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Equations: whiteboard vs slides

  1. Mar 21, 2017 #1

    DrClaude

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    I am struggling with how much math do to on the whiteboard during lectures, and of how much can be put on slides (to which the students have access) instead of me writing everything in detail.

    I have found a very interesting discussion at www.mathoverflow.net/questions/80056/using-slides-in-math-classroom, but I would like some perspective from lecturers in physics.

    I find that writing everything on the whiteboard takes up a lot of time, coupled with the fact that I have to pause to let the students finish copying everything. Often, I find that doing the derivation can be instructive if one tries to do it themselves, otherwise the answer is sufficient. (If anyone is aware of research on whether copying down mathematical developments helps in learning, I would appreciate some references.) At the same time, going through slides sometimes feels like just having symbols dancing around on the screen. with students not really following what is going on.
     
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  3. Mar 21, 2017 #2

    ShayanJ

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    I don't have teaching experience but because I've experienced different kinds of teaching as a student, I think I can have some useful words for you. I've experienced classes in which the professor just projected the textbook itself on the screen and read from it and did some hand-wavy explanations and classes in which the professor proved every single little piece of information and solved every problem he was discussing. Both awful. Of course projecting something different than the book can be of value and I'm not saying its not good based on an almost irrelevant experience but I think I can make some points based on my experiences and what I think is good teaching based on my knowledge and experience.

    I think the sentence in my signature is the golden rule of education. So let's see what we can understand from it for this particular question. As I said its really bad to prove and solve every single thing you say in complete detail. Give some work to the students, give them some blind spots. Give them a compelling reason that makes them to come back to the subject outside the classroom. But you also should give them enough information and skills so that they actually can fill in the blanks. Remember, you're not trying to fill a pail, you're trying to light a fire. So, there are two kinds of things you need to deliver to your students:

    1) Information and skills that are crucial for the students to do some thinking and calculation on their own in the subject presented.
    2) Some facts that actually compels the students to use the information and skills you've given them.

    For the first kind of material, you need to be detailed and comprehensive. A slide simply can't do that. So recognize what parts of your lecture is something that students should have a complete picture of after the class. Not that they should be highly skilled and efficient, but that they should know the outline and have the complete knowledge to be able to understand it completely if they devote some time to it outside of the class. This part should definitely go on the board.

    For the second kind of material, you just need to explain the statement itself, just say what is true. You don't need to prove or solve it completely or even at all. Because either they can prove or solve it on their own using the first kind of material or its just the kind of thing you've preserved as a motivation for the students to come back to the subject outside of the class. So after you realized what are the first kind of materials you want to deliver, the kind that is the foundation of the learning of the students, you choose what are the things that are going to be built upon that foundation. Those are the things that you don't explain/prove/solve completely. Those are the things you leave to students to figure out. Those are the things that should go on the slides.

    As I said I don't have teaching experience and this was a student's point of view but I think its helpful for the teacher to have some idea of a student's point of view. I hope it helps.
     
  4. Mar 22, 2017 #3
    I don't have the sources, but I don't believe that note taking in itself has an effect on improving learning. We had a neuroscience professor do four sessions with our faculty last year (perhaps the most worthwhile professional development I've ever done). He presented a synthesis of recent literature and I do recall having this takeaway about notes. It seemed like many of the studies performed were based on memorization of, say, a list of words, but that isn't too different from memorizing steps of a derivation, if that is what is expected of students.

    Another big takeaway from these sessions included the somewhat obvious (in hindsight at least) fact that one learns best when one does things actively rather than passively – lecture in general isn't a great way to learn (if by lecture we mean that the instructor recites material while students passively listen). One thing I've started to do with worked problems or derivations is that I present the problem to the students and then give them a little time to work on it (or at least think about it) before going through it together. This engages their minds more than simply copying. I don't think that students even necessarily need to finish – simply giving their minds time to think about the question ahead of time is shown to be effective – and getting stuck is probably a good thing. Based on my own experience I can offer anecdotal evidence that this works better that having students simply copy.

