An Empathy Exercise
Three out of four 8th graders in America struggle in math. It’s not because 8th grade math itself is so difficult but because students’ knowledge is a House of Cards waiting to fall down. The shift from additive reasoning to multiplicative (3rd and 4th grades), then fractional (4th-6th), then proportional (5th-middle school) are key stumbling blocks that build on each other. When one isn’t secured, the future knowledge doesn’t stick.
This can be hard for adults to understand, whether that is someone who excelled in math their entire life or even an adult who didn’t, but forgets what it was like to try to learn it. This applies to teachers as well. If that’s you, then below are some problems to help you feel what it’s like to be those three out of four struggling students. It’s just multiplication after all, how hard can it be?
1. 43 x 25
The challenge is that this problem is in base-6, not base-10.
This might illustrate the frustrations students can feel with the invisible concepts in this procedure, such as place value and the distributive property.
See a base-6 calculator to help think outside of base-10 →2. DF x EG
This time let’s replace digits with letters to remove the familiarity we have with the number system. This problem is in base-7.
- A = 0
- B = 1
- C = 2
- D = 3
- E = 4
- F = 5
- G = 6
This setup removes even more of our built-in number sense, forcing us to rely purely on the rules of the system.
See a base-7 calculator to help think outside of base-10 →