August 24, 2019, 02:16:49 pm

### AuthorTopic: Should teachers focus more on the WHY?  (Read 357 times) Tweet Share

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#### JR_StudyEd

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##### Should teachers focus more on the WHY?
« on: May 23, 2019, 02:24:53 pm »
+1
I'm just an average Year 12 student - one whose brain is not particularly geared towards the academic discipline of Mathematics. I've only had experience with one VCE Maths subject - Maths Methods. I know some will disagree, but I find it rather difficult, both to learn and to apply. I think one of the reasons for this is because we don't really delve into why we study Maths. From a young age, I never really got a concise reason as to why we study Maths, and this continued into the early years at secondary school, when Maths became a bit more abstract and more difficult to apply outside the classroom. Maths became merely an exercise of rote-learning formulas and plugging numbers into them. Explanations of the history and origins of these mathematical ideas were non-existent.

There's only so much time that can be dedicated to learning and teaching maths in the classroom, I completely understand that. It's kind of unfortunate that the history and logic that created the maths we learn about today is often forgotten about. Obviously, I can't change the school system and what has to be taught, but maybe if teachers focused on deepening student's understanding rather than getting them to merely memorise would help keep many students engaged in the maths they are being taught.

Further and Specialist students, do you agree?
« Last Edit: May 23, 2019, 02:36:08 pm by JR_StudyEd »
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#### AlphaZero

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##### Re: Should teachers focus more on the WHY?
« Reply #1 on: May 23, 2019, 04:10:51 pm »
+9
UoM 2nd year undergrad studying maths here.

To be honest, I'm not sure one could easily give a "concise" answer to the question of why we study maths, but I'll do my best in a short paragraph.

Mathematics provides the framework for which we can objectively understand the world around us. A good question to ask yourself might be:  what would we be capable of without mathematics? And to be honest, my answer is probably not much. This isn't a good answer, but it's the best one I've got. I'm not sure there's anything that doesn't involve mathematics in some form.

There's only one type of person who says that mathematics is easy. And they are those who are too naive, and don't respect the discipline enough to realise their own incompetence. Mathematics is difficult because it is logical and humans aren't logical. Anyone who says otherwise just needs their ego shot by being presented something more. I'm not ashamed to say that I used to be this type of person. In fact, that version of me sometimes creeps back, and it takes a lot of maturity to stay disciplined, remain critical about your thinking, and not take things for granted.

My students often ask me why I decided to continue studying maths at university, and I usually answer with "because I enjoy how difficult mathematics is". To which, I usually receive a confused look. Then, I tell them to "think about it".

At this point, you're probably wondering what this has to do with whether teachers should focus more on the 'why'. My answer to this question is YES, and I think students will be much better off. I truly believe that high school doesn't foster an environment where both critical and creative thinking in mathematics is allowed. As you said, a lot of it (which is too much of it) is about rote-learning processes without learning the motivations behind it. In saying this though, I'm not sure this will change. There comes a point where you do have to just learn those processes. This is especially true for VCE since investing time into discovering the formation/motivation behind concepts is often more costly than it is useful.

I believe I've been extremely lucky in life - the teachers I had in high school and my parents went to great lengths to ensure I understood and appreciated the bigger picture - the 'why', if you will. It saddens me that there are many people who believe mathematics has been designed to be confusing (or something like that of a beast), and this is why I became a tutor after I graduated - so I could share my passion and try to inspire those who give mathematics a chance.

Last year, one of my students nearing exams said to me "I think I get it... I think I understand why you love maths" - something I'm still very proud of.

So, I ask that you give mathematics a chance. Ask the difficult questions, and put in the effort to pursue the 'why', and I promise you that the inner beauties of mathematics will be revealed. The above example about my student proves that it is possible to "get it".
2015$-$2017:  VCE
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#### JR_StudyEd

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##### Re: Should teachers focus more on the WHY?
« Reply #2 on: June 12, 2019, 03:01:30 pm »
0
This is especially true for VCE since investing time into discovering the formation/motivation behind concepts is often more costly than it is useful.
How is it more costly than useful? Do you mean certain maths concepts are just not worth the time trying to understand (at VCE level)? I think if there was just a fraction of extra time spent actually explaining the maths behind the method, then it would save us a lot of time and tears in trying to solve it ourselves.

Then there's the teachers who say, "That's just assumed knowledge. You should have learnt xyz in Year 10!'
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#### laura_

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##### Re: Should teachers focus more on the WHY?
« Reply #3 on: June 12, 2019, 07:34:58 pm »
0
How is it more costly than useful? Do you mean certain maths concepts are just not worth the time trying to understand (at VCE level)? I think if there was just a fraction of extra time spent actually explaining the maths behind the method, then it would save us a lot of time and tears in trying to solve it ourselves.

Then there's the teachers who say, "That's just assumed knowledge. You should have learnt xyz in Year 10!'

I understand why teachers say that but it still drives me absolutely crazy! Could not agree with you more!
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#### Aaron

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##### Re: Should teachers focus more on the WHY?
« Reply #4 on: June 12, 2019, 08:28:07 pm »
+3
Yes, there's actually a specific term for this called conceptual understanding or knowledge.

Currently maths is dominated (and when I say maths, I don't specifically isolate this to VCE... in theory I am more referring to math teaching and learning up to that point) using an approach called "procedural" understanding where the rules and applications are used, but without a valid understanding as to the why and how.

As a math teacher I really do feel this has to be addressed in the earlier years - that way this leads onto VCE and in turn results in better outcomes and better long term knowledge. Having an idea of the why and the how can result in application of the logic and rules we learn in a more broader sense rather than rote learning a formula without any sort of understanding and regurgitating it for x or y amount of marks and then forgetting about it completely afterwards.

Just my thoughts on it anyway...
« Last Edit: June 12, 2019, 08:29:41 pm by Aaron »
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Current secondary teacher in Maths and Computing.
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