- Building connections and continuities across
year seven to 12, help students develop the knowledge,
the skills and positive dispositions
they need to be successful learners.
Today we're visiting a school
that has just introduced a new inquiry framework
to junior mathematics to support the transition
through to years 11 and 12.
And they've also enlisted the help of a critical friend.
To see what this journey looks like in practise,
we're talking to Associate Principal, Darren Beebe,
and his team here at Cavendish Road State High School.
Darren, how does the implementation
of a mathematical inquiry framework in junior secondary
support your school's improvement agenda?
- In 2020, Cavendish Road implemented
a new research-based strategic plan
based on visible learning.
Within our explicit improvement agenda,
visible teaching and learning,
it builds our expert teaching teams.
We are focusing on evidence-based teaching
to ensure teachers know their impact
and to target teaching in response.
This approach has seen increase in student outcomes,
but school improvement is a team effort.
And, Terry Moran, our head of mathematics,
and his team have been working with Katie Makar
from the University of Queensland on this inquiry framework.
And they'd be very happy to share this practise with you
- Terry, why does the junior school
need a mathematical inquiry framework?
- Yeah, look, my team's always looking to improve practise
and improve student outcomes
and in preparation for the problem solving
and modelling tasks contained
within the new senior syllabuses,
and we identified a problem with practise.
As part of our preparation,
we build up a suite of resources to assist students
starting in year nine, and deal with the demands,
so the literacy demands of a 2000 word assessment task.
This worked well for some students, but we found a lot
of students struggled to engage with the task.
It became clear that we needed to change
our pedagogical practises
to improve student success and disposition.
And to do this, we engaged in inquiry process as a scaffold.
I wanted to ensure that what we were doing
was best practise and evidence-based.
And so, I read some research and this led me to Katie,
and whom I asked to become a critical friend
and help us on this journey.
- Tell us a little bit about how this partnership works.
- Yeah, I look to Katie to provide guidance
on effective ways of implementing the framework
with both teachers and students.
He also gives insight into the markers
to look for and by the student to teacher behaviours
that signal a successful implementation.
- I was delighted when Terry contacted me.
Like many researchers,
I'm always on the lookout to connect with schools,
to help me revise and improve the impact of my research.
I enjoy working with schools as it gives me insight
into how the research is put into practise.
This also lets me see where the research
can have the greatest impact in schools,
and what additional work can be done to support teachers.
- Katie, there were a few useful mathematical inquiry
frameworks that schools are using effectively.
Tell us a little bit
about this particular inquiry framework.
- I think of guided inquiry is responding to the question,
what do you do when you don't know what to do?
Complex open-ended problems
like problem solving and modelling tasks
ask students to negotiate, adapt, and revise their solution.
This can be real challenge for students.
The five phases of guided inquiry are Discover, Devise,
Develop, Defend, and Diverge.
What we call the 5Ds.
This framework was created with my two colleagues,
Dr. Jill Fielding-Wells and C. Almond.
When students see a mathematics problem,
they often jump in and try to solve it
before trying to make sense of the problem.
Unlike a textbook, real problems don't tell you
which mathematical knowledge is relevant.
The Discover and Devise phase
helps students to slow down,
make sense of the problem and its purpose,
and then draught ideas that integrate their personal
and mathematical knowledge.
One of the issues that the school said
students are struggling with was, how to start.
The 5Ds give students permission to try out ideas
in a low stakes setting
before they need to formulate the more formal mathematics.
- How will you know that this strategy has been effective?
- Yeah, to measure the effectiveness of the framework,
where we're using student achievement data.
And we'll also be looking at quality of data,
such as teacher disposition and student disposition
to measure its impact.
I'm particularly interested in indicators
that signal development in teachers capability.
- On walkthroughs and observations,
Terry should expect an increase
in student engagement and mathematical talk
as students start to embrace the Inquiry framework.
As teachers develop more confidence supporting students
to address complex open-ended problems
like problem solving and modelling tasks,
they're able to use questioning to facilitate
class and small group discussion
that allows for more student independence.
Teachers will also develop a common language of inquiry
to share their experiences and strategies
to encourage students productive struggle.
- So, Terry, what process are you following
to introduce this framework to your junior school?
- In this term, we're trialling
the introduction in our year 10 class.
We'll review the way we've implemented the framework,
we'll look at student's feedback and other evidence
and look to scale up the practise
into other classes and year levels.
- So, Kyan, what are the benefits
of this inquiry framework to your students?
- So, Katie and I co-developed these design principles
to help us have a framework
to write lessons to my year tens.
So, in this lesson,
I am to demonstrate a real life application of statistics.
It provides a context of the maths
and consolidates their understanding.
The 5Ds is a way for students to better articulate
their thinking and direct their own inquiry.
Students have been able to understand what,
and how to improve,
based on other classroom language and scaffolding.
Byron, a student that I've taught previously,
has struggled in the past with mathematizing assignments.
This approach, it's allowed him
to discover his own paths to a solution.
- What will you be looking for in your students' work
and behaviour, to know that this framework
is effectively supporting your students?
- First and foremost is engagement with the task
and student disposition.
In the past, our students have sometimes struggled
to engage because of the size of the task.
What we're seeing now is that,
by using the 5Ds students are less stress and more engaged
with the problem solving and modelling tasks,
and in turn, more willing to engage with assessment.
Next would be a checkpoint at the halfway mark
to see how much of these task students have completed.
We can compare this directly
with previous assessment pieces.
Thirdly, we'll be comparing student achievement data.
- You may find that inquiry is really challenging
for your high achieving students.
It can be a real struggle for some students
to embrace the intellectual risks needed
for a complex, unfamiliar problem.
Once students develop more confidence
they can see that their everyday experience has relevance.
Teachers will start to see this represented in student work
through a greater diversity of assumptions limitations.
- Thank you for your time today,
and congratulations on your journey
to transform mathematics teaching and learning.
It's really useful to share these models
of school improvement so that we can scale up what works.
Three questions that can guide the reflection
on the effectiveness of mathematical inquiry are,
what framework do we use to support problem solving
and reasoning across year seven to 12?
How do we know that it's working?
And is there an opportunity to use
a critical friend to support us in our improvement journey?
The M in STEM initiative aims to build
effective pedagogical practises in secondary mathematics
to improve student participation and achievement,
and strengthen the connections and continuities
between the Australian Curriculum: Mathematics
and the QCAA senior secondary mathematics syllabuses.
Visit the M in STEM ed studio
for further information about the 5Ds
and other resources to help transform secondary mathematics.