The Teaching of Math

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  • Reply 61 of 99
    midwinter, what methods do you use in your classes?
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  • Reply 62 of 99
    Quote:
    Originally Posted by BRussell


    midwinter, what methods do you use in your classes?



    Depends on what the class is. But for, say, a composition class, an average day will look like this:



    5-10 minutes of BS at the front

    10-15 minutes of talking about the reading and me asking questions about it to make sure they got it.

    5 minutes at the end of this with me asking them questions that model some skill (say, using multiple texts to make an argument)...so "How would X respond to Y?"

    30 minutes of me asking them specific questions to write about: how would X respond to Y? Find quotations in X that you think Y is responding to? Explain how each quote responds. That kind of thing.



    When I'm introducing them to new skills, I'll do a good bit of group work.



    When we're revising essays, they pass them around. I give them a set of concerns and they tear them up with attention to those. Tomorrow morning, for instance, we're "de-funking" essays (revising for clarity).



    I teach an advanced college writing class that I hardly talk in. We do 5 weeks of literature, which is me asking questions and them talking. Then they present a conference paper and have Q&A afterwards. Then they revise that paper into a 20 pager and we spend an entire class on each one.



    In my upper-division literature courses, it's typically a student presenting on something for 10 minutes at the top and then a free-wheeling discussion of whatever with me trying my best to guide and answer questions. If I need to, I'll lecture. Usually I don't. Tomorrow, I'll probably lecture a good bit, since the poem is 50 pages long.



    In my graduate seminar this semester, one student presents a conference paper (20 minutes) and then we spend 40 minutes grilling him/her. For the rest of the time, I come in with about 15-20 questions. If we get to them, we get to them. If we don't, we don't. Freewheeling, open discussion.
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  • Reply 63 of 99
    I should also add that sometimes, I'll type up questions and have them group up and answer them. That's the discussion for the day.
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  • Reply 64 of 99
    I am a second year student at The Helsinki University of Technology in Finland. At the moment I'm having this maths course called "S3" which means it's the 3rd course of "electricity-oriented mathematics" meaning that it's the kind of maths I will need for my further studies.



    At my university the teaching goes like this: you have three two-hour lectures a week plus two two-hour exercises. The lectures are more theory-oriented and the during the excercises a teacher shows us how to solve the problems that we got. Plus we get extra points beforehand for the exams if we have already solved problems before we attend the excercises.



    Mainly it's a bit boring to try and solve the problems alone, so we tend to call eachother for hints and tips or then we simply work together. Working in groups is more social and more fun. But if you are very good at the subject, it's more like helping the ones who have no idea what to do...



    By the way, right now we are having nabla, div, curl and all that - and I'm loving it! Unfortunately there are not many people who can follow what's going on
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  • Reply 65 of 99
    Here's an example of how American schooling doesn't really teach you how to do math except in a practical way and what I would like to see taught.



    I scored 750 on my Math SAT and passed four Calc classes, so I must be pretty good at it. But I can't really think in mathematical terms except for the step by step recipes. One day I am going to take some time to learn but here is an example.



    For example, at my job new people are supposed to take a call in 10 minutes, but experienced people can take it in 8 minutes. So I wanted to figure out how much more productive they are. I can't do it in my head. First I thought, "they take it 25% faster", but that doesn't mean they are doing exactly 25% more. I'm sure with a pen and paper I could figure it out, but that is not the point. I should be able to SEE the answer and FEEL the relationships intuitively. I mean, the only thing I figured out was that in 8*10=80 minutes they take 10 calls and I take 8, therefore, they are 25% more productive. OK, so maybe the answer is 25%. But I should be able to get to it without fumbling around.
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  • Reply 66 of 99
    I think the word "maths" fell out of favor in American English simply because it is too difficult to pronounce. Also, as is our habit, shorter words usually win out over longer or more confusing ones.
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  • Reply 67 of 99
    I finally got a chance to read through this thread and feel inclined to add my two cents. While I am certainly no expert at either math or education and was in fact a spectacular failure at all levels of schooling my personal bias is that yes, there should be more group discussion and activity in math class. I say this because of personal experience.



