Scientific Mathematics takes place from 3-5pm and this is what the online timetable says. Unfortunately, and unbeknownst to me, a printed timetable had been issued having the class as 9-11am. There was one student in attendance who had got up at 7am in order to attend my class - which was due to run until 5pm!
In a far worse case it transpired that one student was taking her degree alongside a full time job. Her employer was very understanding and had arranged her schedule around the lecture commitments. Since Scientific Mathematics was on a Thursday morning, they had arranged for her to work on a Thursday afternoon. This meant she would only be able to attend very rarely. This is a really terrible consequence of a silly error on the part of the University. It had been agreed that since this student had an A-Level in mathematics it would not be too problematic for her to complete the course in a sort of distance-learning mode, attending where she can.
Wednesday, 26 March 2008
Week 1: Revision of Algebra
I decided since I didn't know what to expect of the students prior mathematical training I would add a column to the register for "previous mathematics". As an example to get the ball rolling I filled in my own line "BSc, 6 years ago." I was hugely suprised when 10 out of the 16 students in the room had A-Level experience of mathematics in the last two years.
One student asked me whether they really needed to attend and I gave the advise I had been asked to give. I said I wasn't going to tell them not to attend, but that they had been sent to me to obtain a certain level of mathematics and that level was represented by the course content. I also made clear that if they failed the module they might have a hard time retaking it if they had a poor attendance record, though I was a bit vague when pressed for more details since I don't know the extent to which this is a bluff. I can't imagine a student will be kicked off their course without being given an attempt to resit. When I finished talking I realised well over half the room had put down their pens to listen in.
When I handed out the course notes, about half the room opened the booklet and supressed a laugh or snort - an involuntary gesture of derision. I was a little dismayed - I had planned to go through the material in the first part of the booklet on the board. Clearly this would be very unwelcomed by most students in the room. I decided that since the material was so basic - really only a revision - and most of the students were obviously over-qualified anyway I would be better off running the whole lesson as a kind of problem class. The students would work through problems and I would be available to assist and answer questions as needed. This is a tried and tested method of teaching mathematics. "Right," I said, "I don't think there's any point me showing you how to multiply fractions, is there? So please have a go at the exercises on page 10 and let me know if you have any problems."
I followed this with a large blunder. I suggested that anyone who didn't feel confident in the materials should come to the front and I would go through it with them. Of course, no one moved. I realised instantly this was such an unwelcome idea. I grinned and said to a chap on the front row "That was a silly thing to say, wasn't it?" He laughed, "there's no way I'm letting you single me out," he said.
The class proceeded at their own pace for about an hour. I wandered round checking how students were doing and answering questions as they arose. The students were all capable and intelligent; some were a little rusty on the specifics of the material but eager to relearn. I tried to engage a few students in discussions about their home disciplines in order to bring them round to being enthusiastic about mathematics. I was suprised that none of them seemed to be questioning why they are learning the mathematics. One or two gave me examples of how the maths would be relevent to their disciplines. This was greater motivation that I had been expecting.
After an hour one student came up to me and said "me and my friends are on this page and we wondered if we could go now." According to the lesson plan I had from a previous year (but had not shared with the students) they were on week 4; and it was only halfway through week 1. I said they could go early; after all I am not their keeper and it is hardly my place to forbid them to leave. They could have simply not attended in the first place. It emerged that most of the room had advanced already beyond week 1 material and all left early. I went back to my room and typed up my register.
On numbers: 6 students in the room did not have A-Level experience. One student had sent word ahead that she would not be able to attend (see next post). This left 8 students who were expected to attend but had not.
One student asked me whether they really needed to attend and I gave the advise I had been asked to give. I said I wasn't going to tell them not to attend, but that they had been sent to me to obtain a certain level of mathematics and that level was represented by the course content. I also made clear that if they failed the module they might have a hard time retaking it if they had a poor attendance record, though I was a bit vague when pressed for more details since I don't know the extent to which this is a bluff. I can't imagine a student will be kicked off their course without being given an attempt to resit. When I finished talking I realised well over half the room had put down their pens to listen in.
When I handed out the course notes, about half the room opened the booklet and supressed a laugh or snort - an involuntary gesture of derision. I was a little dismayed - I had planned to go through the material in the first part of the booklet on the board. Clearly this would be very unwelcomed by most students in the room. I decided that since the material was so basic - really only a revision - and most of the students were obviously over-qualified anyway I would be better off running the whole lesson as a kind of problem class. The students would work through problems and I would be available to assist and answer questions as needed. This is a tried and tested method of teaching mathematics. "Right," I said, "I don't think there's any point me showing you how to multiply fractions, is there? So please have a go at the exercises on page 10 and let me know if you have any problems."
