How do you teach maths?

[MelamineTeapot]

Hi, I'm looking for some recommendations for a good maths syllabus to use with my 9 year old DD who is home educated. She has (suspected) ASD and maths is her weakest academic area, around 2 ish years behind her peers e.g understands numbers but can only add single digits accurately with use of fingers/ objects, doesn't really 'get' number bonds yet.

To date we have just been using a few maths workbooks (KS1) bought from WHsmiths and some of her brother old Kumon worsheets, mainly just to get back her cofidence that she can do maths and we are now at the point where we no longer have a meltdown at the mere mention of the 'M' word. So are ready to start moving on with learning new concepts and trying to consolidate the knowledge she already has so it becomes more automatic (hopefully!)

She needs 1:1 teaching that is explicit, so all the usual baking, weighing, measuring things in everyday life that we do, don't really translate in her mind over to an equivalent sum in a different situation. We use some online programs too but I'd rather keep these as a supplement to, rather than instead of individual teaching.

I've recently read a blog where they used Saxon Math, which looked like it might be good, but its expensive and I worry that as its American we would have to skip chunks that are irrelevant (currency and imperial measurements) or risk confusing DD too much. Is there anything similar to this that anyone could recommend? Another program I have read about is Power of 2 (also Plus 1) which gets good reviews when used for Maths recovery or for use with children with Dyscalculia . Has anyone tried it before?

Thanks :)

I've no experience with any schemes/programmes etc and have only just started HE so can't really advise. Actually I'm looking forward to reading other suggestions!

But what I will say is that repetition is absolutely vital. The problem with workbooks (and I do use them so not against them) is that they tend to have maybe a couple of pages on a topic, and then you move on (it was this way of working that affected my DD at school too - they had to move on even if she hadn't 'got it') - this doesn't work with my DD, we have to go over things several gazillion times.

But also having physical representation of number is really helpful. You might not want to buy any but have a google for Numicon and cuisinaire rods. The way they create an 'image' for a number, and show how they fit together (eg put two fives together, it's the same as a ten) is fantastic and has helped my DCs loads. You can use stuff like lego too. I have found this more useful than counting individual objects IYSWIM.

Anyway I'm not really sure how we are going to approach maths, as we have only just started doing stuff, and I am trying to work out how to demonstrate how column addition works so she can add two digit numbers

Yes thats exactly the problem with workbooks (and the way DD's ex-school taught maths) that they don't spend long enough on one concept before moving on. She needs a LOT of repetition and to securely master one topic before moving onto the next. Otherwise its panic mode and we are back to square one. they have been useful in helping DD overcome her fear of the subject though (as long as we stick to ones that she finds easy) and DS absolutely loved them. He's a child (I was the same ) that only has to glance at a maths problem once and immediately just 'gets it' first time.

Something that uses lots of manipulatives would be great for DD too (she's a compulsive toucher) as long as it doesn't get too expensive. I quite happy to make my own or use substitutes as long as there's an explanation of how to use them really. we do already have cuisinaire rods, but some- the black and white ones- appear to be missing as I think they got made into magic wands when we went through the Harry Potter obsession phase DD's favourite are some little plastic teddy bears in bright colours, that came with a set of scales. She will often use these when counting above 10 (too many for fingers).

:o :o at the missing cuisenaire rods! That would so happen in our house!

Numicon really is fab, it is expensive though and we only have some thanks to a very generous friend. I think you could make your own out of thick card or something? It's the shape that's important.

There are some worksheet generators online where you can set the parameters to make sure they're the right level (eg times tables you could set which tables they know) - these could be good for the repetition so you don't have to buy loads of workbooks just to get enough questions.

I also quiz DCs at random times. Actually it's one thing I miss about the school run as we used to do it then! Just little questions - mostly ones I know she knows IYSWIM and then a couple that stretch her a bit.

I'd suggest you use a lot of physical representations of numbers, so make a collection of something (can be buttons, cubes, plastic teddies or whatever - schools use things called Diennes which come in units, tens and hundreds but TBH anything will do).

So for example 3 + 4 is 3 cubes plus 4 cubes (have her count them out) equals 7 cubes. Lots and lots of repetition. Once she is sound up to ten make a mat from paper with a tens column and a units column and do the same whilst laying the cubes out on the mat in the appropriate column (e.g. 7 cubes plus 4 cubes equals 11 cubes so 11 equals 1 in the tens column and 1 in the units column). Once she has cracked that add a hundreds column and so on.

