1. Introduction to Mathematics
Part time PGCE
Introduction to Mathematics

2. Frogs and toads Activity: To swap over the frogs and toads Rules:
You may either: - slide one square into an empty space
hop one frog/toad over one other frog/toad into an empty space
Aim:
To find the rule for determine the minimum number of moves for any numbers of frogs and toads.
Possible steps:
What is the minimum for 2 frogs and 2 toads? How many slides & hops?
How about 3 of each/ 4 of each etc?
How about 2 frogs and 3 toads?
What patterns are there?

3. For discussion Have you solved the problem?
Have you finished the investigation or is there something else you could do?
What helped/hindered you in solving the problem?

4. A Model for the Primary Mathematics Curriculum
Facts
Skills
Concepts
Processes
Situations
Attitudes
Shuard,H. (1986) Primary mathematics today and tomorrow York:SCDC

5. David Burghes Mathematics Enhancement Project 1997
In his survey, Year 7 / 8 pupils were asked:
‘What do you think are the good qualities of the best maths teacher you ever had?
They gave answers such as:
Patience
Sense of humour
Give individual help
Does not move on too quickly
Checks and helps understanding
Approachable and caring
Makes mathematics enjoyable and fun
Strict and good control of the class
Doesn’t get cross if pupils do not understand
Listen
…..but, by far the most frequent response was
gives clear explanations

6. Independent Study Tasks
Jennings, S.F. (2006) ‘Personal development plans and self-directed learning for healthcare professionals: are they evidence based?’ Postgraduate Medical Journal. 83 pp Available at (Accessed: July 7th , 2010)
Wilcox, S.W. (1996) ‘Fostering self-directed learning in the university setting.’ Studies in Higher Education. 21(2) pp
What are the key messages about independent study?
Task 2
Read extracts from: 
Williams, P. (2008) Review of Mathematics Teaching in Early Years Settings and Primary Schools
What are the key messages about attitudes towards mathematics?