Effects of Instructional Guidance and Sequencing of Manipulatives and Written Symbols on Second Graders’ Numeration Knowledge

Abstract

Concrete objects used to illustrate mathematical ideas are commonly known as manipulatives. Manipulatives are ubiquitous in North American elementary classrooms in the early years, and although they can be beneficial, they do not guarantee learning. In the present study, the authors examined two factors hypothesized to impact second-graders' learning of place value and regrouping with manipulatives: (a) the sequencing of concrete (base-ten blocks) and abstract (written symbols) representations of the standard addition algorithm; and (b) the level of instructional guidance on the structural relations between the representations. Results from a classroom experiment with second-grade students (N = 87) indicated that place value knowledge increased from pre-test to post-test when the base-ten blocks were presented before the symbols, but only when no instructional guidance was offered. When guidance was given, only students in the symbols-first condition improved their place value knowledge. Students who received instruction increased their understanding of regrouping, irrespective of representational sequence. No effects were found for iterative sequencing of concrete and abstract representations. Practical implications for teaching mathematics with manipulatives are considered.

Unlocking the Power of Gesture: Using Movement-Based Instruction to Improve First Grade Children’s Spatial Unit Misconceptions

“…In this sense, it may be helping to slow children down just enough to promote more reflection and engagement with the problem, setting the stage for deeper conceptual learning. Similar explanations may help to explain previously reported phenomena in the field of mathematics education, such as work showing that second grade children learned more about place value when instruction was provided first on symbolic numerals then on concrete manipulatives rather than the other way around (Osana et al 2017).…”

Impairment of Arabic- and spoken-number processing in children with mathematical learning disability

“…External representation as concrete objects could be used to illustrate and manipulate symbolic numbers. Some studies (e.g., Osana, Adrien, & Duponsel, 2017) tested such methods in TD children and showed that children benefit from an instruction starting with manipulatives and pursuing with symbolic numbers in understanding of place-value concept and addition algorithm for example. However, it remains unclear if they would be helping for children with MLD, so that future studies are required.…”

Does Conceptual Transparency in Manipulatives Afford Place-Value Understanding in Children at Risk for Mathematics Learning Disabilities?

“…Because they need instructional support to base their comparisons on structural similarities (Richland et al, 2007;Vendetti et al, 2015), it stands to reason that the more physically similar the two systems are, the greater the likelihood they will abstract the common conceptual structure between them. With respect to manipulatives specifically, proportional manipulatives-those that made the relative sizes of the denominations transparent-were more beneficial for children's transfer of place-value concepts than objects that relied on color alone to distinguish the size of the denominations (Osana et al, 2018).…”