Classroom manipulatives for teaching early mathematical concepts to children: What, how, and why?

Early mathematical concepts are often introduced to children using manipulatives. The term manipulative has been used to refer to 3-dimensional objects that children and practitioners can interact with and move to represent mathematical ideas. This can include a vast range of materials, from everyday objects such as toy animals and pebbles, to more formal mathematics resources (e.g., Dienes blocks, Cuisenaire rods). The choice of what kind of manipulative to use with children may appear to be a relatively minor or intuitive decision. However, research evidence has suggested that different manipulative types (e.g., toy animals, blocks), and their associated features (e.g., colour, shape, similarity, potential to activate prior knowledge), can have important implications for children’s mathematics-related outcomes. In this thesis, I extended current perspectives regarding manipulatives and their associated features. More specifically, I focussed on how four key factors may interact to influence the learning opportunities and constraints manipulatives may provide for children when engaging with mathematical concepts: (1) practitioner perspectives and pedagogical considerations, (2) novel combinations of manipulative features, (3) the instructional guidance provided, and (4) individual learner characteristics.

Given that practitioners are ultimately responsible for the selection and implementation of resources when teaching mathematics, I first considered their perspectives in relation to manipulative use (Chapters 3 and 4). I then used these findings to inform four subsequent experimental studies, incorporating key aspects of the pedagogical considerations reported by practitioners into my experimental designs (Chapters 5, 6, 7, 8). Throughout the experimental studies in this thesis, I also measured children’s behaviour-related outcomes (i.e., strategies, task- relevant behaviour), as well as more standard performance-related measures (i.e., accuracy, time on task), to provide more nuanced insights into how different factors may influence children’s approaches when completing mathematical tasks.

Together, the studies conducted in my thesis have reiterated the complexity of using manipulatives to teach mathematical concepts to children, and also provide novel insights regarding the boundary conditions associated with effective manipulative use. In Chapters 3 and 4, practitioners working with children aged 2-6 years provided novel considerations regarding manipulative implementation in the classroom. These included the use of different manipulative features to provide novel learning opportunities, as well as the incorporation of other pedagogical practices to help facilitate children’s outcomes (e.g., instruction). Subsequent experimental investigations regarding novel combinations of features in Chapter 5 supported existing evidence regarding the influence of different manipulative types (e.g., blocks vs. toy animals), as well as highlighting the potential value of using a homogeneous (identical) set. Results from Chapters 6 and 7 afforded nuanced insights regarding the function of guided instructional prompting when using different manipulative types. Collectively, Chapters 5, 6, and 7 also raised pertinent questions regarding the mechanisms associated with different combinations of features (e.g., activation of prior knowledge), and the potential trade-offs associated with different instructional approaches (e.g., performance vs. active learning). Finally, Chapter 8 provided preliminary insights regarding the importance of behavioural self-regulation in relation to manipulative use. Crucially, by using practitioner-reported manipulative use to inform subsequent experimental work, this thesis has provided a novel, pedagogically relevant perspective, which highlights important considerations for manipulative use both for research, and in practice.