I followed this with a large blunder. I suggested that anyone who didn't feel confident in the materials should come to the front and I would go through it with them. Of course, no one moved. I realised instantly this was such an unwelcome idea. I grinned and said to a chap on the front row "That was a silly thing to say, wasn't it?" He laughed, "there's no way I'm letting you single me out," he said.
The class proceeded at their own pace for about an hour. I wandered round checking how students were doing and answering questions as they arose. The students were all capable and intelligent; some were a little rusty on the specifics of the material but eager to relearn. I tried to engage a few students in discussions about their home disciplines in order to bring them round to being enthusiastic about mathematics. I was suprised that none of them seemed to be questioning why they are learning the mathematics. One or two gave me examples of how the maths would be relevent to their disciplines. This was greater motivation that I had been expecting.
After an hour one student came up to me and said "me and my friends are on this page and we wondered if we could go now." According to the lesson plan I had from a previous year (but had not shared with the students) they were on week 4; and it was only halfway through week 1. I said they could go early; after all I am not their keeper and it is hardly my place to forbid them to leave. They could have simply not attended in the first place. It emerged that most of the room had advanced already beyond week 1 material and all left early. I went back to my room and typed up my register.
On numbers: 6 students in the room did not have A-Level experience. One student had sent word ahead that she would not be able to attend (see next post). This left 8 students who were expected to attend but had not.
A whole hour?
Scientific Mathematics takes place over 2 hours on Thursday afternoons. The format for this, specified in the module specification, is one hour lecture followed by one hour problems class.
I cannot imagine anyone watching me write on the board for a whole hour and still taking anything in. I cannot imagine students, having done this, sticking around for a second hour of doing problems.
I talked with a couple of maths lecturers about this and it was recommended to me that I talk for 5-10 minutes, maybe as many as 20 minutes, then give them 10 minutes of exercises to do, then repeat for the 2 hours. This seemed like a much better plan.
I cannot imagine anyone watching me write on the board for a whole hour and still taking anything in. I cannot imagine students, having done this, sticking around for a second hour of doing problems.
I talked with a couple of maths lecturers about this and it was recommended to me that I talk for 5-10 minutes, maybe as many as 20 minutes, then give them 10 minutes of exercises to do, then repeat for the 2 hours. This seemed like a much better plan.
All the cards on the table
For Scientific Mathematics, all the course notes are printed in a booklet and given out in week 1. This could be problematic, since it invites non-attendance. However, it allows students to work at their own pace between lectures and means that they don't have to copy down their own notes from the board, which has to be a good thing. I haven't been given the notes electronically so can't put them online; they must collect a physical copy from me.
Why is this relevant to me?
I became concerned about the students I would be teaching. If they had avoided mathematics since it stopped being compulsory, only to find themselves at university and being made to study it as part of their course, I could imagine it would be difficult to find motivation.
Mathematics is quite a polarising subject. If they have chosen not to do mathematics at A-Level they are likely do not like it.
I enquired about the courses the students would be taking. Some would be from foresic science degrees, some from business and some from astronomy and computing. This is potentially a real problem, since these are a wide variety of courses. Although there is plenty of mathematics that reaches across these subjects the differences is application mean that the maths must be taught in an abstract way. Business students do not want to learn about radioactive decay, equally forensic science students are not likely to be interested in compound interest; yet these use the same mathematical techniques.
Still, some links to the home curriculum must be useful. Surely students who are not keen on maths, who are being forced to take time out of the degree they chose to read to be taught some, will only be interested if they can see the application in their own subject. This is a great contrast to when I studied mathematics, a lot of which was studied for its own sake, because it was interesting. If these students had this opinion, they would surely not be sitting in this class.
Mathematics is quite a polarising subject. If they have chosen not to do mathematics at A-Level they are likely do not like it.
I enquired about the courses the students would be taking. Some would be from foresic science degrees, some from business and some from astronomy and computing. This is potentially a real problem, since these are a wide variety of courses. Although there is plenty of mathematics that reaches across these subjects the differences is application mean that the maths must be taught in an abstract way. Business students do not want to learn about radioactive decay, equally forensic science students are not likely to be interested in compound interest; yet these use the same mathematical techniques.
Still, some links to the home curriculum must be useful. Surely students who are not keen on maths, who are being forced to take time out of the degree they chose to read to be taught some, will only be interested if they can see the application in their own subject. This is a great contrast to when I studied mathematics, a lot of which was studied for its own sake, because it was interesting. If these students had this opinion, they would surely not be sitting in this class.
Tuesday, 25 March 2008
Prerequisite knowledge
Prior to the first class I was very aware that I knew nothing about the mathematical abilities of the incoming students. There is no prerequisite and consequently no minimum standard. I was told by a physics academic "we must get you teaching a more advanced course." Apparently teaching a more advanced course is far preferred, since you can assume a level of knowledge based on the prerequisites and teach to that assumed ability.