Once she can do it in cubes try it with money too.

Also try a free online resource called Hit the Button. Children love it.

Sorry OP, my dd was very reluctant until recently so we did practical application rather than structured.
Baking - ratio, fractions, weights and measures, number games, coordinates, graphs, collecting data in our local park and supermarket.
Money, through shopping, time through bus timetables etc.

Would Kumon be useful for repetition? It's not very exciting but seems to be good for building confidence.

While not a syllabus, Conquer Maths works well for us (we use Galore Park books alongside it).

The topics are broken down well, and you can repeat them at will, and do them in any order. You can print off certificates, and keep track of work done/marks awarded online.

You also get years R to 12 included in one flat subscription rate ( so you can cover forgotten bits, or skip ahead), and they do a HE discount.

I think the kumon method of repetition is very useful and certainly would be more helpful than rushing through topics - however, having worked for them myself, I definitely wouldn't send my DCs there (not least due to the expense!) - but you can replicate the method at home by setting lots of worksheets (only once DD has grasped the actual concept obviously) which will be free except printing cost :)

I came to post about ConquerMaths too. Tiny lessons of 5 minutes followed by questions. Repeat as often as you need.
One of mine has LD and we take things slowly and go through them together.
Try some of the free lessons and if you like it email them for the home ed discount.

Thousands of worksheets/books here
If a child is reluctant at maths, worksheets can be scary, get a whiteboard (A3 or bigger) or a blackboard and just put up a few problems at a time. Alternatively use a big window, draw the curtain and write all over the outside of the window in board pen. Mistakes and wrong answers can be rubbed out quickly and only successes left as evidence. Beware of writing on fridges, they don't all come clean easily .
Practice times tables on walks to shops, extend your work space to take in the whole world. Let her work out how much 3 tins of baked beans/mushy peas cost.
Make paper cut outs of her hands to help with number bonds to 10. Include feet cut outs to get to 20. Your hands and feet will help her get to 40.
Lego brick, dice, dominos, pencils etc are all great for counting.

Imperial weights are good for cooking cakes.
With balance scales and the knowledge that an egg weighs 2oz, you can build a direct link to the two times tables. You need a couple of extra 2oz weights to get the concept really simple. Caution, playing with eggs causes the odd accident.

BBC bitesize and lots of other websites have online questions and games where you can go and practise without added cost and getting through reams of paper. If I were you, I'd go through the maths you'll likely cover each term and for each concept, find the right material to introduce it, a child friendly workbook to try out the wrok together and see how your DC manages with less and less help (you might need to print additional worksheets). Then line up specific online activities and games where they are using their new skill, as a reward for putting in the hard work.

At your daughter's age my ds used mainly Conquer but we supplemented with Maths Whizz, which your dd might like because it's very visual and brightly coloured and she might think of it as more of a game than proper Maths . Ds got a bit bored when working with the same method all the time so this helped break the monotony.

We also used Schofield and Sims books for practice of concepts - lots of repetition there.

Maths Whizz only went up to KS3 so from that point we stuck with Conquer and supplemented with CGP workbooks as he worked towards IGCSE. He had a tutor for Sciences and he helped out with some of the trickier concepts as the exams approached. He also used Khan Academy quite a bit, and still does, to keep refreshing the bits that go rusty with lack of use .

Have a look at MEP which is available free. You can buy the books though which probably work out cheaper than printing.
Saxon is brilliant for a child that struggles. Is kind of long winded. We adapted the routine of meeting/lesson quite a bit. We only used it for about a year because my son went from lacking in confidence and struggling with basics to having a lightbulb flash moment and started to find it far too slow. There were only a few things we skipped as too US-centred

The thing I liked about Saxon was you wouldn't do 20 sums on the same subject. You would introduce a concept in a lesson and then do a worksheet that included it but also stuff from previous lessons. So rather than practice something a lot one day and then move on, you practice for weeks to reinforce.
Needs a child who thrives on routine though.

Thanks for all the responses :) sorry I didn't come back sooner, been too busy out enjoying the lovely weather (please let it stay until after 9.30am on Friday)

The problem with solely using computer maths programs is, looking at a screen for too long tires DD out quite quickly because of the type of glasses she has to wear. So I'd rather keep that as a supplemental rather than the main focus for learning.

