Effective Mathematics - 6 Strategies

1. Effective Teaching of
Mathematics

2. The Current Context
The Australian Curriculum: Mathematics offers us an
ideal opportunity to rethink the teaching of
mathematics.
We know that many students:
O Forget what they have learnt from one year to the
next
O Are unwilling to engage with challenging tasks and
O Develop negative attitudes to Mathematics early.
It is possible that these issues are a result of teachers
overemphasizing fluency with procedures.
MORE OF THE SAME IS NOT THE DESIRABLE
OPTION!!

3. Some Principles Underpinning the
Curriculum
O The curriculum seeks to encourage teacher
decision making.
O The intension is that teachers will cover
fewer topics in MORE depth.
O The expectation is that all students have
access to the full curriculum for as long as
possible.
O Extension of those who are ready should be
within content at current level.

4. Which of these are your top two priorities?
That students:
• Enjoy the mathematics they are learning
• See the usefulness of mathematics to them
• Be able to interpret the world mathematically
• See the connection between mathematics
learning and their future study and career
options
• Know that they can learn
• Know that they can learn mathematics
• Know that they can get smarter by trying hard.

5. What do you believe
effective teaching of
Mathematics looks like?

6. Key Principles for Effective
Teaching of Mathematics

7. Articulating Goals
O Teacher articulates
the key
ideas/concepts to
be addressed in the
lesson before
students begin.
O Teacher advises
students of the
goals and to make
decisions on
pathways to
achieving the goals
interactively.

8. MakingConnections
O Build on what students know and can
do.
O Link teaching focus to child’s
understanding of their world.
O Experience and thinking

9. For example:
A farmyard has pigs and chickens. There are 10
heads and 26 legs.
Question: How many pigs and chickens might
there be?
REFORMULATION (Kimberley Project)
A ute has some people and some dogs in the
back. There are 10 heads and 26 legs.
Question: How many people and how many dogs
are there?

10. St. Kevin’s Context
At Mr. Con’s house there are many animals.
Altogether we counted 56 legs. What
animals could be found at Mr. Con’s house?

11. Fostering Engagement
Engage students by utilising a variety of
RICH and CHALLENGING tasks that allow
students time and opportunities to make
decisions, and which use a variety of forms
of representations.
- Meaningful and relevant (has to capture
student interest)
- Students are MORE engaged when they
make decisions.

12. DIFFERENTIATING
CHALLENGES
O Interact with students while they engage
in the experience
O Encourage students to interact with each
other (asking and answering questions)
O Specifically plan to support students who
need it and challenge those who are
ready

13. Enabling Prompts
Allow those experiencing difficulty to engage
in active experiences related to the initial
goal task, rather than, for example, requiring
such students to listen to additional
explanations, or assuming that they will
pursue goals substantially different from the
rest of the class.

14. This can be achieved by:
O reducing the required number of steps, or
O simplifying the modes of representing
results, or
O making the task more concrete, or
O reducing the size of the numbers
involved.

15. Extending Prompts
O Challenges a child’s thinking, within the
context of the original task that was
posed.
O Reducing complexity not thinking

16. Structuring Lessons
Adopt pedagogies that foster communication
(individual and group responsibilities).
Use students’ reports to the class as learning
opportunities.
Launch; Explore; Summarise;
Review
Allows for creative and constructive thinking

17. Promoting Fluency and
Transfer
Fluency is important and can be developed
in two ways:
1. By short everyday practice of mental
processes
2. Practice, reinforcement and prompting
transfer of learnt skills.

18. Reflect
Reflecting on your own teacher
effectiveness of Mathematics, what
strategies have you implemented to your
teaching?
O What do you need to improve in?