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Just teach my kid the math

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Re: Just teach my kid the math

#51

Post by sethammons »

boblivion wrote: post #21
ColinWright wrote: post #11

Earlier quoted context omitted.

"Homework" is supposed to be practising skills they have already learned so they can make it more fluent, and have to concentrate on it less when they come to the next thing to learn. Learning things is done with the teacher there to help anticipate, identify, and correct misconceptions. If you want the parent to help with the homework, the parent will have to know the material they want to help with. In maths, that'…

As someone not from the U.S. I wonder, what does "outdated" mean? Can you give a simple example - e.g. comparison - what would be "math back then" and "math nowadays". Because to me math was always just math especially if it comes to numbers.

Here is one potential example from a number of years back. Maybe it counts as "back then." My daughter's algebra teacher was teaching the laws of exponents. When faced with "what is x^0," the teacher gave axiomatic reasoning of "x^0 is always 1. Nobody knows why, you just have to memorize it." When I confronted him about it, his response was along the lines of "we don't have time to get into concepts and teach reasons; we need students to memorize and move on to the next thing for the state tests."

More and more, educators in the US are realizing that memorizing things just wont work. You get students who can't recall if x^0 is 0, 1, or x, and they lack the mental model to figure out the answer. Math nowadays strives to give students the mental models to derive answers. I would hope today's students to go "I know x^3 is xxx, and x^2 is xx, so x^1 is x, so the pattern is divide by x, so x^0 must by x/x or 1".

This applies to even more common things. Many of us who did well in math did so because we saw patterns and relationships. Now educators are striving to help students see those patterns and relationships.

In similar fashion, and to address a concern a few comments up, many older US students (and adults for that matter) can't figure out percents. They were taught a formula of [base * percent / 100] and then they have to unpack the term "percent," where they remember there was something divided by 100, and then they find themselves all mixed up because of failed memorization methods. I can recall in grade school and high school, many kids did not realize they could find 20% of something by multiplying it by 0.2. They first would multiply by 20, then divide by 100, and when I told them they could just combine those two steps, their mental model would break. It got even worse if you tried to tell them "what is 1/10th of the item? now double that, and you'll have 20%".

To summarize, "outdated" vs "nowadays," the students would try to add algorithmic steps to their mental tool box that work in very specific situations, and now, many educators are trying to help children internalize concepts.

[edit, formatting. I wanted the xxx and xx to originally have an asterisk between them to show multiplication, but then everything went italic. Why does formatting have to be such a pain?]

Re: Just teach my kid the math

#52

Post by sethammons »

michaelchisari wrote: post #39
jonsen wrote: post #8

Earlier quoted context omitted.

... makes perfect sense in the context of what the teachers are trying to teach ... What's the point with home work then? School takes the best part of a childs day, and when they don't make it through, the parents can finish with a tired child.

I don't mind this new way of teaching math, but on this note, I liked what Sal Khan had to say about flipping the process for school and homework. He proposed that students should watch lectures at home with a few problems for familiarity, and that classroom time should be spent working through problems in a guided environment. This allows students to pause, rewind, rewatch, etc. the lectures and move at their own pa…

As a former math teacher, I would absolutely love this. I've been a fan of flipping the model ever since I first heard about it years ago from something on Khan Academy.

Re: Just teach my kid the math

#53

Post by gus_massa »

bfung wrote: post #19

Is there a common core method to teach arithmetic in different a different base, like 8 or 16? The "old way" algorithm still works with different bases, you just change extend or truncate the rule for when to carry. Easy to teach your kid hexadecimal arithmetic using old way, like how my parents taught me in like grade 4 or 5 - and now I program for a living, haha

If you ignore the "anchor to 5s" part that is ridiculous, the other parts work in other bases too.

  D3-A7 = (D3-B0) + (B0-A7) = (D3-B0) + 9
        = (D3-D0) + (D0-B0) + 9 = (D3-D0) + 20 + 9
        = (D3-D0) + 20 + 9 = 3 + 20 + 9 = 2C
(I swear that I didn't cheat to make the calculation and I made it in the "string" representation of the hexadecimal form, without looking at the decimal form.)

