tag:blogger.com,1999:blog-2316765421340036602.post519826796379468656..comments2024-01-10T11:38:15.547-08:00Comments on Random Observations: Teaching linear algebraBen Tillyhttp://www.blogger.com/profile/04335648152419715383noreply@blogger.comBlogger24125tag:blogger.com,1999:blog-2316765421340036602.post-75115101126738510282020-11-28T09:22:37.793-08:002020-11-28T09:22:37.793-08:00I am an undergraduate linguistics student looking ...I am an undergraduate linguistics student looking to do my thesis on spaced repetition in the classroom, and I would love to interview you to learn more about your experiences. Please reach out to me at birdseye1109@gmail.com (I can provide an institutional email, but I don't want to post it publicly) if you are available/interested.Anonymoushttps://www.blogger.com/profile/02777611804146046225noreply@blogger.comtag:blogger.com,1999:blog-2316765421340036602.post-59768996350571554472020-01-28T22:30:57.089-08:002020-01-28T22:30:57.089-08:00This blog post and the comments are very useful. ...This blog post and the comments are very useful. I will be teaching Calculus 1 this semester and am looking forward to using spaced repetition and more Q&A during class. Thank you for your post ... way back in 2009! ;-)Anonymoushttps://www.blogger.com/profile/04852759116750465665noreply@blogger.comtag:blogger.com,1999:blog-2316765421340036602.post-28457352078852170862018-03-12T05:10:44.402-07:002018-03-12T05:10:44.402-07:00I would not have gotten through an undergraduate d...I would not have gotten through an undergraduate degree if every course instructor followed this structure, especially re lateness. That policy is so egotistical, inconsiderate, and plainly disrespectful to students. You being a flipping PhD student does not give you the right to demand students adopt your organizational expectations on a daily basis; this has zero relevance to the mathematical content of the course.<br /><br />e.g. I would probably see what you saw as a 30 min task as something that could be done in 10 min, however organising my time to put it at a specific place would result in this taking 4h.FrozenWintershttps://www.blogger.com/profile/07309214249604207549noreply@blogger.comtag:blogger.com,1999:blog-2316765421340036602.post-43861903901701412222017-12-27T05:09:53.468-08:002017-12-27T05:09:53.468-08:00@btilly
When you were giving your lessons, did yo...@btilly<br /><br />When you were giving your lessons, did you write every definition, theorem and proof on the blackboard, or did you use a powerpoint/beamer presentation, or a mix of both?Anonymoushttps://www.blogger.com/profile/10046680473514444774noreply@blogger.comtag:blogger.com,1999:blog-2316765421340036602.post-32045304384809412992016-12-08T19:01:32.960-08:002016-12-08T19:01:32.960-08:00I used spaced repetition somewhat like this for or...I used spaced repetition somewhat like this for organic chemistry 2 last spring. Much of the knowledge for organic requires just short problems, so I was able to cycle through problems more than a few times in the course. In general, the student evaluations were great--they loved it. And the students on average did better than I expected.ianrhilehttps://www.blogger.com/profile/05328507776311550558noreply@blogger.comtag:blogger.com,1999:blog-2316765421340036602.post-31833002523409003172014-04-19T13:06:13.118-07:002014-04-19T13:06:13.118-07:00Well done!
I don't know why spaced repetitio...Well done! <br /><br />I don't know why spaced repetition is not used universally in education at all levels. <br /><br />Spaced repetition during medical school would create less-stressed medical students who panic less before the big board exams, and would train better doctors. <br /><br />A couple of fellow medical school teaching fellows and I implemented a series of quizzes and cumulative review sessions for a dense course. For us, it was an obvious choice. These aids got rave reviews from the students. There was a bit of opposition to the quizzes, but this died down as they realized that quiz contribution to their final grade was tiny while the value of consolidating and reviewing information was high. <br /><br />I still cannot believe that most courses do NOT use these techniques. Actually, I can -- it takes time and effort to implement, and it is seldom required of busy teachers/professors.Freebirdhttps://www.blogger.com/profile/10854389296529044103noreply@blogger.comtag:blogger.com,1999:blog-2316765421340036602.post-72283718728027583212013-12-27T05:24:12.692-08:002013-12-27T05:24:12.692-08:00great!
