I get quite despairing at times when i listen to the political football that is education. It is not all negative however as there are many people who are trying to improve things for everyone. There are many great teachers and tutorials on the internet.
To anybody interested i will recommend an essay you can easily find online called “Lockhart’s Lament” which highlights many of the problems that exist. The first half is full of dubious analogies and dubious understanding of art and music. The second half however is full of concrete examples of where the problem lies. Lockhart diagnoses the problems in great detail and says things we might be thinking but do not know how to articulate. This man is a real mathematician who has a vast wealth of knowledge to draw upon.
One of the developments we have seen in Britain and i am sure there are developments in comparable countries is the calls for basic computer programming to be introduced in high schools. In theory this sounds like a good idea yet there seems to be no evidence given as to why this well help students. There is no better way to kill enthusiasm in a subject than to make it a compulsory part of the school curriculum. People who like these things are drawn to it outside of the school environment in my opinion.
The rise in standardized testing which takes the form of NAPLAN in NSW and “No Child Left Behind” in the United States is an interesting development. I am in favour of some form of standardised testing however i cannot help but notice that there is some confusion as to what the purpose of the tests are.We are always told NAPLAN gives us information yet the information it gives basically disappears into a vacuum and nothing changes at the school level. In other words very little is done with the information once we gain it. Parents of poorly performing students will get tutoring for their children partly because they get little support anywhere else.
Take recent developments in Britain although i am sure it is much the same here. We constantly hear about how we need to make maths “interesting” and “relevant” and the ways in which we need to do this are by using word problems. Word problems such as at the primary school level involving how may donuts can we buy with a certain amount of money or using belly flops to talk about trigonometry or projectile motion. It is suggested sometimes that people who do not take to mathematics at an early age would take to it if only the sort of bells and whistles just mentioned were added. However if the previous mathematics education was not “relevant” why assume that a sugar coated version of the same curriculum will be?
It is furthermore constantly asserted by some people that the best way to get people interested in maths is to make it relevant to the “real world”. As if the “real world” consists merely of mundane repetitive tasks many adults are forced to do for a living.The answers here are usually along the lines of we should teach students how to manage their personal finances as well as fill out tax forms and i would imagine people also mean double-entry bookkeeping. There is nothing wrong with teaching these things however these pursuits are not deeply mathematical in nature and certainly do not compose a mathematical education.
In my opinion if we think about this seriously for more than a couple of seconds this sort of thinking is deeply floored. Do people really think that poor unfortunate students in a class really want to spend a lot of time doing that sort of thing. It would not take very long to adequately teach people how to do these things anyway. Most adults can do their taxes without needing any formal training and have a fairly good idea of what they can spend within their budget. And when students can do these things it begs the question of do students stop maths altogether when they have gained these shallow competencies?
Understanding mathematics gives you a whole new way of looking at the world. That is not an abstract idea as it has many material consequences. Entire fields of thought are cut off if you do not enjoy maths. Maths can give you a lot of solitary pleasure which is the best feature of it.
Notice that many people have missed that simple and honest hard work is the only way to learn mathematics. Furthermore knowing that your hard work has paid off is what makes mathematics and all activities fun. Things like the school curriculum are largely elements on the side as what matters more is what you discover during your own studies of the subject. Like swimming and riding a bicycle mathematics is a skill and can ONLY be learnt by spending a lot of time working at the subject.