Why Does It Matter for Kids?

In traditional schooling, memorizing the multiplication table and calculating quickly were once top priorities. In Hans Christian Andersen’s The Snow Queen, there’s this scene where Kay tries to say the Lord’s Prayer but all he can think about is the multiplication table. That story shows how much weight people once put on memorizing math facts. These days, the focus has shifted. Instead of racing through facts, we want kids to understand what multiplication actually means and how it ties into daily life.

Research shows that using manipulatives when learning multiplication is crucial. Children who worked with blocks, counters, or tokens — compared to those who only received oral explanations and written drills — developed a much stronger grasp of multiplication and division. Even after moving beyond physical objects, these kids could carry their understanding into mental and written math.

Of course, objects alone don’t create understanding. Teachers help kids bridge that gap between hands-on actions and the math behind it. The move from concrete to abstract doesn’t happen all at once — it goes step by step from working with clearly structured objects (like 3 rows of 7 apples) through interaction with pictures and diagrams (like dot grids or a number line) to abstract reasoning (like 3 rows of 7 plus 4 rows of 7 equals 7 groups of 7). Objects should be simple and schematic — realistic toys like fancy cars can distract, while plain counters or squares keep the focus on math.

Multiplication, when kids see it as a neat way of counting, often shown with rectangular arrays, suddenly makes sense. They notice that adding 4 + 4 + 4 + 4 + 4 again and again can be written in a shorter way: 4 × 5. It looks almost obvious once they’ve seen it drawn. Research shows that this kind of early, concrete practice lays a strong foundation and makes the later move into abstract math much smoother. Their skills transfer to word problems, division, and even proportions.

Working with objects also builds a solid foundation for multiplicative thinking — the ability to reason with multiplication and division. Consider a simple example: if 4 oranges cost 13, then 8 oranges cost 26. Children who think in terms of multiplication see this immediately, without first breaking it down into the price of one orange. Multiplicative thinking helps kids manage money problems, notice patterns in the times table, and apply their knowledge to shapes, area, perimeter, or proportion questions involving fractions and percentages without relying on rote memory.