2. Effective Teachers
• Create a mathematical environment
• Pose worthwhile mathematical tasks
• Use cooperative learning groups
• Encourage the use of activities, models and
calculators as thinking tools
• Require students to justify their responses
• Encourage conversation and writing
• Listen actively – actively question
• Include all students
3. The Teaching Principle
Effective mathematics teaching requires
understanding what learners know
and what they need to learn
and then challenging and supporting them
to learn it well.
4. Three ingredients that will contribute
to successful lessons
– Creative climate and conjecturing atmosphere
– Valuing mathematical thinking
– Purposeful activity and discussion
6. “If I ran a school, I’d give all the
average grades to the ones who gave
me all the right answers, for being good
parrots. I’d give the top grades to
those who made lots of mistakes and
told me about them and then told me
what they had learned from them.”
Buckminster Fuller, Inventor
7. Creative Climate
Total Energy available
energy of for task or success
individual
Energy required for
emotional survival
Threatening Adversarial Neutral Cooperative Supportive
Ceserani & Greatwood, 1995
8. Valuing mathematical thinking
What behaviours do we value in
mathematics and how can we
encourage them in our classrooms?
9. Are you excited by a challenge?
The most exciting phrase to hear in
science, the one that heralds new
discoveries, is not Eureka!, but rather,
“hmmm… that’s funny…”
Isaac Asimov
11. Purposeful activity and discussion
Give the learners something to do,
not something to learn;
and if the doing is of such a nature
as to demand thinking;
learning naturally results.
John Dewey
13. We learn
• 10% of what we read
• 20% of what we hear
• 30% of what we see
• 50% of what we hear and see
• 70% of what we discuss with others
• 80% of what we experience ourselves
• 95% of what we teach
William Glasser