In hexadecimal can try to anchor to 8s, it should work. Perhaps anchoring to 4s may be better?

[Disclaimer: I don't like it, but the method to do the calculation works in other bases.]

Re: Just teach my kid the math

#54

Post by sethammons »

dorchadas wrote: post #44
michaelchisari wrote: post #39

Earlier quoted context omitted.

I don't mind this new way of teaching math, but on this note, I liked what Sal Khan had to say about flipping the process for school and homework. He proposed that students should watch lectures at home with a few problems for familiarity, and that classroom time should be spent working through problems in a guided environment. This allows students to pause, rewind, rewatch, etc. the lectures and move at their own pa…

As a math teacher (Algebra II), I think this would be great. The problem is that most of my students won't go home and watch the videos. Either because they can't (lack of internet access, have to work to help support family, etc.) or are just lazy and won't. I've had to quit giving homework, even to the upper level classes, because nobody would do it. They'd just come in the next day and make excuses and have nothin…

As a former inner city math teacher, I feel you. Getting students to do _anything_ outside the classroom was practically impossible. What worked for me for homework for a little while was having the students do 5 push ups for each day they missed homework in a row. I suddenly was getting 90%+ participation on students completing their homework! It was fantastic until someone told the VP, and the VP asked me if I was actually doing that, whereby they informed me that it was corporal punishment and absolutely against the rules. I could rant about that for a bit, but I'm sure you can guess what happened after the pushups stopped: homework stopped.

As for the shift needed in the culture of education, I totally agree. There needs to be a shift in accountability for the students, their families, and for schools. While there were parents who hoped their kids would do well at the school where I taught, there was a pervasive home attitude of school will get you nowhere. Many of the kids had no role models in their life where they could see any value to education. One VP I knew, in a neighboring district, married into a poorer latino family. They valued hard work, but only really understood hard manual labor type efforts. He was constantly hounded as he was going through schooling by them. "Why are you wasting this time at school? Why are you not doing more to provide for my daughter? Go get a real job." After finally becoming a teacher and then a VP and making more money than any other member of the family he married into, they started to see how education could be an investment. I don't know how you do that on a scale where the majority of socio-economically depressed families and communities can be exposed to the value of education.

Re: Just teach my kid the math

#55

Post by sethammons »

yorwba wrote: post #36
lsc wrote: post #14

Earlier quoted context omitted.

I personally find Serge Lang's "Basic Mathematics" to be super useful in explaining the "why" of a particular formula in pre-college level math, as most books at my current level just seem to say "memorize this" He has an explanation of why x^0 is 1 and not 0 that doesn't involve calculus, for instance.

What would be an explanation that involves calculus? The only one I know is that x^(a+b) = x^a * x^b holds for positive a and b, and to uphold that pattern, it's necessary that x^0 = 1, x^-1 = 1/x and so on. For me, all of that was covered long before calculus.

I actually referred to a different pattern to help knowing what x^0 is above. Not from calc, but just a different way than yours. If you start with x^3, x^2, x^1, x^0, x^-1, x^-2, and expand the forms, you get xxx, xx, x, ... where the pattern is each step divides by x. So x/x = 1 is the next, and 1/x is the next, and 1/xx is the next, ...

Re: Just teach my kid the math

#56

Post by JeremyBanks »

garmaine wrote: post #47
ColinWright wrote: post #15

Earlier quoted context omitted.

> And teachers are trying to teach how to make change? No, the "making change" comment is an example of how these techniques of thinking about numbers do turn up in real life. > I understand “anchoring to fives and tens” but I don’t understand why anyone thinks it’s a good way to do anything except confuse kids. It's a part of a broader strategy to talk about the structure of numbers and the operations on them. > Doe…

I’m a parent and I object not because I don’t understand it — it’s not too difficult to pick up — but because it completely misses the why of math. Being able to mentally estimate numbers or do simple arithmetic is a good skill, but having universal algorithms for solving problems and describing the universe is really what math is more about. I can trace my trajectory into computer science all the way back to practic…

Traditional elementary math teaches you algorithms without discussing why they work or the cases where they break down. They seemed arbitrary and untrustworthy. I'm glad that worked out for you, but I don't think many students get the same value.

