Figuring it out

You remember Angel? The child who drove me to distraction over maths while homeschooled? Not so much because she couldn't do it, more that she wouldn't because she had convinced herself she couldn't.

Last week she announced "I'm working as hard as I can in maths, because I want to get moved up to the top set". Why? Because her friends are in the top set. Who says peer pressure is always a negative thing!

This week she showed me the project she had been working on in class. Hard to describe, but it was an investigation into the properties of numbers in a grid - working out general rules to find the difference between products of opposite corners in a number square taken from any part of variously sized number grids. (It truly is impossible to explain without seeing it. So why am I trying?) . She had done pages of immaculately neat - and correct - work, and had stuck only at the final hurdle of working out an overall general rule involving square size and grid size. Given that it was an algebraic formula involving two variables and squares I'm not surprised she stuck. I'm just amazed that she made it that far, happily. What a difference a few months makes!

She also informed me that having to work on maths for an hour at a time was OK ... "when you spend time practicing it, maths is a lot easier". Well yes, dear. I could have told you that. And have. Frequently. But for Angel, it has taken working alongside others to realise that yes, she can do maths, and yes, practice does help.

When not to do your homework ...

Checking Star's homework folder tonight, I found her maths 80% done.

Me: Oh! You've almost finished! When did you manage to do that?

Star: During art lesson ...

Oh. Right. So there we have one of the differences between school and homeschool. When you are homeschooled, your teacher notices if you do your maths when you are supposed to be doing art.

If you are curious about what they do in school, maths homework for Star is always these Delbert's SATs Practice Sheets. In English schools children have to sit SATs (standard assessment tests) in English, maths and science at age 11. As these are used to rate the performance of the school, most schools put a lot of emphasis on them - this means far too much working to the test, in my opinion, particularly when the test is still eighteen months away. However, the Delberts suit Star, as she is strong enough at maths to benefit from the mental exercise of constantly switching between topics. She started the term in one of the middle maths groups, where she was given just one Delbert sheet a week. After a few weeks she was moved up to the top group (out of six for her year) where she was given two Delberts at a time, and since half term this has changed to two twice a week. I can see that her versatility and speed of working has improved already, so for her they are working well.

Rosary arithmetic

After my arithmetical post yesterday I couldn't fail to notice this on Faith's blog, Dumb Ox Academy ...

Today, I happened to glance at my book, A Year with God. I was looking up anything that had to do with the rosary and found this little prayer:

“Dear Mother, may we through your Rosary ADD purity to the world, SUBTRACT evil from our lives, MULTIPLY good works for your Son, and DIVIDE your gifts and share them with others.”

We dedicated each decade we said this morning to either adding, subtracting, multiplying and dividing as the above prayer mentions. For the last decade we prayed to be EQUAL to the tasks that God gives us.

How neat!

Arithmetical adventures

Last week the girls' school ran a workshop for parents to explain how they teach arithmetic to children Star's age. I went. It was ... interesting. For context, I should explain that over the last ten years or so British schools have been encouraging children to find their own methods of calculation. I gather it hasn't worked (how surprising) and they are now teaching selected methods again. Most bear little resemblance to the traditional methods we were taught.

So, for those of you who may be curious, these are the methods that are supposed to produce the most right answers (no marks for efficiency or elegance!) ...

Addition
Straightforward addition in columns with carrying of tens, hundreds and so on.

Subtraction
"Borrowing" tens and hundreds is considered too confusing for this age group because of those horrid problems with zeros in the top line. Instead of subtracting, they are supposed to count on using a number line. So for example, 384 minus 129 could be calculated this way ... start with 129, add 1 (=130), add 70 (=200), add 100 (=300), add 84 (=384). Add together 1+70+100+84 to get 255. It doesn't look quite as bad shown graphically with a number line. Not quite.

Multiplication
For multiplication they use a grid system, which I can't show very well using blogger formatting. Once you see this written neatly, it does make sense as the same method can be used for simple multiplication, long multiplication, problems with decimals, algebraic problems - anything involving multiplication. To find 256 x 34, you would draw a grid with three columns and two rows. Across the top write 200, 50 and 6; down the side write 30 and 4. Then multiply each combination something like this (the asterisks are because blogger won't let me leave a space) ...

**** | 200 | 50 | 6
____________________
30 |6000 |1500|180
4 | 800 | 200 | 24

Then add the six numbers (6000+1500+180+800+200+24) to get the answer (8704)

Angel was taught last week to use this method to expand algebraic expressions such as (3a+2b)(2a-b). It works. You can see clearly what you are doing, and it helps to avoid getting into positive/negative tangles.

Division
Trial and error. Let's try 125 divided by 4 ... you could start with 10 fours. OK, 10x4=40. Not enough. How about 20x4? 80. Not enough. 30x4? 120. Ah! Getting close. Five more to go. How many fours in five? One with a remainder of one. So we have 30 fours add 1 four ... answer is 31 r1. Are you converted? Would you tackle division that way? No, me neither.

Eat your heart out Singapore. Why teach arithmetic the good old fashioned way when you can make it so much more ... um ... interesting.

Bubble Gum Maths

How I wish I had seen this post from Lissa at the Lilting House when she first posted it two years ago. I think it could have reduced Angel's mathematical pain significantly. I plan to stock up on chewing gum and bubble gum and try a scientific experiment when the girls start getting homework.

Personally, I suspect chocolate would have the best SSB effect.

Windows Vist-blah!!!!

