Anecdote: my then 5 year old and I would "practice counting by different numbers" on the walk to school. By the end of kindergarten, she could count by everything up to 12s. In 1st grade, we started reversing it and asking how many 4s in 48 and the like, and by the start of second grade, we were firmly in adding and subtracting fractions with different denominators (though, on paper at this point, no longer mental math).
She had (has?) a solid grasp on numeracy. I recall asking her why, around 7th grade, "0.999..." is equal to 1. I was prepared to show some fancy algebra and she one upped me when she said "well, 1/9 is 0.111... so 9/9 is one and 0.999...".
She never liked math though. She spurned calculus.
What's the point of teaching kids to memorize something that they can't apply? When I was a kid, schools taught multiplication tables in 2nd grade, when most kids are 7 years old. The difference in cognition between a 4 year old and 7 year old is insane.
I'd be surprised if there were any countries where multiplication was formally taught to pre-K students as part of the standard curriculum, but i'd love to be proven wrong.
I don't know if there are countries. I believe that if there actually was a unified accelerated math framework that was really emphasized starting age 4/5 then kids would be absolutely fantastic at math.
> What's the point ... ?
Paraphrasing what I said a comment above, you drill addition and subtraction until everyone is good at it, then you drill multiplication, then you do basic division, then you start introducing basic one variable algebra with "move plus to the other side to get minus" etc. The application is using algebra for word problems; formalism can come later.
In context I meant get really good at addition/subtraction starting pre K and then multiplication once +/- is mastered.
Though empirically, I don't know about age 4 but kindergarten is definitely not too young for learning up to 12*12. And once you figure out multiplication and eventually mental division, it's not too big of a leap to have one variable algebra with "move a plus to the other side to become minus" etc. The formalism can come later but it's fantastic to have some exposure to moving numbers and symbols around from an early age.
My sixth grader and first grader score in the 90+ %ile in mathematics and didn't come close to learning multiplication up to 12 in kindergarten. In fact, the topic isn't even covered until second grade at the earliest.
I think establishing a foundation of addition and subtraction takes far longer for children to master than you're considering, especially since there is evidence that children of this age appear to intuitively view numbers logarithmically rather than linearly [0].
I suppose you could take advantage of this by somehow prioritizing multiplication and division over addition and subtraction, but I think there's too much value in comprehension of linear numbers and addition/subtraction since that is the lion's share of interactions they will experience at that age.
On the other hand, if you're merely talking about abstracting multiplication and division into patterns, then I wholeheartedly agree with you, and there is evidence supporting this [1]. Although pattern identification is already part of kindergarten/1st grade curriculum here.
Ultimately, IMO the most important aspect of education in general is covered in the open letter linked to the OP:
> There cannot be a “one size fits all” approach to K-12 mathematical education.
My children have thrived with their current math curriculum, and I know some of their classmates have struggled in contrast. One size does not fit all in education, nor in many aspects of life.
Out of curiosity, is that a hunch or are you aware of any schools teaching multiplication tables even in Kindergarten? This used to be done in second grade when I was a kid.
I'm not aware of any schools teaching multiplication tables in kindergarten, but I did memorize the 9x9 table when I was in kindergarten because my older siblings' Big Kids Notebooks all had the times table on the back and it formed a rhyme/ditty in the local language. After it was explained to me that multiplication was repeated addition, that made perfect sense.
But don't ask me about division, my siblings/parents/whoever tried to explain it as "the opposite of multiplication", which was complete nonsensical gibberish and I didn't learn division until years later.
When I was in kindergarten, I used to do math booklets at home with my mom for fun. I learned basic multiplication sometime around then. 13 years later I majored in engineering.
So I'm not saying it can't be done by any 5 year olds, but it seems young to teach this to the majority of 5 year olds.