    I use a mix of both slides and white board when I need to present material to students. When I use slides I make sure that the 'steps' are not all displayed at once (at first) and I sometimes also perform derivations 'live' even when they are on the slides. Students have commented to me that they appreciate having both.

    Having students try examples and derivations is even more time consuming than going through the steps and having them copy. Coupled with the common pressure to get through a certain amount of content in a given course perhaps makes this method impossible to implement depending on what you are required to do. Unfortunately (for the standard lecture model of teaching) research shows that the brain recalls more information when it is presented in small chunks (about 20 minute max of focused time on one topic) and then switching to something completely different (like from physics to walking or playing music). A lot of information is consolidated subconsciously and interference affects what is retained. This is why it is believed that using a different part of the brain after learning something will help retention.

    Another thing to consider are the assessments of student learning. Do your assessments assess what you hope students learn by going through a derivation? I certainly value when students are able to explain when/why/how a certain result is valid and where it came from and I needed to add questions to my assignments that assessed this understanding because many of my assignments simply required them to use the result, not explain it (what are the assumptions, why were they made, etc.).

    Something new I've tried this year is to have students 'journal.' My students are essentially writing their own textbook based on the course content. Each topic must be summarized in prose and students must write and solve their own examples. While not a particularly popular activity the students report that they feel they understand the material much better after writing about it. This is something I've noticed in my own work and is one reason that I make sure I write nearly all of my course content.
     
  5. Mar 23, 2017 #4

    symbolipoint

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    You do not need to write everything (up on the whiteboard?). Just write to display the fundamentals, and derive only a few things that might be helpful. Let the textbook be the source of as much as possible. One thing you should do, is to look for what the course textbook does not include as in a useful or important mathematical derivation, AND SHOW THAT IN ALL ITS STEPS. In other words, if the book discusses some mathematical relationships but does not pull all the pieces together, then this is something you, as a professor, should do in class.
     
  6. Mar 23, 2017 #5

    symbolipoint

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    You say, "whiteboard versus slides".
    The whiteboard means putting the internet or computer technology in the way. If it is interactive at least with YOU, then at least you show what you need like in timed doses. Class rooms still have dry-erase boards (and in the past were still using chalkboards), and these are interactive with you and if you like, with your students.

    Slides don't move and don't change. Not so interactive. Then do you need to turn down the lights in the room so students see the image better? Computer screen, if presenting "slides", maybe ok. This saves you writing on a dry erase board. It displays all at once, students read for a few seconds, and then you discuss what you need. Students write their own notes according to what they think they need.
     
  7. Mar 24, 2017 #6

    DrClaude

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    Just to be clear, by whiteboard I mean a blackboard that is white :smile:, aka a dry-erase board.
     
  8. Mar 24, 2017 #7

    symbolipoint

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    That being the case, you are already fast on your way to giving better more organized and powerful instruction. You can change things on your whiteboard at any time during class instruction, or arrange what you show any way you want at the moment, so in this regard, better than a slide.
     
  9. Mar 25, 2017 #8
    imho: it is the best variant when lecturer comes to class having nothing in his hands.He solves problems and proves theorems by chalk and black board now and here. Then students can trace the way of thinking of the lecturer. It is the only way to teach something Slides and other such things interfere the lecturer to feel what students understand\do not understand. Lecturer should feel the feedback
     
    Last edited: Mar 25, 2017
  10. Mar 25, 2017 #9
    I can offer a couple of points from my own teaching experience (17 years).

    1. I find it useful to write out everything on the board. It paces my lecture at a rate that students can absorb it. With slides, you can zip through material at lightning speed, but nothing at all is learned.

    2. I think it is well established that there is an eye-brain-hand connection that is implemented with students copy material off the board that is missed if they simply look at something no the screen. Writing is an important learning activity for the student.
     
