Teaching calculus today in college

[mathwonk]

cdotter, it is hard even to understand your complaint. the point is that any significant math subject is really hard and has many ramifications, not all of which are ever present in anyone particular discussion. Even if you read everything in the assigned textbook you will likely not completely understand it, nor even encounter much of what the professor will say in class. what you will do is prepare your mind to better understand what is said in class.

If indeed you do not want the prof to merely regurgitate what is said in the book, you are even more recommended to read it yourself in advance, to contrast that presentation with the professor's. and if you read the book in advance you just might come up with a question you want to ask.

after reading your post three times, i think your mistake is assuming that moonbear was saying the lecturer is merely going to regurgitate the book to you. the subject itself is much larger than what is said in the book and the professor hopefully has a global grasp of it.

only with a particularly dull class, or one which does not itself ever read the book, does the average professor ever limit herself to saying only what is found there. still some classes complain if the class discussion contains more than the book's does. some students think a course should "cover" the content of one assigned book, and not go beyond.

Actually the idea is to convey a good impression of the nature of the topic, and the book is merely one resource. There is no rule that students may not go to the library and read even more books on the same topic. If they do and they choose a good one, it will barely seem to resemble the one for the course, as only monkey see monkey do books all treat the subject the same way.

 

[khemix]

Except students have the same attitude in biology classes. What the students don't seem to recognize is that if they get lost during lecture, they can make a note about where and now they can save time reading their textbook by going straight to that section rather than having to read the whole book end-to-end with no idea of what is important.

I think its different in biology. If you are unclear about one section in a biology lecture, usually the following sections you can still understand because the subject is intuitive. In math, everything builds up from previous results. Whats worse, is you won't understand any math until you have all prior results down cold. With science courses, you can still sort of ignore past results.

Do you have any idea how long it takes to write a textbook? Even more so, how long it takes to write a GOOD textbook? Why reinvent the wheel if there are good textbooks already available?

I imagine no longer than writing them on the board. The book doesn't need to be a classic with 50 questions in each chapter. But this problem only arises in courses where the teacher does not follow the book closely. In such a case, the teacher should seriously consider adopting a new book. Or atleast type up lecture notes. Is it really necessary to be copying theorems? And at the same time be listening...

 

[morphism]

I imagine no longer than writing them on the board. The book doesn't need to be a classic with 50 questions in each chapter. But this problem only arises in courses where the teacher does not follow the book closely. In such a case, the teacher should seriously consider adopting a new book. Or atleast type up lecture notes. Is it really necessary to be copying theorems? And at the same time be listening...

You "imagine"? Clearly you've never tried this, then. Moreover, it's not like professors simply wing their lectures all the time either; most actually prepare a set of notes beforehand. And have you tried to TeX anything? It's not exactly a pleasurable experience. So if a professor chooses not to waste his/her time typing up lecture notes, I will not hold that against him/her. These people have better things to do.

Your posts in this thread really show a great level of ignorance. But this doesn't come as a surprise to me, having read an earlier post of yours on people who pursue PhDs.

 

[khemix]

You "imagine"? Clearly you've never tried this, then. Moreover, it's not like professors simply wing their lectures all the time either; most actually prepare a set of notes beforehand. And have you tried to TeX anything? It's not exactly a pleasurable experience. So if a professor chooses not to waste his/her time typing up lecture notes, I will not hold that against him/her. These people have better things to do.

Your posts in this thread really show a great level of ignorance. But this doesn't come as a surprise to me, having read an earlier post of yours on people who pursue PhDs.

So scan what you write and compile it into a notebook students can buy. I've used math symbols, and I agree they are time consuming. Still, if I can do 4 page lab reports every week full of them, a book should not be that much of a problem. My point is math classes should focus more on learning instead of writing out the textbook, a view that many students share. This can be done by preparing lectures in advance, the way science courses do.

How do my posts show a level of ignorance? I am sharing my own views that are shared by many undergrad students. I don't pretend to know the master plan behind undergrad work or deny professors know what is best for me. I am just saying that math lectures at their current state are not very useful.

