A radical (and evidently controversial!) proposal that math content should be meaningful to kids
an example of a meaningless question grade 5 (age 11) homework:
"how many groups of 5/3 are there in 1?"
Asked by jscales4 • 01/13/2023 on brainly on 01/13/2023
Answered by shivishivangi1679, Textbook and Expert-Verified
the website claims that question/answer received 30 million likes, 9 loves, 10.8 thousand answers, and was given 4.9 stars out of 5
but i say it is an unhelpful and off-putting type of question for normal kids, for the following reasons:
(1) It is obviously untended as a cute arithmetic manipulation question, but that is precisely the kind of meaninglessness that should be strenuously avoided in a compulsory school curriculum, precisely because it explains nothing about anything tangible or useful or interesting to kids. Offhand, i cannot think of a single practical pre-high school example where a ratio of a ratio says anything useful about the real world. Google Gemini, scouring the internet, claims to have found 4 practical examples of ratios of ratios, 2 of which are simple ratios and not ratios of ratios, and one (ton-miles per gallon) which is a ratio of a product. The only one that is a ratio of ratios is an idealistic economic ratio (P/E)/G that actually has no useful real-world meaning because it omits the vital factor of inflation which must not be left out, so (P/E)/G is a completely nonsensical misinformational number.
(2) the question is poorly phrased by including the word "group", which introduces an anomaly because of the special meaning that word has in mathematics: A group is a set which is closed under a binary operator. If you don't know what that means, you won't know that you cannot have a set of size less than unity, other than zero, and a group is a special kind of set.
"what is 1 divided by 5/3?" is not as bad, because it does at least have an arithmetic answer - but a better question would be:
is 1 / (5 / 3) the same as 1/5/3 ?
if so, why? If not, why not?
brainly "Experts" added a nonsensical "Examples and Evidence" explanation:
"For example, if you have 1 whole pizza cut into groups of 5/3 slices, you would have 3/5 of a group available. This can help us visualize the division and the concept of how fractions work with whole numbers."
No it does not! There are zero slices of size 5/3 in a pizza of size 1!!. The pizza example is an example of integer arithmetic, because a slice is an object, not a quantity! Whoever wrote that example is either a fool or an AI.
"The method described follows the mathematical principle that dividing by a fraction is equivalent to multiplying by its reciprocal, which is a fundamental concept in arithmetic".
No it is not! It is not a fundamental concept, it is a derived relationship*. Division is the fundamental concept.*