  11. Mar 26, 2017 #10
    I get more out of a professor doing whiteboard derivations but that's just me.
     
  12. Mar 26, 2017 #11

    vela

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    How many of these do you have the students do? I took an online course awhile back, and like your students, I didn't look forward to writing in a journal about the material that have been covered. But I found in hindsight that it turned out to be very helpful because it forced me to review what we had done and see it all in the context of a bigger picture.
     
  13. Mar 26, 2017 #12

    vela

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    I think it takes a bit of practice to get the right balance, and the nature of the lecture has to adapt to the medium. The first time I started using slides in physics, I taught physics the way I was taught in college. I ended up switching back after a few weeks to using the whiteboard because I felt I tended to go through the slides too quickly and students couldn't really follow what's going on. Part of this was because I was essentially putting on the slides what I would have written on the board. It's faster to project the slides than to write everything out, so even though I was going through explanations, the pace was still too fast for the students.

    Now my lectures (with slides) tend to focus more on the concepts, so I'm identifying and covering the main concepts in a chapter. I typically don't bother with derivations that are in the book or doing a lot of examples. I figure the students can read the book to get those (though there are still some that I will go over in class). I try to spend class time on having students work out problems together. When I do examples, derive some result, or review a problem students have tried, I do that on the board.
     
  14. Mar 26, 2017 #13
    This is the first year I've done it for my full year introductory course. We have quarterly grades and there have been 4 entries per quarter except for this one in which there will be 5. As an added incentive I allow students to use their journals as a resource on the quarterly tests.
     
  15. Mar 26, 2017 #14

    symbolipoint

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    That last part is a very good idea. Extra encouragement for them to write in their journals, knowing they can use them later that way.
     
  16. Mar 27, 2017 #15
    Once students have taking some introductory courses that handle the basics in suitable detail I think having them study the material before class works best.
    At least as a student I felt like courses that assigned part of the material and reserved lecture time for questions about theory and applications help get deeper understanding.

    This is harder in large groups which is the main difficulty. Both my GR course and analytical mechanics (masters level) used this approach and incidentally those were the courses I felt most confident about. It is tantamount that the materials are very good.
    Often the questions became quite technical when the lecture progressed which I enjoy a lot as did most other students.

    Long story short I would reserve details of derivations etc for questions. This puts some of the responsibility with the student but this also leads them to grow as a student. Some will start using this approach for other courses which generally improves understanding across the board.

    Added later:
    The fun really starts when someone poses a question that the instructor didn't consider before or can't answer immediately. Students and instructors looking for an answer together is (in my opinion) the best way to learn. You get a feel how a professional (as in someone doing the kind of stuff for a living) goes about such questions which is interesting in its own right.
     
    Last edited: Mar 27, 2017
  17. May 9, 2017 #16
    I think writing material in board is more effective than only teaching by screen/slide. I usually use computer/screen to teach only when I need to strengthen conceptual using animation, video, or simulation.
     
  18. May 9, 2017 #17
    Right on.

    Do you like to go at what some would consider a slow speed compared to other teachers? I noticed when I was a student that some professors were zipping through stuff and sometimes seemed to be talking to themselves when they were writing on the board. They really seemed to be in a hurry.

    My favorite counter-example was a rather cranky German physics professor who wrote slowly, spoke slowly, did not really say very much, but managed to cover all the material. I preferred his teaching style. I liked his seriousness. He never made a joke or shared stories about raising puppies, selecting the right wine, or windsurfing as some professors did.
     
  19. May 11, 2017 #18

    jack action

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    My experience as a student is that I need to see how the teacher does it. That is how learning is the easiest: Monkey see, monkey do. So if you will ask the students to solve a certain type of problem in the exams, you should show them how to to solve it "live" on the board. Not «you know how to derive this, I'll skip it», you must do all the work.

    I can read a book by myself, I don't need someone to read for me.

    On the plus side of having the students constantly copying your notes, is that their minds don't wander, they stay focused on the teacher. The students should never stop writing.