[And I still hold my view on PhDs, despite the fact that it is completely off topic. People pursue them for fame, fun, or money; not for the 'betterment of humanity'.]

 

[mbisCool]

So scan what you write and compile it into a notebook students can buy. I've used math symbols, and I agree they are time consuming. Still, if I can do 4 page lab reports every week full of them, a book should not be that much of a problem. My point is math classes should focus more on learning instead of writing out the textbook, a view that many students share. This can be done by preparing lectures in advance, the way science courses do.
QUOTE]

Personally, I prefer when my professors lecture as we get to cover more material in this manner. Any lectures I have gotten in a math or science courses were far from verbatim copies of the text. They offer another unique perspective to the material which increases clarity. The professor generally knows the material well and emphasizes the important or difficult topics

 

[TMFKAN64]

if I can do 4 page lab reports every week full of them, a book should not be that much of a problem.

Congratulations! We have a winner! This is without a doubt the stupidest thing I've ever read on PF! Clearly there is no real difference between a 4 page undergrad lab report and a 300 page textbook!

 

[Moonbear]

This isn't directed towards you, but I really hate this kind of reasoning. I am paying tuition to be taught, and not have a professor regurgitate a textbook.

And if all my students read their book before showing up to lecture, it would be completely unnecessary to repeat the content in the book when giving the lecture. Since the vast majority take khemix's lazy way out, they cannot follow the lecture if we don't repeat much of what's in the book.

I think its different in biology. If you are unclear about one section in a biology lecture, usually the following sections you can still understand because the subject is intuitive. In math, everything builds up from previous results. Whats worse, is you won't understand any math until you have all prior results down cold. With science courses, you can still sort of ignore past results.

You've clearly not taken many biology courses, and certainly not mine. Everything builds on previous subjects. Of course, the BAD students don't see this, because they are missing these concepts, but the astute student recognizes it.

I imagine no longer than writing them on the board. The book doesn't need to be a classic with 50 questions in each chapter. But this problem only arises in courses where the teacher does not follow the book closely. In such a case, the teacher should seriously consider adopting a new book. Or atleast type up lecture notes. Is it really necessary to be copying theorems? And at the same time be listening...

I'm going to say this bluntly. You haven't a clue about how classes are taught or how textbooks are written. Go back and reread the rest of the thread and try to learn something.

You should also look at the contradictions in your own arguments. You complain if a lecturer just repeats the book, then complain if they don't follow the book closely. Which is it? Ideally, lecture and the textbook should COMPLEMENT each other, not be verbatim copies of one another.

 

[mathwonk]

khemix, please go to my website and take a look at a tiny fraction of the notes i have written and provided free for students to use. then see how long it takes you to read some of them. then after you have done so, get back to me.

 

[khemix]

Personally, I prefer when my professors lecture as we get to cover more material in this manner. Any lectures I have gotten in a math or science courses were far from verbatim copies of the text. They offer another unique perspective to the material which increases clarity. The professor generally knows the material well and emphasizes the important or difficult topics

As do I, which is why I suggest they type their own notes up and teach from that. Profs usually have shorter, more elegent proofs than found in the book. Also, if we use notes exclusively written by them, we are more clear of the profs and the particular schools expectations.

Congratulations! We have a winner! This is without a doubt the stupidest thing I've ever read on PF! Clearly there is no real difference between a 4 page undergrad lab report and a 300 page textbook!

For Pete's sake, I'm not suggesting typing up a hardcover text written for use world wide. There is usually 2-3 professors that teach a course. They can easily type up a 300 page course text similar to all the lab manuals we have printed every year. Lab co-ordinators are often writing new ones each year, and they span 200-500 pages. Don't need all the publishing rights things, keep it local. Or at the very least scan the notes online. DO profs have to go through all this when they write manuals or supplementary notes? Lab co-ordinators pull off just fine...

Typing with mathfont is not very fun, but its not as difficult as some make it out.

You've clearly not taken many biology courses, and certainly not mine. Everything builds on previous subjects. Of course, the BAD students don't see this, because they are missing these concepts, but the astute student recognizes it.

