1. Creating Rich and Balanced
Maths Programs to fit the
National Curriculum and AUSVELS
Part One
PD @ RPPS
1st May 2013

5. PD Learning Intentions:
• To establish compelling reasons for
investigating and implementing change in the
teaching and learning of Maths at RPPS
• To introduce the ‘Mathematician’s Model’
• To explore ‘Rich Tasks’ within the context of
Mathematics

6. Mathematics @ RPPS
• State of Maths at RPPS:What does the student data tell us?

7. Mathematics @ RPPS
• State of Maths at RPPS
• What does the staff data tell us?

8. Mathematics @ RPPS
So where to now?
Change in strategy : ‘Mathematician’s Model’
Not 4 ‘number’ 2 ‘other’
but
4 ‘Toolbox’ and 2 ‘Be a Mathematician’ lessons

10. Who is in the photo in the middle?
http://en.wikipedia.org/wiki/Terence_Tao
We celebrate our pop stars, sports stars...
Let’s celebrate our mathematicians too!
Let’s provide our students with positive
academic role models.

12. The Mathematician’s Model
The school has six sessions a week (50
minutes a day). (FYI: ‘Key Characteristics of
Effective Numeracy Teaching’ advocates for 5
x 1hr sessions per week).
For four sessions a week, teachers run
‘toolbox lessons’. ‘You cannot solve any
problems if you don’t have the tools’.

13. Toolbox Lessons
Toolbox lessons focus on:
Mathematical content knowledge
Developing a range of problem solving strategies
Developing student’s mental arithmetic capacity

14. Toolbox Lessons: What do they look like?
BEFORE TEACHING:
• Students prior knowledge assessed via Pre Unit Test.
• Toolbox lessons build skills based on progression of skills according to maths
continuum. Students grouped and placed on continuum according to need (based
off test findings). Planning completed after pre unit test and based on student
need.
TEACHING:
• Lessons progressive, building upon prior learning.
• Learning intentions communicated with students at the start of the lesson.
• Strong emphasis placed on collaboration and discussion between students.
• Strong emphasis placed upon development of mental arithmetic strategies.
• Learning wrapped up with a reflection on learning:
http://www.magicalmaths.org/top-50-maths-mini-plenaries-ideas-to-use-in-an-
outstanding-maths-lesson/
ASSESSMENT:
Observation, Questioning, Rich Tasks (Portfolio), Post Unit, Post Semester (OnDemand)

15. ‘Be A Mathematician’ Lesson
A carpenter is called upon to fix a door which
has come off it’s hinges. The carpenter does
not turn up empty handed – what are they
carrying? Answer: a toolbox – they take one
look at the problem and go rummaging
around in their tool box for the right tool – in
this case, a screwdriver. Importantly, if the
tool is not there, the problem cannot be fixed,
but equally, the only reason for carrying the
tool us to use it in problem situations.

17. ‘Be A Mathematician’ Lesson
In these sessions students get to ‘be a
mathematician’.
Teachers use a range of Rich open-ended
investigative challenges. The investigation is
the mathematics. The ‘toolbox’ skills are
activated to solve a worthwhile problem.
Work completed can be collected and
submitted into a Maths Portfolio, to be used
as part of our assessment schedule.

20. What is a “Rich Task”?
A rich task involves both process and product,
following an inquiry-based model of learning.
Students learn large amounts of new content,
develop important skills and develop in
interdisciplinary learning. This includes personal-
management, interpersonal development,
communication, ICT and particularly in thinking.

21. How to create a ‘Rich Task’?
• Open Ended
• Problem Based
• Inquiry Based
• Wide/Narrow Curriculum
• Process Product
• Collaboration
• Experiential
• Engaging and Relevant

22. Open Ended?
In an open-ended task there are multiple possible outcomes for
success. This assists in catering for different levels of ability
amongst the students. It also allows for student ownership of the
task, as they are able to choose their own directions and work on
their own solutions. Student choice is important! It allows for
student ownership, self-direction, and engagement. This means
students are genuinely thinking for themselves, rather than simply
trying to crack the code to predict an answer/solution that has been
predetermined as being correct by the teacher. Make sure that the
task is genuinely open-ended, and not just that it is possible for
some minor differences in answers, with only one main solution
being possible. It is also a good idea to aim to be open-ended in
allowing for various modes of presenting the final product (ie:
speech, ICT, visuals, movie, drama, print-based text, etc.).

