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Whatever Happened to New Math? (1990)

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Re: Whatever Happened to New Math? (1990)

#61

Post by bpyne »

Minor49er wrote: post #42
hluska wrote: post #26

This is controversial (and shouldn’t be) but what if instead of spending so much time wondering why ‘Johnny’ can’t add, we spent that money and effort on making sure that Johnny was fed properly?? Countries with as much child poverty as Canada and the United States shouldn’t be surprised when their testing results don’t improve. This is pretty fucking basic science yet I’ve been fighting this battle for over twenty y…

Schools in the US serve nearly 12 million free breakfasts and over 20 million free lunches to children every day: https://schoolnutrition.org/AboutSchoolMeals/SchoolMealTrend...

I didn't notice if "participation" meant meals available or actually picked up by kids. Kids, particularly younger ones, who are in unstable households may not get to school in time to pick up what's available. Some districts have adapted by doing grab-and-go available anytime or serving meals in the classroom.

Re: Whatever Happened to New Math? (1990)

#62

Post by jjk166 »

mcphage wrote: post #47
mathgenius wrote: post #23

My grade two teacher demonstrated "venn diagrams" one day, it absolutely blew my mind. She had a bunch of coloured shapes scattered on the floor, then put one hoop over the triangles, another hoop over the red shapes, and then, what to do with the red triangles? My six-year-old brain loved it when she put one hoop overlapping the other one. And yet to this day I refuse to memorize the multiplication table. Rote learn…

> And yet to this day I refuse to memorize the multiplication table. > Rote learning is easier for the teacher: easier to teach, easier to mark. You're right, but there's still a good reason to memorize the multiplication table: more advanced math builds upon lower level arithmetic, and so the less time you have to spend working on the low level details, the more time you can spend focusing on the higher level unders…

Any math higher level than arithmetic doesn't actually require doing arithmetic.

If you want to find the hypotenuse of a triangle with side lengths A and B, the answer is sqrt(A^2 + B^2). It shouldn't matter how long it takes you to multiply A with itself because you shouldn't actually be doing that. Even if one insists on getting a numerical answer for say a word problem, you can use a calculator.

If knowing your times tables provides any benefit to learning higher level math, it's merely in mitigating the inefficiency of bad instruction.

Re: Whatever Happened to New Math? (1990)

#63

Post by jmlundberg »

jjk166 wrote: post #60
TeMPOraL wrote: post #35

Earlier quoted context omitted.

Nice, though I still prefer the trick for 9 that I was taught: 9: 10x, then subtract once.

Another: for X from 1 to 10, the digits of 9x will add to 9, and the leading digit will be x-1. You can do this visually by putting up all your fingers and putting down the Xth one - this splits your fingers into two groups, the first is the tens place digit while the second is the ones place digit.

They keep adding to nine. 137×9 = 1233 . 34457×9=310113. When it breaks down: 99x9=891 sums to 18, sums to 9.

Re: Whatever Happened to New Math? (1990)

#64

Post by TT3351 »

jmt_ wrote: post #28
hluska wrote: post #26

This is controversial (and shouldn’t be) but what if instead of spending so much time wondering why ‘Johnny’ can’t add, we spent that money and effort on making sure that Johnny was fed properly?? Countries with as much child poverty as Canada and the United States shouldn’t be surprised when their testing results don’t improve. This is pretty fucking basic science yet I’ve been fighting this battle for over twenty y…

This reminds me of Maslow's pyramid: https://en.wikipedia.org/wiki/Maslow%27s_hierarchy_of_needs If a child is struggling at the basic needs level of this pyramid then hitting the self fulfillment bit at the top is excruciatingly difficult

Of course I can't find it now no matter how hard I look, but there was an excellent blog post on here many months ago explaining how the pyramid of needs has become somewhat of a lazy shortcut people like to see on PowerPoint slides, which doesn't actually communicate useful information. It made its way into the wider discourse via educators, who were actually using the model incorrectly in the first place according to a few quotes from Maslow himself in the blog. It's a shame I couldn't find the article. Basically, it's an abstraction of needs that is just too good/simple to be true.

Re: Whatever Happened to New Math? (1990)

#65

Post by TT3351 »

Standout passage for me: "The villain, if there is one, might be the country’s penchant for the “quick fix.” Had Sputnik not flown, UICSM, SMSG, the Madison Project, and the other experimental programs might have evolved slowly and carefully into a national curriculum; as it was, they were shoved to center stage, lavishly financed, and told to perform a miracle overnight. They couldn’t, so the country passed on to the next educational fad (“back to basics”), labeled the previous one a failure, and blamed it for low test scores and a decline in skills."