I have taken 1.5 full bio course, and am enrolled in 1.5 now. Yes, everything builds on previous results; this is true for any course. My point is its easier to swing by in a course like bio or chem when you've missed a lecture or two. You can still learn about a new biochemical reaction even if youve missed the old one. With math, its more difficult because everything you do builds on last weeks material, unless you start a completely new topic.

khemix, please go to my website and take a look at a tiny fraction of the notes i have written and provided free for students to use. then see how long it takes you to read some of them. then after you have done so, get back to me.

I have. I found the elementary algebra ones good as they had detailed explanations. The linear algebra ones were way over my head, they were too terse and didnt explain a lot of the terminology (abelian group??). However, I'm sure in a lecture of yours you would elaborate on this or your students would have the proper background.

You should also look at the contradictions in your own arguments. You complain if a lecturer just repeats the book, then complain if they don't follow the book closely. Which is it? Ideally, lecture and the textbook should COMPLEMENT each other, not be verbatim copies of one another.

I don't mind the lecturer repeating the book, but why bother writing our all the theorems on the board? Why not just talk about it (ie. turn to page 105, here we have Sard's lemma, why don't I give some more examples and see why the hypothesis is true). If they don't follow the book, then the text is useless so we have a very crappy source to learn it from - rushed notes on the board w/o any explanation. If you expect students to find the time to read two entirely different spins on the same topic, regardless of whether or not they are insightful, I am not surprised you students don't live up to your expectations.


I don't know why I'm being attacked on this thread. I already said I don't pretend to be the master of any subject or the art of learning. I just thought I'd share some what me and many of my classmates believe. If you'd rather sit there and believe we're all lazy and unmotivated be my guest. The fact is I know a large group of students who love our subject matter, but it is hard to be motivated with all the pressure. Some profs just expect too much. Real learning does not result in the best grade. Because grades are what get me into programs, I am afraid I will continue to learn the course minimum to do well on tests and exams.

 

[CoCoA]

which is why I suggest they type their own notes up and teach from that.

Actually, you suggested that they supply those notes to students, not just teach out of them. The level of polishing of the notes for this endeavor is what will take so much time, not just simply writing them. That's an unreasonable expectation.

I don't mind the lecturer repeating the book, but why bother writing our all the theorems on the board? Why not just talk about it (ie. turn to page 105, here we have Sard's lemma, why don't I give some more examples and see why the hypothesis is true).

I agree with this, at least to some extent. I think referring to the text instead of writing everything out implies that the lecturer has referred to the text also, and supplies an example for the student to do so.

On the other hand, not writing things on the board can easily be taken too far. Thinking about mathematical ideas takes time. If a professor talks too much about several things in a row from the book without writing down enough stuff on the board, the professor will just talk faster than students can absorb. In a sense, the most important part of writing is to control the pace of the lecture.

The fact is I know a large group of students who love our subject matter, but it is hard to be motivated with all the pressure.

Anyone that loves their subject matter will do the extra exercises in homework, the extra problems on the test, etc. Claiming love for a subject and not doing that stuff is like claiming love for a girlfriend and then blowing her off.

if there are 4 problems required and one "extra" problem, some students will not even attempt the extra problem.

funny, this was a talk at the last joint meeting:
Tristan Denley, "Students Don’t Do Optional."

 

[mbisCool]

I agree with this, at least to some extent. I think referring to the text instead of writing everything out implies that the lecturer has referred to the text also, and supplies an example for the student to do so.

On the other hand, not writing things on the board can easily be taken too far. Thinking about mathematical ideas takes time. If a professor talks too much about several things in a row from the book without writing down enough stuff on the board, the professor will just talk faster than students can absorb. In a sense, the most important part of writing is to control the pace of the lecture.

Ideally the lecture would compliment the text and the text compliment the lectures. I personally feel the act of writing my notes helps me remember them very well. I assume this and the reference they provide are why lectures are presented on the board...

