How would you like to learn maths?

Poll

What would you like to be taught?

Every now and then there are calls to reform the mathematics curriculum and/or mathematics teaching. This trend goes back to the 60s I believe (with "new maths") and the most recent manifestations of this were changes to the GCSE, as well as the impending introduction of "Core Maths" courses at 16+. Between then and now there have been many other initiatives. One recent one that I find quite interesting is computer-based maths.

When thinking about that, it occurred to me that during my school years we (as a class) never got maths homework that required us to construct a proof. Every piece of maths homework that I can remember was about applying known rules, sometimes to fairly complex problems, but the problems still obviously had a solution one could arrive at with a bit of effort. This is not about background knowledge either, as there are many proofs that do not require more than high school mathematics. It is about a way of thinking.

So I am curious, would you rather be taught:

1) methods of calculation and their application to clearly "solvable" problems (essentially problems where you know what "type" of problem it is and which technique you probably have to apply to arrive at a solution; NB the way to get there may still require advanced manipulation skills) - I think most current GCSE and A-Level questions fall into this category

2) mathematical methods and their application to "thinking" problems (where at first glance you may not know how to solve the problem, even though it may not require higher order calculation skills - just higher order thinking skills) - these are more like questions you may encounter at a maths competition

3) computer-based mathematics: here you have to think to construct a mathematical model for a real world problem and then program a computer to calculate the solution(s) for you - most real world maths for me falls into this category and I think it is a lot of fun, but perhaps it is too applied for mathematics lessons? (I would love to see this being done in natural science or social science lessons.)

Reply 1

Puddles the Monkey

21

Original post by llys

Every now and then there are calls to reform the mathematics curriculum and/or mathematics teaching. This trend goes back to the 60s I believe (with "new maths") and the most recent manifestations of this were changes to the GCSE, as well as the impending introduction of "Core Maths" courses at 16+. Between then and now there have been many other initiatives. One recent one that I find quite interesting is computer-based maths.

When thinking about that, it occurred to me that during my school years we (as a class) never got maths homework that required us to construct a proof. Every piece of maths homework that I can remember was about applying known rules, sometimes to fairly complex problems, but the problems still obviously had a solution one could arrive at with a bit of effort. This is not about background knowledge either, as there are many proofs that do not require more than high school mathematics. It is about a way of thinking.

So I am curious, would you rather be taught:

1) methods of calculation and their application to clearly "solvable" problems (essentially problems where you know what "type" of problem it is and which technique you probably have to apply to arrive at a solution; NB the way to get there may still require advanced manipulation skills) - I think most current GCSE and A-Level questions fall into this category

2) mathematical methods and their application to "thinking" problems (where at first glance you may not know how to solve the problem, even though it may not require higher order calculation skills - just higher order thinking skills) - these are more like questions you may encounter at a maths competition

3) computer-based mathematics: here you have to think to construct a mathematical model for a real world problem and then program a computer to calculate the solution(s) for you - most real world maths for me falls into this category and I think it is a lot of fun, but perhaps it is too applied for mathematics lessons? (I would love to see this being done in natural science or social science lessons.)

Don't you need to know basic methods of calculation before you can start doing the other two options? :redface:

I haven't been taught maths for a very long time, but I would have liked some explanation as to why things are how they are in maths- we just had to solve pages and pages of algebra by following a given formula; I always felt confused and frustrated and eventually just stopped paying attention when I was about 12 or so.

Someone successfully got me to understand the explanation for me recently on TSR why -1 x -1 equals one, which laid a lot of demans to rest for me. :redface:

Reply 2

llys

OP

17

Original post by Puddles the Monkey

Don't you need to know basic methods of calculation before you can start doing the other two options? :redface:

Yes, that's true, but I think you could do a LOT more of 2) and 3) rather than focus almost exclusively on 1). I think that works at all levels of maths, from prime numbers to geometry and calculus, so you could easily incorporate mathematical thinking and proofs from year 7 upwards.

I haven't been taught maths for a very long time, but I would have liked some explanation as to why things are how they are in maths- we just had to solve pages and pages of algebra by following a given formula; I always felt confused and frustrated and eventually just stopped paying attention when I was about 12 or so.

Yep, and I actually quite liked it :tongue:

but at the time I wasn't really aware that there was more interesting actual maths out there. I really LOVED geometry though - we actually did some proofs in class for that, but never as independent work or homework.