When I talk to older teachers they sometimes mention this mechanical calculating device called the slide rule. Not many people know what it is anymore. It was used to calculate stuff by sliding bits around. The slide rule was invented hundreds of years ago and it seems that humanity only really put it in the obsolete pile in the 70s. It is right for it to be an antique. It was complicated, time consuming and inaccurate.
We have calculators now. They do the job much faster, easier, they’re just better. What people were essentially doing with the slide rule was performing a pre momorised algorithm; if you want to calculate this then do this – It’s a worthless skill now. We can have the electronics do the boring, algorithmic number crunching.
You have to ask yourself, does this skill of algorithmic number crunching have much value? How much time should we spend on teaching current students to perform memorised procedures? I don’t think there is much value in getting future generations really good at number crunching procedures. How could there possibly be much value there? Sure, maybe the basic operations can be understood better by doing them over and over again in primary school, but is it necessary to the degree we are taking it to?
Our current VCE students in Mathematical Methods and Specialist Mathematics still have a non-calculator exam (as well as a calculator one). They’re doing high level Maths here, who cares if they can’t divide numbers really accurately quickly in their heads. And if this is not why they have a non-calculator exam then why do they have it? How much of the exams are based on being able to execute memorised procedures quckly and efficiently? I’d say too much.
I remember teaching this method called ‘completing the square‘. It’s just memorising a procedure and the executing it when asked to. Is this intelligence? Students are rated on there ability to perform this procedure quickly and accurately. It’s robotic, much like a lot in a high school Math text book. If only they could design a robot for that…
We have had computers for a while now. They kick ass at executing algorithms. The speed and accuracy at which they can perform operations seems supernatural to me. The problem with computers is that nobody’s home in there. They only solve what we tell them to solve. I see a massive amount of untapped value in training students how to use computers as a tool in mathematical problem solving. Computers need to be told what to compute; this demands an understanding of mathematics and requires intelligence. Having students learn Maths in this way will make it much less repetitive, more interesting and useful. Using computers + Math in the current curriculum is soo narrow that you could berely say it exists.
Knowing when and how to apply a certain branch of mathematics is, I believe, massively underrated in our curriculum. I’ve seen students that are able to find the answers to complex algebraic equations struggle with the the simplest of problem solving tasks. For example, estimate the number of milk containers that could fit in this room. The hardest math you will have to do to solve that problem is division. It’s primary school math but a lot of high school students can’t figure out how to even start coming up with a solution.
The most heartbreaking thing i see as a Math teacher is students being putt off Mathematics by the overwhelming repitition and lack of creativity. It makes Mathematics appear so dull when its actually a domain of elegance, creativity and vast applications. You might be wondering why us Math teachers dont just teach it in the way we want to. Once you work in the education system for a few years you discover that the way assessment is designed influences EVERYTHING! Differentiating the curriculum is also a huge issue, but it deserves its own blog.
Math should be about logistical problem solving with numbers. It doesn’t make sense to assess students on their ability to execute memorised numerical procedures to the degree we do. We should be teaching students how the math works, and most importantly how and when to apply it. The way the system is designed now has to make you ask, do schools kill learning?