Knowledge of fractions and long division predicts long-term math success • Hacker News Board

Re: Knowledge of fractions and long division predicts long-term math success

#31

Post by yummyfajitas » Sun, Jun 17, 2012, 10:45 PM UTC

tokenadult wrote: post #29

thaumasiotes wrote: post #14

Earlier quoted context omitted.

>> An average United States student is at the bottom quartile level for Singapore, or from another point of view, a top quartile student in the United States is only at the level of an average student in Singapore. http://nces.ed.gov/pubs2009/2009001.pdf Looking at the US-flattering 4th grade scores, it appears that the Singapore average is 599, whereas the US Asian average is a pitiful 582. 8th grade sees the US suf…

I don't know how to get a breakdown of US distributional information by race, but your language is, at best, highly misleading. The last time I saw a comment of this nature in a thread on the subject of mathematics education in the United States and east Asia (both places I have lived), someone advised me not to feed the troll. But that was a different troll, and taking your comment, even where you incorrectly say "h…

...took the lazy way out and said that if "race" is taken into account, then the United States is second to none in provision of public education, which is simply a lie.

As is his norm, tokenadult ignores the data and vaguely appeals to authorities while attacking straw men.

Thaumasiotes didn't claim the US was #1, he merely pointed out that most of the gap Tokenadult cited is caused by student quality, not education policy. Nothing tokenadult has cited (here or elsewhere) addresses this point.

Tokenadult knows all this, but for ideological reasons will attempt to mislead people unfamiliar with the topic. He has already been made aware of the facts Thaumasiotes cited several times, and has repeatedly failed to address them: http://news.ycombinator.com/item?id=3315126 http://news.ycombinator.com/item?id=2463278 http://news.ycombinator.com/item?id=3321276

Re: Knowledge of fractions and long division predicts long-term math success

#32

Post by boboblong » Sun, Jun 17, 2012, 10:47 PM UTC

What we need to do is throw away the idea that smaller class sizes are always better, at least for mathematics. I have nothing against primary- and secondary-school teachers--god bless 'em--but we are letting their egos get in the way of educating our children. If they don't really understand the material themselves--and many of them don't--they need to admit it and let their kids go to someone who does understand the material when it comes time to teach math for the day.

I don't care if there are so few people who both understand math and can teach it to children (and are willing to take the job) that all of our math classes consist of 500 students. If that's the case, bring in bright highschoolers (who also understand the material) either as volunteers or part-time workers to act as "floaters". Let the class consist of one highly-paid individual with a math degree and passable teaching ability and half a dozen low-paid teenagers who understand fractions and are good with kids.

Of course, this would require many adult schoolteachers to admit that, when it comes to elementary math instruction, they are totally unqualified. That's a hard thing for a teacher--or, for that matter, an adult--to admit.

Re: Knowledge of fractions and long division predicts long-term math success

#33

Post by yuushi » Mon, Jun 18, 2012, 12:36 AM UTC

droithomme wrote: post #8

I've mentioned before here that I have taught college, high school, and elementary school. Also adult remedial education. The findings here are well known and have been for a long time, they come up all the time in the placement exams used in community colleges. Most people can do addition, subtraction and some multiplication. Fractions, long division, and everything that follows is a complete void for the majority o…

I disagree heavily with your argument. If the student is struggling with fractions and long division, I don't think you can blame schools "pandering to the slowest student" for such a problem. If they are struggling so much with basic concepts, I'd have to argue that they are the slow students.

> We don't see these results in adults in other countries because they don't burn out their students at such an early age.

If you've looked at education in other countries, I don't understand how you can say this. Many places push their students far harder than the US (for example, Singapore, Japan, South Korea). Rote memorization is pushed far harder as well. How is the material that is taught any less "useless" in the eyes of students in these countries?

I think culture definitely comes into play here. I'm not going to say incompetent teachers don't exist or that there isn't too much bureaucracy in schools; there clearly is, however, laying the blame entirely at their feet is being dishonest. I think culture and parental expectations play a larger part than many people want to admit.

Re: Knowledge of fractions and long division predicts long-term math success

#34

Post by ajuc » Mon, Jun 18, 2012, 5:55 AM UTC

droithomme wrote: post #8

I've mentioned before here that I have taught college, high school, and elementary school. Also adult remedial education. The findings here are well known and have been for a long time, they come up all the time in the placement exams used in community colleges. Most people can do addition, subtraction and some multiplication. Fractions, long division, and everything that follows is a complete void for the majority o…

> push fractions and long division (which, true, most elementary school teachers do not really understand)

Wow.. Really? Then how are they going to teach anything to the students except doing + - *? How about trigonometry, or even Tales Theorem? Hell, how about percentages? That's too hard and not usefull, too?

Is this generally accepted? For me it seems like the fact that parents would riot over?

Re: Knowledge of fractions and long division predicts long-term math success

#35

Post by ajuc » Mon, Jun 18, 2012, 6:04 AM UTC

kjhughes wrote: post #20

Performance on fractions and long division predicts math "success" because those tasks embody math education's emphasis on procedural skills over conceptual understanding. Tokenadult's comprehensive comment includes the 12/13 + 7/8 gem that sums up the problem. Kids see 12/13 + 7/8 and, if they're "good" at math, start turning the procedural crank they've been taught. (If they're "bad" at math, they freeze with a def…

A few years ago there was a long article about math education in USA by Russian math professor that immigrated. He blamed lack of "word problems" solved by intuition and guessing and substituting values at first, only then using algebra.

I can't find it now, but it showed exactly the same problems - math was just pattern mathing problem for most students - no real understanding.

Re: Knowledge of fractions and long division predicts long-term math success

#36

Post by SudarshanP » Mon, Jun 18, 2012, 12:02 PM UTC

Someone wrote: post #12

I haven't read the paper itself, but that text, to me, does not give a "clear message [...] that we need to improve instruction in long division and fractions" . The text talks about correlation between the two, but does not give any arguments for causation. Judging from the title of the paper ("Early Predictors of High School Mathematics Achievement"), neither does that paper.

People who derailed in 5th grade are probably unlikely to get back on track because education in the higher classes stands on the shoulders of the previous classes.

If it not a causation, this may also mean that "non motivated students" never care about math. Either in 5th grade or in high school or later.

Or maybe it is a combination of both. The article only shows correlation. But how can one study causation without destroying the futures of students?

Re: Knowledge of fractions and long division predicts long-term math success

#37

Post by Someone » Tue, Jun 19, 2012, 8:10 PM UTC

SudarshanP wrote: post #36

Someone wrote: post #12

I haven't read the paper itself, but that text, to me, does not give a "clear message [...] that we need to improve instruction in long division and fractions" . The text talks about correlation between the two, but does not give any arguments for causation. Judging from the title of the paper ("Early Predictors of High School Mathematics Achievement"), neither does that paper.

People who derailed in 5th grade are probably unlikely to get back on track because education in the higher classes stands on the shoulders of the previous classes. If it not a causation, this may also mean that "non motivated students" never care about math. Either in 5th grade or in high school or later. Or maybe it is a combination of both. The article only shows correlation. But how can one study causation withou…

Make two groups; give one of them some extra and/or supposedly improved math schooling. Check their math grades and, years later, their success in higher education. See how much they correlate.