    Even if they don't understand everything as you go on, it doesn't matter as they can take their time when they review their notes after class and they can ask questions at the next class (or at your office) in the worst case scenario.
     
  20. May 12, 2017 #19

    Mark44

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    I had an instructor in a university summer class (in '82) in Advanced Fortran, who was pretty much the exact mirror image to your physics prof. The class was to meet twice a week for about 90 minutes a session. After the first class session (and after he had chit-chatted with some students he apparently already knew), I learned that
    1. He didn't know much about Fortran, and
    2. He didn't know much about the new computer system and OS the university had recently installed, Digital Equipment Corp VAX minicomputers, and VAX/VMS, respectively. Prior to that, they probably had IBM 360 systems with punchcard entry.

    On the blackboard (a whiteboard that is actually black and on which you make marks with the decomposed skeletons of marine creatures), he had written exactly one line (unreadable) that ran diagonally down one of the three boards. This was the sole content of what he had written down in 90 minutes.

    After that session, I began to wonder exactly what it was that this prof knew a lot about. I decided that if I was going to have to learn all this stuff on my own, I damned well wasn't going to pay tuition to do that.
     
  21. May 17, 2017 #20

    scottdave

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    I think both, rather than either/or. From what I remember taking classes (and now attending seminars) - sometimes flashing through slides tends to "speed through" information. If there is something that could benefit from working out, a dry erase or chalk can come in handy. Even attending seminars, nowadays, I see presenters using the board (or in venues such as hotels without a board) take the easel and some Post-It style sheets that they write on, then stick on the wall to make room to write more.
    I am a believer that actually taking notes with a pen/paper reinforces learning.

    Another thought - if there is some chalkboard working out that maybe you want to include, but maybe you feel it could take too much class time, perhaps it could be useful to record yourself working it out on the board, then post it online. The students could watch the video outside of class time.
     
  22. May 18, 2017 #21

    DrClaude

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    Interesting idea, although it sounds like a lot of work :smile:
     
  23. May 18, 2017 #22

    scottdave

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    It's just another option. I wasn't thinking the whole lecture. Just maybe certain derivations. If it is 5 or 10 minutes long, you could even assign them to watch before the class, so some of the class time could be spent discussing and answering questions.
    I think that most people of that age group probably enjoy watching videos. Maybe it's just another way to get them to stay interested.
     
  24. May 20, 2017 #23

    epenguin

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    aeay5j.jpg
    What I call a lived-in blackboard.


    Well trying to remember when I started my undergraduate course that blackboards (green) were moderately usual use. Rather less in my final year when we had one formal lecture a day and, the department being under construction, lectures were held in a theatre also used by the faculty of Law. Lecturers had been pressured to minimise use, because the elegant legal gentleman who lectured after them then had to appear in Court and did not appreciate chalkdust on their formal black suits.

    After my degree I have been in any number of seminars, lectures, conferences and meetings for decades, and just never came across backboards. It was slides all the time. I was there around the time of the change over when slide displays were a bit clunky, there were still two formats, and presentations involved a collaborating ‘projector’, i.e. a colleague or a technician detailed to work the projector. Talks were always interrupted continually by the call 'Next Slide Please’. If one incorporated this call within the talk with phrases like ‘so then as the next slide shows' then often nothing would happen – the speaker would have to call out loud 'Next Slide Please!’. This went on for some years but after a time remote controls came in which made it more convenient. Transparences came in, which were at least easier to prepare. And you could write on them during the talk, so they were somehow more like a blackboard and more friendly I would say. But a real blackboard in use I never saw for decades whilst I was in research attending conferences and so on and I forgot about them. (I wasn't teaching, but I think the lecturing where I was was largely with slides too).

    Then my job changed out of research to something of which a small but the most interesting part involved taking in and reporting back on a wide variety of scientific conferences and training activities over all the sciences. It was still nearly all the same. In all disciplines. Everywhere.

