More Abacus Madness

I've been tinkering with ideas for an abacus that hybridises the Montessori place value colours with the RightStart Math Al Abacus... I liked the idea that Joan Cotter uses the reverse side of her Al Abacus for trading exercises with twenty beads for each place value, enabling you to demonstrate trading occuring after the second addend. So here's my hybrid:

But now I'm not so sure that I like the idea of twenty beads per place... could it be confusing?

I shall have to play with it for a while.

Montessori Large Bead Frame/Alabacus hybrid

Today I was using the excellent Montessori Math album from Cultivating Dharma to introduce the Large bead frame lessons. I don't own a Montessori Large Bead frame, so I adapted the Alabacus from RightStart Math. I'd like to make my own large bead frame based on both. Perhaps with the unit beads as 5 dark green, 5 pale green, and the tens beads as 5 dark blue, 5 light blue, etc.,(corresponding to the Montessori colouring, but retaining the pattern of the Alabacus.)

 The bead frame paper was a download also from Cultivating Dharma.
To emphasise the number families (thousands, millions and so on) I adapted a Waldorf based idea on teaching place value from Little Nature Nest, and adapted a math story called "Infinity Street" but changed it to "Infinity Forest".

These are some pictures from previous lessons, before introducing the Bead frame:

Waldorf Grade 3: Measurement and the Wheel of the Year

I can't say I slavishly follow any curriculum, but cherry pick what suits. Year 3 of the Waldorf curriculum is my basic skeleton, though. Inspired by a post on Little Nature Nest's Blog, we created a Wheel of the Year for the Southern Hemisphere that demonstrates the change of seasons as caused by the tilt of the earth in relation to the sun:

 Now I had been in a bit of a quandong about when exactly, say, Autumn starts in Australia. Friends said, "Autumn starts on the first of March". But I've used the Autumn Equinox, the 21st March (as my reference, I'm using the Moon Diary by Shekhinah Morgan and Jude Baderle). If I have my facts right, it's after this point that the days start getting shorter for us down under...

A new year, a new approach: Waldorf and Montessori homeschooling

I've been attracted to Waldorf schooling methods for some time. I've just delved into basic Montessori methods and I find both to have elements that are not just brilliant but compatible.

I will give maths as one example of what we've incorporated this year:
Maths and the Abacus
We have used RightStart math for some time, in fact we have all their material and manipulatives for grades up to 4. RightStart is Montessori inspired, as I understand it. It is a brilliant program, and I cannot rave about their Alabacus enough. It leaves cuisenaire rods and even Montessori beads in the dust: numbers are not just amounts of a certain colour—you can immediately see that 7 is not just 7 beads, it is 5 and 2 beads. This makes such a difference for all kinds of maths skills, especially mental math. For those of a Montessori background, the difference is explained well here.
I remember cuisenaire rods when I was in kindergarten: pretty coloured wooden rods, but what the heck did it have to do with math?? I had no idea. Seven might have been a length of orange or pink wood, but it had no segments in it to show those 7 units. It was just a length of colour. It didn't designate quantity, unless compared with other arbitrarily coloured rods.
I recently enjoyed a lesson with Baby No.2 where I incorporated a gigantic set of math blocks / rods by the German company, Grimm's Speil & Holz Design. This is my first Spiel & Holz purchase, but won't be my last. These are the world's best wooden blocks. They differ from the regular cuisenaire rods (and Montessori coloured beads) in that they follow a logical rainbow sequence, rather than an arbitrary colour order. We had much fun discovering visually how many ways there are to make ten (and other numbers). Did you know 1 + 2 + 3 + 4 = 10? I hadn't thought about it till today.
BUT we did find it frustrating that there were no segments in the rods, to help specify their unit amount. I suppose that with time, a length of pale green would come to be understood as 3, but I don't see 3 units in that piece of wood.
So, with the above in mind, I've hit on an idea. I'm going to make my own number rods out of sawn-up Base Ten (or MAB) ten-unit blocks. They are segmented, so the units are evident. I will colour them to match the AlAbacus; for example, I will have a rod of 7 which will be 5 units blue, two yellow. And so on. Then, I'll use these in the same manner as Montessori coloured beads are used; I have the Checkerboard in mind, in particular. I'll post pictures of these as soon as they are to hand.

