The problem is not the syllabus

The problem is not the syllabus.

In almost 20 years of teaching senior Maths and Physics, I've had plenty of top students go on to unviersity to study Engineering and Medicine, and go on to lead fulfilling, successful careers. Only a handful have decided to become teachers. Each year, I ask the likely candidates why they don't choose teaching, and invariably money is mentioned as the main reason or a significant reason.

Over the last 20 years, I have also noticed a drop in the mathematical ability of my beginning Physics students. The students aren't any less intelligent, so what's happened? We do know there is a huge shortage of maths teachers. In fact, at my school our junior maths classes are currently being taught by PE teachers, English teachers, Home Ec teachers, anyone with a spare in their timetable. These people are all top quality teachers, but not specialists. They can teach the maths, but don't have, nor can enunciate, the broader picture.

We can debate the syllabus all we like, but if students don't have the groundwork for serious Maths and Physics, then all we are doing is bailing out a sinking boat. And if we can't attract the best people to teaching, we're not going to get better results by fiddling with the paperwork.

The problem is not the syllabus.

How to win a Nobel Prize in one easy step

I was highly amused the other day to come across this graph, showing a reasonably strong relationship between per capita consumption of chocolate, and number of Nobel Prizes won by people in that country.





 I'd love to be able to recognise the creator of this graph, but its popped up so many places I'm not sure who's work is actually is.  Still, we can all see from the graph quite clearly that the more chocolate each person in a country consumes, the more Nobel Prizes that country has received over the years.

 

More importantly, how well these two items are related can be measured relatively easily, using something called correlation.  The wonderful person who created this graph has in fact also measured the correlation between chocal consumption and Nobel Prizes being awarded, and you can see it in the top left corner of the graph, where it says r=0.791.

 

Now, there are a large number of ways in which correlation can be calculated, depending on what sort of data you have, but what they all measure fundamentally is how close your data is to a straight line.  If all your points are on a straight line, your correlation or r will be equal to 1.  If all points are spread out randomly, it will be zero (if the line is pointing downwards, the r value will actually be negative, but r=-1 is as good as r=+1).  A value of r=0.791 is pretty reasonable - the two variables are said to be higly correlated.

Now, in no way does this imply causality.  A country could not improve its chances of receiving a Nobel Prize by handing out copious amounts of free chocolate to its school kids or population at large, and expect to start receiving Nobel Prizes left, right and centre.  The set of data above could, in fact, be random.  Or, there could be some other, underlying, relationship.  Perhaps people who receive Nobel Prizes tend to come from welathy countries, countries where people can afford to eat chocolate at will.  Sometimes looking at the outliers can tell you something as useful as looking at the data points in the trend itself.  In this case, what's going wrong in Germany???  All that chocolate eating, and yet its substandard when it comes to Nobel Prizes??  Sweden does alright though, plenty of Nobel Prizes, without all the investment in sweets.

All this thinking about correlation brought to mind a graph that floated around the twitterverse earlier this year, purporting to prove that forcing an economy like Greece to reform and consolidate quickly (ie austerity measures) will only result in a worse result at the end of the day.  Here it is below, again unattributed (but happy to correct if the author lets me know)

Looks pretty convincing, doesn't it.  Nice straight line, lots of points on the line, including, down at the bottom, Greece, trying to consolidate faster than the rest, and getting it more wrong than anyone else (x axis is attempted reduction in spending, y axis is how wrong they got their growth predictions).

 

Using a spreadsheet like Excel, it's pretty easy to get a basic value for correlation here (doesn't really matter what sort for the moment), using the '=CORREL('x values', 'y values') formula.  To get the values off the graph, I simply read off the axes, to the nearest half value (not particularly precise, but good enough for our purposes.

Using my rough and ready measurements, I calculated a correlation of r=-0.68!  Less than that for Nobel Prizes and chocolate consumption.

Remember I said sometimes it is instructive to look at the outliers in any data set?  I redid the calculations, taking out Greece, and got a new value of r=-0.5.  Borderline low correlation.  Much lower than for Nobel Prizes & Chocolates.