    When I was a junior in high school I was assigned to a teacher for my sequential math three class (basically algebra and trig) who I was completely incompatible with. I requested almost immediately to be transferred from this class, but was denied and wound up using the class time to catch up on some much needed sleep after realizing I could learn nothing from this teacher who happened to be a very bitter woman named Miss Weiner. After being forced to have a meeting with my guidance counselor, parents and Miss Weiner where I was accused of being on drugs I was finally granted my request to switch to another teacher. Unfortunately this was way too late in the year to do any good and I still failed the class.



    I then took the same class in summer school and had yet another brilliant instructor, a crazy guy who was only allowed to teach summer classes and would yell at us in German and while I did better I was still a few points short of a passing grade.



    I next took the class in my senior year with a teacher named Doctor Hormuzzi. The kind of teacher whose name you remember because he was brilliant and genuinely helped you learn. Dr. Hormuzzi started off teaching us in a normal fashion, but over the course of the first few weeks the class developed a unique rythymn whereby he would randomly and without warning give us a test and we would all cheat. At first we did this in a low key fashion, but after awhile we realized he didn't care that we were cheating. What ended up happening was that we developed our own groups and we would go through the problems together or we would do them by ourselves. Whatever we preferred we could do. Some students always worked together, some worked mostly by themselves, but ask the occassional question of others and no one was forced to work with anyone they didn't like. I wound up getting about an eighty-five or so on the NYS Regents and to this day I don't think I would have passed with any other teacher.
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  • Reply 68 of 99
    Quote:
    Originally Posted by BRussell


    midwinter here's an article about elementary math education that might interest you.



    Thanks for that link. I saw it and forgot to save the article.



    I've known plenty of professors to use "group work" to break up topic pace in the classroom, but I've never seen it used effectively for actually getting students to learn how to do something in a skills class. In a discussion class, it works to keep the number of opinions expressed down to a manageable number, but also gets students to participate who normally would just sit there, so it can be effective.



    But for skills (traditional lecture stuff), forget it. I've only been teaching 18+ years, at four regional schools, in several subject areas, so I may have some learning to do yet. Groups mean that the folks who did their homework get to explain it to those who didn't, so the teacher doesn't have to work as hard.



    And in some cases, it means the professor doesn't have to work at all. We can just have a "discussion" and all go home feeling good about what we talked about.
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  • Reply 69 of 99
    brussellbrussell Posts: 9,812member
    Quote:
    Originally Posted by finboy


    Thanks for that link. I saw it and forgot to save the article.



    I've known plenty of professors to use "group work" to break up topic pace in the classroom, but I've never seen it used effectively for actually getting students to learn how to do something in a skills class. In a discussion class, it works to keep the number of opinions expressed down to a manageable number, but also gets students to participate who normally would just sit there, so it can be effective.



    But for skills (traditional lecture stuff), forget it. I've only been teaching 18+ years, at four regional schools, in several subject areas, so I may have some learning to do yet. Groups mean that the folks who did their homework get to explain it to those who didn't, so the teacher doesn't have to work as hard.



    And in some cases, it means the professor doesn't have to work at all. We can just have a "discussion" and all go home feeling good about what we talked about.



    I have noticed that lazy teachers seem to love the group discussions. And it's also true that other students' ideas probably aren't as valuable as an expert in the topic. "Well, one time? my friend? one time he blah blah" - WHO GIVES A FLYING FUCK?!?



    On the other hand, I remember getting some really good help from other students in classes, and it being helpful to me to explain things that I understood.
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  • Reply 70 of 99
    x xx x Posts: 189member
    Quote:
    Originally Posted by midwinter


    I find it difficult to believe that the most effective way to teach math is to have someone at the front of the room writing things on the blackboard.



    It's not, and to use the example that skatman gave...



    The math teachers are teaching you how to use the hammer and not when to use it.
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  • Reply 71 of 99
    Quote:
    Originally Posted by finboy


    I've known plenty of professors to use "group work" to break up topic pace in the classroom, but I've never seen it used effectively for actually getting students to learn how to do something in a skills class.



    Interesting. How have you seen it used? What kinds of skills? What kinds of instructions?



    Quote:

    In a discussion class, it works to keep the number of opinions expressed down to a manageable number, but also gets students to participate who normally would just sit there, so it can be effective.



