Why remembering the rules of maths is important

Just this morning I gave my (third year) students a set of x-y data. During the previous lecture (which was on ultrafiltration) we derived a mathematical model that predicted

y=b*ln(a/x)

where a and b constants.

Their challenge was to use the data to evaluate a and b. Only a small minority of the 30 or so students came up with a solution. Why did such a simple data analysis problem challenge them so much?

My theory is this: the students I teach are learning on a multidisciplinary programme and they do not get immersed in mathematical and computational reasoning to the extent that I would like them to.

Consequently, they do not have the basic rules of mathematics, the grammar of the mathematical language, ‘at the ready’, waiting to be called upon when they have to solve engineering problems. They are not ‘triggered’ to make the leaps that an engineer or a mathematician might make.

So in the above instance they don’t make the first logical step, the step that anyone who is fluent in the language of mathematics would make, i.e., they don’t simply write

y=b*lna-b*lnx

Some, but not all, will then be able to extract a and b from the slope and the intercept of a plot of y versus lnx.

This tells me two things: (i) remembering the rules of mathematics is important because having immediate recall is usually the thing that drives mathematical problem-solving and (ii) multidisciplinary programmes are hard to deliver.

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About Greg Foley

A lecturer in Biotechnology in Dublin City University for more than 25 years. Trained as a Chemical Engineer in UCD (BE and PhD) and Cornell (MS). Does research on analysis and design of membrane filtration systems.
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3 Responses to Why remembering the rules of maths is important

  1. Pingback: Ninth Level Ireland » Blog Archive » Why remembering the rules of maths is important

  2. Would be interested in your views on this.
    The teaching council produced an e magazine for maths week. They also put on a webinar hosted by Dr Aoibhinn Ní Shúilleabháin (UCD) with guest speaker Professor Alan Schoenfeld (University of California, Berkeley) on the topic of Maths Pedagoy: Problem Solving,
    http://www.teachingcouncil.ie/en/News-Events/Latest-News/Maths-Ezine-now-available.html

    The webinar is aimed at primary and scondary school teachers. Would be interested in your opinion on how relevant/useful it is.

    • Greg Foley says:

      Alec

      I’ll have a look (apologies, my management of this site has been a bit sporadic – I tend to just write stuff when I’m frustrated!). To be honest, my overall feeling about education generally, not just maths, is that there is a generation of educators who are over-complicating things and trying to fix what are essentially cultural problems by tinkering with pedagogy. Kids are growing up in a highly-distracting environment and it is very difficult for them to put in the time and practice that learning requires. We now have a sort of teaching and learning ‘mafia’ who are ignoring the fact that traditional education underpinned the phenomenon that was the 20th century and seemed to be determined to throw the baby out with the bathwater. The ironic thing is that with all the talk about ‘growth mindsets’, many of our education ‘experts’ seem to be very reluctant to challenge their own beliefs.

      One thing I do feel strongly about when it comes to maths is that maths educators should pay more attention to the those who actually use maths for a living. I’m talking about engineers, scientists, applied mathematicians etc. Talk to any of these people and they will have a very simple view of things: you have to acquire the basics, you have to know them off by heart and you have to do lots of practice. It isn’t always fun or ‘engaging’ but that’s the nature of things. Going from novice to expert is always hard.

      The other important thing is this: traditional teaching is hard! It is far easier to float around a room while students work on problems. It’s fun, you can have a bit of banter with the students and it’s easy to mistake ‘engagement’ for learning. I think a lot of those who would espouse a progressive philosophy need to stand back a bit and ask themselves if they have a vested interest in all of this.

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