you have rediscovered
what made education w...great!<br />you have rediscovered<br />what made education work fifty years ago.<br /><br />we lost it. <br />even those of us who went through it.<br /><br />there was so much nonsense around pandering to the students, that we lost even the memory of what worked for us.<br /><br />your post is the most<br />wonderful thing, i have read in ages.Unknownhttps://www.blogger.com/profile/17563983459289070045noreply@blogger.comtag:blogger.com,1999:blog-2316765421340036602.post-26004788759102522652012-10-16T12:53:29.888-07:002012-10-16T12:53:29.888-07:00Wow! You seem like such a great teacher! I took li...Wow! You seem like such a great teacher! I took linear algebra in college and totally was that kid writing down what was on the blackboard 2-3 minutes behind the prof, doing homework during class, and eventually just skipping class altogether. I got lucky to get a B, but I definitely don't remember anything from that class. Wish I'd had you as a teacher!Mirandahttps://www.blogger.com/profile/11625617954303243845noreply@blogger.comtag:blogger.com,1999:blog-2316765421340036602.post-74331790616949431072011-01-12T12:30:01.273-08:002011-01-12T12:30:01.273-08:00> That's impressive, imposing discipline is...> That's impressive, imposing discipline is and will always be the best technique. Thanks, you crystallized many thoughts in my mind.<br /><br />But Basel, note that the discipline is just a small part of it. The important thing is the questions and spaced repetition.<br /><br />Suppose Ben had run the course as a mediocre one, except you failed if you missed a class. Strict discipline, surely, but would his student have learned so impressively? I think not.gwernhttps://www.blogger.com/profile/18349479103216755952noreply@blogger.comtag:blogger.com,1999:blog-2316765421340036602.post-9381925814772703932009-10-29T00:36:52.443-07:002009-10-29T00:36:52.443-07:00For @Scott.
I don't see things the way that y...For @Scott.<br /><br />I don't see things the way that you do, for reasons I explained in <a href="http://bentilly.blogspot.com/2009/10/why-write-blog.html" rel="nofollow">my latest post</a>.<br /><br />To illustrate why I don't feel I have more to say of interest, let me answer the questions you pose. The pattern is that I generally did things in the most obvious and generic way possible, and don't think I have any particularly valuable insight.<br /><br />I planned the course by using the textbook used the last time it was taught, starting at the beginning, and going as far as I got. I did this because I was satisfied with the textbook and knew it covered the curriculum for the course.<br /><br />The textbook was conveniently split into sections which took approximately one lecture each to get through. Therefore I'd approach each lecture by taking the next section, reading it, coming up with an outline for what it would take to present it, and adding in appropriate examples, deciding what to stress, etc. Sometimes I'd do a little more or less than a section, but a section per day was my usual pace.<br /><br />Each section had a list of problems to choose from which ranged from easy to hard. So I'd grab 3 of the easiest questions from the current section, 0-2 from each section from the previous week, and then I'd pick 3 random topics from the whole course to pick a hard question from. As I selected I marked off the questions in my copy of the text so I didn't accidentally ask the same question twice. My rule for picking hard topics was to prioritize things by whether people showed confusion on it in question/answer, and then by how long it had been since a question was asked on the topic. Honestly it was haphazard, and I probably spent about 5 minutes preparing homework.<br /><br />After the first day the daily Q&A section ran itself. Because of the homework policy, class started on time. People came with questions, and I never again had a shortage.<br /><br />I didn't encounter any unanticipated gotchas. The anticipated ones were already covered in my post. For instance I anticipated that question and answer would be weakened by disruptions from people coming in late. Hence a homework policy set up to get class to start on time.