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!

Best wishes,

Dr Feinstein

**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.)