**Mood:** hug me

**Now Playing: **Mexican Joe (Jim Reeves)

As part of my Postgraduate Certificate in Academic Practice, I have to write an essay on:

Identify an existing module or unit of learning which may be enhanced by the use of technology. Critically consider the impact of the changes you suggest.

And I have to demonstrate the following:

- Critical consideration of the use of technology in own teaching
- Proposals and justification for choices / rejection of technology
- Critical consideration of the impact of proposed changes
- Knowledge of the literature

Great, so I sort of know what I have to do – but still don’t know how to do it!! AHHHHHHH!!!

I have an idea for the essay, it’s just not hitting the things I need to demonstrate 😀 .

Okay so here is my idea which I have already incorporated into a unit. I want to look at the use of Autograph when teaching functions and graphs. Autograph is a mathematical software which is able to plot complex functions, so students are able to visualise the maxima and minima quite easily and also able to see how differentiated and integrated graphs look like as well.

Well, I think the first thing I need to do is to critically consider the use of technology in my teaching. Let’s start with practical issues. The class on functions and graphs is a 3 hour intensive class which is focused on building students’ concepts of mathematics. Secondly, it is already scheduled for the current classroom hence using a computer room becomes difficult. So, I have timetabling constraints. I have no clue what I’m saying – I just know that I don’t want to do it 😀 .

Alright let’s describe the scenario – maybe that would get my brain going (I know what is annoying me … previously when I was writing my thesis – I always had to make sure I was satisfied with it and didn’t have to meet any targets but in an essay you have to meet the targets – and that is kind of scary … I don’t know how to just let it flow …)

Okay, my example is the use of limits to find what is differentiation at a point. I used Autograph to show students the gradient of a line, and then decrease the change in y and the change in x, to show how it was approaching the gradient at a point. I think showing students this visually they did not have to imagine it and I think that is good. I think I need to find the difficulties associated with teaching differentiation. Okay, I found a paper by Tall (1985) which talks about teaching the concept of differentiation from first principles. He however uses the graphing calculator and suggests that students explore on their own the concepts of a chord tending towards a point for a tangent. He explains that helps with developing a cognitive manner and suggests that this relates to Skemp’s idea of relational understanding. He then goes on to draw from Ausubel that the learner is able to get an idea of the whole concept first and this person can be an “advanced organiser”. This is interesting because Pea (1985) also mentions that the computer can be used as an organisation tool for a learner – I wonder if it is in this context that he meant?

Now the question may be asked why I chose to use Autograph. Well, there are several reasons for this:

- It has a site licence here at Liverpool Hope and hence makes it easier for the students to have a play with it
- I chose not to use graphing calculators although there were some available, because would have spent more time teaching students how to use a graphing calculator rather than them seeing the context
- But, I didn’t give the students an opportunity to use Autograph, I demonstrated it instead, the reason being of course I wasn’t time-tabled for a computer room. This is really a 15 minutes task to learn – if used in a computer room it may take several minutes to learn (okay I can’t seem to make an argument right now! )

I think I have a sufficient amount to make a start. I was going to bring in cognitive load theory – I could suggest that learning software itself is too high an intrinsic load and hence there wouldn’t be any germane load …?? Making this stuff up as I go along …