or Connect
AppleInsider › Forums › Other Discussion › AppleOutsider › The Teaching of Math
New Posts  All Forums:Forum Nav:

The Teaching of Math - Page 2

post #41 of 100
BTW, I was just kidding. Greg made me laugh...
"If I had played my career hitting singles like Pete (Rose), I'd wear a dress." - Mickey Mantle
Reply
"If I had played my career hitting singles like Pete (Rose), I'd wear a dress." - Mickey Mantle
Reply
post #42 of 100
yeah i could only name three.

...and one's not even a real person.
post #43 of 100
Quote:
Originally Posted by ShawnJ

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


Who Natrilova? Yeah I don't think she is a she either...
"If I had played my career hitting singles like Pete (Rose), I'd wear a dress." - Mickey Mantle
Reply
"If I had played my career hitting singles like Pete (Rose), I'd wear a dress." - Mickey Mantle
Reply
post #44 of 100
I think she was from the old Czechoslovakia, too.

Czech girls can be gorgeous.
post #45 of 100
Quote:
Originally Posted by dmz

midwinter, check out the Saxon math program. I think this is the silver bullet. A rotation of concepts that seems at first pointless and painfully redundant, but it will have your 8-year old doing algebraesque operations.

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

Quote:
Strengths

Saxon Math prides itself on its ability to help marginal students acquire relatively high scores in standardized tests. It is extremely strong in the areas of arithmetic computation and mathematical principles (i.e., the "distributive principle," "commutative principle," etc.). It is relatively easy to teach and, from fourth grade up, requires little parental involvement.

Weaknesses

For students who don't require the drill, Saxon Math can be boring. In early elementary grades, it is relatively pricey. Compared to other programs on the market, it is weak on application and presentation.

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...
post #46 of 100
Quote:
Originally Posted by tonton

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.

In our desire to impose form on the world we have lost the capacity to see the form that is there;
and in that lies not liberation but alienation, the cutting off from things as they really are. --...

Reply

In our desire to impose form on the world we have lost the capacity to see the form that is there;
and in that lies not liberation but alienation, the cutting off from things as they really are. --...

Reply
post #47 of 100
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".

In our desire to impose form on the world we have lost the capacity to see the form that is there;
and in that lies not liberation but alienation, the cutting off from things as they really are. --...

Reply

In our desire to impose form on the world we have lost the capacity to see the form that is there;
and in that lies not liberation but alienation, the cutting off from things as they really are. --...

Reply
post #48 of 100
Thread Starter 
Quote:
Originally Posted by Guybrush Threepwood

Come on...

The Russian from Rocky IV?

That dude is fascinating. Swedish. Four languages. Captain of the Swedish Olympic Karate team. MA in Chemistry and won a Fulbright to go to MIT but turned it down.
Gangs are not seen as legitimate, because they don't have control over public schools.
Reply
Gangs are not seen as legitimate, because they don't have control over public schools.
Reply
post #49 of 100
Quote:
Originally Posted by midwinter

That dude is fascinating. Swedish. Four languages. Captain of the Swedish Olympic Karate team. MA in Chemistry and won a Fulbright to go to MIT but turned it down.

And looks like Groverat!
"If I had played my career hitting singles like Pete (Rose), I'd wear a dress." - Mickey Mantle
Reply
"If I had played my career hitting singles like Pete (Rose), I'd wear a dress." - Mickey Mantle
Reply
post #50 of 100
Quote:
Originally Posted by dmz

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.

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.
You can't quantify how much I don't care -- Bob Kevoian of the Bob and Tom Show.
Reply
You can't quantify how much I don't care -- Bob Kevoian of the Bob and Tom Show.
Reply
post #51 of 100
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.
post #52 of 100
Quote:
Originally Posted by Placebo

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?
post #53 of 100
Quote:
Originally Posted by BRussell

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).

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.

In our desire to impose form on the world we have lost the capacity to see the form that is there;
and in that lies not liberation but alienation, the cutting off from things as they really are. --...

Reply

In our desire to impose form on the world we have lost the capacity to see the form that is there;
and in that lies not liberation but alienation, the cutting off from things as they really are. --...

Reply
post #54 of 100
Quote:
Originally Posted by Guybrush Threepwood

Russian accents?

