What exactly is 'rote learning' in maths? (2 Viewers)

[planino]

Does this refer to simply memorising formulae? What else does this refer to?
I used to rote learn formulae, and it didn't get me very far (not that I'm doing any better now), but how can we undo this/any other aspect of 'rote learning' maths?

 

[someth1ng]

Rote learning is essentially memorising methods of many questions without actually knowing why it works.

To some extent, everyone rote learns the formulae since it allows faster application to questions but not everyone understands how these formulae came to be.

 

[seanieg89]

Memorising formulae and procedures without understanding why they work and the scope of their applicability. The pragmatic reason why this is bad is that for questions that are even slightly different from those you have done before, you may be completely stumped because you cannot adapt the procedures you have memorised.

The higher the mark you aim for, the less efficient this method of learning is. (Efficient in the sense of exam marks relative to time spent.)

Worst of all though, you don't get a feel for what mathematics really is if you rote learn. Its sort of like the difference between driving a car and knowing how cars work. Which is a shame, because the process of drawing logical conclusions about (and connections between) patterns through rigorous argument is far more enjoyable than memorising formulae. I cannot blame most secondary school students for disliking mathematics if it is presented as a boring memorisable list of techniques for solving really contrived problems!

In mathematics more than most subjects, the "why" is far more important than the "what".

To counter this culture, I advise you to always question why things are true for the rest of your education (not just in mathematics!). If you can not answer this question about a particular method in mathematics then you do not truly understand it.

 

[Drongoski]

+1⁵

 

[Carrotsticks]

Rote learning:

If the discriminant of a quadratic is less than zero, then the polynomial has no real roots.

If equal to zero, exactly one root.

If greater than zero, two distinct roots.

Because the textbook said so.

Not rote learning:

The quadratic formula is .

But the 'inside' of the square root cannot be negative, otherwise we get complex roots (can't square root a negative number). So if the discriminant is less than zero, there are no real roots.

If it is equal to zero, we simply have , hence one real root. Notice that it is also the 'formula' for the vertex. This is because we have EXACTLY one root, and this can only occur in a quadratic if it is a double-zero ie: the root IS the vertex.

If greater than zero, we have two DISTINCT roots because of the plus/minus.

===================================

tl;dr rote learners can't explain how it works so don't do it (unless in exceptional circumstances where things MUST be rote learned ie: FTA).

I could go on for ages about the concept of rote learning, but I will save that for a later post.

 

[seanieg89]

+1⁵

That's still just +1 .

 

[seanieg89]

An elaboration of my post:

https://docs.google.com/viewer?a=v&...x7Mrwv&sig=AHIEtbS4BuWwbEGSdTY_SQ4UuwnBXHqt6g

One of my favourite pieces of writing on what is wrong with high school mathematics in its present form.

 

[planino]

Thanks for the responses You've all dissected the concept of rote learning in maths really well for me to understand this. I'd love to hear more

 

[Kat92]

One may also rote learn some common terminology.

I have seen hundreds of mathematical proofs performed, but it is rare that instructors will describe their thought processes (i.e., a metacognitive analysis of their proof) as they perform them.

Overall, I agree with @seanieg89 that interactive discussion is key for maths- allowing for a shift opportunistically between working through tasks (ie. solving a math problem) and reflecting on the process + why it is so (ie.strategies for learning math). The article is so very true indeed-- quite annoying really... as we should be encouraging students to move towards SCL learning only with recursive support if they become really stuck!

 

[cutemouse]

Admittedly I "rote learnt" maths in Year 11. For example, for the subsidiary angle method I used to memorise that when cos was first I would use the transformation R cos(x-a) and when sin was first I would sue R sin(x-a). I had no idea why though... I still did fairly okay though.

 

[darkfenrir]

Rote learning is essentially memorising methods of many questions without actually knowing why it works.

To some extent, everyone rote learns the formulae since it allows faster application to questions but not everyone understands how these formulae came to be.

