The Teaching of Math - Page 2

BTW, I was just kidding. Greg made me laugh...

yeah i could only name three.

...and one's not even a real person.

Who Natrilova? Yeah I don't think she is a she either...

I think she was from the old Czechoslovakia, too.

Czech girls can be gorgeous.

From http://www.sonlight.com/saxon.html


Really, really really doesn't seem appropriate for my 8 year-old...

DMZ, please let us know, were you home schooled? This gives me an idea for a new thread...

Yes, from about the 6th grade on -- I essentially taught myself (with curriculum) from there, and started college early.

I hear a lot of stories from people who talk about the less savory aspects of high school, politics, etc. -- I feel like I escaped a prison sentence.

On the Saxon review, that is the polar opposite from what I've experienced. (weak on application, etc.)

They got started in the homeschool market --- the curriculum was created by a guy who was once told "he could never learn math". It's a hit in charter schools and I think some public schools are looking at it as well (Harcourt bought Saxon a year or two ago).

****Breaking news
...my wife just leaned over and read that review and quipped, and I quote: "that's such bullshit it's not even funny".

And looks like Groverat!

Saxton math is great, I did their "pre algebra" book cover to cover, every exercise in my 8th grade year, and slept through high school algebra.

I think math past high school sophomore year should be taught as a two-week crash course at the start of college. So much of the material is such that it will never be applied outside of a math/science career.

Unfortunately, that is how it seems to go in many cases: People going to college are tested and often found to be so poor at basic math that they are required to take remedial math (that usually doesn't count toward college graduation).

But I have to ask about "never being applied outside of a math/science career." Is college supposed to be job training? How much of what people take in college is career-related? English? History? Geography? And is this a good or bad thing?

I hear that -- if I set one "pre" Algebra text a year, I set a dozen; it's a total disgrace. In some cases, my 11 year-old could get a C.

Crazy.

Russian accents are the sexiest.

Ouch! Goes to show that one should not post when one is drunk

Sometime things that are difficult to believe actually work pretty well.
Classroom instruction is only one part of the puzzle... alone it's not the most effective, but when combined with after class activities and seminars it works well.

Did you go to public school? If so your behavior doesn't support your arguement of public education 'improving' one's social skills. You do realize that in this post alone you've gone out of your way to insult two posters?

Midwinter,

Do you teach at the college level or high school? Just curious to know, I'm not a teacher but find the discussion interesting.

PS I did stay at a Holiday Inn Express a few weeks ago.

Midwinter,

Does it have to be an either or proposition? Couldn't you use several methods of teaching in your class? For example, couldn't you do traditional blackboard instruction and then also have groups that solved complicated problems?

Most definitely, I did attend public schools.

And no, I don't care that you think I 'went out of my way to insult' anyone.

midwinter, what methods do you use in your classes?

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

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.

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.

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.

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.

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.

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

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.


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.

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

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.