23. Problem Based?
Having a task where students have to respond by
solving a problem ensures that there will be the
need for both creative and critical thinking (ie:
brainstorming ideas, critiquing suggestions,
evaluating, etc.). Solving an open-ended problem,
where students have the power of task-
ownership and self-direction provides a context
for deep thinking and engagement. In order to
solve a problem, students have to engage in
thinking and not merely rely on the pre-
established ideas of others.

24. Inquiry Based?
In short you could say this means that a task follows the
pattern of Bloom’s Taxonomy: “gathering information,
processing information for comprehension, applying
information to solve a problem and evaluating the results“.
Following this model ensures that students build skills and
content knowledge in a lot of disciplines. It also helps to
develop interdisciplinary learning, such as group-work,
personal-management, thinking and communication. You
don’t want a rich task just to be all about gathering
information and presenting it – there need to be tasks that
require students to apply their new-found knowledge by
thinking creatively and critically in order to solve an open-
ended problem with opportunities for self-assessment and
reflection throughout.

25. Wide/Narrow Curriculum?
A rich task should provide opportunities for wide
study and learning of content from a wide
selection of areas. There should also be
opportunities for narrow inspection of important
details that are crucial to the outcomes of the
study. Students need opportunities to learn
broad concepts, with broad examples from the
broader world, while also having opportunities to
ensure that they comprehend important details
and key skills and concepts through targeted
teaching and learning.

26. Process Product
Process comes before product and that the process in itself is
a bigger aspect of learning than just the end product by itself.
A rich task should have a significant process of learning and
discovery as well as difficult challenges in the tasks
themselves. When assessing a student’s work on a rich task, it
is important that a teacher includes some process-related
indicators as part of the assessment. For instance, a student
may have displayed excellent thinking, group-work and
personal-management throughout the task, but their product
may have failed for some particular reason. It is valuable for
the student to receive feedback about both the process and
product so that they understand their strengths and areas for
improvement as a learner. It is important to realise that the
rich task is both the process and the product.

27. Collaboration?
Collaboration is important for developing interpersonal skills as
well as personal-management. It is also important for developing
the ability to think creatively and critically and to engage in
discussion and work in ways that are respectful to others. If a
student simply works by themselves, then they are less likely to be
challenged in their thinking. Working in a group means that
students are more likely practice important mathematical
vocabulary to justify their answers and ask clarifying questions of
others and develop the ability to learn from others and accept
differences in thinking. Collaboration provides a good context for
group discussion and exploratory talk using key mathematical
vocabulary. Collaboration also provides many challenges and
supports for students as individuals, in that they are challenged to
improve in certain areas, whilst also being supported by the
variation of skills and abilities of their peers throughout the learning
process.

28. Experiential?
Not all students have the life experience and knowledge
required to tackle a open-ended, problem-based task. Not
all students have the same degree of skill with print-based
texts or receptiveness to “chalk and talk” teaching to rely
on these methods for gaining new knowledge. So, the
learning experiences that go with the rich task should be
ones that offer students different ways to learn new
content. For instance, excursions, interactive activities,
experiments, discussions, hands-on activities, movies,
documentaries, ICT, games, software, websites, audio,
guest-speakers, books, drama, etc. Do not discount the
value of print-based texts, but certainly don’t limit
resources and texts just to print-based versions.

29. Engaging and Relevant?
Ask yourself these questions; Is the task
relevant for students as individuals? Is the
task relevant to the wide curriculum? Is the
task relevant in relation to the broader world
(both local and global)? What is it about the
task that is going to engage students as
learners? A rich task may not necessary tick all
of these boxes initially, but it should tick most
of them.

30. “I have a challenge for you today: Take
six squares and try to construct a cube in
as many different ways that you can...”

31. There are 11 different possibilities. These are
referred to as ‘hexominoes’.
What would you do next to extend this activity?

32. Mathematics @ RPPS
Paul Halmos:
• “It is the duty of all teachers, and of teachers of mathematics in particular,
to expose their students to problems much more than to facts.”
• “The only way to learn mathematics is to do mathematics.”
• “Mathematics is not a deductive science – that’s a cliché. When you try to
prove a theorem, you don’t just list the hypotheses, and then start to
reason. What you do is trial and error, experimentation, guesswork.”
Paul Halmos:March 3, 1916 – October 2, 2006) was a Hungarian born American mathematician who made
fundamental advances in the areas of probability theory, statistics, operator theory, ergodic theory,
and functional analysis .