I see my blog has just passed the 100,000 views mark.
(Rather more people watch my YouTube videos!)
This year I have about 260 students in my first year module G11FPM Foundations of Pure Mathematics.
I invited feedback using an online anonymous comments form, but only 12 students responded to this. So on Monday I handed out a paper-based version. Given that attendance was high, it was a bit disappointing that only 42 forms were placed in the box at the end, but the comments were still interesting. (I expect that it didn’t help that we had to evacuate the building for a while when the fire alarm went off!)
I put together some “feedback on feedback” for the students. Here it is! It is rather long, so perhaps relatively few people will read the whole thing.
G11FPM: Feedback on feedback
Thanks for all of the comments you provided on the form I handed out in today’s classes. If you do have any further comments, you can use the online form (link available on the Moodle page). There will also be an official set of Student Evaluation forms which I will issue in a class towards the end of the module.
See below for a summary of your comments, and some of my thinking on these. This is rather long, but I hope some of you may find it useful!
What works well?
- The use of voting packs and multiple choice questions provides an interactive aspect. This helps to keep you engaged in lectures, and also helps you to confirm your understanding of the material.
- The videos of classes (both from this year and last year) are very popular.
- The common notation sheet I issued today also gets some mentions.
- You appreciate my clear explanations and my thorough approach to proofs on the board (but see below for some comments on pace).
- You like having a chance to prove things yourselves.
- You feel that help is always available if you need it.
- You find the slides well structured, with good uses of boxes and highlighting (though some of you would like a little more variety in the colour).
- You find the examples very helpful when trying to understand the concepts.
- You like the ‘slides with gaps’ system (but some of the gaps need to be a bit larger).
- Generally you find the workshops are working well in their current form (but see some comments below).
What else would be helpful?
Requests here include:
- Some computer-marked multiple choice practice questions on Moodle for instant feedback.
I have been thinking about the best way to do this for some time: I plan to develop some software to generate tens of thousands of random questions!
- Slower pace in proofs. See also comments on pace below.
- More discussion of how to start and end proofs, and possibly some handouts on this.
I agree that there are some routine aspects to doing proofs which can be learned, though there are creative aspects too. I hope that the additional comments I include in my solutions to question sheets may be helpful, and my feedback on last year’s exam performances. You may also find my videos on ‘How and why we do proofs’ useful (available online). But the main thing is to try to do as many proofs yourselves as possible.
- Annotated slides/workshop solutions available online.
[For blog readers: note that the unannotated slides with gaps are all available to students online via Moodle.]
Generally I make annotated slides available if the recording fails or if we don‘t finish all of the questions. I prefer not to put everything online, as that might discourage some students from attending the classes.
- A sheet with all the definitions from the module
This might be a bit long. Perhaps I could extract some of the more commonly used definitions.
- Some of you want more votes in classes, but others want fewer.
I won’t be able to please everyone here! I could cut down on the votes to allow more time for my own explanations, but I feel that it is really valuable to let you discuss the material in class. It is probably impossible to find a perfect balance, but it may help if the fire alarm doesn’t go off!
- More sets of lecture notes in one go if possible.
I will probably move to issuing two lectures at a time regularly now.
- More questions with solutions available online
There are a lot of questions on Dr Zacharias’s question sheets (available on Moodle), and I will make solutions to these available as the module progresses. Where I don’t make solutions available, you are welcome to come to see me to discuss your attempted solutions. I prefer not to make all of the solutions available, as that may encourage some students to give up to quickly and look at the solutions before trying hard enough on the questions.
- Sometimes my writing may be a little hard to read.
I’ll do the best I can. It can help if I write a little more slowly.
- Some of you want more hints for workshop questions, others want fewer
Again, I won’t be able to please everyone here. Hopefully you can get some more guidance from the helpers if you need it.
- More visual examples
Diagrams are often helpful. I’ll try to incorporate a few more!
- Let us know which proofs could be examined: do we need to memorize them all?
You may find it useful to look back at the first workshop ‘About this module’. Everything in the annotated slides from lectures is ‘examinable as bookwork’ unless it is explicitly stated otherwise. You can expect to be asked for the statements of a number of definitions and named results (theorems lemmas etc.) from lectures. You can also expect to be asked to reproduce some standard proofs from lectures and/or slight variations on these. Of course, as well as the bookwork portions of questions (described above), there will also be lots of “non-bookwork” portions to exam questions, which will often require you to demonstrate your understanding of the material, and your ability to write proofs, and your ability to work with or to think up suitable examples.
Memorization without understanding will be of limited value. More constructive, if you can manage it, is to understand the key ideas needed in the proofs, and to practice doing proofs until the proofs start to almost write themselves. This will become more and more important as you progress through the course, if you continue to study pure mathematics.
- More examples and practice questions
I do have to balance my use of time in classes. But you do have quite a lot of question sheets available now. (See the G11FPM Moodle page. Don’t forget about all of Dr Zacharias’s question sheets, which are available there.)
- A sheet summarizing all the lemmas and standard results we can use/quote without proof in the exams when proving something else.
This might be a bit long again, though perhaps the detailed summary of lectures (available on Moodle) could help.
The general rules here are: (i) you are not allowed to quote a result to prove itself and (ii) you should usually not quote a result from later in the module to prove a result from earlier in the module (as the earlier result might have been used to prove the later result). You are generally allowed to quote earlier results to prove later results. If you are proving something completely new to you, then you can usually quote and use any standard result from lectures.
