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January 28, 2011

Maths topics (phase 2): Mathematics for 14–19

Writing about web page http://www2.warwick.ac.uk/fac/soc/wie/teaching/pgce/secondary/subjects/maths/topics/14to19/

The session began by discussing the techniques and concepts in A-Level mathematics. Concept-wise, differentiation, integration, exponentials, trigonometry, surds and complex numbers are the main concepts that are introduced.

We looked at a way of using a spreadsheet to introduce rates of change (and thus differentiation). It contains good ideas, and if nothing else provides an alternative way of introducing the topic.

Overall it was an interesting session and a reminder that encouraging understanding is important even (especially?) when teaching A-Level.


January 04, 2011

Maths topics (phase 2) – Cross–cultural Mathematics

Writing about web page http://www2.warwick.ac.uk/fac/soc/wie/teaching/pgce/secondary/subjects/maths/topics/culture/

4th January 13:30-16:30

We discussed how the majority of mathematicians that pupils come across at school are White, Dead and Male. It was an interesting perspective, encouraging us to think about how to involve mathematics from other cultures, although I am not sure that I know enough about many other cultures to do it true justice.

We then created some Rangoli patterns, using squared dotty paper. It was an interesting way to approach symmetry, that I will consider using in my teaching

We then did some work on numbers, apparently first investigated by Kaprekar, who also looked at
Kaprekar numbers (297*297 = 88209 and 88+209 = 297). I didn’t enjoy this as much, though I can see that it might be a useful idea as basic numeracy work.

The groups then presented on examples of maths from non-European cultures. The presentations were on
  • an ancient Inca way of representing data using strands of knotted string (Quipu);
  • the Egyptian method of writing non-unit fractions;
  • Chinese multiplication (an adaptation of the grid method);
  • a very neat method to geometrically represent completing the square by a 9th century Iranian mathematician;
  • the use of a tangram when studying perimeters, etc.;
  • the Chinese remainder theorem, that states that we can find a number given the remainder after division by a set of numbers
  • various number systems, including discussion of the importance of place values.
  • weaving, including creating different patterns, and thinking about sequences (e.g. what is the colour of the seventh row?)

Many of these provided surprisingly useful ideas, and I will try to remember to try these out when the opportunity arises.


Maths topics (phase 2) – Attributes of a Mathematics Teacher

Writing about web page http://www2.warwick.ac.uk/fac/soc/wie/teaching/pgce/secondary/subjects/maths/topics/attributes/

4th January 09:30-12:30

In this session we looked at the qualities that can make up a good Mathematics teacher. We came up with the following list. A good teacher,

  • is enthusiastic and exciting
  • is patient: allows time to think!
  • is organised, with good time management
  • reflects on their practice
  • communicates clearly and effectively
  • has high expectations
  • builds constructive relationships
  • makes good use of continual assessment.
A good maths teacher,
  • is highly numerate,
  • allows time to practice,
  • breaks concepts down to its simplest form,
  • predicts and addresses misconceptions,
  • relates to real life,
  • teaches creatively.

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