Why 4x8 and 6x8 are, surprisingly, some of the hardest times tables to remember
Certain multiplication facts like 4x8 and 6x8 are difficult for students due to associative interference. Educators can improve recall by spacing out related facts and gradually mixing them after initial learning.
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The article discusses why certain multiplication facts, specifically 4x8 and 6x8, are particularly challenging for students to remember. It highlights the concept of associative interference, where related knowledge can hinder recall. For example, when trying to remember 4x8, students may confuse it with similar facts like 4x6 or 3x8, leading to errors. Research indicates that a significant percentage of multiplication mistakes, potentially up to 90%, stem from this interference. The author suggests two pedagogical strategies to mitigate this issue: first, educators should avoid introducing related multiplication facts simultaneously to reduce cognitive load; second, once students have learned these facts in isolation, they should gradually mix them to help students differentiate between them. This approach mirrors weight training, where individuals start with manageable weights and progressively increase difficulty. By applying these strategies, educators can enhance students' ability to recall multiplication facts effectively.
- 4x8 and 6x8 are among the hardest multiplication facts for students.
- Associative interference can lead to confusion and errors in recalling multiplication facts.
- Over half of multiplication mistakes may be due to interference from related facts.
- Educators should space out the introduction of related multiplication facts to reduce cognitive load.
- Gradually mixing learned facts can help students distinguish between them and improve recall.
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9 commentsFor something like 6x8 I'll still almost immediately decompose it into either 2x(3x8) or 6x8 = 8x8 - 2x8 = 64 - 16. And if I did the latter, I'd second guess myself as to whether I'm going to make fence-post errors in the subtraction.
Even something basic like 5x7 I might mentally turn into 5x5 + 5 + 5 and just mentally step through the answer 25..30..35 on a number line. I get more error prone when incrementing by 7.
As an aside, it kind of blew my mind when I discovered that my wife seems to work a completely different way "in floating point". She'll often come out with a good answer for the mantissa but having lost track of the exponent. My mental calculations don't work this way at all.
https://www.youtube.com/watch?v=WLMHWtregmw (at 1:38).
Because 24 is a multiple fo 6 and 8 it's causing interference.
This seems believable, curious if there's hard data on this (that indeed 6x8 is the hardest and other numbers with shared multiples) but not curious enough to look it up.
6(8)
= 6(10 - 2)
= 60 - 12
= 60 - (10 + 2)
= 60 - 10 - 2
= 48- 6x8 = 48 : 4-6-8
- 7x8 = 56 : 5-6-7-8
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