 

[mathwonk]

khemix you inspired some heat because you complained that your professors were being paid to teach you, but when we also tried to teach you something you apparently rejected it, revealing that you are not so easy to teach. you are at least partly your own problem and you seem to be blaming someone else. you remind us of why it is so hard to help some people. but we piled on a bit. my apologies.

and if you look at my notes for math 8000, abelian groups are defined on page 1.

even in the math 4050 notes the qords are used but no knowledge of them is required. don't be afraid of words which are explained in context in the sentences where they appear.

those notes state explicitly that the abelian groups being discussed are products of Z/n 's, which presumably all elementary algebra students have seen.

 

[Moonbear]

Some students also just learn better by listening than through reading, so lecture serves them far better than a textbook ever will. And, as we all know from the various misunderstandings that occur on forums such as this, speaking to someone carries a lot of non-verbal information that helps convey context, importance, relevance, and understanding in a two-way direction between both lecturers and students that cannot be accomplished in any written text.

I give my students my notes...I say a lot more than is written. I had one comment this week that there is a LOT in the textbook, and what should she focus on while studying (this is a student who actually attends lecture). I was a bit taken aback, because my impression is that the book is incredibly skimpy on the subjects we were covering in this unit. I suggested focusing on my lecture content, because there was a lot more covered in lecture than in the book. They don't realize that my hour of talking covered more material than 3 hours of them reading.

Of course, reconsidering what khemix has been saying, perhaps he just has bad experiences with bad lecturers. We do know they exist, the lecturers who just practically read the book to the students and provide no additional information or insight, and don't take time to help them connect concepts or make associations between related materials. Perhaps that is khemix's only experiences. Of course, that is not the intention of this thread to complain about the bad lecturers, but to focus those interested in improving their teaching on the GOOD lecture techniques.

So, I'm going to ask that we get this thread back on topic. I really don't want to lock it when there is possibly still valuable information to discuss, but non-constructive complaints are not going to keep this thread going.

 

[buffordboy23]

The biggest task I have seems to be helping students learn how to learn. Some fail to come to class, others never look at the notes they take, and many seem not to even open the book.

Many never ask questions, and those who do, often ask things that could be found immediately by looking them up in the index of the book. People who ignore office hours for weeks expect me to schedule extra help sessions the day before the test. Questions more often focus on "what will be tested?" instead of how to understand what has been taught.

Everyone seems to have taken calculus in high school, but most also seem not to know anything about algebra or geometry or trigonometry. With the advent of calculators some also do not know simple arithmetic, like how to multiply two digit numerals. (I have had students who had to add up a column of thirteen 65's on a test, apparently not knowing how to multiply 13 by 65.)

Many think that having taken a subject "2 years ago" is a valid excuse to have forgotten the material, and to expect the teacher to reteach the prerequisites. Appparently no one ever dreams of reviewing the prerequisites before the course starts. Books like "Calculus for cretins" are apparently more popular than books like "Calculus for science majors".

When I was in college students like this were just ignored, or expected to flunk out, but in today's setting there are so many like this that they form the primary market. With all good faith to teach these stduents, the failure rate is still about 50% in college calculus across the nation, in my opinion. What are some ideas on how to improve this?

I realize that this is an old post, but I saw that it has been resurrected. I am an ex-teacher who returned to college to study physics, so I have recent experience regarding both educational windows, as a student and as a teacher.

I see what you are saying in my upper level physics courses. Basically, many students don't perform well due to many reasons, so grades are curved and a large majority of students pass the course although maybe a significant number of them shouldn't. What is the overall benefit to the mathematics or physics student for such behavior from an academic institution? Because they get away it, these students do enough to get by, but not enough to gather a deep understanding of the material and to develop a serious discipline in regards to their learning. So, the student never matures. Eventually, they will graduate with a degree, but they are not adequately prepared for graduate school or to enter into their job field.

If I were a professor, nothing would be more easy than to take the hard line with students; if you don't understand the material, you fail. However, like you said above, the common college student entering university will not likely meet these expectations, so we must look at alternative strategies.

