Practicing Math in the Classroom

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As many of you know, I instruct courses in mathematics. I recognize that

1) most of you hate math here, so you are the perfect audience to ask
2) most who hate math don’t get much practice in it.

So I focus my instruction on practicing problem solving in math after providing a key formula. As the hipsters you are that despise math, I’ll sum my questions up as succinctly as possible.

1) You exist as you are. You find yourself in a math course, and you struggle to solve problems. What is something you would like to see from an instructor (in a problem solving session) that will help you to solve it? Do you prefer it if the instructor solves everything out mechanistically and then asks you to help him solve the next similar problem? Or do you prefer he start from scratch on the first one, and encourage participation on each step of the process?

2) You’re too shy to ask a question you’re struggling with. As someone who doesn’t read minds, we cannot anticipate your difficulties. How would you like your instructor to approach the problem, assuming he did anticipate your difficulties?

3) Do you prefer seeing alternative ways to solving a problem, or would you rather see one method used universally to every problem you see (I strongly advise against the latter).

These are the core questions, and feel free to bring up anything you would like to see or not see as well if you were in this scenario. All suggestions are welcome.

Note: I ask not because I struggle to teach—I ask because many of my students share your disdain toward math and are too shy to speak out toward their difficulties and what they want to see. I also instruct the derivations in lectures—this is a separate class which supplements the material taught. My presentation skills are already fine—this topic is poised in such a way to ask what you, in particular, seek when you struggle.

Of course, I won’t do exactly everything you say since Math needs to teach critical thinking, which many of you lack (waah waaah). So it stands to reason that some of your suggestions will not fall into line with what math teaches.

Is it notation that bothers you that you want to learn? Is it the inability to see step 1 to step 2? Of course everyone has different difficulties, but share your difficulties and what you think may help.

Format: First, address your difficulty in as much detail as you can, and then suggest any number of ways you feel this difficulty may be alleviated by a problem solving session and what your instructor can do to help.

I think this will benefit us all, since you will tackle your math phobia head on (if you actually care to provide a legitimate reply) and will help me to produce people that don’t cower in the fetus position when they hear fields of math.

Nota Bene: This is college level mathematics; try to seclude your answers to the realm of college. You may include others as I think many methods carry over, but not all will. If you can provide insight for calculus that would be lovely.

 
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Wow, you have a major superiority complex, your post is pretty much toxic with the condescending attitude. I worry that you are a teacher, and I think I may see why you have a problem with getting through to your students. You claim it is maths your students disdain, but I have read one post by you and disdain you as the writer rather than your subject matter. As for your student’s being ‘too shy’ to speak out about difficulties, can you blame them? If you talk to them the way you speak to us then I wouldn’t approach you for anything.

 
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I’m quite thankful I never had a professor as much of a douche as you are.

 
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I myself have never really had trouble in math, but I’ll drop my two cents. Many of my friends on high school had some trouble, and I can convey many of the things that they described.

1) I (and many of my friends) have found it extremely helpful for the teacher/instructor to show how a problem is done first, so that I can see what technique we are actually trying to learn. If the teacher simply writes up the initial problem and asks “What now?” when the problem revolves around an entirely new concept that we have not yet learned, it seems to end up being a big waste of time. Think about it like this: If someone were to write a sentence in a foreign language, one that you have not learned, and they ask you to fill in the words one by one, how much are you actually going to learn?

2) I like it very much if the teacher simply approaches and asks something along the lines of “How are you doing?” or “How’s it going?” – This makes it very easy to just say “It’s going alright, but there’s this one problem…”

3) This one varies strongly from individual to individual. For someone with a naturally high capacity for math, it might be easier and more beneficial for them to learn a few different ways to do each variation, and they can sort of adopt one as their own based on what they are more comfortable with. However, I know that some people, regardless of how hard they try, how long they study, or how much they practice, continue to have a difficult time when a new concept needs to be learned. It’s just the way their brain functions be it due to a learning disability or simply due to genetics. For these people it may be beneficial to teach them a method that is more easily adapted to different concepts. Personally, I see no harm in learning a broader and more efficient, universal method, but I’ll trust that you have valid reasons for advising against it.

