November 30, 2010

Task 2.3 c

TASK C: The history of zero

The concept of zero seems obvious to us nowadays, but actually has a long and complex history, not coming into widespread use in Europe until the 17th century.  Read the article A history of Zeroat the MacTutor website, and answer the following questions:

  1. Why is zero an important concept in mathematics?
  2. Why did zero take so long to become established within number systems?

Zero has become important within maths as a place marker and a “digit” in its own right. Within mathematical place systems it has become vital as a means of separating numbers and showing place value. Other systems had developed punctuation marks to show that there was a gap- ie 2”6 where we would write 206 but systems based on pictures/ symbols had no need for a zero- there just wasn’t a picture there. Rather than there being any misinterpretations the use of zero makes numbers explicitly clear as the 0 shows one space. a gap could be one zero, none or more.

Zero is also important as a means of separating positive and negative numbers- a neutral space so show that something was there but has now been taken away (or added) – a little like a debt being paid off. The zero records that there was a debt but that it has been cleared.

Mathematicians also perform numerous calculations with a zero- the concept of infinity arises when a number is divided by zero.

Zero was “invented” by different civilisations over time- Mayans, Babylonians and Greeks had some form of zero which was used and then died out. It wasn’t until the Indian mathematicians developed it that it eventually came into widespread use- even then it took hundreds of years to become established.

Some civilisations didn’t really see the need for a zero – as mentioned earlier – within systems using pictures and symbols the zero was depicted by a lack of symbol. The context in which the number was used appears to be more important than accurately the number. Indeed some mathematicians suggest that Christian teachers didn’t like the concept of zero and shied away from its development. They believe that it took Hindu mathematicians who believed in a void to develop the concept.

Much of the historical use of maths was in a very practical way and so that if you have 5 horses and sell 5 you don’t have any left and there is no need to record that fact. Historical mathematicians used maths to record passages of time or to map the movement of stars- again the use if zero is not relevant. Only when maths was started to be used in theoretical ways – what was called pure maths when I was at school- that the zero became relevant.

September 26, 2010

Initial Assessent

I would say that the vast majority of my teaching skills have been self taught. I have my teaching qualifications but they are generic rather than subject specific. I have a friend who is a maths teacher at a secondary school who has been invaluable in terms of letting me have resources and helpful suggestions. At the WEA we work very independently and rarely meet other tutors let alone numeracy specialists. I work a lot on instinct and trial and error. If a student has difficulty with a subject I work hard to relate it to everyday life and something they would use- I find many students understand how to do something if they know what is being asked of them (eg relating decimals to money always helps).  Most difficulty is in interpreting the question. For those students where this is not the case I would find it really helpful to have some underpinning knowledge and theory of how to unravel the problem.

I feel I do have enough subject knowledge as I have always found maths relatively straightforward at this level (not so much when it came to vectors!).

My barriers to learning which we completed in class all related round time. I have given up being a Chair of Governors at my son's school this year to free up some time but this is a perennial problem of mine. I have such a full calendar now I am really worried how I can do all the work- lots of late nights coming up I think. My personal (therapy) work has become quieter at the moment which is a blessing in a way but rubbish financially. I need it to get busier to pay the bills but then to fit in studying- I will do it but its a worry.

One target I would set myself is to be more organised in my teaching (the irony in this is that I have a reputation amongst my friends of being totally organised in my life). Although I never run out of materials to use I then carry tons of worksheets round with me to cover every eventuality. I work very much on the hoof and tend to follow the students' needs which is fine as it does help them but I can feel underprepared. I am looking forward to observing other tutors as I have never seen anyone else deliver a numeracy lesson. I have a colleague who has a fearsome reputation amongst her students and although I wouldn't want to go that far it will be interesting to see how that works.

Another target could be to use less materials in class. I know literacy tutors seem to manage to work with very little - I would like to develop a similar approach in my teaching.

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