Fostering the Development of Mathematical Thinking and Number Sense in Kindergarteners through the Interactive Reading of Mathematical Stories: A Small-scale Intervention Study in the Context of Saudi Arabia

Abstract

This study contributes to the existing research by offering a well-designed empirical study with the aim of investigating the effectiveness of reading mathematical stories interactively on the development of number sense and mathematical thinking in authentic interactive reading scenarios in kindergartens, which involved reading to a group without additional supportive activities. In this way, it also explores the contribution of stories’ features and interactive reading to such development. Mathematical stories are fictional narratives that depict the struggles of characters of interest as they attempt to resolve a problem by employing mathematical knowledge. Based on the inclusion of several key features, mathematical stories have the potential to improve number sense and mathematical thinking. Taking into account the fact that most kindergartens incorporate daily storytelling sessions, exploiting such sessions to teach mathematics through mathematical stories may thus offer a strategy for improving children’s mathematical thinking and number sense. Mathematical thinking in this study is viewed as a style of thinking rooted in the mathematical processes of specialising, conjecturing, generalising, and convincing. As mathematics is widely described as a science of patterns, which play a crucial role in stimulating and developing mathematical processes, the development of mathematical thinking may be seen as central to the study of mathematics, and thus taken as the primary focus of mathematical education, including early years settings. As the key properties of operations are crucial generalisations in mathematics, and also offer rich data regarding mathematical thinking, the commutative property of addition and the inverse relationship between addition and subtraction were used to stimulate mathematical thinking in this study. However, students must already have some number sense to be able to think mathematically about these properties. In addition, number sense is believed to act as a foundation for the acquisition of mathematics proficiency in later years. The working definition of number sense in this study was set as the capacity to make comparisons between quantities using concepts such as “more” and “less”, to employ counting principles, to identify number position within a sequence, and to evaluate the comparative magnitude of numbers, as well as to solve addition and subtraction problems without the need for concrete objects. A quasi-mixed methods small-scale intervention study was conducted on 46 kindergarten children aged five to seven years old. The study adopted a non equivalent quasi-experimental design involving comparison and intervention groups and utilised pre-, post-, and delayed testing. Eight mathematical stories were presented in interactive reading environments, and the pretest, posttest, and delayed test were used to measure number sense. The resulting data was then subjected to ANCOVA statistical testing. All reading sessions were observed and recorded using a video camera to capture the responses and behaviours of the class, though only the teacher’s voice was captured. The recorded data for all reading sessions were transcribed using MAXQDA software, and the reading sessions for three of the eight stories were then analysed qualitatively to explore the expressed mathematical thinking processes evoked during those sessions. This also allowed exploration of how the stories’ features and teacher and peer interactions contributed to the development of number sense and mathematical thinking. The quantitative results indicated that the intervention had promising effects on number sense, in that the experimental group significantly outperformed the control group not only on the posttest but also on the delayed test. Moreover, the differences between the experimental and control group's posttest and delayed test results were more prevalent with respect to the addition and subtraction items, two operations that may be expected to be refined when pupils think mathematically about the commutative law of addition and the inverse relationship between addition and subtraction. The findings of a qualitative analysis of the video recordings of the reading sessions indicated that the kindergarteners engaged in mathematical thinking processes throughout the storytelling process, although they did encounter certain difficulties with this. The results thus highlighted the crucial role of specialisation in assisting pupils progression to more advanced mathematical processes. Regarding the expected relationship between number sense and mathematical thinking, evidence also emerged that understanding mathematical content is one of the main variables that influences the ability to think mathematically about certain topics, while practising mathematical thinking gives pupils the opportunity to develop and enhance their understanding of related mathematical content. The qualitative analysis also demonstrated the significance of including well designed mathematical stories with content supported by mathematical language that contains several mathematical representations, examples, and interesting mathematical problems, actively in kindergarten settings, based on the evidence of using this strategy in a kindergarten setting. Even for well-designed mathematical stories, reading the story interactively helped to provide a questioning atmosphere conducive to mathematical thinking and number sense. This study was therefore successful in addressing one of the gaps in prior mathematics education research, answering the call for research to explore the “effectiveness of the intervention in more typical schools, for example when delivered by teachers to larger groups” (Purpura et al., 2017, p. 133). The study also provided insights about the potential reasons for such effectiveness, thus, surpassing mere examination of the effect of the intervention (i.e., measuring number sense and investigating the expressed mathematical process) to investigate various anticipated factors that might contribute to the occurrence of such an effect through an analysis of the influences of various story features and reading style. Through this process, alongside the development of greater comprehension of the consequences of each story's characteristics and the reading interactive strategies, a framework for structuring and presenting mathematical stories was established. In addition, the work has provided a detailed framework for analysing both mathematical thinking and number sense. There are several implications for practice within the study findings. Not only do they confirm that teachers in kindergartens should use story time to teach mathematics, but also suggest that such teachers should take into consideration several additional factors that might influence the effectiveness of utilising this strategy. The study also provided a framework for the design of mathematical stories, which might be considered a helpful tool for teachers in selecting, developing, or creating well designed mathematical stories, as well as illustrating the reading styles that teachers may best use to deliver such stories more effectively. The findings of this study should also encourage teachers of young students not to underestimate their students’ abilities regarding this type of thinking, thus promoting the planning of ways to encourage students to think mathematically in various regards. Teachers may also prefer to use stories designed specifically to evoke pupils’ mathematical thinking while at the same time developing their own understanding of the nature of mathematical thinking to determine how young learners might express concepts, using the detailed conceptual framework for encouraging mathematical thinking processes presented in this study as well as the related findings.