# Good ways to help people learn math.

I have a student position at my university, which involves helping people who are struggling with basic calculus, precalculus, and discrete math. In general, the students that I help are hostile towards the subject, and are easily frustrated. For instance, many people have told me that "we don't need anyone that good in math"--in earnest--after I answered their question about what I'm going to do after I graduate (go to grad school). For anouther example, and I regretfully say that this is common, students frequently have trouble with online homework systems. They do no enter their, say equation of a line, in the format required by the system. One time, I helped someone who was using this software to pratice for a test they had in one hour. I solved the problem for them (it said not graded on the page), to show them how to go about solving the types of questions that were being asked. I told her the answer was $2y+3x=4$ , 4and the machine marked it wrong. What was going on was that it wanted the equation to look like $3x+2y=4$... She was angry at me, and asked me if I knew "even know wtf this even means."

All in all, I am asking a few questions:

1. How do you deal with students who treat you like garbage?
2. How do you help a student who is learning extremly basic math without frustrating them, or somehow making them feel stupid.
3. How do you deal with people who think that your disipline is pointless, but want your help anyways?

Obviously, these 3 questions are subjective, and this post should be in as a community wiki, rather than on the Q and A part of the site. However, I do not know how to do this. If anyone knows how do that, feel free to make it a community wiki.

-
Dear Chris. I'd like to address question 2. As I am not sure I really understood correctly, I am doing so in a comment: If it is really the case that the programmer who implemented the online system was too lazy or stupid to implement it in such a way that obviously correct answers get accepted as being correct it is clearly not acceptable. Already insecure people will get even more confused if they think they enter a correct answer, then get marked wrong and subsequently spend hours trying to find the (non-existent) mistake. –  Matt N. Jul 27 '12 at 8:31
Yeah, I agree. It is unacceptable. And, unfortunately, what I said was correct. I checked my work, and her entries into the computer many times. –  Chris Dugale Jul 27 '12 at 8:33
Dear Chris. Then I suggest that you put effort into fixing this issue first: the programmer is liable to deliver correct code hence if there are bugs they must fix them for free. Or else convince your university that the online system should be abandoned completely. I am on the side of the students being angry and frustrated as a consequence of an online system that is wasting their time. –  Matt N. Jul 27 '12 at 8:35
Of course I am aware that there are students who "hate" or "despise" maths and people pursuing it. But one should ignore these and cater for those who genuinely are trying to learn the subject. –  Matt N. Jul 27 '12 at 8:37
You're right. I should look into one of the two options you gave me. I personally dislike online systems because I find that they rarely give students quality advice and feedback, and grade solely on whether or not they entered the correct expression. THey could, of course, have done everything correctly, except for a lost negative sign. The student would be assured by a human being that they had understood the overall process, but had just made a careless error. –  Chris Dugale Jul 27 '12 at 8:51

You ask a subjective question and here is my (very) subjective answer. I have TA'd a couple of math lecture courses for non-math people and this is what worked for me.

Let me describe an exaggerated worst case scenario:

There are two sides: On one side there is evil math. An utterly useless subject which is for some reason very hard - obviously just to been mean. On the other side are the innocent students. Actually they are very smart but just not good at math. Why is this annoying subject destroying their average?

The lecturer is usually on the dark side. He/she really believes that people should learn math since it's useful. In his/her clouded point of view just learning for the exam is pathetic. He/she deliberately includes very hard problems in the exam, just to make sure many will fail and just the very best will pass.

The key for me was to somehow manage to be perceived as an ally of the students. You are the person who is actually good at math but understands the students. Then the students will feel more comfortable asking their "stupid" (in reality simple but helpful) questions and actually expect that they might learn something from the answer.

In my very first lesson I just ask the provocative question "Who thinks math is useful?" and then "And who thinks math is actually fun?" If enough people answer those questions with yes you can just forget everything I just said and have a good time. If most people say no, I continue with something like: "Here's the deal, I am one of those people who thinks math is both, useful and fun, but I understand that some of you might think differently. Actually this is not really a problem since we have the same goal, namely that you score as high as possible in the exams. This is what counts, right? If we have the time I will maybe sometimes try to say why this is all useful but first of all I will try to give you enough tools to ace your problem sets...

Something like that.

Then I think there is a big difference how math people tackle a problem than how many non-math students do it. We try to understand the problem first, find a solution conceptually and in the end writing down an "algorithm" to solve these kind of problems is pretty clear. When I am asked a question in a lesson how to solve a problem, I start with explaning the recipe without saying to much about the reason. In theory the students should be able to plug the problem into the mechanism and get a solution without thinking. Obviously I explain afterwards - following the steps of the solution - why this all works. I sell this part as "a way to memorize it". I am usually amazed how many people actually listen to the second part (one could expect they just stop after part 1), but apparently once they know that they have the tools no matter what they are able to follow a proper explanation with less pressure.

Obviously this is all very subjective and perhaps pretty declamatory but maybe it helps.

Edit To actually answer your three questions:

1. They treat you like garbage since they think you are one of math's evil minions who is there to torture them. Once they realise that you are actually another human being who is just doing his/her best to help they will treat you more gently.

2. You are super good at math, right? For you all of math is very easy and you obviously never make mistakes. Wait, no? The math you are learning makes you struggle as much as they do? Sometimes you are incredibly frustrated after starring at a paper for days without making any progress, aren't you? Let them feel that! The math they are doing is very hard (for them), you are obviously at a different place but that doesn't mean you can not totally relate to them! Obviously it is hard at times but if they ask the very simple questions then you can help.

3. Yeah ok, you disagree so far, but who cares? Your common goal is a good result in the exam. You might be somewhat happy if they appreciate what you are doing but if not, you are satisfied if they just realise that you might personally like it for some reason. Potentially you will never agree, but in the end it's also a matter of taste.

-
Wish I could give you a +1 for every paragraph. +3 for the explanation of the difference between how math and non-math people approach math problems. –  dj18 Jul 27 '12 at 14:41
Thank you dj18! –  Simon Markett Jul 27 '12 at 14:48
I just think these people were victim of the "system" described at A Mathematician's Lament... –  Ian Mateus Jul 27 '12 at 19:31
Of course I make mistakes--loose negative signs, ect. And, I wouldn't consider myself 'super good.' I do not think that I'm so utterly brilliant, nor do I think that there is any real reason to think so. Some people think I'm brilliant, but they're wrong! –  Chris Dugale Jul 27 '12 at 19:57
Chris, I hope you notice my occasional sarcasm. Point is that no matter how brilliant you might be, you will always find your master in math - sooner or later. –  Simon Markett Jul 28 '12 at 12:27

In my opinion mathematics/science should be taught with some history. Showing the original work of the author of a mathematical concept, for example, will help the student see, hopefuly understand, the thought process behind it and a question like "Why was this concept was introduced?". Study the discovery step by step and then see how it evolved and how it assumed its current form.

-

For problems in teaching I would consider the personal side as well.. maybe have a look into "non-violent communication" to deal with the frustated behaviour (for example with Rosenberg's book).. this is aimed to make it possible not to feel offended by offensive behaviour, instead seeing the needs of the other person behind his behaiour and still being in touch with one's own needs in this situation (being respected for example)..

-