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Education in Victoria is succeeding in some areas, but failing in many others – we have new school buildings, but they are overflowing and the school rolls climbing so quickly that teachers and principals have no bandwidth left for improving educational outcomes. Schools are adapting to technology, but failing to handle the wide range of ability and rates of learning our kids have. The system is not flexible enough to handle the needs of low achievers and high achievers in specific areas.

Every couple of months there is a new study showing how badly Australia is doing compared to other countries in areas such as Math. We know there are approaches that have worked elsewhere but we seem unwilling or unable to change and adopt them.

Homeschooling is an important right for Victorians – in many cases it is the only way to solve problems with bullying, with low achieving students and with high achieving students. Homeschooling is a rising demographic which serves as an important barometer of how well our schools are serving students and parents.

If the government understands this, then it will understand the value in Homeschooling, and will preserve that right as a legal option, and keep the current registration regulations intact. Homeschooling also serves the Dept of Education – it relieves pressure form a strained system, and gives a flexible way of educating students who are not well served by schools. It is part of the solution, not part of the problem.

It is so important that the Department of Education _listen_ to Homeschoolers, not try to tell them how to educate, or punish them – rather use it as important feedback. I was surprised to find many ex-teachers among Homeschool parents, and other parents had studied education theories in some depth. Homeschoolers as a rule are those who value education highly – they are pro-education, not anti-education.

I can say personally, it is heart rending to make the decision to take your child from school, you would only do it if there was a real problem to solve, or a clear benefit in doing so.

My son has just turned 13yo, he is by some accounts gifted – but the reality is simply that he was read to a lot from an early age, and had some opportunities for books and learning and discussion, and excelled because of normal healthy genes and a supportive environment. He has attended public schools in inner Melbourne for 3 years, the other years being Homeschooled – so I have some basis on which to compare the good and bad of each approach.

Early this year he was accepted into the SEAL program at a very good new school in inner Melbourne. The SEAL program is great for many kids because they immediately skip a year and jump ahead closer to their current level. I’m in favor of the SEAL program, its a good thing – but its not the complete answer. In my sons case he was repeating material he had done a couple years earlier in Math, so the homework was ‘busy work’.

I tried him out on year 10 questions and he worked through them well, so it seemed he was at that level. I asked the teacher if he could work ahead in Math, then asked the year coordinator and finally the deputy principal – and was surprised that this request was politely ignored in every case. At first I was angry, but then I realized that they probably just saw my request as “more work” for them, and they are already straining to keep up with massive expansion in student numbers. The roll is growing at a massive rate, and I think this is why they just don’t have bandwidth to gather a real focus on learning outcomes, let alone catering flexibly to students who fall outside the norm.

As an aside, there are ways to teach and learn math that are vastly better for all students than the approach we have in most Australian schools now. You don’t have to invent new methods, they are tried and work well overseas – you can read about Jo Boaler, ProofSchool, MathCircles, KhanAcademy, AoPS.com, Australian Math Competition etc. You can read any review of our current math texts by university mathematicians, or look at any comparison study with other countries to know we are doing it badly. The system needs to be flexible enough to accommodate and experiment with these new methods. Its not the curricula per-se, it is the way its communicated – it is not visual enough, it is too topic-centric and should be more problem-centric, it is not interactively explored.

Id like to see schools adopt these approaches – but right now they are too busy handling roll growth alone, and in moving from paper books to ipads.

This means the only solution, for now, is to Homeschool your child if they excel in Math – school is a hostile environment towards learning math deeply.

We need to change the way we think about Homeschooling – it is valuable for mainstream education in Australia, it is a place to see how new methods work and take the needed risks in new approaches to learning. It is a pressure valve for a school system experiencing the stress of rapid growth, and it is the only way to accommodate that small minority of students who will not excel at schools, no matter how good those schools become in future.

To this end I propose that the Victorian Government / Department of Education Victoria consider supporting Homeschooling in the following practical ways :

- Preserve the current lite-touch Homeschool registration regulations in Victoria [ realise that making regulations tighter will likely result in mass non-registration ]
- Fund a fulltime Homeschool liaison specialist educator in DETV [ to support homeschoolers, not police them ! ]
- Establish an open registry of public school events that Homeschoolers can join in with
- Fund several masters/phd opt-in studies on Homeschool education approaches and attainments
- Fund Math and Science specific programs for both schools and homeschoolers, eg: [ alternative curriculum materials, such as AoPS.com books, Math Circles and Robot workshops ]
- Establish a yearly tax deduction for extra costs associated with homeschooling your child [ taken from the money that homeschooling saves the government on schooling ]

Some comments in response to a video TED talk that Conrad Wolfram gave called “Teaching Kids real math with computers”

I did enjoy Wolframs video, but I think its too tempting to take away computations.. in doing so we risk losing the math understanding behind them. I just think we need more of both : more understanding and more facility with actual practical problem solving.