Hmm.  What does this mean for all those economists claiming that austerity is not a good plan?  Not a lot really.  They may well be right.  But this graph doesn't really prove that convincingly.  Nor does it disprove it either, for that matter.  what we can take from this little analysis is that whatever is happening in Greece is somewhat different to what is happening in the other parts of the world, given that it has such a disproportionate effect on the data.  Certainly makes it an interesting place to look at, economically speaking.

For our students, its a nice little study on the importance of looking at data critically.  Graphs can be a great way to communicate information, but they need to be aware both that correlation is not causality, and also of the impact of outliers

Facts, Lies and Statistics

Facts

Facts matter, and most of us will know the phrase Fact Checkers, which came up quite a bit during the recent US presidential election.  But Facts are only part of the story.  The Choice of Facts matter just as much as the facts themselves, and nowhere is this seen more than wherever statistics and data are discussed.  Western mathematics education doesn't serve most people well in this regard, and I could explain to you why, or you could watch this TED lecture by Arthur Benjamin.

The lecture is only 3min long, but for those time-short readers I can summarise by saying: we should teach less algebra, and more statistics at school.  Going to be an engineer?  You need algebra.  The other 99% of the population, you really, really need statistics!
 

You really, really need statistics

Why, I hear you ask?  I'm glad you asked!  Below is an poster of the Incredible Shrinking Doctor, an image commonly used in high school maths classes to explain distortions caused by the misuse of statistics:

The image is linked from this page, which has a great discussion on the ambiguity of data.  Ambiguity?  How?  The image is meant to show the shrinking number of doctors in California between 1964 and 1990.  The reduction in doctors was, in actual fact, approximately half.  But, because the images were shrunk by half in both height and width, it appears as if the number of doctors actually shrunk to a quarter of what they where (the small doctor is about 1/4 the size of the original doctor).  The Facts are right, but they are presented in such a way so that the loss of doctors to family practice is much worse than it actually is. 

 

Statistics

Facts matter.  In fact, Facts matter so much, that some people are willing to choose which Facts they use very carefully to make sure they give the right impression to people who don't know any better (like voters and investors).

Here's an example from a post on twitter today from Stephen Koukoulas (@thekouk), an experienced economist (you can read his Bio here).

Is it a Fact?  Absolutely!  Perfectly correct.  Doesn't look good for the profligate Howard government, does it! As far as I can tell, it comes from here, the 2012 MYEFO documents, table D1 (see screenshot below).

In fact here is the table partially reproduced below (with the relevant data I believe used by @thekouk highlighted).

The 'last 8 Howard Budgets'

Why did he choose the 'last 8 Howard Budgets'?  Is 8 some magic figure, or some standard Economic rule of thumb?  Not as far as I know, but I do know that by choosing the last 8 years, he maximises the point he is trying to make, that the Howard government was a wasteful spender.

Note the first figure in the list - a 10.7 increase in real spending over the previous year.  What happened?  To be honest, I'm not really sure, but I do know that the inclusion of that one, large value significantly biases the average over those 8 years. 

 

The last 7 Howard Budgets

What if 7 was the magical economic rule of thumb?  Then the average increase in spending under the Howard government in its last 7 budgets was less than 2.3% per year, much less than under the current Rudd/Gillard government. So much for the 'profligate' Howard government!

(@thekouk could have used 9 years, and arrived at the figure of 3.6% increase in real spending per annum, still worse than under the current government, but not as usefully 'bad' as using 8 years of data.)

 

Teaching Stats and the Choice of Facts

Don't get me wrong, I follow @thekouk on twitter, and I have learnt quite a bit from doing so.  He has a broad range of experience in both the private and public sector. 

He always uses Facts.

And Facts matter, but our students also need to know that the Choice of Facts also matters. For this reason, Statistics should matter more than algebra when it comes to maths education, and we should always, always question the Choice of Facts that are presented to us, and teach our students to do the same.

NT Education Department aquires C2C units from Qld Education Department

I've written previously in regards to the difficulties faced by Queensland teachers in implementing the Australian Curriculum, mainly due to the faults in the units of work written by Education Queensland, known as the C2C units.  Despite some earlier confusion and mixed messages, the Director-General of Education did finally confirm that the use of C2C units were not mandated, and that they were written as examples of how the Australian Curriculum could be taught.