I do think that you should clean up your post in a couple of places, though. Namely the second sentence in the ‘hipster’ paragraph and the entirety of the ‘critical thinking’ paragraph – it is completely unnecessary and uncalled-for. You can leave the “I’ll sum my questions up as succinctly as possible” part of the prior, but the rest is condescending and superfluous. You won’t get helpful feedback from people if feel they are being degraded by the asker.

 
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Personally I don’t hate math I’ve just never been good at it. It seems that I needed things explained to me a bit more than the average candidate. Unfortunately it seems that teachers misread this as meaning I have a low level IQ and need to be in a lower level class set. I’m sure this has probably been similar for others. But I’m actually quite fascinated by maths and wish I didn’t need things explained to me so much during secondary/high school, because now I find myself interested in most of the compulsory subjects I struggled learning back then but, I have very little foundation to build upon.

However, I did notice a dramatic shift of perspective and understanding when I had things explained to me one on one. When it was getting close to my final Maths exams, I would pay a visit to my Maths teacher’s classroom at the end of the school day to get things directly explained to me. Maths seemed a lot easier than I had originally thought when I took this approach, my only problem now was memorizing formulas and methods to solving equations. I didn’t do great in my exams as I only got to get these things explained to me a few times but I believe I did much better than I would have without taking this approach.

1) So personally I would advise to spend short one to one periods (when possible) with the students that appear less able in the class. To find out whether they really are less able or are just struggling to understand your phonetic explanation of the mathematical formula to given problems.

2) Also I think it may be very beneficial to emphasize the importance to the class that they understand what you just explained or taught, before moving on with a lesson. And then like you said with your second question – if you anticipate or suspect particular students are not quite getting it, ask them directly if they got it or not. If you get the vibe that they’re getting it, I guess it’s all good. If not, you could always try a different approach to explaining a particular equation or something.

3) Personally I’ve always found examples and scenarios useful when trying to understand something.

 
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I hate meth, its addictive and harmful.
Oh, you mean math?
1- I would like my instructor to do a math problem in front of me explaining each step in the way, then I do the similar problems following his steps.
2- I would tell him that I would like him to explain the point that is causing the problem.
3- If there are hundered ways to solve a problem, I want learn atleast fifty.
4- I usually understand a problem in first try unless if I am not payinf attention.

 
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My usual approach is trying to find alternatives while watching the instructor attempt to solve a problem. It also brings in at least some fun to try and solve each problem without using the methode you are supposed to use (today we had to prove whatever or not Σ((-1)^n*n/(1+n^2))) was convergent. While you can try to look at this using Leibniz you can also try it using it’s simulairy to (-1)^n*n/n^2=(-1)^n*1/n which is conditionally convergent.

 
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I love math. I learn best when I am given the basic blocks, and then given a more advanced problem. I am currently taking calculus, and we are addressing rectangular approximation. I am currently trying to figure out the “better way” to estimate that sort of area, using calculus. I have a feeling it will be something along the lines of linear regression, but I am having difficulty proving it. You might scoff at me missing something that probably seems obvious in retrospect, but this is fun for me.

Vihart’s videos are enjoyable. Look at those.

Also, you sound like an asshole.

 
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Personally I think his arrogance and insults are hilarious.

 
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Well, while we are helping you with your teaching skills, let me help with your asking for help skills.
Here’s some comments that I dont like from your post and reasons for them.
1) Math teaches you critical thinking, which many of you lack (waah waaah)
DID WE JUST BECOME BABIES?!? If you are gonna make me into a baby, just dont even bother asking me a question; cuz apparently you think I’m too stupid to know.

2) tackle your math phobia head on (if you actually care to provide a legitimate reason)
This, first of all, assumes that we all have math phobias. I myself, love math. Then again, if I had you as a teacher, I might DEVELOP A PHOBIA. But I digress. Second, if you assume that we have a large capacity to give you bad reasons, WHY ASK US AT ALL? Try not making us sound like trollish idiots.

3) (i strongly advise against the latter)
If you are asking for a whole hearted opinion, dont craft the responses before they respond to you. Let them answer their own way. If you dont like their answers, there’s no point in asking.

