You are currently browsing the tag archive for the ‘education’ tag.

Here are my thoughts on sitting the British “A-Levels” in Australia as a possible path to University Entrance for Home Educated students.

Disclaimer :  This is a guide only – our current plan which we have not yet verified/ completed – so please check for yourself before making any decisions.

Questions :

  • What are A-Levels ?
  • Why do them ?
  • How to do them ?
  • Costs / Logistics ?
  • Does it really work ?

In a nutshell, the A-levels are the UK / British approximate equivalent of the Australian VCE/HSC/ATAR, or the American CollegeBoard/AP exams, or the IB International Baccalaureate.  That is to say, they are the highest secondary school qualification, and are used to gain entrance to University and satisfy tertiary prerequisites.

A-levels are sat in many international schools worldwide, and are quite well known by universities in many countries, so the qualification is reasonably well regarded and can usually be compared/converted to the local equivalent.  The exams are standalone and not based on coursework, they are marked by an independent body and have few formal prerequisites or formal age requirements.   There are plenty of course materials, books and past exam questions available, and A levels cover a wide range of subjects in depth.

In Australia, the BritishCouncil in Sydney run the exams in May/Jun and Oct/Nov, and some in Jan.  There are various exam “boards” which set the exams and mark them, and BritishCouncil offer the option of EdExcel or CIE ‘flavor’ exams.

In our case, DS15 – code for ‘my 15 year old Darling Son’ – has worked a couple of years ahead in Math, using materials from KhanAcademy.org, AoPS.com and amt.edu.au.    Doing some fairly rigorous academic tests in Math next year seems a good fit, in preparation for University the following year.   If we could have done VCE methods, ‘spesh’ and physics next year that would have worked out fine – but we could not find a school that would allow us this flexibility.

In the UK it is normal to sit 3 A-levels, so our plan for 2019 is roughly :

  • “Maths” in May/Jun
  • “Further Maths” in Oct/Nov
  • “Physics” in Oct/Nov

I think this gives us a reasonable chance of getting into a good science/math program at an Australian university, but they may insist he also sit an entrance STAT exam to show evidence of English / Reasoning / Writing skills at university level.

The A level exams are not super cheap – each test is around $300 AUD, with usually 2 or 3 tests per subject on different days, so around $2400 in our case.  There is also the issue of travel and accommodation to sit the tests in Sydney and lesser costs for books and materials.  There are some online distance ed providers for A levels, but in our case we prefer to self study from the books.

If things go well, we will report back on our success and this pathway might prove useful for other home educated students.  If things don’t go well, we can review what went wrong, and DS will still have time to find other pathways to get into Uni.   I admit this is a pretty “geeky” approach with so much emphasis on Maths, but it suits us well and DS does have wider interests – he plays the violin, reads voraciously, writes, does computer art and programming, loves cooking etc.   Even with good marks in A-levels a 16yo student will most likely need the University Dean of Schools approval, so we shall see what they say about our best-of-british quals !

Some links :

I was discussing with other parents online, about the merits of various school Math multiplication approaches.

In the “Japanese Line method” you draw lines for each digit, and then count the intersections and add them up.

In the “Box-Method” you draw areas for each sub-product, and in “Longhand Multiplication” you just use the square grid to keep track in a table, without use of a diagram.

My main issue with the Line Method is that for problems like 97*98, you’ll be drawing a lot of lines .. its a lot of work even for 64×34 :

line_method_64x34

I also like the idea that Box Method starts with a physical / visual intuition – you can start children counting rows and columns, then progress to counting areas such as “How many 1ft square tiles do I need to tile the 3’x7′ kitchen floor ?”

Then you can discuss the distributive law a(b+c) and (a+b)(c+d) and explain the method behind longhand multiplication .. and then go on and show some handy tricks, such as using negative numbers to make less work, vis :

grid_97x98_two_ways

The above example, which does the same problem in 2 different ways, shows the kind of approach Jo Boaler recommends, called “Number Sense” – where students are encouraged to find their own way of doing a math problem.  The idea is that there are many valid ways to do it, and struggling to find your own way is a good thing [ even if you fail ], and students tend to engage more, and certainly recall more when they have actively discussed with other students.

The same Box Method diagram can lead onward naturally to algebra and quadratics.. and even the beginnings of calculus 🙂

A MathCircle is where a group of young people get together and work on some interesting Math-related topics introduced by a mentor.

The topics are sometimes problems like you find on ArtOfProblemSolving.com or Math Competitions [ vis AMC Sample Questions ].  They can cover quirky topics that aren’t normally seen in the school curriculum, such as Catalan Numbers.

The idea sounds geeky, and is un-apologetically so, yet has the potential to engage students who might be bored with the traditional material.   It preps interested students for careers in science / finance / medicine / engineering and helps the school do well in math and science competitions.  Math Circle meets can also be a lot of fun.

Why

Question : “Why do we need more math.. we already do that in school, right?”

Answer : “yeah..but you don’t learn enough Tennis in PE class to become a club player, and you don’t get enough Instrument practice in Music class to get into music school .. you really need to train, to play in an ensemble and have dedicated practice for that.”

MathCircle takes the same approach of intensive practice which you find in Basketball practice, Dance club, Swim meet or musical instrument group … except focused on math-related skills.

Practice with Duration + Intensity

One important aspect that both Math problem solving and programming share is the sustained concentration on one task – in my opinion we have gone too far in the direction of byte size chunks of learning.  Sometimes you need to chew on things for a while.

We can look at how Basketball and Music are learnt, and apply what works to math.   Training sessions often last for 2 hours, and this is accepted as a social norm – it is well understood it takes time to get into the zone.. repeat the basics, introduce a new skill, practice it, and integrate and perfect it over time thru a range of scenarios.

Its also not about the one or two elite players – the whole team improves and transfer skills around and offer peer-support thru the shared activity.  It can help develop individual qualities that are useful for success in other areas of life, namely ‘character’.

With Code

MathCircle is something most parents haven’t heard of .. but teaching young people how to program is an easy sell – it has had a lot of positive marketing over the last year or so, and its a clear pathway to a good salary.

I also think that writing small programs is a great way to introduce and discover math ideas .. its tactile, interactive, hands on, iterative, experimental.  Your also working with the real concepts – a lot of educational apps and games seem to win in terms of engaging and entertaining, but lose in terms of conveying deeper ideas.  When your making a program you are really tinkering under the hood with the engine, not just zooming around the racetrack.  So a MathCircle with an emphasis on making your own programs to investigate math topics, and using tools like Geogebra, might work really well.

Example Topics

A MathCircle which has a code-things-up emphasis, we could call a MathCodeCircle.

Here are some topics that might be covered in such a MathCodeCircle :

  • find prime number factors, use for solving lcm/gcf problems
  • pong game variant – balls bounce around and collide
  • adding waves together – beats, square waves
  • simulate jumpy stock prices, compare with compound interest
  • planets orbiting / solar system simulator
  • circle inversion using GeoGebra

Most of these would be developed in javascript, and run in the browser – using the canvas api to render 2D graphics – its real programming.

More

Some links if your interested :