Technology can help to explain math better. I just found this video today, which contains a superb intro to Bezier curves, among other things. I think this would be pretty engaging to high school students, be a motivation for them to learn calculus.

One of the things I wanted with GridMaths is to take some of the pressure off long working out but also have the student solve the problem for themselves. Its easier to line up numbers in long multiplication and you tend to make less typos. By design, GridMaths is _not_ a calculator, there are other apps that do that well.

I’m currently working on a hybrid approach where you can use ASCIIMathML to get good looking math expressions, which should open GridMaths up to wider use at high-school level. Maybe we can make worked problems less of a chore and more about understanding … but still keep the facility and practice with computations at a good level.

I can remember an awful lot of fiddling around with sharpening pencils and erasers at school.. push-pencils solved that, but I must have bought 15 different compasses :] Once a person can write legibly, maybe the emphasis should segway from paper to electronic tools, but still keep the ability to do the constructions, structure the essay, think critically, type well, organise computations etc.

I recently saw a report from one school where they moved to 1-to-1 tablets, where they saw savings of ~20k/month in stationary costs.. maybe exaggerated and an affluent school, but paper is kind of expensive at volume.

Its certainly a lot quicker to make a GeoGebra construction on a tablet, than to do it with ruler, compass, dividers, protractor and pencil … you can concentrate on the concepts and specifics, rather than paper-management. Then the diagram you construct is malleable, you can drag and interact… that’s a big innovation, and helps understanding.

I wonder what ways software can help take the load off teachers, so the mechanics are easier for them, and they can spend more time teaching face to face.

I much enjoyed Kalid Azads Interactive Guide to Fourier Transform article on BetterExplained.com [ and was much impressed he mentioned my animated sine demo, which he extended upon in wonderful ways. ]

With recent javascript and web 2D/3D, I think we’re at the cusp of a kind of interactive learning renaissance.. because Math concepts can be made really physical, tactile and intuitive : **Show-me-how-it-works + let-me-drive** beats **verbose-monologue** every time.

I wanted to mention another variant of the animated sine demo, where you can add a second circle and slide back and forth to see the first 2 terms of a Fourier series.

It seems like a gentle intro that would get young people thinking..’hmm, what if I add another circle… and how big should that circle be…’.

Obligatory Tolkien quote : “*It’s a dangerous business, Frodo, going out of your door. You step into the Road, and if you don’t keep your feet, there is no knowing where you might be swept…”*

### Counting with coffee Beans on grid paper

When I started teaching my son maths we did a lot of counting coffee beans. We would arrange 12 beans in groups of 3 and groups of 4… The idea was to start building up intuition and then segway into multiplication.

Don’t ask me why coffee beans.. I must be a bad parent! The beans just happened to be handy, being dark they were easily visible when put on 5mm math grid paper and fit nicely in the squares. You can use small buttons or raisins even. Its pretty tactile, so works okay for young kids [ as long as they are old enough not to swallow small things ]

### Abstracting to Multiplication

Later we drew the ‘beans’ in the squares and then just drawing a circle in the box instead of placing a bean. This gradually led to tracing out the rectangle outlines of the groups and let the squares on paper take the place of actual beans.. so it abstracts really well in a fairly natural and unforced way.

There are some nice ‘tricks’ you can do on squared paper that grow out of this approach –

- every rectangle is a multiplication product, so you can use it to figure out any times table question
- you can work out all the times-tables and write them in the top right square before reciting them
- introduce distributive property (a+b)*c = a*c + b*c by showing the rectangles add up
- ask.. are there any numbers that cant be made by a rectangle product? [ yes..prime numbers]
- show square numbers – 1,4,9,16 …
- you can show how to add 2n+1 to n squared to get the next square number
- you can introduce series – 1+3+5+7+ … and show how they sum to make the square numbers
- make a stepped-triangle 1+2+3+4+5+6 and show how two of these can be put together to make a rectangle, which leads to sum 1 to n = n(n+1)/2

So this approach leads very naturally into some really nice mathematics. Along the way it reinforces the rote learning of times tables (auditory repetition) with visual intuition.

### The web app – introducing Doctor X

I thought there was probably an App or web page to do this kind of thing interactively. I googled around and found lots of times table grids, math systems but nothing that seemed to take the grid-paper-rectangles-and-counting-beans approach into an interactive medium.

I made notes on what the app might look like, and then spent some time making a quick prototype in Javascript. I found It needed a way to step through some basic usage notes and examples, so I added a howto box. Then we came up with a silly name for this thing.

Anyway, here is the current version of the visual grid calculator for kids, which I’m calling :

“The Doctor X Amazing Griddable Multiplication Contraption”

When I get time Ill make some more in-depth tutorials and worksheets on some of the concepts I mentioned above. Let me know what you’d like to see,

enjoy!

gord.