Here is my basic plan:

Don't get rid of the hard line approach completely. Enforce it with strict discipline with junior and senior level mathematics courses. Let this knowledge be transparent to freshman and sophomore majors, so that they are fully aware of the expectations ahead, while at the same time supplementing their education with objective tasks to transition them towards these higher expectations. This will give the student a few years to develop an academic level of maturity to be successful in the higher-level courses, or at least enough of warning to switch to a new major, like physical education, without having to stick around at college for another 2 years.

The objective tasks for freshman and sophomore students could include "gateway" examinations. For example, you said students don't have basic trigonometry, algebra, and geometry skills. Well, have your department make them learn these skills and prove it by taking a rigorous test at some point, maybe in their first semester. If they don't pass, they don't take higher level courses until they do. Of course, many students will need to review these concepts, so professors teaching intro courses should develop tools to help students accomplish this task. As another example, after the third calculus course, students are required to take a comprehensive calculus test, which will force them to go back and learn concepts they forgot.

When I returned to college, I had to take a calculus III course. One of the components of the course was a weekly lab using Maple software. Often, I found myself confused with the code as did many other students, so assignments were difficult to complete although the problems were basic in design. Graduate students ran the course and there were about 40-50 students in the lab so it was difficult to get assistance. Outside of lab, it was even more difficult, since the graduate students are extremely busy themselves. Overall, I thought the labs were a waste of time, although they had potential to be great learning tools if designed effectively. The code should already be developed so that it is easy to manipulate, which allows the student to focus more so on conceptual understanding than programming the correct code. It would also be of benefit if the labs were developed around interesting phenomena associated with the students current background of study (physics, engineering, etc.).

Hopefully, there will be more to follow when more comes to my mind and I have the time.

 

[buffordboy23]

Here is another thought that comes to mind. In your intro courses, assign a lot more problems as homework. Practice makes perfect, right? In a typical section of calculus books, there might be numerous ways of applying the concept. For example, there are numerous ways to compute a line integral. I see that professors assign about 10 problems per week in a math course as homework that span a few sections of the textbook, which is only a couple problems per section. So, the student doesn't get much practice solving line integrals unless they take they initiative to do it themselves. Therefore, many students probably forget how to solve these problems a short while later because they have so little experience except for the one or two examples, and likely won't even care to go back to relearn it.

So, as a professor I would assign more problems. Many of these problems would be easy munching to the student and take little time, yet they would reinforce the concepts and hopefully enter into the student's long-term memory storage. Solutions should be available to a decent number of these problems pertaining to each concept, so that students have a target to work towards and don't get easily discouraged. Hints should be given from the outright to teach supplementary ideas not necessarily discussed in the book that will appear in a certain problem and offer simplification. In this case, it may be necessary to design your own problem sets since the problems in the book may be sparse or their integrals time-consuming to calculate.

 

[buffordboy23]

Another idea for intro courses. We know many students don't read the textbook, so hold the students accountable. Assign sections to be read for each class. Every so often, give students a short 2-3 minute quiz about very basic ideas in the reading at the beginning of some classes. This would likely increase the number of students who are prepared for lectures and promote discipline with their studying.

 

[mathwonk]

those seem like good ideas. the reality we face is very serious however.

e.g. what would you suggest when faced with the following data that actually occurred to me?
My department does not give placement tests to my knowledge, so at the beginning of a calculus class, in an attempt to measure readiness, for my sake and the students', i gave a precalculus quiz, mostly covering facts on equations of lines and circles and the definition of sine and cosine.

the average score was 10%, although one Chinese transfer student got 100%. So I gave it back and made it a take home test. The next day, several students did not come back at all, and of those who did and turned in the take home test, the average score this time was 15%.

I was so discouraged I never did this again.

The only thing I know of that seems to work, is to send students to the board for presentations and detailed discussion and critique of their work, but this takes about 4-5 times as much time as is allowed in a semester.

my calculus classes think i am teaching a very theoretical class if i ask them to learn the statement of a theorem, including hypotheses, or to state a definition, although i essentially never ask them to prove anything, or even to learn a proof.