Progress by Degrees

Today we had a great day! Baby No.1 and I sat down with "What your 5th Grader Should Know", and turned to the History and Geography Section. I decided we'd discuss reference points on maps and atlases, including latitude and longitude and which was which and how to remember that. We talked about how these points are measured in degrees, and we use degrees to measure temperature and angles, too. Latitude always comes first, and is like a waistband around the earth, you measure it north and south of that waistband. Longitude comes next, and you can remember it easily as running around the earth north to south (Long-itude; like hair is long and it runs downwards). Then we located different areas on the globe by navigating to them using their Lat-Long co-ordinates. This seems to have taken an easy hold in her mind, and we then went and got a street atlas to test if she remembered how to find the street we were staying in. She located several more streets easily.

Baby No.2 had obviously been listening in, unnoticed by us at the time, and now knows latitude and longitude too, and which comes first. Sometimes simple little associations can make such a difference to learning (they did for me, anyway).

Then it was on to the maths lesson for the day, and by some coincidence it was about degrees and temperature. She wizzed through it without effort and was very pleased with herself. She sometimes makes easy mistakes when she's feeling confident and as a result not paying 100% attention, but we managed to correct one mistake without fuss.

Homeschool on the Road

Well, we've been on the road for a month and a half now, fieldwork and photographing in remote areas of Western Australia. The girls are literally skipping through fields thick with everlasting daisies of all kinds.

Schooling is going well. I had to whittle down the materials we brought with us to the bare essentials, and to that end we purchased "Maths Power". It's a great program, and the children cannot progress to the subsequent lessons until they have a 100% (or perhaps 95?) score on their previous work. It also helped me in that it is an Australian program, designed by and for Australian teachers and curriculum. So now I know that Baby No.1 is up with what's happening in her grade regarding mathematics. Not that RightStart wasn't wonderful, just that I was unsure where we were in the scheme of things as far as Australian schooling was concerned.

I think that back home I was getting bogged down by the sheer quantity of material I wanted to cover, and worrying about whether I was doing it perfectly... so being forced to stick to the desert-island-essentials has been a revelation.

For English and spelling, we're continuing with Spell to Write and Read, and spelling is improving every day. Baby No.1 still resorts to more "phonetic" spelling when she's writing in a hurry, but does very well when actually thinking about it.

The girls love traveling and being out in the bush, discovering and identifying new animals and plants... we encountered an echidna and followed it as it nuzzled under logs for ants. I decided to make "echidna" the spelling word for the day, which proved popular: they both now know how to spell it! The girls sketch things we find, too. For long hauls on the road, we've bought Beatrix Potter's Tales on CD. Baby No.1 at first dismissed this as beneath her but now loves listening to them. We all enjoy them! They are such wonderful tales, and use beautiful language.

After much frustration scouring bookstores whilst in Perth, Baby No.1 has found a book to read that appealed to her: The Shadow Thief and is tearing through it. We'll have to get her the sequel when we next pass through town... She's really missed not having access to her books at home (she reads avidly every night in bed; tales and myths, history, anything she can get her hands on.

Baby No.1 is also studying along with the Institute for Excellence in Writing DVDs, practicing writing structure and style. She has a great hold on producing keyword outlines, and is starting to introduce some strong verbs, adverbs etc. I'm going to get her a nice hardcover journal for her to write in, so she can document her adventures.

I also brought along the "Core Knowledge" book for 5th grade (What Your 5th Grader Needs to Know) and we'll be going through it gradually. This material is fantastic for expanding and testing the kids' general knowledge.

We'll be on the road in WA till December, and so far the mobile schooling is a great success. Combined with their daily explorations and discoveries, the girls are having very full days indeed. So are we!

A New Year begins...

Well, our first 6 months or so of homeschool has ended, and we begin another. Baby No.1's spelling has greatly improved from the use of "Spell to Write and Read" and today I tested her on all the phonograms and she wrote them down correctly with very little trouble. Baby No.2 did the same with some simpler ones. Then it was keyword outlining practice for No.1 with a story of her choosing from an Usborne Stories of the World book. Baby No.2 practiced some cursive "qu"s and was very proud. I've purchased a set of Base-10 blocks and I'm painting them to match the colured beads of the Al-abacus that they use for RightStart Maths. Baby No.1 is progressing with visualising addition problems etc, and Baby No.2 now understands the concept and quantities of 100, and even had a game with herself skip-counting by 100s. The girls like to do work on the whiteboard, so I photograph their work every now and then which they really like. A good day today—very little conflict!