Re: Whatever Happened to New Math? (1990)

#66

Post by jmlundberg »

soVeryTired wrote: post #27
mathgenius wrote: post #23

My grade two teacher demonstrated "venn diagrams" one day, it absolutely blew my mind. She had a bunch of coloured shapes scattered on the floor, then put one hoop over the triangles, another hoop over the red shapes, and then, what to do with the red triangles? My six-year-old brain loved it when she put one hoop overlapping the other one. And yet to this day I refuse to memorize the multiplication table. Rote learn…

I found myself thinking about multiplication tables in the shower today. I think you can get away with knowing the tables for 2, 3, and 7 really well. The rest is just tricks: 4: 2x twice 5: add a zero and divide by 2 6: a 3x followed by a 2x 8: 2x three times 9: 3x twice Beyond that, it’s repetition of those tricks, plus the distributive property of multiplication over addition.

Also (x+1)(x-1) = xx -1 helps if you know the squares 1x3 = 2x2-1, 2x4 = 3x3-1, 3x5 = 4x4-1, 4x6 = 5x5-1, 5x7 = 6x6-1, 6x8 = 7x7-1, 7x9 = 8x8-1, ...

Re: Whatever Happened to New Math? (1990)

#67

Post by Technically »

Minor49er wrote: post #42
hluska wrote: post #26

This is controversial (and shouldn’t be) but what if instead of spending so much time wondering why ‘Johnny’ can’t add, we spent that money and effort on making sure that Johnny was fed properly?? Countries with as much child poverty as Canada and the United States shouldn’t be surprised when their testing results don’t improve. This is pretty fucking basic science yet I’ve been fighting this battle for over twenty y…

Schools in the US serve nearly 12 million free breakfasts and over 20 million free lunches to children every day: https://schoolnutrition.org/AboutSchoolMeals/SchoolMealTrend...

Lunch debt is also used to separate children from parents: https://www.washingtonpost.com/education/2019/07/20/school-d...

The black panthers used to serve free breakfast to schoolkids for a reason.

Re: Whatever Happened to New Math? (1990)

#68

Post by emteycz »

jhardy54 wrote: post #59
harperlee wrote: post #54

Earlier quoted context omitted.

> children were still the poorest age group What... does that mean? I see how someone who cannot (legally) work yet can be poorer than other age groups, but I am sure that’s not what is meant. But is a child somehow deemed poorer than its caregivers? Or perhaps is the child as poor as its poorest caregiver? Or how does that fact appear?

I'm curious about this too. My best guess is that they're measuring household income and there are a lot of kids with low household incomes (more than adults with low household incomes, especially when you have more kids than adults in a household). /shrug

Poor households tend to have many kids, and the parent/s are often very young, sometimes even under 18. It's not unseen to have 32-year old parents living with their 16-year old daughter and her two babies, a 14-year old child and another ~12-year old child. Of course these are extremely poor compared to even most of low income households. Perhaps that's what was meant by the comment.

Re: Whatever Happened to New Math? (1990)

#69

Post by jjk166 »

pfortuny wrote: post #18
brazzy wrote: post #8

Earlier quoted context omitted.

> There's an endless search for an effortless way to learn math. Nonsense. There is a search for more effective ways to teach math. And there most definitely are differences in effectiveness, so no reason to believe that any given way is optimal. > Just like there is no way to get strong without hard work. There are, however, lots of ways to spend a lot of hard work for little gain.

Nonsense is such a strong word when experience shows otherwise. Learn playing! Gamify! But people DO NOT LIKE MATHS despite them needing it. I am a professor of the thing and am not ashamed to own it. It is what it is. Like cleanin your room, doing your bed or... shaving!

People love math. Look at youtube channels like 3Blue1Brown - 3 million subscribers, 160 million views, or Numberphile with 3.4 million subscribers and 511 million views. Millions of people of their own free will go out of their way to at least get an introduction to math concepts. Most of this isn't practical knowledge that they need, but rather abstract concepts they learn purely for fun. Think of what fraction of the population who would rather do puzzles instead of what they actually are supposed to be doing at the time. Strip away the tedium of rote arithmetic drills and people can't get enough of real math.

Saying people simply don't like math because their eyes glaze over in math class is like saying people don't like stories because they're bored by Great Expectations.

Re: Whatever Happened to New Math? (1990)

#70

Post by jjk166 »

jmlundberg wrote: post #63
jjk166 wrote: post #60

Earlier quoted context omitted.

Another: for X from 1 to 10, the digits of 9x will add to 9, and the leading digit will be x-1. You can do this visually by putting up all your fingers and putting down the Xth one - this splits your fingers into two groups, the first is the tens place digit while the second is the ones place digit.

They keep adding to nine. 137×9 = 1233 . 34457×9=310113. When it breaks down: 99x9=891 sums to 18, sums to 9.

99 on its own is also an example where it breaks down, which is why I stopped at 10, but yes all multiples of 9 in base 10 have digits summing to a multiple of 9.
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