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I would like to have a comparison or a big picture of how and why the approach for teaching math varies from primary (or pre primary) to middle to higher classes.

I understand at every level one need to learn concepts and procedures, so why I see so much compartmentalization for teaching math at different levels?/

I accept that in pre-primary classes focus should be on learning how to learn and learning using 5 senses. But is there anything more than this that nessicitates a different approach especially when moving to upper primary, then to middle, secondary and higher and finally to university? I would like to know about those approaches and contrast the same to have a big picture.

I am new to maths teaching, so kindly bear with me if you find this question too naive.

Thanks and regards

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It's a very broad question (to do the comparison you want). And made even more difficult when you consider that best pedagogy for any of the stages is not agreed on.

My personal opinion is that much of the methodology should be similar, because humans are similar. Much more than people think. There's probably some social sensibilities that are different. For example, teaching skiing I can't treat adults or pre-schoolers how I treat 5th graders (10 year old boys are the bomb...I would semi-literally go to war with them). But a lot of the drills and practice required are same (much more than different).

I went to a school that taught college classes "just like high school": similar class sizes, teachers rewarded for teaching not research, homework drill problems rather than project-style questions, being called to the board, more frequent tests versus just a midterm/final, etc. In talking with sisters that went to normal schools, I thought it was a total gyp what they were getting. From a student perspective, this sort of support/attention/methodology was much more time efficient in training us than the college lecture halls at Enormous State Universities or non-native English speaking grad students whose real priority was their thesis work.

I think a lot of the rationale for "not spoonfeeding", etc. ignores human behavioral traits. They are generally, instead, excuses for the economic setup involved in US colleges. (Which is why I recommend to kids not to go to an R1 school but go to a liberal arts school on a ROTC scholarship instead.) It's even worse in graduate school courses in terms of the "go teach yourself" excuses, grade inflation, etc.

P.s. "It never gets easier. You just go faster." -Greg LeMond.

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Math seems difficult for most of the students. I'm a student at university. What makes mathematics easier for a student is concepts. Like, for instance, trigonometry lesson is introduced in 9th Grade and 90% of teachers don't explain what actually trigonometry is! Also, it's introduced as a difficult topic. According to me, if it's in the following pattern every student would love to solve the math problems :

1.Introducing the topic with real-life examples


If someone's going to teach me differentiation conducting some fun activity related to the topic, I would be eagerly waiting for the next class. Why this thing is necessary? What usually happens is students actually don't know the applications of the topics taught.

2.Explaining the theory and methods of solving


You can introduce some basic theory to students, for instance, what d/dx symbolizes. It has two good things: your students will have some extra knowledge outside the textbook and secondly they'll know the importance of understanding the concepts rather than learning them. My favorite part in notes was: method of solving. My teacher added a stepwise method of solving in her notes. When students have stepwise instructions they would be able to solve the problems faster. Also, divide the lesson into subtopics!

3. Practice


Giving sums to practice in after explaining the theory. Explain the theory and method of solving for a subtopic and then give 5-10 different types of sums that students will solve in your presence.

This really helped me in building good concepts and improving my results. Also, if not needed don't disclose difficulty levels of lessons.

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