How do you 'teach' maths?

[catnipkitty]

Been HEd my twin 6 and half yr olds since beginning of October and still finding our feet - I lurch between autonomous and structured hoping to find a happy medium and things seem to be working well so far.... I'm just not sure how to do the maths, whether to use workbooks/worksheets, or just incoporate numbers and sums etc into everyday stuff like cooking/baking, shopping etc. I do do this already, but is it enough?? How about things like long multiplication and division and all the other stuff I can vaguely remember doing at school? What do you do? Thanks in advance

C x

If you only remember the long multiplication and division of your school days vaguely, it sounds like it is not very useful to you in your daily life.

I think it can be handy to pay some attention to what you DO use all the time, and introduce that to your children as they are ready. Understanding money is an essential skill, for example. As an adult I need to have an idea of speeds and distances so I can work out how ling it might take me to walk or drive somewhere. The ability to estimate is tremendously useful.

These things will all arise in the course of your lives so you may not need to make a special effort.

More abstract computational skills are easier to pick up at an older age and especially if the child has a use for doing it. For example, when my dd was ten she was very keen on various moneymaking schemes and was doing complex calculations to do with importing toys. This involved exchange rates, import duties, shipping costs, the relative savings made by importing in bulk, etc.

My ds7 wants to decorate his room and get a new carpet. I have sat with him and taught him about areas and now he has to work out the area of his walls and floor so we can buy the paint and carpet. That's worked really well. We always do fractions when we have pizza. Weights and measures when baking. Lots of counting pocket money/anything he's lucky enough to find lying around. We sing times tables in the car. That was fun, I didn't realise we did so much!

You could try getting them to learn their times tables through chanting - not formally but whilst they're playing or through singing, times tables snap cards, and games etc. Also there are lots of good story books that introduce math concepts, like this or this one

As with so many things, it depends on what you and your children enjoy and how they learn but when DS came out of school aged 9, we played lots of number games and did practical stuff that involved maths - measuring for a vegetable plot, baking, shopping etc.

We did very little formal maths for a couple of years but when he decided he wanted to try a GCSE, he didn't find the course a problem. I agree that cards, songs, stories and games are a great way to learn the concepts.

Workbooks are fine imo if your children enjoy them but not necessary if they're not interested. I've also found that DS has never had the fear of failure around maths that I had when I was a child, which is a huge bonus, and I think it's because he's done it at his own pace and taken as much time as he needs to understand something through play.

For tables, we found an ancient Carol Vorderman video with songs and we used to sing them when we were out and about. I don't know if that's still around but there are lots of singalong tables - try Amazon.

(Something must have worked as he's now 17 and doing maths as one of his A levels!)

I really like Numicon and Cuisenaire rods. They are amazing resources! (and no I don't sell them :o) I use them in a yr1 class. My DD has some and she sees them as a toy, but through playing with them she comes up with her own 'theories' about numbers rather than me telling her IYSWIM?

They are expensive so try getting some 2nd hand if you're interested.

tbh at this age I'd keep it all experiential. Lots of practical stuff. If you want something a little more formal, I'd look at miquon which is very very hands on, using cuisinere rods. I don't tend to move into formal homeschooling with mine til they are around 7 1/2 or so, but my 6 year old loves miquon.

I think, unless you have serious prodigies on your hands, that you are probably a way away from needing to remember your long division! I'd have thought if you want to keep up with the schools (and no especial reason why you should) you'd need to start introducing algebra, long division and multiplication etc around the first year of secondary.

If I were you, I would get some workbooks for myself. You don't need to put them in front of the DC but they may guide you to what the DC should be becoming familiar with. (and if you are as old as me they will remind you of how to do some things)

I could do multiplication, long multiplication, short division and long division by age 9, maybe even fractions.

I think you need to think of maths as a language, piece of piss when you are young, much harder to understand the older you get.

We like Miquon math available in the uk from here

We have got lots of maths stuff to fiddle with (formally known as 'manipulatives') - have a look here
(their online 'basket' is rubbish and often crashes but the bargains can be good!)

I googled math manipulatives just now and found this website of online stuff to fiddle with :)
math playground
Loads of other maths games on that site too

It's taken me ages to remember the name of the things one of children liked for 'doing' maths, but I finally got there and remembered Cuisinaire Rods

Expensive-but worthwhile if you can get them secondhand.

If you are inclined towards letting your kids find their own feet without instruction, you may be interested in Peter Gray's account of an experiment in which some schoolchildren were taught no maths at all until the age of 11. They were then tested and it was found that, in the case of questions which could be answered by common sense and basic arithmetic, they were far ahead of their peers who had received maths instruction for the previous six years. In the case of questions which required rote computation, they were behind their peers.

The children were then given a year's instruction in maths and tested again. In the case of the "common-sense" problems they remained ahead of their peers. In the case of computational skills they had now caught up.

The argument is that explicit instruction in computation at an early age may actually hinder mathematical development rather than helping it, and that computational skills are easy to pick up later.

www.psychologytoday.com/blog/freedom-learn/201003/when-less-is-more-the-case-teaching-less-math-in-schools

Thank you for that Saracen, that's a really interesting link.

C x

oooh thanks for that Saracen. always nice to have ones laziness laissez-faire attitude supported by scholarship :)

Yes ommmward, and of course one benefit to being lazy laissez-faire with my kids' education is that I have more time on my hands to surf the net aimlessly research the validity of my methods than I would if I were hunting up curricula and marking papers.

It is possible that this explains why the people advocating a laissez-faire approach seem to post more links to research which support that approach, rather than because we are actually right.

On a more serious note, here is a video I like. Possibly more relevant to slightly older children than yours, Catnip, but worth thinking about: www.ted.com/talks/dan_meyer_math_curriculum_makeover.html

This maths teacher points out some of the bad habits into which traditional textbook learning can lead children. He observes, for example, that the neatly-packaged "problems" encountered in textbooks bear little resemblance to real-world situations:

"I believe in real life. Ask yourselves: what problem have you solved - ever - that was worth solving, where you knew all of the given information in advance, where you didn't have a surplus of information and you had to filter it out, or you didn't have insufficient information and you had to go find some?"

"[Einstein] talked about the formulation of problems as being so incredibly important, and yet in my practice, in the US here, we just GIVE problems to students, we don't involve them in the formulation of the problem."

Dan Meyer may be radical within the school system, but from a home ed perspective it was slightly sad to see him still foisting artificial "problems" on children (even if he has gone and filmed A Real Water Tank Being Filled for the benefit of his students) rather than advocating allowing them to go out into the world and find whichever questions are meaningful to them at the time. A home educated kid would be playing about with an actual water tank (or with something else which caught her interest), and not because someone had led her up to it and made her do so! She would be wondering whatever she was wondering, which would probably be quite different to what 29 other children might be wondering at that moment.

He describes his job this way: "I teach high school math. I sell a product to a market that doesn't want it but is forced by law to buy it" which is very different to how I experience my role as a home educator!

Oooh- fascinating stuff. Thank you ommmward and saracen- really interesting info (my DDs are only 4 and 2 but committed to HE already and looking for ideas). I'm thrilled that we've done absolutely no formal written maths but my elder DD uses basic mental addition and subtraction to solve problems when she comes across them and I'm completely convinced by the argument that this will just continue without being forced. Thank you so much for sharing your experience with the rest of us!