<br /><br />The general principle in math when students don't "get" something is to try to break it down into pieces. One of two things happens. Either breaking it down clarified things, or a particular piece and be identified as trouble. In the latter case you repeat until you identify the real problem. Then reverse the process step by step to get back to the original question, and find whether there are any other misconceptions.<br /><br />I didn't succeed in making the class fun, so I don't feel qualified to offer advice on how to do so...<br /><br />As you see, I don't think I have anything particularly surprising to say on any of those topics. But if you wish to continue this conversation by email, my email is btilly@gmail.com.Ben Tillyhttps://www.blogger.com/profile/04335648152419715383noreply@blogger.comtag:blogger.com,1999:blog-2316765421340036602.post-13211450428926744082009-10-28T07:14:24.146-07:002009-10-28T07:14:24.146-07:00I can't find an email address for you so I'...I can't find an email address for you so I'll just post here.<br /><br />I think you have a big opportunity here and you're blowing it by fiddling around in your blog comments instead of writing a whole series of articles on this topic.<br /><br />Clearly there's a lot of interest in teaching using spaced repetition. I couldn't care less about linear algebra and I'm not a teacher... yet the <i>comment feed</i> of this one blog post in my RSS reader (and it's the only comment feed. the others are regular blog feeds). <br />Why? Because I'm really interested in spaced repetition learning and you're one of the very few people who's used it successfully. (Maybe some not-on-the-internet people are doing it... I don't care. I live on the internet)<br /><br />Why not write a whole series on the different elements here? Just off the top of my head I can see you've got<br />+ planning out the course<br />+ choosing how to split the lessons up<br />+ selecting homework assignments<br />+ running the daily Q&A session<br />+ specific gotchas to plan for and how to deal with them<br />+ dealing with topics the students just don't "get"<br />+ but it wasn't FUN.... (how to make it more fun)<br />+ ideas for how to tune this idea for teaching non-math topics <br />+ etc etc etc<br /><br />Do you realize that you're an authority on this now? Just by posting your success story and answering some questions about how you did it? Who cares if you only did it once... and that was a long time ago. It's still relevant and interesting and you're one of the very few talking about it.<br /><br />You're making people beg for more information in the comments... why? It's like that TED video with the kid that made his own windmill to power his family's house. When he gets up to talk about it he basically says "yeah, I built it out of parts I found. It was pretty cool"... <br /><br />We want to make something like what you made... teach us how.<br /><br /><br />Regards<br /><br />ScottUnknownhttps://www.blogger.com/profile/11319518842433436196noreply@blogger.comtag:blogger.com,1999:blog-2316765421340036602.post-76542876901861892592009-10-28T00:09:05.194-07:002009-10-28T00:09:05.194-07:00Answers for @toposphere.
1. Yes, homework was ass...Answers for @toposphere.<br /><br />1. Yes, homework was assigned every lecture and due the next.<br /><br />2. I forget exactly what portion homework was of the final grade. However I do remember that it was small, but you had to pass the homework to pass the course. Of course that turned out to be a non-issue since everyone did well on the homework. :-)<br /><br />3. Each day I would come up with a lecture plan, and then I would assign questions based on what I expected to cover. If there was material that I was unsure I would reach I wouldn't ask questions on it - after all I could always ask those questions next time. :-)<br /><br />4. Questions asked during question and answer time were almost entirely from previous material. However I also got asked questions during lecture from people who had clearly read ahead.<br /><br />5. I certainly mentioned that I thought it was a good idea to read ahead, but I didn't push the idea. I certainly didn't try to enforce it in any way.<br /><br />6. Yes, I would have reduced questions asked during regular lecture from the blackboard. I still think asking those questions is a valuable thing to do, but it also stresses the students out, and I don't think I found the right balance.Ben Tillyhttps://www.blogger.com/profile/04335648152419715383noreply@blogger.comtag:blogger.com,1999:blog-2316765421340036602.post-44850142861488538902009-10-27T23:39:35.936-07:002009-10-27T23:39:35.936-07:00I have a few questions:
