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Karatsuba’s algorithm is a shining example of creative applications of simple concepts. I used to teach math to gifted elementary school students and used some

Karatsuba’s algorithm is a shining example of creative applications of simple concepts. I used to teach math to gifted elementary school students and used some problems from Japanese exams for the talented. I think the creativity and complexity of thought required to come up with this algorithm is about the same as some solutions to a harder problem in those exams. (The creativity required to solve them is significantly more than for American Math Competition, which typically involves difficult but quite conventional thinking.) [1] More countries should adopt these Japanese-style problems in their gifted education as well as simpler versions for normal students. They are a great training ground for creative problem solving, which has become increasingly essential for successful careers in most fields. PS. Hong Kong holds annual creative math problem solving competition for primary and secondary school students: https://www.edb.gov.hk/en/curriculum-development/major-level-of-edu/gifted/resources_and_support/competitions/local/cps.html https://www.edb.gov.hk/en/curriculum-development/major-level... There was also at least one international math competition for primary students in Asia-Pacific which focuses on creative math problem solving. [1] AMC problems and solutions https://artofproblemsolving.com/wiki/index.php/AMC_Problems_and_Solutions https://artofproblemsolving.com/wiki/index.php/AMC_Problems_...

brianpgordon 8y ago
Interesting; I thought that a common criticism of Japanese-style education was that it's based to a large extent on rote memorization, whereas the West tends to focus more on concepts and creative thinking. Can you speak to that? Is the conventional wisdom wrong, or am I just wrong about what the conventional wisdom is?
- jbay808 8y ago
  One anecdote: My North American math education seemed to focus on rote memorization, with little creative thinking at all. Did you have a different experience? Not sure how they teach math in Japan though.
  - 52-6F-62 8y ago
    Not necessarily related (and avoiding the attached political junk)— here in Ontario (Canada), the current government as ... strongly advocated... for going back to the "good old days" of rote memorization for the math curriculum versus modern discovery math methodology—ie: problem solving and creative thinking. There tend to be pillars of thought in NA.
    - chmln 8y ago
      Don't see what the current ON government has to do with the abhorrent state of math education here. It was just as bad under the previous governments
      - 52-6F-62 8y ago
        I was not getting into the political junk, as I said. Only pointing out that there are pillars of thought in NA who think that rote memorization as the sole method for learning mathematics was “the good old days” and is the only worthy method (with a practical example).
- nopinsight 8y ago
  I do not know much about Japanese education system in general (I used translated version of the problems) but from what I observe in their challenge math problems used for admission into selective schools and creative output in other industries like popular mangas, the culture clearly values creativity. The emphasis on skill mastery is most likely there and popularized in the US and globally by Kumon which might skew the perception somewhat. The component which I am unsure if they emphasize enough is the understanding of math concepts, which is possibly a strength of American math education relative to Asia from what I see from textbooks for training American teachers. I would appreciate more insight from others here.

brianpgordon 8y ago

Interesting; I thought that a common criticism of Japanese-style education was that it's based to a large extent on rote memorization, whereas the West tends to focus more on concepts and creative thinking. Can you speak to that? Is the conventional wisdom wrong, or am I just wrong about what the conventional wisdom is?

jbay808 8y ago
One anecdote: My North American math education seemed to focus on rote memorization, with little creative thinking at all. Did you have a different experience? Not sure how they teach math in Japan though.
- 52-6F-62 8y ago
  Not necessarily related (and avoiding the attached political junk)— here in Ontario (Canada), the current government as ... strongly advocated... for going back to the "good old days" of rote memorization for the math curriculum versus modern discovery math methodology—ie: problem solving and creative thinking. There tend to be pillars of thought in NA.
  - chmln 8y ago
    Don't see what the current ON government has to do with the abhorrent state of math education here. It was just as bad under the previous governments
    - 52-6F-62 8y ago
      I was not getting into the political junk, as I said. Only pointing out that there are pillars of thought in NA who think that rote memorization as the sole method for learning mathematics was “the good old days” and is the only worthy method (with a practical example).
nopinsight 8y ago
I do not know much about Japanese education system in general (I used translated version of the problems) but from what I observe in their challenge math problems used for admission into selective schools and creative output in other industries like popular mangas, the culture clearly values creativity. The emphasis on skill mastery is most likely there and popularized in the US and globally by Kumon which might skew the perception somewhat. The component which I am unsure if they emphasize enough is the understanding of math concepts, which is possibly a strength of American math education relative to Asia from what I see from textbooks for training American teachers. I would appreciate more insight from others here.