1. Introduction to the course

2. Plan for today Introductions
Outline of the course and your participation
Getting started

3. Outline of sessions 6 sessions
Getting started
Learning from mistakes and misconceptions
Looking at learning activities
Managing discussion
Developing questioning
Using formative assessment
Emphasis on working collaboratively with colleagues to develop active learning

4. Getting Started

5. Aims of the Session
To reflect on our current assumptions, beliefs and teaching practices;
To consider the aims of the approaches in this course;
To begin exploring ways in which our pupils might become more actively engaged in their own learning.

6. Beliefs about learning and teaching
Put the statements you all agree with into one pile. (Alter the statements if you wish.)
Put the statements you all disagree with into a second pile.
If you cannot reach agreement about a statement, then place it in a third pile. Make a note of the reasons that you disagree.

7. Most common teaching methods
Statements are rank ordered from most common to least common
1 = almost never, 2 = occasionally, 3 = half the time, 4= most of the time; 5 = almost always. Source: Swan (2005)
Mean (n=120)
Learners start with easy questions and work up to harder questions.
4.26
I tell learners which questions to tackle.
4.02
I teach the whole class at once.
3.90
I know exactly what maths the lesson will contain.
3.80
Learners learn through doing exercises.
3.67
I try to cover everything in a topic.
3.56
I avoid learners making mistakes by explaining things carefully first.
3.31
Learners work on their own, consulting a neighbour from time to time.
3.30
I teach each topic from the beginning, assuming they know nothing.
3.29
I tend to teach each topic separately.
3.19
Learners use only the methods I teach them.
3.18
I draw links between topics and move back and forth between topics.
3.03
I tend to follow the textbook or worksheets closely.
2.99

8. Least common teaching methods
Statements are rank ordered from most common to least common
1 = almost never, 2 = occasionally, 3 = half the time, 4= most of the time;
5 = almost always. Source: Swan (2005)
Mean (n=120)
I only go through one method for doing each question.
2.95
I encourage learners to make and discuss mistakes.
2.63
Learners work collaboratively in pairs or small groups.
2.57
Learners learn through discussing their ideas.
2.53
I jump between topics as the need arises.
2.51
I find out which parts learners already understand and don’t teach those parts.
2.44
I teach each learner differently according to individual needs.
2.43
Learners compare different methods for doing questions.
2.24
I am surprised by the ideas that come up in a lesson.
2.08
I encourage learners to work more slowly.
2.03
Learners choose which questions they tackle.
1.98
Learners invent their own methods.
1.73

9. Principles for effective teaching
Build on the knowledge learners bring to sessions.
Expose and discuss common misconceptions.
Develop effective questioning.
Use cooperative small group work.
Emphasise methods rather than answers.
Use rich collaborative tasks.
Create connections between mathematical topics.
Use technology in appropriate ways.

10. Make a poster Make a poster showing all you know about one of the
following.
Decimal numbers
Shapes
Time
Show all the facts, results and relationships you know.
Show methods and applications.
Select only the most important and interesting facts at a basic and more advanced level.

15. Follow up work
Write a paragraph about your beliefs about what mathematics is and another one about how you teach it
Use the strategy of asking your pupils to make a poster as a way of assessing their prior knowledge at the beginning of a new topic