more discussion of maths

[~*heket*~]

So we've decided that maths as taught by schools is not only boring but time filling and grossly overrated (or I have anyways :p)

But what maths DO we actually use in daily life? And what maths are we likely to use in our careers? (there'll be lots of answers to that question, Bring it on!)

Personally I find timestables to be a useful thing (I learnt them in primary school). Adding and subtracting are useful (thanks to primary school again). Graph reading is useful for reading transport timetables, and food labels and surely other things too (a primary school lesson again). I'm confident that algebra has uses in it's early stages, but that it gets taken over board in highschool. Fractions and percentages ..... well percentages are helpful. But past halves, and quarters, you're unlikely to be adding fractions with different denominators in the real world aren't you? (but I learnt to do it in primary school) Measuring is useful for cooking (primary school).

Anything else you can think of that's useful? Or anything that's specific to a certain career path?

[Duchessa]

TBH, I can't think of any math that I learned at school that didn't help me understand the world around me in a more thorough way and therefore make it a more intricate and beautiful place. Even the stuff I found hard and boring and unnecessary, like calculus for instance, has proven to be far more useful than I ever would have imagined - it has allowed me to read about the world, to understand the world, to see beauty in the world in ways that I never would have been able to before.

I don't htink it is maths itself that is the problem, it is the stultifying disconnected way it is taught. Using nature, engineering and design of all varieties (from biota to bridges), to illustrate the beauty and wonder of maths can really make it absolutely fascinating.

[Kezia]

I think that the way to determine what maths our children "need" in the real world is to wait until they do need it. My son is learning times tables for fun (!) but he also uses very basic maths skills in everyday situations. Eg, division to work out how to share food or toys among a given number of children, addition to work out how many place settings to put on the table when we have visitors. Even fractions: the other day he figured out that if we have five people, the adults want twice as much pizza as the children, and B doesn't eat pizza, we'd need to cut it into 1/3 + 1/3 +1/6 +1/6. Granted this is all on a very basic level, but he's only five, and I think that if we don't let him learn that maths is horrible and boring, he will continue to be interested in it and want to do algebra, calculus or whatever when he's older and can use it. We will probably also try some "strewing", I think the main thing is not to require them to "do maths".


ETA: Remember I don't know any more than you do at this stage, so this is only my theory. Looking forward to input from the more experienced home school parents. :)

[Currawong]

Good idea for a thread! Ooh, there are so many things...Someone told me the other day that the seeds in sunflowers follow a certain type of maths pattern that goes like this (can't remember the name of it): 1, 2, 3, 5, 8, 13, 21...
Working in the garden opens up all sorts of maths possibilities. Problem is I can't think of any of the names of the maths concepts I'm thinking of. Hmmm...anyone heard of sin, cos, tan? Used to calculate distance and height. Also the concept that rectangles are made up of two triangles can be used to calculate how much dirt is in a slope (I'm currently doing this right now as we are about to excavate our front garden).

Oh, I need about two hours to think about this question and I don't have that right now! BBL

[esp]

Yes we use Maths en every aspect of our days. From as simple as calculating what we might spend pocket money on (or not) to working out just EXACTLY how old we are with fractions (yes it goes deeper than I am 6 and a half - there are 12ths!). Then there is cooking, gardening, driving (we are learning to estimate distances together because i am no good at it and the navman telling me how far to go is giving us all a better perception of distance).
I loved Duchessa's response actually.
Math is useful in art, in moving furniture in the house - building or buying furniture. For making toys or tools or jewellery.
Math's is useful for giving directions - working out the sale price on an item, paying bills. Even for making lists and tables, for mapping out how we will spend the day (each 24 hour period). I could go on forever really... Is it easier to say what we don't need math skills for?
Fractions you need for working out how to plot a garden, or how to draw a grid - and halves and quarters just wont cut it.

[gemi_ny]

Pythagoras's theorem is about the only thing I can remember from high school maths :lol (well maybe a little more, but not much! I wish I could remember how to do permutations & combinations for some strange reason!)

DH & I have both noticed how innumerate many teenagers in shops are these days. If they don't have a cash register in front of them, they can't calculate change.

When I was buying some glass a few weeks ago, the guy was trying to work out how much GST to add. He couldn't work out 10% of the ex GST price without a calculator (or me telling him before he pressed all the buttons on the calculator).

If this is what the school system is producing, home schoolers could surely do better with encouraging an enjoyment of learning maths.

[~*heket*~]

:lol I know! People are always amazed when I can calculate percentages off .... it's not that hard people! :blueroll

[Beatrice]

You're thinking of Fibonacci numbers, Currawong :)

[Quickening]

It is how they teach it. The times tables are rote learning over and over by memory. You may find that useful but how much real understanding do you have of the numbers? You're just remembering a formula. They've completely minced the path to adding and subtracting as well and the other stuff.

