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

[seanieg89]

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.

Well creativity is the antithesis of rote learning . Of course there will be some memorisation involved, even an artist or musician relies on memory to build his intuition for what will look/sound good in a particular landscape.
The fact that you experiment with mingling bits from different methods is a good sign, trust me...it is exactly this fumbling in the dark that leads the developing of intuition. By the time your hsc rolls around if you keep up your work you will likely have a good sense for when a particular technique is likely to work etc.

 

[seanieg89]

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.

Lol. Even the proof of the fundamental theorem of arithmetic is a bit beyond the expectations for mx2 students. The uniqueness part is a little subtle for high school material. (Try proving it on your own if you haven't read a proof before, it is still definitely doable yourself).

 

[RealiseNothing]

Lol. Even the proof of the fundamental theorem of arithmetic is a bit beyond the expectations for mx2 students. The uniqueness part is a little subtle for high school material. (Try proving it on your own if you haven't read a proof before, it is still definitely doable yourself).

I've read a proof on it before unfortunately lol.

 

[Carrotsticks]

I think some people have differing definitions as to what rote learning is.

It appears that many students mistake 'sort of getting the concept, but not 100%' with rote learning, which isn't the case IMO. It is okay (and perfectly normal) for students to initially have a weak grasp on a new concept.

Just because you can't use your mathematical tools creatively, it does not necessarily mean that you are rote learning. It just means you haven't developed that degree of versatility, which is oh-so-important when it comes to higher mark ranges.

Rote learning would moreso be:

"When I implicitly differentiate f(x,y), I chuck a y' at the end of everything with y in it, because it just is."

 

[GoldyOrNugget]

What do people think of the number of questions on the MX2 exam for the 3hr time limit? I often felt like the need to get marks on questions 1-6 (which generally require little creativity, and let's face it, can more or less be rote learned) meant that I rarely had time to really dig in to those more interesting questions near the end. However, there are clearly people capable of getting full marks or very close to full marks consistently...

I've heard that the STEP exams only require candidates to solve 3-6 questions, and maths olympiads are generally 3-5 questions too. Which format do people prefer, and why? What should be the required ratio between candidates' speed, accuracy and creativity?

 

[seanieg89]

What do people think of the number of questions on the MX2 exam for the 3hr time limit? I often felt like the need to get marks on questions 1-6 (which generally require little creativity, and let's face it, can more or less be rote learned) meant that I rarely had time to really dig in to those more interesting questions near the end. However, there are clearly people capable of getting full marks or very close to full marks consistently...

I've heard that the STEP exams only require candidates to solve 3-6 questions, and maths olympiads are generally 3-5 questions too. Which format do people prefer, and why? What should be the required ratio between candidates' speed, accuracy and creativity?

I think to truly assess mathematical understanding/ability, shorter (in terms of number of questions) and more difficult exams would be ideal. Especially for differentiating the top end of the cohort. The board would NEVER go for this though.

 

[seanieg89]

That said, it should not be to the extremes of olympiad. There is a sizable difference between contests and exams, and so there should be.

 

[asianese]

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.

Just finished reading this piece. My jaw dropped at the 'geometry proofs'... No wonder American maths standards are dropping!