The more I read about Saxon I find I'm leaning towards trying it out. The way it is structured and slowly moves from 1 concept to the next and builds on knowledge in a logical way is definitely something I'm keen on. The scripts are useful too as I find maths naturally easy, so struggle a bit with having to explain things I just 'get' to someone who doesn't at all.

DD is definitely one who thrives on routine. She decided that Maths happens at 9.30 every morning (followed by drink/snack then reading- her 'easy' subject) and that is what we do! Hopefully she will be like your DS itsstillgood and suddenly not need it after a year, but no matter if she doesn't we are in this for the long run.

Its just the cost that's putting me off a little. also I'm not totally sure which grade to go for, I'm between 1 and 2. If I get 1 and its too easy, its an expensive mistake. But if I get 2 and its too hard, I risk scaring her off maths all over again. Then there's the manipulative kits (more expense) that I'm not sure how necessary they are. I think we already have some of the stuff and I could probably make or buy cheaper the other bits if we really need it all.

You don't need the manipulative kits. Buy what you need when you need. For the level we did (3) all we found we needed were some measuring cups and pattern blocks (already owned the second, love pattern blocks). I'd go for harder level as Saxon is set easier than most US grade levels. Worth asking on the HE selling pages if anyone is selling on their teachers manual.

I struggle with that too MT - maths is my first love :o so I find it hard to explain it to DD in a way she can understand!

I thought I would let you know how I taught dd maths.

I used the Letts revision guide and workbook. Also their mythical maths series. As well as this I used a Wilko's A4 graph paper book, coloured crayons and pencils. We also turned to Khan Academy when I could not understand the maths or when she just wanted to do some computer maths for a change. Senteacher also has some good printable resources.

We would work through 3 sections of the revision guide each time. (it is split into boxes and sometimes for easy sections we might do 2 at once). The first section would be what we had already done for the past 2 days, the second section we would have done the day before and the third section would be something new I was introducing. So we would progress through with one new section each day. I would have set her examples on the A4 pad prior to the lesson or would work through and scribble things for her to work out as we went. I would give her one or two examples to work through for each section on the A4 pad at the end and get her to do the "quick test" when we reached it.

She would then do work book by herself and would only ask for help if she were stuck. This may be after a break or for the lesson next day, depending on how time was going and how she was feeling. The pages she did in this would be from topics she had done a few days to a week earlier.

If she wanted to take things easier or just have a bit of a change (or I wanted a break) she would do some of her Khan Academy or Mythical Maths book.

What I found helps with lessons is:

Lots of colour and diagrams. Eg: "To get an improper fraction multiply the whole number by the denominator, so 2 1/5 becomes 11/5" How much more fun for a child to actually see 2 coloured circles divided into 5. Your drawing does not have to be perfect, you can ask the child to imagine you have drawn perfect, equally sized 5ths.

Pick interesting examples. Aliens on spaceships, dragons dividing up a sponge cake. Bearings can be taught as easily by a teddy bears' game of hide and seek as by a tanker driving into harbour.

Stop talking and start listening. Your child will learn so much more by doing the maths than by having it told to them. Give lots of examples for them to have a go at as you work through the sections. If your child gets stuck, it is so tempting to jump in with the answer. IME it is a balance between encouraging the child to work it out with a few hints and completely helping if the child is finding it difficult to the point of tediousness. Often a child will sit quietly because they are trying to work something out. They just need time, not hints. Judging what to do takes a lot of listening to the child.

Maths takes time. If you can't understand something the best option is often to walk away and come back later. The subconscious seems to work on it while you are doing something else. If introducing something difficult just tell the child you don't expect them to understand it this time, you are just telling them about it. It does not matter if the child does not understand it first time and it is surprising how much easier they learn if the anxiety of failing is taken away. Getting them to indicate with their thumb how well they are understanding it will help them see they are making progress and only understanding it a bit is success, not failure. Also, repeating it next day then in a few days helps it on its journey from short term to long term memory. Do not worry you are not explaining it right, as they will interpret this as their failing. You too can also "leave that bit" and come back to it next day.

Keep it fun. Stop as soon as the child is getting tired. It is no use just getting to the end of a section is your child really wants to stop. Pick a time when both of you are not tired. A child will return so much easier to a lesson they found fun last time.

This has turned into a bit of an essay, so I hope you find some of it useful. You can just take the bits you want and ignore the rest. Maths too comes fairly easily to me. so for me the challenge is finding clear and interesting ways to explain it. I often see maths problems as diagrams and drawing these out helps dd understand also.