Re: Just teach my kid the math

#57

Post by jfaucett »

meuk wrote: post #32
mratzloff wrote: post #23

When calculating in my head or on paper, I value quick estimations moving to greater refinement. Common Core math seems somewhat similar to this. I never subtract, only add up from low to high. If the two numbers have the same number of differing digits, I move from most significant digit to least: 73-57=10+6. If they cross a round number threshold greater than 10s, I get to a convenient base first: 2018-1995=5+18; 1…

Well, it is super useful do be able to do exact arithmetic. For example, to not get scammed when you buy anything, or share a bill. I've seen American university students who don't know how to compute a percentage of a given amount - so I'm not very impressed by common core math to be honest. That being said, it's probably a cultural thing too. I noticed that in the USA (at least in California?) it is customary to ex…

> When I go to the grocery store, I usually keep a sum of the price in my head while I pick products. That way I'll know if something is off at the counter.

I do the same thing, but it does depend on how much I'm shopping. If its big for the whole family I keep a rounded tally in my head, and use that sum to determine whether or not I look at the actual receipt to see if something was wrong. If on the other hand I'm buying say less than 15 items then I'll keep up with the actual to the cent sums when I'm paying in cash.

You get a weird look sometimes when you get to the counter, they say 23.45 and you hand them the money immediately.

I've done this ever since I can remember, but growing up in the USA you just had the added step that you needed to know what the sales tax rate was for the area you were currently in, and if you didn't know it then I'd just use a default rate of 8%.

Re: Just teach my kid the math

#58

Post by sethammons »

nitwit005 wrote: post #18

What seems to happen in practice is the parents end up asking the teachers why they're teaching that way, and the teachers can't actually explain it. Obviously, the parents don't walk away impressed.

When I got my teaching credential for high school math, it became apparent and was openly recognized that many grade school level teachers choose that level of certification because they are, themselves, afraid of "math expected at the high school level." We expect many teachers who are math-phobic to lay down the foundational layers of mathematics with our kids. They cling to whatever the pre-made material and lessons are in the texts and often don't know why things are to be taught the way the texts want. Scary stuff.

Re: Just teach my kid the math

#59

Post by sethammons »

maximexx wrote: post #17

There is a reason why most people hate math. IMAO the current system of teaching math is ancient and above all deprecated. We should not punish our kids with it. I mean, what's the point of drilling stupid sums if you'll hardly ever need it in your life? I think it is totally stupid and irresponsible if anyone does calculations without a calculator for almost any application, not excluding: store checkout, health car…

The idea is to give them "number sense." Kids trained on calculators don't bat an eye at 12+6=72. "The calculator said so." "What do you mean I pressed the wrong button?"

Re: Just teach my kid the math

#60

Post by contravariant »

ColinWright wrote: post #3
noir_lord wrote: post #2

I did A-level maths, I've programmed computers for 30 years since I was a kid. Ive implanted algorithms to calculate solar irradiance varying by orientation, inclination and latitude. I don't understand what my 7yo stepsons maths homework is asking him to do/learn. It's just weird and I'm not sure he always does either, it teaches the how (weirdly) but never the why, I've started teaching him how to understand the pr…

My (very limited) experience of more recent homework is that it makes perfect sense in the context of what the teachers are trying to teach, but no sense out of context to people who learned their maths decades ago. If you'd care to send me a photo of an example of the homework then I can try to give you some context and understanding. My contact details can be derived from my HN profile. I might be a little slow to…

It's a bit weird when your mathematics education enables you to understand a book written several millennia ago, but not homework written several decades later.
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