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14:4+1-6*5-7*14:3+5 = ? ( )

13 Tips For Being Successful in Math Courses at University

13 Tips For Being Successful in Math Courses at University

The natural development of the number sense is less that encouraging. This post suggests some rules for success in math courses. The emphasis is on solving proofs, but I think most of these are good advice to take issue with any math course.

1 . Take responsibility for your learning.

I have never seen a student succeed who did not make a concerted effort to understand this material. It’s a very long road if you think of learning mathematics as a matter of accumulating facts, and it can be a very frustrating one. Math is about understanding concepts, not equations or formulas.

2 . Be willing to devote time outside of class to do your own work.

You will have homework in every one of your math courses; you will have exams in every one of your math courses; at some point during both of these processes, you will suddenly feel like it’s all too much.

The key to success is not ease but intensity. How deeply do you think about the concepts involved? Do you understand how they work or are they just another problem that you can solve mechanically?

3 . You should know what to expect in any class.

A math course is not like an English course, which has lots of things that are optional. There are assigned readings (and questions about those papers), there are sets of problems (possibly with solutions) that help you learn the material better than merely reading or hearing someone explain it.

If you aren’t doing these assignments then you’re wasting time even being in this class. This does not mean that you have to do all the exercises in a book before moving onto the next one; but when I give a quiz on a certain section, make sure to actually read and understand this stuff before coming to class unprepared.

4 . Do your homework carefully and thoughtfully.

Homework is not a test of your ability to remember what I told you in class, though this might be useful from time to time from an educational point of view. Homework is designed to make sure that you understand the material and can apply it.

If you don’t get this right then doing well on exams will be a matter of luck rather than skill or intelligence. The reason for grading homework is so that we have a baseline for how much effort you’re putting into understanding the assigned material.

It’s also very common for students to have difficulty with certain homework problems because they lack basic tools or expertise even before the course has started! Or because there were things mentioned in lecture without being covered in detail, which can make it easy to not understand the instructor. If you struggle with a problem, ask me for help (in person if possible).

5 . Do not make excuses!

There is no one else who can know as much about what happens in your brain when you solve problems; no one but you knows why that equation didn’t come out exactly right or why two lines look like they should intersect here even though they’re clearly supposed to be parallel.

The only way to improve this skill is by continuing to work on it, so please stop making up unverifiable stories about how it’s really hard for you or something happened outside of class and now homework isn’t fair. Self-pity has never overcome impasse : there are people who have devoted their lives to making math accessible to everyone, so if you have difficulty with it, work harder or find another course!

6 . Learn to listen in class.

This is not just for your benefit , but also mine : when I explain a difficult concept that I expect you to spend the rest of the class working on, I want you in class working on that material instead of chatting away in some parallel world.

If there’s something unclear about what I’m saying then please stop me and ask questions–I can never explain something as well as when it’s fresh in my mind after having said it aloud.

The reason I give examples is because most students will appreciate an illustrative example over an abstract set of axioms. The reason I don’t give formulas is because most students are capable of abstracting the basic ideas behind how a formula works, even if the subtleties of applying these to specific problems are lost on them.

7 . If you can’t see your mistakes, how do you expect to fix them?

You will make errors in this class. That’s expected–if everything worked perfectly then there’d be nothing for you to learn. It is important that you identify where and why you made these mistakes so that they won’t happen again!

When trying to solve a problem, it’s easy to focus on all the parts that are going right instead of the ones that aren’t working out correctly–but by ignoring those errant results entirely, you’re just proving to yourself that you don’t know how to deal with them and should avoid those problems at all costs, instead of figuring out why they went wrong.

The last thing I want is for someone to get the answer right but not be able to explain what happened or where their method broke down.

8 . Acknowledge your confusion!

It’s far better for me as a teacher to spend fifteen minutes explaining something that I can tell you didn’t really understand than it would be if I stayed after class for an hour trying to make you see how it works.

Even better is when students are willing to ask questions about something in front of the whole class–this means that everyone else also benefits from having listened or watched! Your chance to speak up in class is entirely dependent on how much you contribute while the rest of us are listening, so if you don’t ask questions then it’s not likely that I’ll call on you.

Likewise, writing your questions anonymously to me days or weeks after a lecture has happened doesn’t get me anywhere : I wouldn’t have been able to answer them during class and may not even be able to remember explaining this material at all!

9 . Provide evidence for what you’re saying.

I’m perfectly willing to take someone’s word for something–but I can only trust that they’re correct if their argument makes logical sense to me.

For example: “this problem is hard” isn’t a valid reason because there could be many different reasons why it’s hard for someone, and without knowing exactly what those are then I’d be just as lost as you. Likewise, “the new curve is curvy” isn’t a convincing argument because without any evidence of what makes curves “curvy”, there could be many different definitions of the word–and therefore this observation means nothing to anyone else but the speaker!

This sort of thing may seem nitpicky to some people, but if you can’t explain your reasoning behind things then you’re going to have a very difficult time getting anyone else on board with your ideas/beliefs/etc.

10 . Know how much they know before trying something new.

You don’t want to ask me a question during lecture that I’ve already answered in a previous class, because then I’m just going to tell you that this is old information–which means you’re wasting both your time and mine.

Likewise, if you have a question about how something works but can’t be bothered to find the book/paper/class notes where it’s been discussed before, then I’ll ask you to go back and check it out so that I don’t give you more details than are actually necessary.

Lastly, please don’t walk into class on the first day having read all of the textbook or all of some paper–not only does this set impossibly high expectations for what I’m supposed to do for you, but it also means that everything I say on that day will be completely lost on you because you’ve already figured things out.

You can read ahead if you like, or ask me to explain anything more than what’s in the book/paper/class notes–but please don’t expect me to cover any material that isn’t covered by them!

11 . Take advantage of office hours.

I know how tempting it is to send email after email until someone finally answers something for you–which means there are plenty of people who try this technique and succeed at getting their questions answered.

Unfortunately, no one enjoys having their time wasted like this… which makes me less likely to want to help anyone else who does the same thing. I answer the questions that are asked to me in person, so please stick around after class if you have anything you want clarified for yourself!

12 . Get your question answered too.

This isn’t just about getting your own question answered–it’s also about being sensitive to who else might be asking it.

For example: when everyone is trying to ask a professor something at the same time, it gets much harder for us to figure out what people are asking because we can’t hear them well enough.

This problem doesn’t go away when only one person tries talking over everyone else; all of you still end up looking like you’re all talking at once! The best technique here is to politely state that you’d like everyone else in the room to give you a chance to ask your question, and then wait for everyone to quiet down before you begin speaking.

Similarly, when everyone tries chiming in on an already-given solution, it makes it much harder for the instructor to figure out who wanted what answered–and if no one speaks up then that’s even worse because there are likely many other people who were also trying to get their questions answered but couldn’t!

So please take responsibility during these moments by deciding which question is most important so that I can take care of all of your needs in order : whether they relate directly or indirectly to the current problem.

13 . Ask at the right time.

If you have a question about something that I haven’t finished covering yet, then please ask it when I’m about to move on to something else!

That way, I can keep the discussion moving by referring back to your question instead of having to stop mid-sentence so that you can feel better about understanding something now.

On the other hand, if you have a question for me outside of class time (e.g., during my office hours), then please don’t let its timing interfere with whatever else I might be doing at that moment; if it does, then these sorts of questions would be another reason why people choose not to take advantage of them or attend them at all.

The end result is that all questions are answered more quickly and everyone benefits from this–except for those people who try getting away with asking questions at the wrong times.

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14:4+1-6*5-7*14:3+5 = ? ( )