A typical incoming student has never apparently seen a definition. Even if I write
DEFINITION:...

in front of every one, almost no students, even the brilliant ones, can answer a question asking for a definition to be given. only a few think hypotheses are part of a theorem.

I am going to try to make this point this week by making up a list of series that do NOT converge even though they may appear to if you fail to check the hypotheses of the tests we have learned.

But I am worried that my students will simply give up if they are confronted with the fact that theorems are not true unless the hypotheses are true, and the need to verify this. Math has been dumbed down so much for them, some of them seem saddened by the thought that this level of precision is part of the subject.how is it possible there is such a disconnect between what an incoming student thinks of as theory and what i think? i have even been criticized for teaching "with words".what else should i have used to teach with?

What is going on in some high schools? teaching with pictograms?

 

[mathwonk]

as to gateway exams, we have turned to them in an unlikely setting: for graduate students in our phd program. we have admitted so many grad students who do not have even basic college math skills that we now have a remedial program for graduate students. and presumably it is working.

in america apparently failing students is never an option, so our educational system is built around remedial programs at every level, since students arrive in every grade without any reason to be there, except time spent in previous grades.

in your posts b23 the main thing that strikes me is that you are a returning teacher. that is a universal qualifier in my experience. i have never had a returning teacher who did not have the dedication to succeed that i look for. so maybe we could kick students out sooner, and put them in practical settings where they will learn quickly that they do need to actually know something to perform in their jobs. i.e. maybe work - study is the answer.

 

[mathwonk]

we tried labs for years, and they were universally considered a waste of time (as you found them) except by the people who designed them. students simply refused to put in the time needed to benefit from them. the time needed to deal with the software and hardware was overwhelming to them, and the program was a huge time sink for the few faculty who lavished enormous effort trying to make them relevant, interesting and potentially beneficial.

my feeling is that there are many things that would work on a more motivated population. so motivation is the key.

how do we motivate students to work hard, harder than they have had to in high school? to ask themselves to understand what they are doing rather than just memorize procedures?

 

[Tobias Funke]

What is going on in some high schools? teaching with pictograms?

I'm a high school math teacher and I ask the same thing about middle school. Like you said, these students are never held back when they should be and thus you have the problem all the way up to grad school. The problem doesn't start in high school, it starts with fractions and maybe even earlier.

I bet you won't be surprised since I've read a lot of your horror stories involving unprepared students, but about 90% of my freshmen algebra 1 class can't add fractions unless you stand over them and tell them every step. I'd say about 20% can't consistently do computations like -3-10. They simply can't remember which of 1/0 or 0/1 is undefined (and I try to explain to them why, but you must know more than anybody that they don't want explanations, just facts to remember). How can I possibly bring them from that level to the algebra they need to know in a year?

I've worked with middle school math teachers too. I was told we were covering prob and stats and I was a bit worried because stats is not my strongest area. I soon realized I had nothing to worry about because I was absolutely shocked when I saw the level these people were at. Only a few of them actually wanted to learn and the rest just suffered through the course to get more credit for a masters (in education. Many math teachers don't even seem to have a degree in math). It was embarrassing.

Of course there are the good students who make it all worth it though. A few of my calc students were genuinely excited when we took a day off of related rates to prove the formulas for the sum of the first n squares/cubes in several different ways (no boring induction), something of no relevance to the class. They actually enjoyed going through the proofs, and hopefully it will inspire them to try their own proofs.

 

[buffordboy23]

e.g. what would you suggest when faced with the following data that actually occurred to me?
My department does not give placement tests to my knowledge, so at the beginning of a calculus class, in an attempt to measure readiness, for my sake and the students', i gave a precalculus quiz, mostly covering facts on equations of lines and circles and the definition of sine and cosine.

the average score was 10%, although one Chinese transfer student got 100%. So I gave it back and made it a take home test. The next day, several students did not come back at all, and of those who did and turned in the take home test, the average score this time was 15%.

Wow. These scores really are dismal, even when given a second opportunity. Are these students mathematics/science majors?

