What Are “Jigs”? Why Do Schools Use Them?

Using math manipulatives to build the problem 7 x 12 is not only a physical action. It also develops a mental bridge to the concept of how multiplication AND division are related. This relationship cannot be learned by a “jig” like memorizing the times table or doing 30 similar problems in a workbook. For schools, “jigs” are tools that help students score well on tests and help teachers conform to school mandates.

Here is an example of the difference between “jigs” and real learning. For regrouping in addition or subtraction, a child is told to add two numbers together in a column.

If that column’s total is more than 9, they are told to carry a digit over to the column on the left. If she adds 7 + 6 and gets 13, she writes the 3 down and “carries” the 1, putting it above the next column. She can do a whole worksheet of such problems and get 100% but cannot explain why or how it works!  

Her brain needs to understand that underlying the “jig” is a concept called place value: A child is not really carrying a “1” to the next column, the child is really adding one “10” to it.

If you like math, it might be obvious to you. But you are not a second or third grader learning what numbers mean in the real world. And those meanings must be as concrete as possible. A poor “concrete foundation” can create middle school headaches and high school dropouts.

Failed concrete understanding leads to a gap in abstract thinking.  “Jigs” are not bad, they just do not bridge the gap. A “jig” gets problems right but can kick the abstract thinking challenge down the road where the deficit is even more difficult to overcome.