- A quick revision/summary at the end of the lecture or the start of the next one
There probably isn’t time to fit this into the actual classes. However you may find the detailed summary of lectures available from Moodle is helpful here.
Any other comments
Here is a selection of some of your comments, and my thoughts on these.
- Although you generally approve of my pace, some of you feel that I spend too long on easy bits at the start of classes, and that I then have too little time for harder parts at the end of classes.
I agree that I don’t always spend as long on some aspects as I would like. However, I do usually try to spend extra time on those more basic aspects which have caused difficulty in previous years (based on frequently asked questions and on common confusion shown in the exam performances). For example, there are usually many students who do find the precise logic behind ‘less than or equal’ confusing. So it may be that material that some of you find obvious is nevertheless hard for others. I prefer to go a little slower at the start of the class so that more students are able to keep up for longer.
Hopefully the recordings will help with those parts of classes where I go faster. If I do omit some details, see if you can fill them in. Please feel free to ask me if there are parts which you are unable to figure out after some studying and/or multiple viewing!
- Some of you would like a slightly faster pace overall, but others would like me to go slower.
- Some of you can’t find this year’s recordings, or can’t make them work. I will email you all with more details on this. (See also earlier emails concerning some possible problems with using the Chrome browser to view recordings.)
People talk about issuing “Stop, Start, Continue” questionnaires to their students … though I hear that these days an alternative is to ask “What Works Well” and “What could be even better?”.
I generally make online forms available to my students so that they can give me anonymous feedback. Of course you generally don’t get many people filling these in. I may issue a paper-based form requesting early comments.
So far three of my 270 first-year Pure Maths (G11FPM) students have responded to my request to fill in the online form. There are already some interesting suggestions there: could they have a summary sheet listing commonly used notation to help them while they are getting used to it? That may be a good idea, though I wouldn’t want them to become dependent on such a sheet, and I wouldn’t allow it to be taken into the exam.
I included a question on pace. Two of them said the pace was mostly good. One of these said it was sometimes a bit slow and the other said it was sometimes a bit fast. The third one says that the pace is too fast for them. (Hopefully the videos will help those who are finding it hard to keep up.)
The start of teaching is approaching!
Soon I will have my second attempt at teaching Foundations of Pure Mathematics to the incoming first years at Nottingham.
We have a record intake in maths at Nottingham (again) this year, and I expect to have about 270-280 in this class. I will make heavy use again of my coloured card Voting Packs (which we have modified slightly this year). I will also record videos of classes using the resident Lecture Capture system (Echo360). I hope to publish the module videos in some form on iTunes and YouTube.
Recordings from this module as given in 2012-2013 will remain available too, at least for this year.
Off topic, but for those interested in autism, here is a message I just received (sent to the Awares mailing list) from my brother Adam.
Dear Joel Feinstein
The wonderful Liane Holliday Willey is the latest presenter in the monthly series of one-day online autism conferences in the Awares conference centre. I will be putting Liane’s excellent paper on the conference site over the next day or so and Liane will be online all day on Monday, May 20, 2013
Please register right now at www.awares.org/conferences
Dr Liane Holliday Willey, Ed.D. (www.aspie.com) is an inspirational speaker who helps her audience truly understand the importance of accepting people with differences. All her life, Liane knew she was different, but only after one of her family members was diagnosed with Asperger’s syndrome did Liane realize the reason behind her own differences; she too was diagnosed with Asperger’s syndrome. Liane spends much of her time working with horses at the equestrian facility she owns. Dr Willey has authored several internationally best-selling books all published by Jessica Kingsley Publishers, including Pretending to be Normal: Living with Asperger Syndrome (foreword by Tony Attwood), Asperger Syndrome in Adolescence: Living with the Ups, the Downs, and Things in Between, and Asperger Syndrome in the Family: Redefining Normal and Safety Skills for Asperger Women: How to Save a Perfectly Good Female Life. Liane has contributed to many additional books and journals, and is currently the senior editor for Autism Spectrum Quarterly. In addition to her numerous interviews on national and international television and radio, Liane’s life story was an inspiration for the film Normal Folk, currently in pre-production, and the feature film, Adam, as well as the focus of the video Asperger Syndrome: Crossing the Bridge with Dr Tony Attwood. Liane believes the Asperger’s syndrome community is a wonderfully rich world that is populated by some of the most interesting and incredible individuals on the planet and she is exceptionally proud to be a part of it.
For further details about this and all other Awares online conferences, please contact me at: email@example.com
The University of Nottingham’s May Fest this year will be on Saturday 18th May, 11AM to 5:30PM.
For more details, see http://www.nottingham.ac.uk/mayfest/index.aspx from where I quote:
Saturday 18 May!
Following four successful years The University of Nottingham will once more open its doors to the local community for May Fest 2013. Come along and join in with the free, interactive activities for all ages and interests.
The May Fest programme is now available from http://www.nottingham.ac.uk/mayfest/documents/mayfestprogramme2013.pdf
Here is what we are offering in Maths:
Try your luck at the roulette table (no real money involved!) and learn how
to solve Rubik’s Cube. Or look at fascinating mathematical exhibits, games
and puzzles while chatting to staff and students.
Time: Just drop in 11am-5.30pm.
Location: Room C20, Portland Building (No.7).
Recommended for age: 3+