Sometimes you need "negativity" (though GP's was very mild) to dissuade people from bad ideas that will have negative consequences later. Prioritizing emotional state now over consequences later has worse consequences than reasoned negativity.
If this numeral and base system is used to supplement children's understanding of basic principles, that's fine. I think there were lessons on alternate bases, and there was plenty of interaction with cuisenaire rods, when I was in pre-k/kindergarten/1st and maybe 2nd grade. The emphasis placed on Kaktovic numerals and number system by the article, suggests something more than a supplement.
If teaching this system distracts at all from children building a core fluency in arabic numerals and base-10 arithmetic, it does them a great disservice, and makes more advanced math more challenging than it would otherwise be.
Arabic numerals and base 10 (which is also based on digits, but only hand-digits and not hand+feet digits) are not fundamentally better than anything else, but they are the primary system used to communicate concrete math, and as such have to be the primary system taught in school, or children suffer far more than any negativity you're worried about in these hackernews comments.
This is a written representation of the number system used in their native language. It's not intended to replace arabic numerals. It's a pedagogical tool to internalize and apply a system they will be using already.
> At first students would convert their assigned math problems into Kaktovik numerals to do calculations, but middle school math classes in Kaktovik began teaching the numerals in equal measure with their Hindu-Arabic counterparts in 1997. Bartley reports that after a year of the students working fluently in both systems, scores on standardized math exams jumped from below the 20th percentile to “significantly above” the national average.
It's not clear to me what that paragraph is saying. One interpretation is:
- They were using standardized textbooks with problems that used standard arabic numerals.
- Students converted to kaktovik numbers (in words, since they didn't have the symbols until 1994?) before working the problem, and back to arabic after solving it.
- The change in 1997 was to teach students to solve problems directly using arabic numerals in addition to being able to solve problems directly using newly-arrived kaktovik numerals
I realize that interpretation goes against the tone of the article, but I wouldn't put it past journalists to gloss over an inconvenient fact in an article that's intended to champion an alternative number representation system.
It would make a lot of sense that students would do better on (timed) standardized tests after they're fluent in arabic numerals, which was the entire point and concern in my earlier post. I don't care what else is taught to supplement basic arithmetic, or to reinforce concepts, but students have to be fluent in using arabic numerals for arithmetic, without conversion to some other system, or they will suffer.
By the article's own admission there, students were using kaktovik numerals before 1997, and their scores were lower, so whatever change was made in 1997 did not involve students learning kaktovik numerals when they didn't know about them before. Were they taught them better, so they understood abstract concepts in basic arithmetic better... or were they taught arabic numerals better, allowing them to use those numerals natively to solve problems? My speculation, as above, is the latter. There's nothing inherent about learning kaktovik numerals that would help on standardized tests.
If this numeral and base system is used to supplement children's understanding of basic principles, that's fine. I think there were lessons on alternate bases, and there was plenty of interaction with cuisenaire rods, when I was in pre-k/kindergarten/1st and maybe 2nd grade. The emphasis placed on Kaktovic numerals and number system by the article, suggests something more than a supplement.
If teaching this system distracts at all from children building a core fluency in arabic numerals and base-10 arithmetic, it does them a great disservice, and makes more advanced math more challenging than it would otherwise be.
Arabic numerals and base 10 (which is also based on digits, but only hand-digits and not hand+feet digits) are not fundamentally better than anything else, but they are the primary system used to communicate concrete math, and as such have to be the primary system taught in school, or children suffer far more than any negativity you're worried about in these hackernews comments.