Russian accents are the sexiest.
post #55 of 100
Quote:
Originally Posted by gregmightdothat

Well, they were probably looking at you confused cause that's 6 dollars change

Ouch! Goes to show that one should not post when one is drunk
post #56 of 100
Thread Starter 
Quote:
Originally Posted by tilt

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


But if TWO are drunk, it's totally OK.
Gangs are not seen as legitimate, because they don't have control over public schools.
Reply
Gangs are not seen as legitimate, because they don't have control over public schools.
Reply
post #57 of 100
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.

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.
post #58 of 100
Quote:
Originally Posted by hardeeharhar

You should do that AND send them to socialize/learn with other children; but seeing as you live in a town of ~3500, I can see where you can rationally argue that your family constitutes the only source of children for the school system.

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?
post #59 of 100
Thread Starter 
Quote:
Originally Posted by skatman

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.

Sometimes things that are difficult to believe suggest a discipline throughly untouched by developments in pedagogy since the 1970s. Or since the 18th century.

I started this thread because it stuck me as mighty odd that classroom activities that are common in many other disciplines (something as simple as group work) are foreign to so much of math instruction, and I wanted to know whether my experiences were an anomaly. It would seem they are not.

Now I'm curious to hear how other countries do it. How is math taught in Japan? In India?
Gangs are not seen as legitimate, because they don't have control over public schools.
Reply
Gangs are not seen as legitimate, because they don't have control over public schools.
Reply
post #60 of 100
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.
post #61 of 100
Thread Starter 
Quote:
Originally Posted by backtomac

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.

Yes. Like a few other people around here, I'm a university professor.

/me frantically tries to finish prepping for class this evening....
Gangs are not seen as legitimate, because they don't have control over public schools.
Reply
Gangs are not seen as legitimate, because they don't have control over public schools.
Reply
post #62 of 100
Quote:
Originally Posted by midwinter

Yes. Like a few other people around here, I'm a university professor.

/me frantically tries to finish prepping for class this evening....

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?
post #63 of 100
Quote:
Originally Posted by backtomac

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?


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.
"In a republic, voters may vote for the leaders they want, but they get the leaders they deserve."
Reply
"In a republic, voters may vote for the leaders they want, but they get the leaders they deserve."
Reply
post #64 of 100
Thread Starter 
Quote:
Originally Posted by backtomac

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?

I would argue that not only can you mix methods, but that you SHOULD do it. Were I a math instructor (and if you knew me, you'd know what a laugh that idea is) I would push your example even further: have the groups then teach the class, then position weaker students together and stronger students together, then mix weak and strong students, then have groups come up with lists of things they don't understand and have other groups figure them out, and on and on.
Gangs are not seen as legitimate, because they don't have control over public schools.
Reply
Gangs are not seen as legitimate, because they don't have control over public schools.
Reply
post #65 of 100
midwinter, what methods do you use in your classes?
post #66 of 100
Thread Starter 
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.
Gangs are not seen as legitimate, because they don't have control over public schools.
Reply
Gangs are not seen as legitimate, because they don't have control over public schools.
Reply
post #67 of 100
Thread Starter 
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.
Gangs are not seen as legitimate, because they don't have control over public schools.
Reply
Gangs are not seen as legitimate, because they don't have control over public schools.
Reply
post #68 of 100
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
post #69 of 100
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.
post #70 of 100
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.

Proud AAPL stock owner.

 

GOA

Reply

Proud AAPL stock owner.

 

GOA

Reply
post #71 of 100
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.
post #72 of 100
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.
Never had ONE lesson.
Reply
Never had ONE lesson.
Reply
post #73 of 100
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.
post #74 of 100
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.
post #75 of 100
Thread Starter 
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.
Gangs are not seen as legitimate, because they don't have control over public schools.
Reply
Gangs are not seen as legitimate, because they don't have control over public schools.
Reply
post #76 of 100
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

"During times of universal deceit, telling the truth becomes a revolutionary act." -George Orwell

Reply

"During times of universal deceit, telling the truth becomes a revolutionary act." -George Orwell

Reply
post #77 of 100
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.
Never had ONE lesson.
Reply
Never had ONE lesson.
Reply
post #78 of 100
I found this video of midwinter teaching one of his classes.
post #79 of 100
Thread Starter 
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.
Gangs are not seen as legitimate, because they don't have control over public schools.
Reply
Gangs are not seen as legitimate, because they don't have control over public schools.
Reply
post #80 of 100
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.
New Posts  All Forums:Forum Nav:
  Return Home
  Back to Forum: AppleOutsider
AppleInsider › Forums › Other Discussion › AppleOutsider › The Teaching of Math