    I don't know about under-involved students, but I guess it depends on what the task is.



    Quote:

    But for skills (traditional lecture stuff), forget it. I've only been teaching 18+ years, at four regional schools, in several subject areas, so I may have some learning to do yet.



    Well, you have 7 years and one regional area on me.



    Quote:

    Groups mean that the folks who did their homework get to explain it to those who didn't, so the teacher doesn't have to work as hard.



    Well, that depends on what the task is.



    Quote:

    And in some cases, it means the professor doesn't have to work at all. We can just have a "discussion" and all go home feeling good about what we talked about.



    Yeah. That's when it's bad bad bad. Of course, you could make the same argument about any level of discussion; rather than the professor filling up the students' empty heads with his superior knowledge, everyone talks about whatever the topic is.
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  • Reply 72 of 99
    trumptmantrumptman Posts: 16,464member
    I obviously don't teach math at a college level. I teach it daily at the elementary level though and do use a combination of methods to try to pound this information into the heads of children.



    On the days where we have purely independent work, we do your very traditional lecture followed by guided practice and finally end with independent practice. During the lecture portion, I will always attempt to help the children some how relate this skill to real life so they understand why they are doing more than solving problems.



    There are days where I tell the children that I am not grading their answers, but I am only grading their work related to the answer. On these days, I leave the teacher edition of the math book, and all the answers in it out and available. The students are allowed to go look in it as long as they do not have anything to write with in their hand.



    One strategy I use is called partner pair share. The students work with a partner, share a paper and the grade associated with that one paper. They trade off each problem and while the one partner is doing the work, the other is supposed to be monitoring their work and insuring it is done accurately. During partner pair share, the partner is self selected using criteria I provide. (examples, must be in a different row, different gender, different shoe color, etc.)



    Another partner strategy I use is simply rotating partners. The children all have numbers and I have a wheel that simply changes their partner each time it is moved. If number 4 worked with number 23 last time, he or she will have to work with number 24 this time. Children keep their own respective papers but it is understood that having the same work and answer is not copying.



    Studies have shown that even toddlers can tell if someone truly needs help and so the students are told that they are allowed to help their partner, but that they may refuse help and send the partner to me if the partner is trying to "borrow their brain." This phrase helps the students understand that if your partner needs assistance with understanding, it must be provided. If they don't want to think or learn, and just want to copy, they don't have to endorse that.



    Nick
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  • Reply 73 of 99
    finboyfinboy Posts: 383member
    Quote:
    Originally Posted by BRussell


    I have noticed that lazy teachers seem to love the group discussions. And it's also true that other students' ideas probably aren't as valuable as an expert in the topic. "Well, one time? my friend? one time he blah blah" - WHO GIVES A FLYING FUCK?!?



    One of my favorite comments that I hear from students is "The class should allow us to express our opinion" (not in my class, obviously, b/c there's very little opinion to it, but about others). Given that most students haven't any experience with the topic at hand, how much is their opinion worth, exactly? Of course, with graduate students it's different, and for different areas other rules apply, but I used to get so frustrated hearing this from other students, even back when I was in school. Your opinion about something that you know nothing about isn't relevant. I once had a history teacher say that to a student, and I laughed about it for weeks. It wasn't demeaning in the way it was done, but it was true.



    Quote:

    On the other hand, I remember getting some really good help from other students in

    classes, and it being helpful to me to explain things that I understood.



    Yeah, me too. But those discussions were outside of class. On our own time, unless we all had relevant experience to bring to class. Otherwise, eyes would roll.



    I've discovered another great time waster: presentations! I had a student tell me the other day that 6 out of 14 sessions this semester were reserved for group presentations. In a graduate course. Man, gimme some of that. Sounds like Fat City. Of course, the student was complaining that the class seemed kind of "fuzzy" to him. I remember taking that class, and it was far from "fuzzy" back in the day. Kinda important, as I recall. Oh well.



    I'm all about teaching innovations, and I try to improve the class each week, each semester. In fact, a large part of my career has been about bringing innovative techniques and technology into the classroom. But I wonder about the flavor of the month and the drive to "innovate" for the sake of changing one's syllabus. Maybe that fits some disciplines, but standardized test scores and my experience on the other end of the process indicates that innovation in skills classes leads to poor outcomes.