EDIT: I think this would be reason enough to require placement tests. Your students are in a hole before the course even begins. In a sense, your quiz is kinda similar to a placement test. You have determined that the majority of the class is not adequately prepared for calculus, yet you are stuck with them the whole semester.

The only thing I know of that seems to work, is to send students to the board for presentations and detailed discussion and critique of their work, but this takes about 4-5 times as much time as is allowed in a semester.

This is good because it holds students accountable, but like you said it consumes a lot of time. I currently have a physics class that does something similar. Two times during the semester, each student has to give a brief 3-5 minute review of the previous lecture. The students seem to handle it well and understand the content, but, overall this consumes a total of about 2-3 whole classes throughout the semester. This further supports the idea that students are capable when they choose to be.

my calculus classes think i am teaching a very theoretical class if i ask them to learn the statement of a theorem, including hypotheses, or to state a definition, although i essentially never ask them to prove anything, or even to learn a proof.

A typical incoming student has never apparently seen a definition. Even if I write
DEFINITION:...

The thing I like about mathematics is that it is a subject that is in black and white. The basic rules are given, from which other rules follow. You always win when you play by the rules. However, I think that, in general, students don't understand the rules and why they exist. I would argue that many students find proofs very difficult, and I would wager that this is due to their high school education because they probably aren't exposed to the rigorous aspects of the mathematics.

What is going on in some high schools? teaching with pictograms?

Probably. =)

 

[buffordboy23]

Since my return to college, I have been very critical of the manner in which professors run their courses. I find that many of them do the basics and cover what is exactly in the book--write the theorems/definitions on the board, talk about the gist of the concept, do some examples. For a student like me, I often won't go to class like this because I read the book and learn nothing new from their lecture. I can't blame them though, since they are catering to the average student. Plus, it takes a lot of time on the part of the professor to be original with his presentation, since professors often exist in a publish-or-perish environment and have exhaustive workloads themselves.

In light of this, I thought of an alternative approach in offering a course to students. I am sure that you probably have quite a few sections of calculus each semester, with multiple professors carrying this workload. I wonder if it would be beneficial for these professors to record video-taped lectures and develop notes for each concept, so that their students can view them online. As a supplement, students can post urgent questions on a forum, where another student or another professor can respond. Essentially, it would be just like going to class, but instead, students can watch the lecture videos from their dorm and at their convenience. Of course, there needs to be student accountability somewhere in the mix for this to potentially work. There would still be regularly scheduled class to attend.

These are the immediate and foreseeable benefits:
1. Students often have trouble following the professor during a lecture, and many are scared to ask questions, so they can review the lecture over and over again as need be. This also gives more time for reflection, and the student can come to class with good and quality questions about the content.
2. Many students choose not to go to class for one reason or another, so they miss out. With this idea, students have no reason for missing a class because they can go anytime they want.
3. In the long run, this will likely reduce a professor's workload. If the video-lectures are designed effectively, they can be used semester after semester, freeing the professor from putting basic content together.
4. During the regularly scheduled classes the professor has a lot more freedom, since they don't have to cover basic content. They could discuss ways of how to think mathematically, elaborate on key ideas/theorems, introduce interesting applications, solve some examples, dedicate more class time to holding students accountable, etc.

I don't know of any college that has tried such an idea. The closest thing that comes to mind is the online courseware offered by MIT. Perhaps, my thinking is too idealistic, but it would be interesting to see how such an approach works out.

 

[buffordboy23]

how do we motivate students to work hard, harder than they have had to in high school? to ask themselves to understand what they are doing rather than just memorize procedures?

I think this is the fundamental problem. I think many students get discouraged easily because the work is difficult and requires time. But if they get passed through the course just by going through the motions, is intrinsic motivation necessarily an issue for them? Personally, I think many college students still need scaffolding to be successful. Should it be this way? Probably not, but this is the current state of our education system.

 

[mathwonk]

the video model is hard for me to imagine. i try to learn my students names and lecture with them in mind. i call upon them i class, and if i see a puzzled face i stop and ask what is bothering them. if students seem receptive i am encouraged to go beyond usual bounds and present things that are more advanced. i model the lecture on their response, and plan the next one based on questions from this class. without an audience i would be very bored and have trouble knowing what to say without the stimulation of the faces.