Bro, fuck understanding, anything that gets you maximum marks in HSC is worth doing, especially since most super high ATAR kids who get state rankings in mx1 and mx2 do medicine, where high school type maths of ext 1 and 2 won't be required, so not understanding what you did, won't be an issue at all in later life. It was a stage of your life where u simply had to rote a lot of stuff. If ur doing advanced maths in uni then u obviously want to try to be as thorough and deep in understanding in mx1 and mx2 as possible, otherwise do whatever it takes to just get high marks.

 

[Galapagos]

Rote learning maths will make maths very very painful and boring. It's so much more rewarding when you understand WHY something works, not to mention you will probably do 50%+ better in your course if you actually understand the content.

When I did calculus this year, I went over some of the older concepts from high school that I found so hard to understand at the time (rote learned almost everything...laziness maybe?), and the contrast of clarity was amazing. If only I put more effort in high school. /Sigh/

IMO rote learning is "learning" for people that don't actually want to learn.

 

[GoldyOrNugget]

Bro, fuck understanding, anything that gets you maximum marks in HSC is worth doing, especially since most super high ATAR kids who get state rankings in mx1 and mx2 do medicine, where high school type maths of ext 1 and 2 won't be required, so not understanding what you did, won't be an issue at all in later life. It was a stage of your life where u simply had to rote a lot of stuff. If ur doing advanced maths in uni then u obviously want to try to be as thorough and deep in understanding in mx1 and mx2 as possible, otherwise do whatever it takes to just get high marks.

='( this makes me so sad. Year 12 doesn't have to be a year that you throw away just to get into your desired uni course. It doesn't have to be a stage of your life where you "simply have to rote" stuff. It's possible to achieve your aims without compromising on everything else.

Also, the critical thinking skills you gain by learning maths properly are applicable to every facet of your academic life. Even if the specific formulas don't come up again in future studies, the ability to deconstruct a problem into logical components and solve them systematically will be relevant in everything you do.

 

[iBibah]

Bro, fuck understanding, anything that gets you maximum marks in HSC is worth doing, especially since most super high ATAR kids who get state rankings in mx1 and mx2 do medicine, where high school type maths of ext 1 and 2 won't be required, so not understanding what you did, won't be an issue at all in later life. It was a stage of your life where u simply had to rote a lot of stuff. If ur doing advanced maths in uni then u obviously want to try to be as thorough and deep in understanding in mx1 and mx2 as possible, otherwise do whatever it takes to just get high marks.

But rote learning doesn't get you maximum hsc marks.

 

[planino]

Bro, fuck understanding, anything that gets you maximum marks in HSC is worth doing, especially since most super high ATAR kids who get state rankings in mx1 and mx2 do medicine, where high school type maths of ext 1 and 2 won't be required, so not understanding what you did, won't be an issue at all in later life. It was a stage of your life where u simply had to rote a lot of stuff. If ur doing advanced maths in uni then u obviously want to try to be as thorough and deep in understanding in mx1 and mx2 as possible, otherwise do whatever it takes to just get high marks.

Rote learning basically prevents you from enjoying the subject. I see where you're coming from, but what's wrong with enjoying what you're doing? The numerous epiphanies that result from not rote learning are enjoyable and good for study anyway

 

[darkfenrir]

Yeh guys what I meant was if you "understand" everything on a superficial level simply because of roting the process for a question similar to it before, then there's no reason you cant get 100 in mx1 and mx2. It comes down to how many processes you've seen.

But yea enjoyment comes into it, me personally I just made that comment because I myself am not sure whether I rote learn maths or not, I just know that up until now ive really enjoyed maths, am topping MX1 and MX2 at a selective school, and have not really known if I "understand" stuff or not. I know whats what and what to do in most situations but whether I actually "understand" i cant tell.

