the social and sociomathematical norms established within group intervention sessions with two groups of four Grade 2 learners across 9 weeks of intervention in a suburban school which serves a historically disadvantaged learner population.Methods: The frequency of specific norm codes was used to determine the normative behaviour within groups across intervention lessons.Results: Two significant inferences are drawn from study results: a culture of co-operative working based on social norms was needed in the grouped learning space before sociomathematical norms could be foregrounded within the same space; and one particular sociomathematical norm – ‘use the structure of 10’ – was particularly important as the ‘hand hold’ that allowed for progression in participants’ early number skills.

Increasing the Number Sense Understanding of Preschool Students With ASD

Teaching children with autism spectrum disorder (ASD) academic skills supports their future opportunities. For example, early number sense skills are predictive of future mathematical success for all children including children with ASD. Yet, research on foundational early childhood mathematics skills of children with ASD is limited. This study used an adapted version of Number Talks to increase the number sense skills of preschool children with ASD. Number Talks is a constructivist approach that was combined with systematic instruction (i.e., system of least prompts and modeling) in this study. A multiple probe across participants design established a functional relation between using an adapted version of Number Talks and the early number sense skills of preschool children with ASD. Findings suggest using an adapted version of Number Talks can increase the early number sense skills of preschool children with ASD. Implications for practice and future research are discussed.