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Just teach my kid the math

solipsys.co.uk

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Re: Just teach my kid the math

#41

Post by tomxor »

> We need to be sure not to insist on one approach when analyzing a problem

It's encouraging to hear from educators out there who understand communicating the value of problem solving and comprehension is more important than rigid adherence to methodology and procedure.

I remember the most useful aspect of my secondary school education (12-16yr) was learning how much I liked problem solving. However I came to this realisation through solving various simple math homework problems without following procedure (procedures which I remember finding particularly irritating for not explaining themselves) only to be lectured on how I had not followed the rules in spite of arriving at the correct solution and understanding the problem (albeit not well enough to figure out how the procedures worked).

My teachers did exactly the opposite of what the above quote is saying - they insisted on one approach, without explanation, and it totally alienated me from math at the time. Thankfully I was never a very "good student" and it didn't dissuade me from enjoying the problem solving aspect, but it did leave a lasting impression of "i'm not good at math".

Re: Just teach my kid the math

#42

Post by dorchadas »

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…

You want us to teach them best practice? Then we need to teach them maths, without relying on calculators. I teach secondary maths (specifically Algebra II), and they can't understand what I'm supposed to be teaching them because they have no clue how numbers work. Why don't they know this, if they're 15/16? Because they were given calculators at too young of an age and know "just push the button". What you're arguing is for a complete removal of teaching math, period. Also, why would you want to pull out a calculator every time when it's often quicker to do some mental calculations in your head? For instance, I've seen my students multiply by two in the calculator. Then be amazed when I can just say it.

Over-reliance on the calculators is already a huge issue, and we don't need to make it worse.

Re: Just teach my kid the math

#44

Post by dorchadas »

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 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 nothing done. This includes when they're homework was just to watch videos explaining problems they missed on a standardized test they took. Most just refused to watch the videos at home. It'd be great if they would watch the lectures and then be able to practice in the hour I see them daily, asking questions to clarify and such. But I can guarantee you it won't happen without a huge shift in the culture of education.

Re: Just teach my kid the math

#45

Post by dictum »

> For instance, our standard arithmetic algorithms are somewhat bizarre - they are the end result of a human process of codifying arithmetical thinking, designed with the extra goal of using as little of precious 17th-century ink as possible

I've long thought that this is partly why Mathematics are, paradoxically, at once terrifying and tedious for students. To learn a second language, you must immerse in it, using it as much as you can. Math has been attached to a language that is not used in daily life (except in a few situations, mostly very basic usage) and where the parallels to real usage feel contrived. If they weren't contrived, the question "what's the point of learning this" would get much clearer answers.

When I was a student, I found it curious how I had trouble expressing certain concepts in that language, but when working with the same concepts in a programming language, things were much clearer.

I can't offer a solution, but I think learning programming at a young age can help, though I'm personally against requiring it in classrooms, increasing the pressure on kids who are already exhausted with the rest of the curriculum.

Re: Just teach my kid the math

#46

Post by ghaff »

TheAdamAndChe wrote: post #24
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…

This is why I'm not opposed to the Common Core approach. It seems that they really emphasize math conceptualization and chunking instead of a formulaic process list that was used when I was a kid. Given the poor math scores in the US compared to other advanced countries, I really hope that this helps more younger people understand math.

These things all go in cycles though. People were complaining about the "new math" back in the 1960s. As Tom Lehrer put it "Understanding what you're doing is the important thing, rather than to get the right answer."

https://www.youtube.com/watch?v=wIWaJ0sy03g

https://en.wikipedia.org/wiki/New_Math

Re: Just teach my kid the math

#47

Post by garmaine »

ColinWright wrote: post #15
TheOtherHobbes wrote: post #12

Earlier quoted context omitted.

And techers are trying to teach how to make change? 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. Does independent research prove these approaches increase numeracy?

> 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 practicing multiplication tables and discovering that I could multiply numbers in long form too large to fit in my head and yet get the exact result. It is the power of the algorithm. My kids are entirely missing that in their common core education...

Re: Just teach my kid the math

#48

Post by zaphar »

yorwba wrote: post #40
empath75 wrote: post #38

Earlier quoted context omitted.

Learning by rote doesn’t teach you anything.

Spending lots of time on the treadmill won't make you a great soccer player, but still trains a basic skill useful for the game. Similarly, doing lots of arithmetic by hand isn't enough to solve all kinds of real-world problems, but it does help develop an intuition for numbers, which then helps with the problem-solving part.

Rote arithmetic may help you develop an intuition for numbers. It's hit or miss though and there are more effective and efficient methods than just doing a large volume of arithmetic. I believe the current trend in Math education is intended to take advantage of the more effective and efficient methods.

Your treadmill is a good example actually. Much of the exercise world has realized that just jogging for a long period of time while effective is also not the most efficient way to exercise. Instead mixing periods of hi intensity workout with periods of lower pace workout can allow you to get more value with less time from you routine.

Re: Just teach my kid the math

#49

Post by credit_guy »

empath75 wrote: post #38
credit_guy wrote: post #16

My problem with the "new math" is the lack of volume. Developing a sense for the numbers is best done by working more with numbers; in the "old math" kids had to do thousands of additions in the first and second grade, and developed ten times the sense of numbers compared to kids today. Theory is theory, but practice is practice. Just get over the addition and multiplication, please. That's not where the true math is…

Learning by rote doesn’t teach you anything.

Are you sure that it doesn't teach you anything? Somehow the students of "old math" were able to put a man on the Moon.
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