# Why 4x8 and 6x8 Are, Perhaps Surprisingly, Some of the Hardest Multiplication Facts for Students to Remember

by Justin Skycak on

There's a cognitive principle behind this: associative interference, the phenomenon that conceptually related pieces of knowledge can interfere with each other's recall.

Cross-posted from here.

Let’s do a little experiment. I want you to take a guess at the top 4 multiplication facts (within $10 \times 10$) that students have the most trouble remembering.

Most people know that higher-number facts are typically harder than lower-number facts, but the 10s are really easy and the 9s follow a pattern that makes them fairly easy as well.

So, we arrive at the following guess: $8 \times 8$ is the hardest, then $7 \times 8,$ then maybe $7 \times 7$ tied with $6 \times 8.$

This is a decent guess. These are all some of the hardest facts. But when you look at the results, such as here, you maybe surprised by the following two observations:

• $6 \times 8$ is the hardest
• $4 \times 8$ is at least as hard as $7 \times 7$

What gives?

There’s actually a cognitive principle behind this: associative interference, the phenomenon that conceptually related pieces of knowledge can interfere with each other’s recall.

For instance, when recalling $4 \times 8,$ related facts like $\mathbf{4} \times 6 = \mathbf{24}$ and $3 \times \mathbf{8} = \mathbf{24}$ interfere with the spreading activation during the recall process and increase the likelihood of the error $4 \times 8 = 24.$

(Spreading activation is a method by which connections between information can be used to recall information in response to a stimulus. The stimulus activates some piece(s) of information, and the activity flows through connections to other pieces of information.)

Here’s a diagram that I made to illustrate:

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