It turns out that the Northern Territory government has recently aquired the rights to the C2C units, and has mandated all teachers in the territory to teach the C2C units, down to pre-written the lesson plans. 

Apart from the loss of professional choice and responsibility, some of the provided materials potentially breach existing copyright, and some of the science experiments may be dangerous to students and staff.  Forcing teachers to follow such a highly prescriptive curriculum is not just  insulting to teachers, but also highly regressive.

I can only encourage teachers in the Northern Territory to have serious discussions with their Principals and Regional Directors, and do their best to fight such a decision that will only result in lower standards of education and morale amongst students and staff.

Technology

Breakthrough!
Read a couple of articles recently that showed technology use in education being pulled in two different directions.  I'm talking about the devices that we place in students hands here.  I really prefer not to get too worked up about which laptop/tablet/device is best for students, as it is really the use of the device, the pedagogy, that is key.  But these two articles came out on the same day, which tweaked my curiosity.


Faster Computers
More traditionally, this first article looks at the development of a new chipset for PCs and laptops, with much smaller transistor size.  Smaller transistors allow for a more complex CPU, as well as faster switching and information processing.  This one, the Ivy chipset is particularly exciting for a number of reasons.  I'm not sure why, but the article specifically refers to its use in education, but it will really improve processing speed in PCs in all sorts of industries.

Computing in the Cloud
The second article (here) to me is the really exciting one, and I think indicates the real future of computing for many schools - cloud computing.  Google is offering a much expanded Google Drive, as well as online productivity apps.  I use them a bit and find them more than adequate for most purposes.  Cloud computing, along with the NBN (either the Labor or Coalition model) offer some real benefits to schools in Australia.


Benefits
Cloud computing means that a lot of the storage and processing of documents happens offsite, somewhere over the rainbow.  It almost makes the choice of technology redundant.  As along as you have quick enough accesss to the 'net, you can do your work.  You don't even need to use the same device each time (even your smart phone will do it).  For schools, it means no need to run and maintain their own servers, no backups, less technical support required.  Potentially large savings.


BYOD (Bring your own device)
And then the device - Hawker College in Canberra is doing what a lot of switched on businesses are doing - allowing students to provide their own device.  While Education Departments in Qld and NSW are tying down their networks tighter and tighter, the ACT is opening theirs up. Benefit for the school?  Lower costs for maintenance and technical support.  And for students, they can choose a device that matches their own needs and budgets.


For school administrations, Cloud computing and BYOD has to be the way to go.  The financial savings from reduced maintenance and technology can be put to much better use in the classroom, and the savings in time can allow them to focus on what really matters in the end - teaching and learning.

A Flying Start with iPads! But who will cop the bills?

Far be it from me to criticise our government for spending money on technology in education!  Technology has been responsible for some of the most innovative changes in education, and we ain't seen nothing yet.  Within a generation, we'll see a change in schools that will make them almost unrecognisable compared to what we see now.  So, why do I have such an issue with Qld Labor's policy to give iPads to year 7 students over the next year or two? 

It is relatively easy for governments to spend money on technology in schools - it goes down well with most of the punters, and makes you look like a politician with an eye on the future, a bit of a thinker.  Unfortunately, it is also easy for govenrments to waste money on technology.  Technology by itself doesn't do anything for education, and the general public would be horrified to know of the number of laptops and computers sitting unused in classrooms, in cupboards, in bags, right across the state.

The Electronic Jellybean

There were plenty of stories from early days of computers in Queensland schools of teachers covering them with tablecloths and flowers to hide them from students, or using them as an 'electronic jellybean', a reward for good behaviour or hard work.  Very little impact on actual education.

Education Queensland has developed some really good programs over the years for making good use of computers in classrooms.  Most of it is based on two really simple principles - get the technology to teachers before the students, and give them time and training in best how to use them.  The department also regularly rewards high flyers who develop good, scalable ideas for the use of technology in education.

So, how does the Flying Start iPad rollout stack up?

