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

The Potentials of Tangible Technologies for Learning Linear Equations

“…Moreover, the findings from the thinking aloud data suggest that X-is facilitated the achievement of equation learning (i.e., modelling and solving equations successfully) among diverse students, particularly low and medium achievers. These findings are consistent with those of Pires et al [14], who found that children with no proficiency in number combinations benefited more from their TM compared to their virtual manipulative.…”

“…Particularly, their argumentation indicated that they had a good understanding of mathematical equivalence (e.g., the equal sign as a relational symbol) and the equation-solving process. The evidence that X-is is advantageous for students' learning achievement corroborates the findings of earlier work [14,45,81] in tangible technology-enhanced mathematics learning. Moreover, the findings from the thinking aloud data suggest that X-is facilitated the achievement of equation learning (i.e., modelling and solving equations successfully) among diverse students, particularly low and medium achievers.…”

“…Studies have shown how TUIs have enhanced mathematics learning in different content domains and various educational levels. For example, number composition for primary school [14], fractions for primary school [42], geometry for pre-primary and primary school [43,44], trigonometry for undergraduate school [45], and algebra for lower and upper secondary school [20] have been studied. The potential benefits of TMs were used to inform our TM design and to guide our result analysis and discussion.…”

“…Thus, tabletop systems are neither portable nor affordable. Another possibility was a vision-based tracking mixed reality system, where a mirror is placed in front of a tablet camera and enables the system to detect objects on a flat surface in front of the tablet (e.g., Ceibal Tangible (CETA) [14]). This system is inexpensive, portable, and would be able to detect our objects.…”

“…Different advantages of virtual manipulatives include providing the simultaneous link between pictorial and symbolic representations, step-by-step scaffolding, immediate feedback [11], and drawing learners' attention to the to-be-learned mathematics [12]. However, there has been concern about the disadvantage of replacing rich physical interactions using physical manipulatives with clicking a mouse or tapping and scrolling a touch screen when manipulating virtual manipulatives [13,14]. A body of research signals that the combination of physical and virtual manipulatives may facilitate students' mathematics learning [11,12,15].…”