Subject: 5 most critical mathematical concepts

Posted by Niall Palfreyman on 12/2/2010
In Reply To:5 most critical mathematical concepts Posted by Tim Joy on 12/2/2010

Message:

Am 03.12.2010 05:01, schrieb Tim Joy:
> I am not asking about skills, but about numeracy. For instance, is knowing the basic curve and climb of exponential growth the most important mathematical concept?
>
> Why that question as the lead, what are the FIVE most critical mathematical concepts that can also be most ably delivered via system dynamics?
I feel a bit uncomfortable about this combination - it sounds like we're only interested in those issues which we already know how to tackle in SD. But what if there's something important that we still need to find a solution for? And maybe with a bit of thought we might then find an SD solution.

So: What is for me the most critical mathematical concept related to numeracy? I guess for me it depends on whether I'm an everyday person wanting to make a living or some kind of decision-making person, so here are my two:

For everyday life: A thorough understanding of what fractions _mean_.
So many of my students come to me not knowing that the fraction "2/3" is equivalent to "2 divided by 3", which hampers them in following mathematical derivations. And this seems to me to be related to a lack of understanding of what exactly a fraction is - in terms of 2 pizzas divided between 3 people, for example.

For decision-makers: The concept of accumulation.
We tend to assume that the "things" in our world are active, but in truth "things" only afford responses - what is far more important are the processes which alter these things. So, for example, "I" am not this collection of flesh and blood writing this mail, but rather "I" am the process which daily intelligently accumulates this flesh and blood in ways which enable the "I" process to keep on running. This is the basis of calculus: What counts is not the quantity itself but changes in the quantity. This is clearly an SD issue, and the leaky barrel is an excellent way of introducing it in class.

In both of these cases the critical skill is in my opinion the ability to generate spontaneous examples of the relevant concept: Understanding fractions means that I can spontaneously generate an example of the fraction 2/3; understanding accumulation means that I can spontaneously generate examples such as the leaky rainbarrel.

Best wishes,
Niall.