    Until one day my scientific butterfly samplings took me to the Newton Institute, Cambridge. Many mathematicians here will no doubt know it, or at least its standing. For others I should say this: if you have read some of the popularisations of modern, last few decades, mathematics you may have the impression that it is just a different thing from what you know as mathematics. The calculations you do a little of resemble it the same way that your school experiments verifying Hooke's law with weights and springs or something resemble the work at the Large Hadron Collider. You can't do anything on your own just in the study, it seems, unless you can insert yourself into some such large-scale structure. At the Newton they have six-month research binges on some topical theme to which anybody who is anybody in the specialist field tries to get to for a time, perhaps for months, and exchange or collaborate with others, including one or two weeks climax conference where the top people talk (all confirming another impression you may have got reading the pop maths maths books as well as those about abstruse theoretical physics like Theory of Everything and its generalisations, that the lifestyle is rather enviable in comparison with even the most fashionable biologist, who must be tied to his laboratory mainly.)

    I reported back that the facilities were Excellent, or rather, hors categorie. You cannot compare it to any other meetings facility, it is more an intellectual Accelerator”. An Excellerator I should have said, but I only thought of that just now, I expect I'm not the first.

    One instrument illustrating the peculiarity of mathematics among the sciences: in the sessions attended they were making heavy use of a visual aid I haven't seen used before – blackboards. (Well now I cast my mind back a not dissimilar device was in use when I was at school – it must be a rediscovery.) There are also overhead projectors but more often than not they remove them as being 'in the way'. This leaves eight blackboards in a lecture room which they cover with formulae, just like you see in those old photos of Einstein etc.

    The whole Newton Institute is made from blackboard plus of course glass windows, otherwise it would be too dark to see what is written on them.
    This is not an exaggeration

    At all moments in any discussion anywhere in the place there are several handy where the discussants can write down their ideas and calculations.

    Visiting journalists as they find math a bit hard to understand or explain fix the reports rather on the blackboards, also found in the lifts and the toilets where I was told one can see theories evolving collaboratively over a period. Who knows how many mathematical inspirations were in the past lost forever for lack of this means of immediate capture? And how many trees saved by it?

    (I don't have any pictures of the wall–and–pillar blackboard-covered general areas, but here from the Institute site is seminar room 1)
    2heaa36.jpg

    For lectures I was told that one of the advantages of blackboards is that they slow lecturers down. (This may be somewhat offset if the calligraphy is impossible to read, as I found in one case, though for the mathematical audience familiar with what the squiggles are about this was not a problem.) They usually use eight at a time, but this is not enough for most lectures, so they use that other schooldays technology the blackboard eraser.
    It must have been a wish to not confess my total overawe that induced me to conclude with this overthetop suggestion for an improvement:
    The only thing lacking is a complete polygonal (e.g. Euclideanally constructible heptadecanal) or polyhedral auditorium so the audience could appreciate the whole argument in the round but this will come someday somewhere no doubt of it.
     
    Last edited: May 20, 2017
  25. May 26, 2017 #24
    There doesn't seem to be much difference here to me. If you write the derivation or problem in the same amount of steps, whether it is on a whiteboard, a powerpoint, or outside on the ground in chalk, the speed at which the students write isn't going to change much if anything at all. I think you'll have less writing to do if you make a powerpoint since you only have to do it once. Either method you'll still have to talk the students through the problem or about the problem. Also I second Scottdaves suggestion. The reason being is because I can rewind this video and get a better understanding of what is said and I go to class better prepared because I already know the math involved. I would recommend making the video less than 20 minutes. This is about the time most people start to lose focus and much math in Physics can be explained within this time. I haven't taken Quantum or E&M yet, but the only math derivation I've seen that requires more time is solving Schrodinger's Equation.
     
  26. May 30, 2017 #25
    I learn better when the professor or teacher writes the equations. At least he/she will be obliged to explain every variable he/she writes, as they tend to explain while writing.

    Some professors that run slides on formulas... My eyes, really.

    It looks like a formula freakshow, you know you sit there while you get bombarded by flying formulas everywhere
     
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