4) Most of you hate math here
Again, thank you for assuming! Jeez, thats like saying that most of us are trolls, or most of us are teenagers. You got no proof buddy. LEARN TO BE NICE TO THE PEOPLE YOU ARE ASKING FOR ADVICE!

5)hipsters you are that dispise math
a) asumptions. b) the word hipster is very outdated. Also, thanks for labeling us.

6) As someone who doesnt read minds
You now assume that we expect you to know our problems. This is really an unnessecary comment.

Obviously, you have ALOT of problems with teenagers. This scares me, especially since you are a “teacher”. If this is how you talk when you need something, then I would hate to talk to you when you feel you have an advantage; which when you are a teacher, must happen alot. Learn to repect others and people will actually tell you their troubles in math. Then you wont have to go on forums and demonstrate to us why you have a hard time connecting with students.

 
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Don’t assume a student is stupid if they don’t get it, some just need it taught a different way. I know I did, but I got left in the dust all through my junior high and high school math classes. I needed very personal instruction that was slow where every little detail of the problem is explained.I needed a teacher that had enough patience not to get angry when I made simple mistakes or when I asked questions that you would think everyone should know.

Please DO NOT MAKE THE STUDENT FEEL STUPID!!!

 
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From my experience as both a student and a teacher, if the students are afraid to come up to you privately to ask for your help, then there’s something wrong with your classroom environment. A lot of times it isn’t the fact that a student is shy so they won’t ask a question, it’s that they’re afraid of being ridiculed. Your demeanor in the post speaks volumes about how you might treat your students, both publicly and privately, in the classroom. Before you can really expect to see any kind of change and acceptance of what you’re teaching, students have to accept who is teaching it and feel a comfortable enough relationship to trust the person who is teaching them. Without that in your classroom, you can’t expect students to take anything you say seriously, or believe you care enough about them to truly want to help.

If you knew your students well enough, they should feel comfortable around you, and you should already know and understand their needs in the classroom environment, without them having to explicitly tell you.

 
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I assume where you say college level you mean further education, most likely degree level. That means that your student’s chose to do maths, and are likely paying for their studies. You also say your students disdain maths…

This makes no sense to me. Why would students choose and pay to do something they dislike. I am sure many school students do hate maths and that leads to teaching difficulties, but at college level the students have chosen to do maths, have they not? So clearly they do not hate the subject as they would not of chosen to study it if they hated it.

Though I am guessing from the lack of replies the OP has retired back under his bridge like a good troll, either that or you cannot take criticism, but then why ask? Though you did try to set up your post in such a way to only get the answers you wanted to hear which sadly, for you, we have not obliged in.

 
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This makes no sense to me. Why would students choose and pay to do something they dislike. I am sure many school students do hate maths and that leads to teaching difficulties, but at college level the students have chosen to do maths, have they not? So clearly they do not hate the subject as they would not of chosen to study it if they hated it.

Many colleges (in the US at least, not sure about other countries) have required classes that the student must take in order to graduate. So you may have gone to college to learn Chemistry and you ma be only interested in Chemistry, but o still have to pass a math class and an English class before you can graduate (for example). Different colleges have different required classes, some don’t have any at all, but the point is they can be in a college math class without liking math if only so they can get the required credit.

 
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Rather belated, but I certainly couldn’t imagine directly engaging an instructor when struggling with a topic. I would simply look into the matter with available materials at hand. But ultimately it boils down to what sort of personal relationship we have, and my confidence in their ability as an instructor, beyond their familiar with the subject.

But, I’ve never done any college level math courses. Last math I chewed on was the Monty Hall problem, which balked me at first but seems obvious in retrospect. Can’t say I ever felt math phobic, but never felt a need for greater math in my life. It became little more then a game, idle speculation.