1) To fit in 27 assignmen...I have a few questions:<br /><br />1) To fit in 27 assignments into a semester it seems you would have to give out a new assignment each lecture which was due in the following lecture. Is that correct?<br /><br />2) What percentage of the total mark was made up by the assignments?<br /><br />3) How much material was on each assignment? Did you aim for a certain number of questions or a certain estimated time until completion?<br /><br />4) You talk about both concretely in this situation 'starting the question session with questions' and abstractly 'the advantage of reading ahead and turning up with questions'. Did these two overlap in practice: ie did students turn up with questions on the material to be covered that day? Or was it mainly from the previous sessions?<br /><br />5) As a follow on, did you enforce or encouraging reading ahead? If so, how? Was it just a matter of saying "Next lecture I want to look at .... ."?<br /><br />6) In the conclusion you say you'd ask "somewhat fewer questions". Is this in reference to the questions you'd ask students whilst in the 'blackboard teaching' part of each lecture?<br /><br />Thanks for taking the time to write this up. :)topospherehttps://www.blogger.com/profile/16696336657266156205noreply@blogger.comtag:blogger.com,1999:blog-2316765421340036602.post-25031379180479355272009-09-30T12:09:34.964-07:002009-09-30T12:09:34.964-07:00That's impressive, imposing discipline is and ...That's impressive, imposing discipline is and will always be the best technique. Thanks, you crystallized many thoughts in my mind.Baselhttps://www.blogger.com/profile/17887809687689974873noreply@blogger.comtag:blogger.com,1999:blog-2316765421340036602.post-71509648989934647882009-09-30T10:34:09.867-07:002009-09-30T10:34:09.867-07:00@Basel: After the final exam I went to the course ...@Basel: After the final exam I went to the course coordinator and had the following amusement conversation.<br /><br />Me: "I have a problem with the class that I'd like to discuss."<br /><br />Her: "What is it?"<br /><br />Me: "I think it would be easiest if you read the final exam first."<br /><br />(she read it)<br /><br />Her: "Your problem is that they all bombed?"<br /><br />Me: "No, my problem is that they all aced it and I want to give half of them A's in the course."<br /><br />Her (laughing): "If they passed that test you can give them any grade you want."Ben Tillyhttps://www.blogger.com/profile/04335648152419715383noreply@blogger.comtag:blogger.com,1999:blog-2316765421340036602.post-11387438087349292212009-09-30T10:00:07.464-07:002009-09-30T10:00:07.464-07:00Was there a certain reaction from the course coord...Was there a certain reaction from the course coordinators or the dean regarding the general high performance of the class? Sometimes supervisors have certain expectations with regards to class performance, and alarms go off if it goes significantly up or down.Baselhttps://www.blogger.com/profile/17887809687689974873noreply@blogger.comtag:blogger.com,1999:blog-2316765421340036602.post-87994430330289311492009-09-29T23:37:24.908-07:002009-09-29T23:37:24.908-07:00I like your idea of reading the text before a lect...I like your idea of reading the text before a lecture and not taking notes in the lecture.<br /><br />I also like the thought of building in recall at different points in the course (especially promoting recall when students are just about to forget the material).<br /><br />Thanks for posting.Paraghttps://www.blogger.com/profile/16885449156962300704noreply@blogger.comtag:blogger.com,1999:blog-2316765421340036602.post-75880669658381463712009-09-29T17:29:33.367-07:002009-09-29T17:29:33.367-07:00@rick: Beyond some conversations a few months late...@rick: Beyond some conversations a few months later, I did not follow up to see how they did later. And it can't be published. All I have now are my memories and no real data. Someone would have to set it up as a proper experiment, and properly measure how the students did against other classes taught with more traditional means.<br /><br />@Peter: Sorry, I don't have the homework sets. I can't even remember what text I used, though I'd probably recognize it if I started to read it. But all I did for homework sets was pick problems out of the textbook. The trick was that a homework set would be drawn from different sections of the book.