    Makes the teaching profession easier though. In fact, I'd argue that anything that makes teaching easier makes education worse. I've never found teaching to be any kind of easy. Fun, yes. Rewarding, yes. But easier? Nope. There are always new challenges.
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  • Reply 74 of 99
    brussellbrussell Posts: 9,812member
    I found this video of midwinter teaching one of his classes.
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  • Reply 75 of 99
    midwintermidwinter Posts: 10,060member
    Quote:
    Originally Posted by BRussell


    I found this video of midwinter teaching one of his classes.



    I have a friend who used to do something like that in his classes, although not on the first day. He would have one of his buddies post as a "cheater" during the first test, and he would "catch" him, start screaming at him, throw him against the wall, and forcibly remove him from the class while screaming he was going to have him expelled.



    In short, I'm pretty sure that cell phone is a plant.



    I have, however, answered a student's cell phone before.
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  • Reply 76 of 99
    brussellbrussell Posts: 9,812member
    You know, I didn't even consider that. I guess I'm just not devious enough. I thought it was a fake, because of the way the camera moved to the phone before the teacher smashed it. But I assumed it was all an act, rather than a real class with a plant.
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  • Reply 77 of 99
    regreg Posts: 832member
    I had a teacher in 7th grade that made the same type of statement the first day of class. I went to a very strict catholic school and one of my friends was always getting into trouble. The first day of class Mr. Smith ( good teacher, not as scary as some of the nuns) had Mike sit in the front row right in front of him. Mike gave this defiant look to him. Mr. Smith walked over picked him up by the front of his shirt and put him out the window. Mike was told to stand there and pay attention for the rest of the class. No one ever did anythng wrong in his class. He turned out to also be one of the better teachers. You could do that 40 years ago.
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  • Reply 78 of 99
    midwintermidwinter Posts: 10,060member
    Quote:
    Originally Posted by reg


    I had a teacher in 7th grade that made the same type of statement the first day of class. I went to a very strict catholic school and one of my friends was always getting into trouble. The first day of class Mr. Smith ( good teacher, not as scary as some of the nuns) had Mike sit in the front row right in front of him. Mike gave this defiant look to him. Mr. Smith walked over picked him up by the front of his shirt and put him out the window. Mike was told to stand there and pay attention for the rest of the class. No one ever did anythng wrong in his class. He turned out to also be one of the better teachers. You could do that 40 years ago.



    God I wish I could do that now. My students get all upset when I just throw them out of the classroom.
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  • Reply 79 of 99
    trick falltrick fall Posts: 1,271member
    Quote:
    Originally Posted by midwinter


    God I wish I could do that now. My students get all upset when I just throw them out of the classroom.



    I had this one teacher Mr. Lamb who had a very monotonous voice and he insisted on reading us the Illiad. Anyway many students would fall asleep so he came up with the "alarm box" so you would fall asleep at your desk and he would throw an empty copy paper box at your head. Either that or he would sneak up on you and bang a rolled up copy of the times on your desk. Scared the crap out of you and was very amusing for the rest of the class.
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  • Reply 80 of 99
    midwintermidwinter Posts: 10,060member
    Quote:
    Originally Posted by trick fall


    I had this one teacher Mr. Lamb who had a very monotonous voice and he insisted on reading us the Illiad. Anyway many students would fall asleep so he came up with the "alarm box" so you would fall asleep at your desk and he would throw an empty copy paper box at your head. Either that or he would sneak up on you and bang a rolled up copy of the times on your desk. Scared the crap out of you and was very amusing for the rest of the class.



    Heh.



    a) any time a teacher insists on reading an entire book TO a class, my first thought is "Well. That's a lot less prep, isn't it?"



    b) Students falling asleep in my classes is rare (for reasons unrelated to my magnetic personality), but once, a student fell asleep in class. Hard. Snoring. I continued talking and wrote on the board "Slowly, and in small groups of no more than three at a time, begin putting your things away. When everyone has put everything away, slowly, quietly, TURN YOUR DESKS AROUND. We will continue our discussion as you do this. When you are finished, slowly, and in small groups, leave the classroom. Have a nice weekend." We left this guy in the classroom, asleep with his desk facing the wrong direction.
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