Learning number symbols from multiple concrete representations carries a cost compared with consistent single representations, whether concrete or abstract¶

Claim · All claims
Evidence · 1 study · causal r2 · q3
Currency · newest study 2018 · not yet checked against its sources · not reviewed by a person

Subclaims¶

q3 i? Across three experiments, children learning from multiple concrete representations performed worse on symbolic comparison than those learning from a single consistent representation. → Amy Bennett 2018

Evidence¶

Amy Bennett 2018¶

Amy Bennett, Matthew Inglis and Camilla Gilmore. (2018). The Cost of Multiple Representations: Learning Number Symbols with Abstract and Concrete Representations. https://doi.org/10.1037/edu0000318

q3 · i? · causal · r2

The general discussion synthesises the three experiments: multiple concrete representations, the dominant format in children's number books, produced lower symbolic comparison accuracy than either consistent concrete or consistent abstract representations in each experiment. No summary effect size is printed.

"Overall, we found that there is a cost to multiple representations. Learning number symbols from multiple concrete representations – the approach adopted by the majority of children's number books (Ward et al., 2016) – seems to be less effective than learning from a consistent concrete representation or a consistent abstract representation"

Discussion¶

Learner Variables¶

• Number Sense — outcome: instruction changes it

Related Claims¶

• The abstract advantage stems from the use of multiple representations rather than concreteness itself: single concrete and abstract conditions did not differ, and both outperformed multiple concrete representations — possibly the same claim (merge candidate)
• In Experiment 1, abstract representations produced better symbol learning than multiple concrete representations, but only for children who completed the concrete condition first — related
• A systematic review argues that concrete materials aid mathematics and science learning when they are explicitly and gradually connected to the abstract symbols they represent — a broader claim this one bears on
• Concreteness fading studies in mathematics show mixed transfer results, with some studies favoring fading and others favoring generic symbols or reversed sequences — related