I just stumbled across this today.

http://www.youtube.com/khanacademy

I have only looked at part of a couple of videos so far, but it looks at least as good as my high school physics teacher. Who wasn't as good as any of my math or chemistry teacher but I think I would have loved this in 7th grade. The advantage of this over live teachers is the ability to play it back as much as desired.

Any thoughts?

umbra

Sorry it took awhile for me to reply. You posted this when finals week was in full swing.

But ... this might be good for some learners. But frankly, I think a lot of college kids would have problems following this presentation.

There's too much "mathese" (i.e., I feel that the language should be adjusted for younger people). The presentation is a bit abstract (basically it doesn't differ too much from the typical college lecture) and even I feel uncomfortable with the disembodied voice over. But this criticism mainly applies to the more advanced discussions (like ferris wheel trig). The SAT prep stuff is aiight.

When I was in the 8th-9th grade range, I immensely enjoyed this PBS series:

http://www.its.caltech.edu/~tmu/

It had a live instructor (who you actually SAW). It had cool graphics/cartoons illustrating the concepts (a cartoon Einstein racing light beams and such). It even had actors and historical re-enactments shot on location. It was on the TV in the living room. And it was free.

But having said that ... to each his own. Some folks might like it. And being able to play back is an advantage.

This message has been edited. Last edited by: HonestBrother,

I'M AN ELITIST TOO.

quote:

Originally posted by HonestBrother:
Sorry it took awhile for me to reply. You posted this when finals week was in full swing.

But ... this might be good for some learners. But frankly, I think a lot of college kids would have problems following this presentation.

There's too much "mathese" (i.e., I feel that the language should be adjusted for younger people). The presentation is a bit abstract (basically it doesn't differ too much from the typical college lecture) and even I feel uncomfortable with the disembodied voice over. But this criticism mainly applies to the more advanced discussions (like ferris wheel trig). The SAT prep stuff is aiight.

When I was in the 8th-9th grade range, I immensely enjoyed this PBS series:

http://www.its.caltech.edu/~tmu/

It had a live instructor (who you actually SAW). It had cool graphics/cartoons illustrating the concepts (a cartoon Einstein racing light beams and such). It even had actors and historical re-enactments shot on location. It was on the TV in the living room. And it was free.

But having said that ... to each his own. Some folks might like it. And being able to play back is an advantage.

Last thought:

If you're going to present math in this fashion, I think you should at least use Powerpoint or something comparable. At least that's what I would do ... because it looks neater. IMO this presentation is a bit messy and disorganized.

This message has been edited. Last edited by: HonestBrother,

I'M AN ELITIST TOO.

quote:

If you're going to present math in this fashion,

I wasn't intent on presenting it, I was just intending to let other people know it was available on the internet, primarily for home schoolers. It looks better than the crappy job the nuns did when I was in grammar school.

I wanted to see what other people thought of it.

The disemdodied voice doesn't bother me since I focus on the subject and not the teacher. But their writing is often rather poor, but I have seen that same problem with live teachers.

um

quote:

Originally posted by umbrarchist:

quote:

If you're going to present math in this fashion,

I wasn't intent on presenting it

My "you" was generic. I didn't mean you personally.

quote:

I was just intending to let other people know it was available on the internet, primarily for home schoolers. It looks better than the crappy job the nuns did when I was in grammar school.

Good point.

quote:

The disemdodied voice doesn't bother me since I focus on the subject and not the teacher.

I've found that a good number of people are effected by the teacher.

But I'm generally the same as you. When I want to learn something, I get a book or something.

When I first started teaching I could not understand my students. I wondered why they had such difficulties when they could simply read the textbook to clear things up. If there was something in the book they didn't understand then they could ask me and I would clear it up.

I eventually discovered that it's probably the case that a large percentage of students really can't even comprehend the textbook.

quote:

I've found that a good number of people are effected by the teacher.

What age group were you teaching?

