Original title: Exploring how understanding of the equals sign relates to additive and multiplicative equivalence performance beyond arithmetic fluency
Phoebe Mills, Sabrina Di Lonardo Burr, Lisa Jane Rodgers, Ella Denvir +2 · September 2026
Many students think the equals sign just means "find the answer." But it really means equivalenceTwo things that have the same value., showing that both sides of an equation have the exact same value. Researchers wanted to know if understanding this real meaning helps kids solve math problems, even if they are already fast at basic arithmetic. They tested 277 students in their final year of primary school. Almost all students recognized the equals sign, but most still saw it only as an instruction to calculate. However, students who understood that the symbol connects two expressions of equal value did much better on equivalence problems. This understanding boosted their performance in both addition and multiplication, even after accounting for their basic arithmetic speed and gender. It helped even more with multiplication, which seems harder for learners. Understanding the symbol really matters.
Imagine you have a balance scale. You put a pile of coins on one side and a pile of coins on the other. Most people just count the coins on each side and say 'that side has more.' But some people understand that the scale is balanced when the total value on each side is the same, even if the coins are different. Here, the equals sign is like the balance point. Most pupils see it as a signal to add up the coins on one side and write the total. But those who see it as a statement that both sides must have equal value do better on harder problems where both sides have different combinations of coins.
For years, math instruction focused on drilling arithmetic facts. This study shows that even after controlling for arithmetic fluency, a deeper understanding of the equals sign as a symbol of equivalence significantly boosts performance on equivalence problems, especially in multiplication. Teachers should explicitly teach the relational meaning of the equals sign to help students tackle more complex math.
The abstract doesn't say what the limitations are. It describes a correlational study with 277 pupils aged 11.4 years in their final year of primary school, so causality and generalizability to other ages or contexts are not established.
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Exploring how understanding of the equals sign relates to additive and multiplicative equivalence performance beyond arithmetic fluency — Phoebe Mills, Sabrina Di Lonardo Burr, Lisa Jane Rodgers et al. — Journal of experimental child psychology — doi:10.1016/j.jecp.2026.106652
Abstract licence: CC BY
Explanation generated by Synthesis from the abstract — it is not the original paper.