 

[seanieg89]

Yeh guys what I meant was if you "understand" everything on a superficial level simply because of roting the process for a question similar to it before, then there's no reason you cant get 100 in mx1 and mx2. It comes down to how many processes you've seen.

But yea enjoyment comes into it, me personally I just made that comment because I myself am not sure whether I rote learn maths or not, I just know that up until now ive really enjoyed maths, am topping MX1 and MX2 at a selective school, and have not really known if I "understand" stuff or not. I know whats what and what to do in most situations but whether I actually "understand" i cant tell.

If you enjoy maths (and are topping it) you are almost certainly not COMPLETELY roting it. Roting in its rawest form is just imitation of things you have seen before (changing numbers here and there). someone who completely rotes definitely can't answer the hardest of mx2 questions and hence cannot get 100.

If rote learning is good because it is a practical way to get high marks leading to uni entry my counterarguments are that:

a) the efficiency of rote learning drops off rapidly at the higher marks, it will bring you from 75 to 90 easily, but it would take MUCH longer to get from 90 -> 95+ by rote learning than by taking the time the understand the material.

b) you are reducing a beautiful area of human knowledge to somewhat boring exercises in memorisation. the creative side of mathematics is incredibly enjoyable and it is a shame to deprive yourself of this before you even know what it is.

c) the logic skills picked up through studying mathematics are universal in applicability, even if specific things like calculus may not be. I am sure a good english teacher would say something similar about his/her subject, the ability to formulate coherent arguments is a far more valuable upshot of english education than knowledge about any particular novel.

 

[RealiseNothing]

Bro, fuck understanding, anything that gets you maximum marks in HSC is worth doing, especially since most super high ATAR kids who get state rankings in mx1 and mx2 do medicine, where high school type maths of ext 1 and 2 won't be required, so not understanding what you did, won't be an issue at all in later life. It was a stage of your life where u simply had to rote a lot of stuff. If ur doing advanced maths in uni then u obviously want to try to be as thorough and deep in understanding in mx1 and mx2 as possible, otherwise do whatever it takes to just get high marks.

But rote learning doesnt get you maximum marks in maths.

I don't think anyone sitting the 2003 HSC MX2 paper went in to the exam with a proof that is irrational memorised.

 

[darkfenrir]

If you enjoy maths (and are topping it) you are almost certainly not COMPLETELY roting it. Roting in its rawest form is just imitation of things you have seen before (changing numbers here and there). someone who completely rotes definitely can't answer the hardest of mx2 questions and hence cannot get 100.

If rote learning is good because it is a practical way to get high marks leading to uni entry my counterarguments are that:

a) the efficiency of rote learning drops off rapidly at the higher marks, it will bring you from 75 to 90 easily, but it would take MUCH longer to get from 90 -> 95+ by rote learning than by taking the time the understand the material.

b) you are reducing a beautiful area of human knowledge to somewhat boring exercises in memorisation. the creative side of mathematics is incredibly enjoyable and it is a shame to deprive yourself of this before you even know what it is.

c) the logic skills picked up through studying mathematics are universal in applicability, even if specific things like calculus may not be. I am sure a good english teacher would say something similar about his/her subject, the ability to formulate coherent arguments is a far more valuable upshot of english education than knowledge about any particular novel.

yeh like, I enjoy being creative, but I cant help thinking is it just the fact i know so many different methods of doing questions that I start intermingling things to get an answer quicker, or am I actually understanding it. Hmm that actually sums up quite well what I feel about myself in maths, I have encountered so many methods that I just use them where applicable and If I see mingling bits and pieces of methods gets a result quicker then I just do that.

 

[RealiseNothing]

tl;dr rote learners can't explain how it works so don't do it (unless in exceptional circumstances where things MUST be rote learned ie: FTA).

Why? It doesn't seem too difficult to understand, unless FTA stands for a different thing to me than what it stands for to you (Fundamental Theorem of Arithmetic?)

edit: obviously you're talking about fundamental theorem of algebra, /fail.