Do you think this might be affected by how they were taught in grammar school? A lot of teachers behave as though the student is supposed to be dependent on them.

um

quote:

Originally posted by umbrarchist:

quote:

I've found that a good number of people are effected by the teacher.

What age group were you teaching?

Do you think this might be affected by how they were taught in grammar school? A lot of teachers behave as though the student is supposed to be dependent on them.

um

Chicken or the egg? That's a good question. The majority of my experience is with college age students in freshman or sophomore classes.

My experience with them suggests that the weaker students are coming from a high school education in which either they weren't expected to intelligently read a textbook for information or they were supplied with very poorly written textbooks (of which I've seen a few). A few with whom I've spoken have said that they depended largely on class notes and their teacher's presentation.

For the most part, these students seem to study mathematics in a way that is almost completely opposite to the way that highly math literate people understand mathematics. For example, their retention of concepts is extremely poor. They'll study something (read "cram the night before the exam") and seemingly know it well enough for the exam for which they think it relevant. But by the time the next exam rolls around, what they supposedly "knew" for the previous exam is gone.

That poses a challenge for me. Mathematicians and most college math textbooks understand and present the subject linearly. What you learn in the beginning needs to be retained because it will be used for what is studied later. And this can be true for an entire of sequence of courses stretching over several semesters (a typical 3 part Calculus sequence culminating in Differential Equations is one example)

In the semester that just passed, I taught a course in college algebra. In the beginning of the course, we talked about solving linear equations. By the end of it, we were talking about more general polynomial equations. It's a fact that if you can't recall the basics of how to solve a linear equation or a general quadratic, then it's hopeless to try to understand polynomial or rational equations. But that's exactly what happens for many students. I'm lucky if I can get them to be cognizant enough of when and how to use the quadratic formula.

Expecting them to rely on the textbook? Forget it. Their math reading literacy tends to be poor. I spend a great deal of time teaching them just how to read. It's like a foreign language to them.

This message has been edited. Last edited by: HonestBrother,

I'M AN ELITIST TOO.

What is your teaching philosophy? How do you think your students learn best? What is(are) the best method(s) to apply to this end?

quote:

Originally posted by Khalliqa:
What is your teaching philosophy?

That is evolving. I like to think that it is student centered. So my expectations for the class depends on the class (to the degree possible).

It gets a lot easier with higher level classes. But these tend to be much smaller anyway and students in those classes are not lacking basic skills for the most part.

So my complaint is largely aimed at the lower level classes. The ones that bridge from high school to more advanced coursework. These classes also typically fulfill degree requirements for students who only need a few math credits to graduate.

The class I mentioned in the previous post was a large lecture. I started off with 150 students enrolled. It is practically impossible to be student centered with 150 students.

And in these classes, weak basic skills is a tremendous issue. See below for elaboration.

quote:

How do you think your students learn best?

By being drilled in preparation for multiple choice tests - which is half a joke since I don't give multiple choice tests.

quote:

What is (are) the best method(s) to apply to this end?

I hope you don't mind if I don't answer this question. See previous comment.

Instead, I'll elaborate on what I actually do.

The biggest problem - as I see it - is that there is a tremendous disconnect between the way students are trained in mathematics at the primary and secondary level ... and what's expected of them in the college classroom.

Going back to the course I mentioned ... in many ways, I have little choice about how to teach that course:

1. It has upwards to 150 students enrolled.

2. The textbook (which I don't really care for) is selected by the department.

3. The course syllabus is more or less uniform to ensure that students in different sections of the class learn roughly the same things.

4. The syllabus is too long. There's too much that needs to be covered.

So in this situation, my role - as I see it - is primarily to facillitate the students as far as possible ... and to orient them within this framework.

Secondarily, my role is to adjust that framework to my own conception of what I believe is most important for students to know from the course.


Having said that ...

My method:

• To distill the course to as few basic ideas as possible. These are the key concepts. The conceptual leitmotifs.
  
  
• Repetition. Repetition. Repetition.
  
  
• Elaboration and development.
  