I couldn't help thinking about my own degree. I had several modules where I had barely scraped through the assessment for the prerequisite in semester 1, only to find it assumed that I knew the material perfectly in semester 2. I would therefore get immediately lost. Running to catch up, I would fare badly in the second module also. I think it is important to remember that even if you have an agreed level of knowledge on paper, it may not be reasonable to assume that everyone is up to that level. In the case of Scientific Mathematics, since there is no agreed level all students are at, I could assume everyone needed to know everything in the course equally, unless proven otherwise.
The other aspect of this was my own prerequisite knowledge. My first degree was in mathematics but I graduated from this almost 6 years ago and have done little advanced mathematics since. I was nervous enough at the prospect of teaching; at least in Scientific Mathematics I knew the material fairly well. Teaching some advanced module my first time out I would be petrified in case any of the students started asking questions!
I couldn't help thinking about my own degree. I had several modules where I had barely scraped through the assessment for the prerequisite in semester 1, only to find it assumed that I knew the material perfectly in semester 2. I would therefore get immediately lost. Running to catch up, I would fare badly in the second module also. I think it is important to remember that even if you have an agreed level of knowledge on paper, it may not be reasonable to assume that everyone is up to that level. In the case of Scientific Mathematics, since there is no agreed level all students are at, I could assume everyone needed to know everything in the course equally, unless proven otherwise.
The other aspect of this was my own prerequisite knowledge. My first degree was in mathematics but I graduated from this almost 6 years ago and have done little advanced mathematics since. I was nervous enough at the prospect of teaching; at least in Scientific Mathematics I knew the material fairly well. Teaching some advanced module my first time out I would be petrified in case any of the students started asking questions!
Mixed abilities
In preparation for teaching Scientific Mathematics I asked if there was anything I should know. I was told to expect little from the students – I shouldn't be surprised if I encounter reasoning such as 1/2 + 1/2 = 1/4. (Of course, 1/2 + 1/2 = 1; the confusion arises from 1/2 * 1/2 = 1/4). I was also told that there may be one or two students who have taken an A-Level in mathematics and so already know this material. The point of the module is to demonstrate to the student's course that they have a level of mathematical ability and this is achieved through passing this module assessment. I was told that if the one or two students who have an A-Level in mathematics approach me and ask quietly if they need to attend lectures then I am to tell them that if they feel they do not need to attend that is their choice but that if they fail the assessment they may find it very difficult to retake it if they have poor attendance.
Doing the deal
I was approached by my supervisor at the end of 2007 who told me there were more mathematics courses to teach than mathematics lecturers to teach them and so they were looking for postgraduate students willing to take on some part time lecturing. My first degree was in mathematics and so I went along to find out what courses they were trying to fill. When I got there I was told that all the "interesting" courses had been filled and all that was left was Foundation Mathematics and Scientific Mathematics. I am familiar with Foundation courses from a previous job at the University of Nottingham. Students take a Foundation degree, which is roughly A-Level equivalent material and designed to feed into an undergraduate degree course (at Nottingham often in some form of Engineering). Scientific Mathematics was pitched between GCSE and A-Level and I was told the students would be those who have not taken an A-Level in mathematics or who had one from perhaps 10 years ago and needed the refresher.
I was asked if I minded teaching the more basic level Scientific Mathematics. I was told that the remaining course would probably have to be assigned to an academic and that person would be more upset by this if the course they were made to teach was Scientific Mathematics. A bit ominous, but I said I didn't mind. I was given a copy of the course materials and asked to think about it. That night I read through the course. It seemed basic but okay. I was said I was happy to teach this.
A few days later I was talking to another lecturer. I told him I was going to be teaching Scientific Mathematics and he gasped and made the sign of the cross. This didn't bode well!
I was asked if I minded teaching the more basic level Scientific Mathematics. I was told that the remaining course would probably have to be assigned to an academic and that person would be more upset by this if the course they were made to teach was Scientific Mathematics. A bit ominous, but I said I didn't mind. I was given a copy of the course materials and asked to think about it. That night I read through the course. It seemed basic but okay. I was said I was happy to teach this.
A few days later I was talking to another lecturer. I told him I was going to be teaching Scientific Mathematics and he gasped and made the sign of the cross. This didn't bode well!
Monday, 17 March 2008
A reflective journal
This blog is for me to keep a reflective journal on my experiences of teaching Scientific Mathematics. I am prompted to do so by taking the Postgraduate Certificate in Higher Education.
As I started the PGCHE after most of the teaching had been completed this journal is, for the first part, retrospective. In the next several posts I will tell the story of Scientific Mathematics so far and try to outline what were my worries, etc.
As I started the PGCHE after most of the teaching had been completed this journal is, for the first part, retrospective. In the next several posts I will tell the story of Scientific Mathematics so far and try to outline what were my worries, etc.