I still do not believe school is able to teach or give children a real understanding of maths and numbers because they can not make them truly relevant to the real world. Each child has their own pathways of understanding. School doesn't allow for that. They teach one way to do something, and if you do it differently and get the same answer, you're wrong.

We can learn basic maths better, quicker, easier and actually UNDERSTAND it. If we truly understood it then there wouldn't be a need for rote memorisation of the times table or complicated ways of working out large problems, requiring memorised formula to work out.


Look at this example from John Holt's Learning All The Time


2 + 3 = 5
5 - 2 = 3
3 + 2 = 5
5 - 3 = 2


Those four aren't four seperate facts to be memorised like school teaches. They're all ONE fact. They are simply four different ways of looking at one fact. It is not just a fact of maths to be memorised or taken on faith, it is a fact of nature which children can discover and rediscover and verify for themselves as many times as they need to. Take away the numbers and you are left with the very basic fact:


***** <-> *** **


This is developing the basic understanding of grouping. You can make the group of five look like the group of three and two, or two and three. Or you could make the group of two and three look like the group of five. A baby playing with blocks will begin to see that the difference between ***** and ** *** doesn't make any difference.

It helps us to develop a real understanding of the number 5. A property of the number 5 is 2 and 3. Another property is 4 and 1. Five can only be separated two ways into smaller numbers.

See how school mangles that now? They teach many different isolated facts. They do not teach basic understanding of numbers or facts. Children will retain better, learn, and actually UNDERSTAND if they are allowed to work it out for themselves.

As for the times table look at this


****** <-> *** ***

See how the number 6 has one fact but many different ways of looking at it, including multiplication and division?
3 + 3 = 6
6-3 = 3
6-2 = 4
4 + 2 = 6
5 + 1 = 6
1x6 = 6
2x3 = 6
3x2 = 6
6/2 = 3
6/3 = 2
1/2 x 6 = 3
6 x 1/2 = 3
2 is one third of 6
3 is one half of 6
2 and 3 are factors of 6

[Kezia]

Yes! That is exactly what my son is doing playing with numbers atm.

[Blossomtime]

This was always my problem with maths at school. I had so many arguments with teachers over how the maths was applied, only to be told that I needed to learn it to get into university :blueroll (umm yeah, cos calculus is exactly what they are looking for in an art folio)... My Mum helped me learn so much more about maths than anyone because she helped me apply it. She was an excellent teacher :) Wish we'd been homeschooled now :lol

In response to the question... yep gardening is great for maths and pattern. I've also needed maths, particularly fractions and percentages in my work as a textile designer to calculate repeat patterns, stitches and rows in sock design and color separations. Music can help with fractions and vice versa too :)

[gemi_ny]

They teach one way to do something, and if you do it differently and get the same answer, you're wrong.


Oh, that was such a HUGE issue for me at school! I could often get the right answer, but could not show the working out that THEY wanted - sometimes not at all. I knew the answer, but couldn't explain for the life of me how I got that result.

(OT - but I used to get frustrated when writing essays for other subjects, too - particularly for one English teacher. You're told to write something "in your own words" or "give your opinion", only to be told that your opinion is wrong. My sister got the same crap at Uni. Oh, how the issues around my own schooling are re-surfacing!)

[Kezia]

Snap! I had that problem too. Even in highschool, where I was the only student in the school to be described as "creative" in my maths report :rofl

[SandraDodd]

My husband thinks in patterns. He said he always has. I think in words, and sometimes in pictures. His pattern-thinking is visual, partly, maybe. But before we ever had children we had talked about those ways of organizing our thoughts and perceptions.

Genetics have been interesting with our kids. The one who's most like me (Kirby, the oldest) is very verbal but he's also fantastic with games and gaming (patterns). Marty, who is very much like his dad (physically and left handed and his hair and many other similarities) just understands how things go together (spatial) and is great with money.

Here's my collection of commentary on mathematics by many unschooling parents over the years: http://sandradodd.com/math

[Currawong]

:lol Sandra, I have to say, your site makes me salivate. I guess it's because there is SO MUCH juicy stuff in it, I just want to eat it all up at once!!!

ETA: I hope it's ok to quote this juicy little tidbit from that link in the previous post. The response to the question is by Linda Wyatt:

'I "make" my kids do their math...lying in a puddle of sunshine on the front room floor, wrap-ups in the recliner, Math Minute drills, etc. Right now, the two younger ones are playing dominos...MATH!'
'No, it's playing dominoes. Why not let it be that?
Why separate math out of everything all the time? Why do people do that?
The way to learn math naturally is to let it be a natural part of everything, like it is, and not make such a point of it all the time.
For example, what if, in writing and speaking, you had to stop and make a point of every time you used the letter "e"?
Look, I'm writing an e-mail... USING THE LETTER E!
How ridiculous is that?
Yet people do it to math all the time.'