 
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Well my personal tips as an instructor:

1. Teach your pupils how to use Math books. Good Math books generally start with a index, then alternate a formula section with a practice section, and include solutions and vocabulary/definitions at the end.
Its generally very important for those struggling to be able to look up Formulas they are struggling with.
Sadly most formula sections are only written in one version with the explanations being a combination of math example and Math language written explanation. Neither of which many students can fully understand. That makes it quite important to teach math language as well as just the formulas. Having students keep a note book for Math vocabulary and testing on it regularly can be helpful as can presenting alternate versions of the formula sections(that use a different style of speech/vocabulary).

2. As with the vocabulary, tests are commonly the best way to find out what problems a Student has. Here its important to not just grade the test but put in some effort to understand and keep track of which mistakes which students make.
Is it just careless slip/mistake or a repeated mistake.
Quite often students struggling with a new Formula are doing so because they lack understanding in a old formula thats used in the new one. For example a new formula using percentages or fractions that are already supposed to be known. Some never really understood the old formula and some have just forgotten, either way they often need help understanding the old one before they can master the new.

Now, where are you going to get the time to do all this stuff, especially what has to be done with students during class? With the common class sizes caring individually for each student is commonly near impossible. And setting the pace for the class can be very hard. Too fast and the slower students get left behind and too slow and the faster students get bored and held back. Here you can commonly hit a hare and turtle with one stone, by having the class break in groups of 4-8 (ideal number is commonly 6) with 2 of the better students teaching the other 2-6. The better students get the benefit of repetition and an added insight one can only gain when one has reprocess the know data in a way that other slower students can understand. While the slower students get their individual education.

Homework is also important since math is in much parts about perfect form. Knowing how to do it and actually doing it right are quite often not the same. Generally only repeatedly solving Problems in perfect form can help here. Time in school is generally not enough. So homework is practically necessary. Do not use grades as primary punishment for not doing homework. Most students have no idea how valuable grades can be. Its generally not a now and here punishment that will change their behavior, but instead a 2-4 times a year kick in the Ass(when the parents notice the bad grades).

 
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after reading your post, I can conclude that your students don’t hate maths.. they hated you. If I’m one of your students, I will not be interested to learn the subject you’re teaching because you are arrogant and yeah, scary.

Anyway, I’m a maths student and I teach maths too. First thing I do before teaching is learning the students’ characteristics. And well, every person in that class has different ways of learning. Some might learn really fast, some might learn a bit slower, some might need to play games to understand/adapt the formula and more.

Maths is fun, make a fun learning environment.

 
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For me personally I feel that most math classes I have ever attended is that the Lecturer will plow trhough the work at breakneck speed and assume everyone to be on the same level as ihim or her forgettng that most students are not at their level, This is why I feel that when lecturers take the time to break the problem down into its core components to solve a lot easier for students to understand.

Another bug bear is when someone enquires into a subject they are not comfortable in (e.g. rearranging equations) and the lecturer mentions that they will come to that later when it is required in the problem in hand.

To reiterate from my personal experience I have alwasy found it easy when the problem can be broken down into its core components

 
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Originally posted by Fishyninjabread:

For me personally I feel that most math classes I have ever attended is that the Lecturer will plow trhough the work at breakneck speed and assume everyone to be on the same level as ihim or her forgettng that most students are not at their level, This is why I feel that when lecturers take the time to break the problem down into its core components to solve a lot easier for students to understand.

Another bug bear is when someone enquires into a subject they are not comfortable in (e.g. rearranging equations) and the lecturer mentions that they will come to that later when it is required in the problem in hand.

To reiterate from my personal experience I have alwasy found it easy when the problem can be broken down into its core components

yeh. my teacher just read everything in the book and then gave us exercises to do. woulda bee nice to thoroughly work through it all and explain everything.

but doing the same lessons every year multiple times proly made the teachers very tired and lazy.

 
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I sometimes wonder whether you and Janton are having a private competition to be the most curmudgeonly bastard on the forum.

Now this may be going off at a bit of a pointless tangent, but then again it could be relevant. When I was at school I could do maths, but had little to no interest in it. Then I joined the school’s cadet corps and learned gunnery. When I found out that quadratic equations were used in the compliation of the aiming tables we used, they suddenly became a lot more interesting, and I was keen to learn more. For me, pure theory was deadly dull, but a practical and (at the time) relevant application made it important for me to learn the subject properly.

 
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