<abstract xmlns="http://www.w3.org/1999/xhtml">

<bold><italic>Introduction:</italic></bold> 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.
<bold><italic>Methods:</italic></bold> 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.
<bold><italic>Results:</italic></bold> 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.
<bold><italic>Discussion:</italic></bold> 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.
<bold><italic>Limitations:</italic></bold> 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.
<bold><italic>Conclusion:</italic></bold> 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.
</abstract>

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.

Different Types of Subitizing Activity: A Teaching Experiment with Preconservers

Acta Educationis Generalis

This work is licensed under the Creative Commons Attribution 4.0 International License.

{"article-title":"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....

Different Types of Subitizing Activity: A Teaching Experiment with Preconservers

Published Online: Dec 17, 2021

Page range: 35 - 52

Received: Apr 26, 2020

Accepted: Jun 15, 2020

DOI: https://doi.org/10.2478/atd-2021-0020

Keywords
subitizing, number conservation, early math, teaching experiment

© 2021 Derya Can, published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Different Types of Subitizing Activity: A Teaching Experiment with Preconservers

Published Online: Dec 17, 2021

Page range: 35 - 52

Received: Apr 26, 2020

Accepted: Jun 15, 2020

DOI: https://doi.org/10.2478/atd-2021-0020

Keywordssubitizing, number conservation, early math, teaching experiment

© 2021 Derya Can, published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Keywords
subitizing, number conservation, early math, teaching experiment