<br /><br />@Max: Being an adult means taking responsibility for your own actions, and accepting the consequences of the same. Believe it or not, adults have to follow lots of rules that they don't like. Frequently those rules revolve around being on time for things. Because, like it or not, wasting just a few minutes of a lot of people's time means you've wasted a lot of time.<br /><br />Besides which I <b>didn't</b> get significant resistance on that policy. Yes, one kid was unhappy at the start of one class. But on another day 2/3 of the class was happy because they were free to skip their homework to study for a midterm in another course. In the end I got far more thank yous than complaints.Ben Tillyhttps://www.blogger.com/profile/04335648152419715383noreply@blogger.comtag:blogger.com,1999:blog-2316765421340036602.post-82165007776189935572009-09-29T15:55:04.801-07:002009-09-29T15:55:04.801-07:00I don't think we need more teachers treating s...I don't think we need more teachers treating students like kids and not letting them turn in HW when they are only 2 minutes late. You deserved to be resisted on that one.Maxhttps://www.blogger.com/profile/10128548902346094251noreply@blogger.comtag:blogger.com,1999:blog-2316765421340036602.post-35413882108624379142009-09-29T15:22:27.714-07:002009-09-29T15:22:27.714-07:00Do you still have the problem sets available? I am...Do you still have the problem sets available? I am currently doing an intro to linear algebra course with proofs and I would love some material other than class assignments to work with.Peter Goodmanhttps://www.blogger.com/profile/08872907341973496185noreply@blogger.comtag:blogger.com,1999:blog-2316765421340036602.post-51786240263557604932009-09-29T10:30:21.210-07:002009-09-29T10:30:21.210-07:00I'd imagine that the students resisted your me...I'd imagine that the students resisted your methods early on, but it appears that they came to accept, if not appreciate them over time. I like your recipe. You had obviously given much more consideration than most regarding how to effectively convey the material. Have you ever gone back to your students (or have any reconnected with you) to get a sense for 1)how they've done in their career, particularly as it relates to the material you taught, and 2) retrospectively, how they felt about your methods. I'd ask that you make your "experiment" more broadly published, as those methods which are truly and thoughtfully designed to help students "absorb" complex material (rather that simply talk and expose them to it) are those which can help shape a future classes of kids who understand math and other complex subject materials. We, as a country, need more kids who get math, not fight it.<br />Many thanks.rjanezichttps://www.blogger.com/profile/01791397267087441465noreply@blogger.comtag:blogger.com,1999:blog-2316765421340036602.post-60393778126904394942009-09-29T09:57:23.609-07:002009-09-29T09:57:23.609-07:00@John: Homework was only on material that had been...@John: Homework was only on material that had been covered. But questions on the first week's material could show up on the last homework set. And if they did, you could be sure that they would be the hardest questions available.Ben Tillyhttps://www.blogger.com/profile/04335648152419715383noreply@blogger.comtag:blogger.com,1999:blog-2316765421340036602.post-26619750751666461832009-09-29T08:46:17.430-07:002009-09-29T08:46:17.430-07:00@John: I would presume from the material already c...@John: I would presume from the material already covered. <br /><br />I like the idea of taking notes before class and then just paying attention during class. In general, students learned to take notes any time the professor writes something down and that didn't seem the best way to learn to me even though I was also doing the same thing.Wanghttps://www.blogger.com/profile/13245484090260821651noreply@blogger.comtag:blogger.com,1999:blog-2316765421340036602.post-48592146185802157712009-09-29T08:26:27.903-07:002009-09-29T08:26:27.903-07:00>>and 1/3 from anywhere in the course
Was t...>>and 1/3 from anywhere in the course<br /><br />Was this material already covered? Or any material in the course?<br /><br />Thanks,<br /><br />JohnUnknownhttps://www.blogger.com/profile/15527092012999133171noreply@blogger.com