Son’s math test sparks internet outrage – Mind Your Decisions

Recently, a parent uploaded a son’s math test question to Reddit which has sparked an uproar on the internet.
A student solved 3 times 4 as 3 + 3 + 3 + 3 = 12. The teacher marked it wrong, saying that 3 times 4 means 4 + 4 + 4 = 12.
What the teacher did made no sense to many people, especially since multiplication is commutative and 3×4 = 4×3. So why did the teacher mark the answer wrong? I take a deeper dive into the question to reveal a bit of math history and a convention that perhaps many people were never taught.
Son’s math test sparks internet outrage
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“All will be well if you use your mind for your decisions, and mind only your decisions.” Since 2007, I have devoted my life to sharing the joy of game theory and mathematics. MindYourDecisions now has over 1,000 free articles with no ads thanks to community support! Help out and get early access to posts with a pledge on Patreon.
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Answer To 3 x 4 = Wrong
(Pretty much all posts are transcribed quickly after I make the videos for them–please let me know if there are any typos/errors and I will correct them, thanks).
Given the anger this question brought about, it would be easy for me to pander to the crowd that the question is stupid or the teacher is bad. But I think we should not mix our feelings into a fact fight.
As an outside observer, I just want to share a perspective on why the teacher gave this marking. I am not saying this Common Core standard is the best way to teach, or that the teacher is doing the best job. I am simply trying to focus on the facts.
Multiplication of whole numbers is motivated by a concept that a×b means a groups of b. This is a standard that is taught in American schools, and it has a history of thousands of years of mathematics. It does appear people have never heard of this standard so I do wish to provide some examples.
I looked up the official Common Core standard to find this:
“Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7.”
Therefore 3×4 is 3 groups of 4, which is 4 + 4 + 4.
This same concept is taught in the Khan Academy videos of multiplication as well:
This idea is nothing new. It is mentioned hundreds of years ago in Euler’s Elements of Algebra (1765) which explains that 3 × a means a + a + a so you want to repeatedly add the second number.
But the history extends even further. Euclid, the famous ancient Greek geometry, also published about number theory. A modern translation shows the definition of multiplication is: “A number is said to multiply a number when the latter is added as many times as there are units in the former.”
So 3 × 4 has the latter number (4) added as many times as the former (3), so we need 3 groups of 4, or 4 + 4 + 4.
So going back to the original problem.
You can see at the top there is a cropped out problem. The student has written:
3 + 3 + 3 + 3 = 12
4 × 3 = 12
It seems the previous problem is about 4 groups of 3, which is 3 + 3 + 3 + 3.
The next question asks for 3×4, which would be 3 groups of 4. But the student has written the same 3 + 3 + 3 + 3, which the teacher marked wrong and indicated should be 4 + 4 + 4.
Now you may still be angry about the exercise and find it all to be pointless. That is your right.
I personally would do whatever the teacher wants in class, but then I would learn all the interesting math concepts I wanted to outside of class.
References
Reddit
https://www.reddit.com/r/mildlyinfuriating/comments/1gq3j2j/sons_math_test/
askmath
https://www.reddit.com/r/askmath/comments/1gslqhc/arent_they_the_same/
theydidthemath
https://www.reddit.com/r/theydidthemath/comments/1gudc3j/requesti_have_gotten_into_an_argument_over_this/
Khan Academy – multiplication
https://www.khanacademy.org/math/cc-third-grade-math/intro-to-multiplication/imp-multiplication-intro/v/introduction-to-multiplication
https://www.khanacademy.org/math/cc-third-grade-math/intro-to-multiplication/imp-multiplication-intro/v/multiplication-as-repeated-addition
5×3 is wrong video
https://www.youtube.com/watch?v=FG0vtPa0UrM
Common Core Standards Math
https://corestandards.org/wp-content/uploads/2023/09/Math_Standards1.pdf
Multiplication
https://en.wikipedia.org/wiki/Multiplication
Euler Elements of Algebra originally published 1765
https://www.google.com/books/edition/Elements_of_Algebra/vV1NAQAAMAAJ?hl=en&gbpv=1&pg=PA9&printsec=frontcover
https://en.wikipedia.org/wiki/Leonhard_Euler
Euclid Elements Book VII (around 300 BCE)
http://aleph0.clarku.edu/~djoyce/elements/bookVII/defVII15.html
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