I do not like it, Sam I am, I do not like ... Windows Vista. Grrr! It makes my new laptop - which has more memory than the old one - run like a snail. It does not like my software. My software does not like it.

On the other hand I do very much like Maths2XL - now known as Conquer Maths. Not only has it reduced the trauma resulting from the combination of Angel and maths (if not quite eliminated it), but they are really nice people. I could not get it to run on the new laptop and phoned their help line. "Ah!" said a very man with a very nice Geordie accent, "let me guess ... Windows Vista?" Got it in one! "Mmmm" says he, "we've had a number of those lately. Don't worry, we'll sort things out!" He kindly replaced my discounted end-of-line CD-Rom version with a free subscription to their online program, which I can use on any computer, including my nice new iMac. To make my day even better, Angel then whizzed happily through a lesson on fractions.

Maths manipulatives ... eek!

This morning I wanted to demonstrate division with remainders to Star and asked her to bring me five of something ... anything she liked. What did she bring? Eggs. Raw eggs ... or more precisely, four raw and one boiled. Why???? What was wrong with spoons ... or pencils ... or soft toys ... or Playmobil people ... or something normal.

Yes, we did use the eggs as a manipulative. And yes, they did stay in one piece ... but the combination of Star and raw eggs is not good for my peace of mind.

Moral ... when dealing with Star, always be specific. Giving her carte blanche is not a good idea.

Temperamental monster

Being curious about where visitors to my blog come from and go to, I couldn't resist signing up with MyBlogLog when I heard about it a while ago. I was mystified today as to why someone found their way to me through a Google search on "temperamental monster". It turned out to be a post on Angel and maths. Should have guessed. Still, I am delighted to report that despite the odd blip, the Maths 2XL CD-Rom is still proving a pretty good cure for temperamental-monsteritis. And that alleviates the associated disease of frustrated-motheritis. Phew!

Note: My Blog Log is free, so long as you are happy just to see the top ten hits to and from your blog. I may be curious, but not so much so that I'm prepared to pay for the privilege of having my curiosity satisfied!

What is it with maths?

I have been enjoying reading the responses to my homeschooling meme. One thing struck me. What is it about maths? Why is it that for so many people the resource they wish they hadn't bought is a particular maths curriculum?

The Lilting House - Right Start Math
Karen Edmisten - Singapore Math
Cirque de Moi and Adventures With Books - Saxon Math
Dumb Ox Academy - MathUSee
Myself - Miquon Maths
... and most thoroughly, A Room of My Own's "vast collection of math curricula"

Perhaps I should have answered the "one resource you wish existed" question with a foolproof maths curriculum, guaranteed to be a good fit for all families.

Next year: Maths

Angel: Maths 2XL (Key Stage 3)
Star: Finish My Pals Are Here 3, then either My Pals Are Here 4 or Maths Enhancement Programme Year 5
(UK Year 5 is equivalent to US / Singapore Grade 4)
Schedule: Angel - two lessons weekly; Star - daily (4 days per week)

Maths with Angel is my bugbear. Every time we begin a new maths topic, virtually without fail, a blank look spreads over her face and she becomes incapable of remembering how to add two and two (that may be an exaggeration, but only a slight one). This would be less frustrating if she truly struggled with maths. In fact, she has a good maths brain once she stops panicking enough to use it. When we come back to the new topic a day or so later the trauma miraculously disappears and she discovers she can do it after all. You would think that over time she would learn that it is never as bad as it looks at first sight, but no. Over the years I have tried everything I can think of to try to overcome this maths resistance - carrots, sticks, flexibility, inflexibility, dropping maths for a while, and so on - all without success. Despite occasional forays into other maths programmes Singapore Maths and then the newer Singapore My Pals Are Here books seemed to work best with Angel in terms of more progress for less trauma ... until last year we finally hit an impenetrable wall somewhere in My Pals Are Here 5. We switched to a UK maths scheme for a short time until, thanks to maths trauma combined with pregnancy debilitation, I simply gave up and we took a break from the dreaded subject. Faced with maths my normally pleasant daughter turns into a temperamental monster; faced with the a temperamental monster I turn into a bear ... and I just did not (do not!) want to go there any more.

This year I have found the wonder-programme that is going to solve all our maths problems. OK. Dream on. I have enough experience to know that wonder-programmes are never quite as wonderful in practice as they look. What I have found is something sufficiently different to be worth a try, and that just might be the programme that will get us out of the trauma / reluctance loop. Maths 2XL is a CD-Rom covering the entire UK Key Stage 3 (ages 11 to 14) maths curriculum in over 250 lessons. An Australian teacher presents each lesson with an audio-visual demonstration; the student then completes a practice worksheet, and is required to score 90% or more before moving on to the next lesson. The explanations are clear, and the combination of the computer with an audio-visual approach should fit Angel's learning style better than the traditional textbook and workbook. Best of all, someone else will be doing the teaching. A computerised someone who will be impervious to emotional meltdowns.

Star is generally strong at maths and likes to work independently. Until now she has used Singapore Maths and My Pals Are Here in a laid back way - sometimes working through it quickly, other times slowly, and often jumping between topics in a different order to the book. We are currently jumping around in My Pals Are Here 3A and 3B. Next year I want her to finish these books, then move on either to My Pals Are Here 4, or try the Maths Enhancement Programme. This is a maths curriculum being developed by a UK university, based on a Hungarian maths scheme. At the level she would be using it is available freely online, so I am tempted to at least test it out. The challenge this year is not so much mastering the maths concepts, but working on Star's concentration - Charlotte Mason's "habit of attention".