  
• Repetition. Repetition. Repetition.

This approach addresses multiple student issues:

Problems

• The course takes for granted many basic skills in which the students are lacking and I have only 1 week in which to directly address those deficiencies.
  
  
• The text (and syllabus) covers too many topics - which many students find disconnected and unmanageable.
  
  
• Many students have poor long term retention.
  

So my approach does this:

• Makes explicit at the beginning what I think students should learn from the course (set expectations).
  
  
• Isolates a handful of basic skills which I know will be drawn upon most often and so are most critical to achieving the course goals. These will be reinforced throughout the course.
  
  
• Focuses attention on what is most essential in the course and textbook. I essentially rewrite the book. I've at least extensively edited it for the purposes of the course. This is emphasized in the lecture, the assignments and exams, and the study guides I make up for the exams (repetition).
  
  
• Constant reinforcement (repetition again). Every time we move to a new topic (development and elaboration), I point out how that topic relates to the basic concepts (repetition) and how the most basic skills are being used again. I might even briefly review them each time we draw upon them to do something new. The best students might even get a little bored.
  
  
• Each time we move to a new topic, I try to motivate the reason why we're interested in that topic, how it relates to previous topics, and what we stand to gain from doing something new (development and elaboration). I'll announce something like, "The bad news is we're doing more math. The good news is it's really the same stuff in a slightly different form."
  
  
• Emphasize how the most basic ideas and skills can be understood from multiple perspectives (mainly symbolic and visual ... but also practical if there is time). I try to get them used to translating between these different points of view and understanding the advantages of being able to do so. Hopefully they develop conceptual fluency over time. Development and elaboration. Repetition.
  

I've had a few students tell me that though they struggle with math, I make it easy - at least understandable.

This message has been edited. Last edited by: HonestBrother,

I'M AN ELITIST TOO.

I have a chatty and conversational lecture styles. I like to engage. I'm not one who spends the entire period talking, writing, and looking towards the board. I spend just as much time facing the students and asking them questions. I also encourage them to ask questions. And as a policy, I always answer them. No matter how dumb. No matter how much the stronger students roll their eyes. I find that you can often take an apparently dumb question and turn it into a pivotal learning moment.

For a small class, this works fine. But it can be quite challenging for a larger class and so it makes me that much more efficient in the presentation.

I like to think that I'm witty (though I wouldn't necessarily say "entertaining"). I'm at least self deprecating enough to make myself the punchline of a corny math joke. At any rate, I try to convey my own enthusiasm and excitement for the subject. It is something to be discussed with interest. Not something to be lectured to about. It is something to be intimately understood ... down to the marrow in your bones ... and not something to be merely memorized by rote. At some point, I tell many of my classes that I can't even remember my own phone number ... If * I * had to depend on memorization ... well then ...

I'm teaching this course again next semester and will probably incorporate more technology: meaning more and better graphics.

This message has been edited. Last edited by: HonestBrother,

I'M AN ELITIST TOO.

While I'm being sleepless ... I will add that for the most part, students who attend class regularly aren't a big problem.

My irritation is with those who'll miss a whole week and write email asking if they missed anything important (I don't have an attendance policy) ... and with students who are failing and show no interest in their grades until after the semester is over and suddenly they want you to make a special office hour in which to discuss their grade (IN PERSON they demand by email). It's cold outside. And I don't have to be there. Not going to happen.

Why are they taking mathematics courses? What are their majors?

um

quote:

Originally posted by umbrarchist:
Why are they taking mathematics courses? What are their majors?

um

The course I've been talking about fulfills a general education requirement. There are no math majors taking the course. The majors represented run the gamut.

In the same way, you don't have to be an English major to be required to take an English composition/literature class in order to get an undergraduate degree.

quote:

The course I've been talking about fulfills a general education requirement. There are no math majors taking the course. The majors represented run the gamut.

That explains their attitude. They see it as useless junk they have to take and just want to pass. If they wanted to be engineers I would be worried. LOL

um