# Thoughts after first two lectures

Some thoughts on how teaching went. But first a summary of how lecture is organised.

## Summary of how I organise lectures

- Printed notes are provided with gaps throughout.
- I use a “document camera” or “visualiser”, not a slideshow.
- Lectures always start with warm-up questions.
- Throughout the lecture I pose questions to the students and give them an appropriate amount of time to answer them. While students are attempting them, I walk along the two sides of the lecture theatre and see how students are doing, and sometimes ask for students’ thoughts.
- I get students to tell me their answers. Either I go along a row of the lecture theatre (and hence put students on the spot), or I just ask anybody to just shout out the answer, or I get them to raise their hands for yes-no questions.
- When they are not attempting questions, I am doing standard lecture stuff: introducing a new idea, going through an example question, etc.
- The university I am at automatically records all the lectures. It records the lecture theatre with a camera at the back, and it can also record what is being shown on the document camera and on the PC screen.

## First lecture. Lecture 1.1

This was an introductory lecture.

- Warm-up questions were two *very* easy Sudoku puzzles, except the second one had two possible answers. Gave 5 minutes for this. I walked around to see how students were doing and all the students I saw were attempting it and at good pace. Then went through answer: went along rows asking students for their value in certain gaps. No student resisted answering when put on the spot. For second Sudoku puzzle, I just started attempting doing it myself and people in audience voluntary shouted out answers (especially if I made a mistake!). Nicely, many students noticed there were two possible answers for 2nd puzzle(but I have no idea how many students did not notice).
- I then went through various introductory information about the maths module: what is maths (comparing pure and applied maths), what is aim of this particular module (mastering basic ideas and patching any weaknesses), differences between uni and school (learning from fewer examples, we are more open to critique and feedback), info about my teaching style (interactive lectures, and here I said that if you are particularly anxious or uncomfortable being put on the spot, just say “No thanks” and I’ll move on. I then said that if you are not anxious, you should make an effort to answer. Few other minor things that I do differently to most teachers).
- I then posed the question: It is 1pm. How many times do hour-hand and minute-hand overlap in 24 hours? Gave them 5 minutes, and I walked around asking people for their thoughts. Most people said 23 with the explanation: They cross once every hour, but since it stops at 1pm, it does not reach 1:06 where they would have crossed 24th time. For most students, I pointed out that the hands have already overlapped at the time 1:06 twice, so you shouldn’t be subtracting one. Then, went back to front, and said: “I’ll first just state the answer, and then go through 4 explanations discussing the merits of each one.”
- I went through answer, and went through explanation. Each explanation gives the correct answer, but the amount of understanding increases each time. The purpose was to illustrate how the answer is not everything, and to illustrate difference between knowing the answer and understanding it.
- Then went through final few bits of info, and what I expected them to do between the end of this lecture and the workshop which started in an hour. (Explicitly, they should review the lecture and make a start on the workshop questions.)

Overall thoughts. First, I was surprised by how engaged the students were in lecture and how willing they were to answer. My only previous experience was during Semester 2 of last academic year, where students presumably already got used to a certain style of lectures (i.e. minimal interaction). I think the two main points for anybody wanting to make lectures interactive are:

- Do it from the first lecture
- Ensure the questions are selected so that
*every*student can actually understand the question and*every*student can come up with some reasonable ideas. If this is not the case, then naturally students will be more hesitant to answer. Also, from a pedagogic point of view, if a question does not meet these criteria (in particular the first criteria), then you should be questioning the value of asking the question.

Second, I learnt a valuable lesson. If you want to hand-out three pages of printed notes (which are not stapled), then have three separate piles (so each student selects one sheet from each pile) instead of one large pile (in which case each students has to take three sheets from that pile).

Third, I re-watched parts of the lecture and I need to make a habit of repeating explanations more than once. This is because I noticed how easy it is to miss a word or two in an explanation (I did not enunciate clearly, or momentarily zoning out, or trying to think of something a minute ago, or …).

## Lecture 1.3

(Event 1.2 is a workshop. This is why the second lecture is not Lecture 1.2).

This lecture was on addition. Here is a summary of what happened and my thoughts on it:

- Warm-up was basic mental arithmetic. Went along rows and people did not hesitate in answering. (One person did make a mistake, but corrected it when it was pointed out.)
- Then I discussed the pattern that 4+8=8+4. I described the pattern in words (adding one number to second is same as adding second number to the first) and then using algebra (for any numbers a,b, a+b=b+a). I then made a historical remark that algebra did not already exist, and it is worth observing this benefit of algebra. Then discussed pattern 3+(5+7)=(3+5)+7, and again wrote it out in words and then in algebra. It is worth noting describing these patterns was worthwhile — during warm-up I overheard somebody explaining to their neighbour “it doesn’t matter which order you add”.
- Then I gave them task of translating a worded description into algebra. They were “adding zero to a number equals that number” and “given any four numbers, adding first two is equal to adding second two.” I walked around side of theatre and almost all answers I saw were correct. However, one person wrote “4+0=4” as their answer for first question. After going through answers, I then asked for a show of hands for whether the statements were true or false. All people thought first was true, but to my surprise, there was a mix of answers for the second. I do not know what to make of this — either they do not actually understand what the sentence means or they had no idea how to determine if such a statement is true or false. I ended up just saying it is false, with the example 1+2=3+4 is false.
- Next had exercise with translating symbols into words. Can’t remember anything noteworthy.
- Next had exercise of using algebra to describe real-life variables. First one was D+F=T, where D is cost of drinks, F is for food and T is total. Questions included translating from words to symbols, doing simple calculations, and asking if what happens to T if D increases by 1, and what happens to T if F decreases by 1. I then highlighted that if you can answer these previous two questions, you have understood the main idea behind differentiation, which is all about understanding how changing one variable affects another.
- Then had similar question, but with hours awake, hours asleep and total hours in a day. Had similar questions. But afterwards, I highlighted difference between these two very similar looking equations — the difference being that in second case total hours in a day is a constant. I stressed that there is ambiguity in formulas and one skill you need to learn is keeping track of which letters represent constants and which letters represent variables.
- Then had few questions on estimating addition.
- Then showed them the online resources available (on the so-called Blackboard VLE).
- I then went through an online “Mastery Exercise” with them, which had 35 simple addition to be done in 2 minutes. I asked if anybody was brave enough to attempt it, but nobody was, so instead just had people shouting out answers while I typed them.

The main problems I have are this. My cohort consists of people who are reasonably good at maths and some who are very weak. The most vocal students seem to be the ones who are good (and they generally indicate boredom or ease with the lecture), so I have no idea if I am actually helping the people I intend to help by going over this basic maths. I will need to think of some ideas quick before they fall to far behind!