 

[will.c]

If you can expect the students to watch your lectures on their own free time, why can't you expect them to crack the damn book?

expecting students to prepare outside of class in any way is, unfortunately, not tenable - not the way basic math and science classes are expected to be taught anyway. More unfortunate yet is that these will always remain to be service classes, and so deviating from student expectations is dangerous.

 

[buffordboy23]

If you can expect the students to watch your lectures on their own free time, why can't you expect them to crack the damn book?

You raise a good point. I am throwing out ideas, even radical ones, to spur discussion. If one of my ideas is of any use, then I consider my time well spent.

To answer your question. Students are not held accountable to read their book. If they come to class without having read their book, then the only immediate consequence they suffer is not understanding the lecture. I believe accountability is a necessary prerequisite to improving student performance. Having the lectures already recorded will free up more time to focus on accountability. You can still find numerous ways to hold students accountable with a traditional course (e.g. presentations), but do you think more things would need to be sacrificed to do so in comparison with the video-lecture idea?

 

[buffordboy23]

expecting students to prepare outside of class in any way is, unfortunately, not tenable - not the way basic math and science classes are expected to be taught anyway. More unfortunate yet is that these will always remain to be service classes, and so deviating from student expectations is dangerous.

Yes, people fear change. When you take them out of their comfort level they have no choice but to adapt to a new situation. Unfortunately, to obtain some goals does require change. The widespread availability of technology in our society today has changed our society in ways unimagined in only a relatively short period of time, so why shouldn't we incorporate this in our education system? Some public schools have chosen to give their students a personal labtop computer; I don't yet know if any schools have replaced traditional textbooks with digitized copies.

EDIT: Some teachers are now required by their districts to run online chat/forum sessions with students outside normal school hours.

EDIT2: I agree that deviating from expectations can be dangerous, but only if such expectations are not conveyed clearly and maintained with consistency. This was a large reason why I saw students having difficulty in some of their classes when I was a teacher. The students did not understand their teacher's expectations on an assignment. They sometimes would ask me for assistance, and so I would look at the assignment given to them and I did not understand the expectations either.

 

[buffordboy23]

the video model is hard for me to imagine. i try to learn my students names and lecture with them in mind. i call upon them i class, and if i see a puzzled face i stop and ask what is bothering them. if students seem receptive i am encouraged to go beyond usual bounds and present things that are more advanced. i model the lecture on their response, and plan the next one based on questions from this class. without an audience i would be very bored and have trouble knowing what to say without the stimulation of the faces.

My original intent with the video-lecture idea was to still hold classes. If students are held accountable by completing short questions at the end of a video-lecture and submitting them, you now have foresight about misconceptions and can structure the next class meeting to rectify their misunderstandings. By holding students accountable before they arrive to class, more of them should be prepared to engage in meaningful discussion and permit you to have greater probability of success in introducing any interactive class activities. Students will still need some form of accountability sometimes during class meetings or there would be no reason to go to class. So you would still have your audience.

 

[CoCoA]

i gave a precalculus quiz, mostly covering facts on equations of lines and circles and the definition of sine and cosine.

the average score was 10%

This is bad enough to wonder about a systemic problem - then I saw a web log (can't find it now) from a prof in state of Wash with a child in high school algebra using a book with essentially NO algebra in it! Students "solve" problems by looking up values in tables and creating graphs.

California has a "algebra for every 8th grader" initiative (perhaps failing to legel challenges, perhpas not) that just has to water down the curriculum severely to accomplish this. Every level of our educational system just seems to be underminig the teaching of math, no wonder colleges can't get good math students.

 

[CoCoA]

I wonder if it would be beneficial for these professors to record video-taped lectures and develop notes for each concept, so that their students can view them online.

I took an line course a few years ago with recorded video lectures online. It was actually pretty good.

On the other hand, about a year ago I was "talked into" (forced into?) teaching a course onlilne that I thought wasn't that amenable to online delivery. It turned out to be pretty bad.