Firstly, there is no indication that the teachers will be receiving iPads themselves.  Even if they do, it seems they will get them at the same time as the students.  Now, for some teachers, that's fine.  There will be some teachers that will run with them and do some very good work with them.  But there will many others that just won't know what to do with them.  And to be honest, between preparing lessons, marking, behaviour, talking to parents and colleagues, and actually teaching lessons, finding time to work out what to do with a class full of laptops will be right down the bottom of the list of priorities.

What about the finances?

$5.7million for 5000 iPads for 5000 students averages out to $1140 per iPad - how does that stack up to real costs?.

The policy specifices a WiFi only 32GB iPad (or equivalent).  A runout model iPad 2 at these specs currently costs about $649.  Sounds good so far. 

But the policy also calls for a warranty (Apple Protection Plan).  That's another $99 for 2 years.

Schools also need a way of charging a class set of iPads, Syncing, and uploading Apps. Apple sell a cart for that, for the sum of $2600.  You'd  need one per class, let's say one per 26 iPads, or an extra $100 per student iPad.

Even with a warranty, you want to protect the iPads from accidental damage, so there's another $50 for a case for each iPad.

Want an Office suite software package so students can actually create documents, spreadsheets, slideshows and so on? Add a few other simple Apps in, and you're easily talking $50 at a bare minimum.

So how much is left now?  The school would be lucky to have $200 per iPad left.  For a school with 100 year 7 students, that's $20,000 to fund a technician, teacher training, teacher iPads, network infrastructure, increased internet usage.  And unless the government is going to stump up the cash each year, that $20,000 would have to last the lifetime of the iPads, probably about 2 years before they become obsolete.

$10,000 a year?  You'd be lucky to get a technician 1 day a week.  And if you think iPads are pretty rugged and won't need much maintenance, sit outside a school at 3pm and watch how the kids treat their bags as they get on the school bus or take off on their bikes each day.  There will be breakages.

So who pays?

Schools will have a few choices.  The money to really run the iPad program and make it work can come out of existing school funds set aside for maintenance, painting, furniture and so on.  It could come from increased fees for parents of students receiving iPads.  Or, they could just run a half-baked program where there is no teacher training, no technician, and no increased internet bandwidth. 

What  next?

It's great that the government wants to spend money on education.  But if it wants the money to be effective, they need to slow down, give schools time to plan, and in this case, double the price tag to cover all the costs.  Do that, and they can step back and let schools do what they're best at.

C2Cs and through the looking glass

Curious.  That's how it felt as a teacher in a Queensland State School last year as the new Australian Curriculum came closer and closer.  Curious because, for one thing, the Australian Curriculum is Australian in name only.  So far, Queensland is the only State ready and willing to start teaching to the Australian Curriculum in 2012. 

When I say 'ready and willing', I mean of course the politicians and bureaucrats.  The people that actually have to teach the curriculum, that is, the teachers, were certainly not ready.

...and Curiouser.  The Education Department, on orders from the Director General, hired a crack team of top notch teachers and started creating sample work units, assessment items and so on, to assist the teachers in their work.  Great!  Good idea.  Except that it was never clear if the sample units were just examples, or were mandatory for all schools across the state.  So most of us just sat on our hands and waited.

Down the Rabbit Hole
The sample units came out a lot later than originally planned.  Some work for term 1 2012 was only released on the last day of term 4, in 2011.  Too late to really plan with your colleagues, organise equipment, and so on.  And definitely no clear idea of the year ahead.  And to be honest, the units of work were not exactly cutting edge material.  Only a few weeks in and a lot of teachers and schools have already started to shelve the C2Cs, or to start looking themselves at how the Australian Curriculum could be delivered best for their own students in their own schools - work that should have started a year ago.

Teachers across the world are working hard to integrate IT into schools, in ways that are engaging for students, and model real world use of IT.  Queensland has teachers the equal of any in the world in the use of IT, and EQ in general is ahead of the game there.  There are some fantastic models that we use in our classrooms that could have been used to collaboratively develop good quality units, for much less money, using expertise from across the state, from teachers currently in the classroom - not from an office somewhere in Brisbane, by people often with perhaps no understanding of the broad and diverse needs of our schools and students.  I'm hoping to share some these models and ideas, and I'm hoping others will here as well.

So feel free to add in your two bits.  Share ideas, share frustrations, and we'll see if we can survive until Christmas.