Building Blocks of Mathematical Learning: Virtual and Tangible Manipulatives Lead to Different Strategies in Number Composition

Ana Cristina Pires,Ewelina Bakała,Bruno Fleisher,Gustavo Sansone,Fernando González Perilli,Sebastián Marichal

doi:10.3389/feduc.2019.00081

Ana Cristina Pires, Ewelina Bakała + Show 4 more

Open Access

https://doi.org/10.3389/feduc.2019.00081

Copy DOI

Abstract

Multiple kinds of manipulatives, as traditional, virtual or technology-enhanced tangible objects, can be used in primary education to support the acquisition of mathematical concepts. They enable playful experiences and help children understand abstract concepts, but their connection with cognitive development is not totally clear. It is also not clear how virtual and physical materials influence the development of different strategies for solving instructional tasks. To shed light on these issues, we conducted a 13-day intervention with 64 children from first grade, divided into three groups: Virtual Interaction (VI), Tangible Interaction (TI), and Control Group (CO). The VI group played a fully digital version of a mathematics videogame BrUNO and the manipulation of virtual blocks took place on the tablet screen. The TI group played the same videogame with digitally augmented tangible manipulatives. Finally, the CO group continued with their classroom curricular activities while we conducted the training, and only participated in the pre- and post-test evaluations. Our results highlighted that the use of tangible manipulatives may improve children’s mathematical abilities. Of most interest, we recorded children’s actions during all the training activities, which allowed us to achieve a refined analysis of participants’ operations while solving a number composition task. We explored the differences between the use of virtual and tangible manipulatives and the strategies employed. We observed that the TI group opted for a greater number of blocks in the number composition task, whereas the VI group favoured solutions requiring fewer blocks. Interestingly, those children whose improvement in mathematics were greater were the ones employing a greater number of blocks. Our results suggest that tangible interactive material increases action possibilities and may also contribute to a deeper understanding of core mathematical concepts.

Highlights

IntroductionLearning mathematics at an early age is fundamental to ensuring academic success in STEM (science, technology, engineering, and mathematics) disciplines and maximizing future integration into professional life (Wang and Goldschmidt, 2003)
Learning mathematics at an early age is fundamental to ensuring academic success in STEM disciplines and maximizing future integration into professional life (Wang and Goldschmidt, 2003)
Current findings indicate that the use of tangible manipulatives had a positive impact on mathematical learning

Summary

Introduction

Learning mathematics at an early age is fundamental to ensuring academic success in STEM (science, technology, engineering, and mathematics) disciplines and maximizing future integration into professional life (Wang and Goldschmidt, 2003). Additive composition is the knowledge that larger sets are made up of smaller sets; the commutative property implies that changing the order of the operands doesn’t affect the result; the associative property allows us to add (or multiply) numbers, no matter how the factors are grouped [(a + b) + c = a + (b + c)]; while mastering the basic number combinations leads to understanding how numbers can be composed These properties are crucial for cardinality and number concept acquisition; and lead to the development of key strategies in arithmetical problem solving, such as addition and subtraction (Fuson, 1992; Verschaffel et al, 2007)

Objectives

Methods

Results

Discussion

Conclusion