Blended learning and e-learning
support within the Cornerstone
Maths Project
Alison Clark-Wilson
a.clark-wilson@ioe.ac.uk
Plenary overview
The aims and objectives of Cornerstone
Maths
The professional development content
Design and evaluation of professional
development at scale
Ongoing findings
Future directions for our research
Cornerstone Maths
Collaboration of SRI International
(USA) & the London Knowledge
Lab (UK), funded by the Li Ka
Shing Foundation.
Design-based research approach
in England derived from extensive
work in the USA (over 15+ years)
for middle school mathematics.
Acknowledgements
England (UCL
Institute of
Education)
Celia Hoyles
Richard Noss
Teresa Smart
Bola Abiloye
Eileen Coan
James O’Toole
US (Stanford
Research
International)
Jeremy Roschelle
Phil Vahey
Ken Rafanan
Jenifer Knudsen
Design principles:
the curriculum units
Cornerstone Maths exploits the dynamic and visual
nature of digital technology to stimulate mathematical
thinking by:
focusing on the ‘big mathematical ideas’ in middle
schools mathematics (11-14 years)
making links between key representations
embedding activities within realistic contexts
providing an environment for students to explore
and solve problems within guided structured
activities
at s
ca
Research foundations
design of digital mathematics resources (Hoyles and
Lagrange 2009; Hegedus and Roschelle 2013;
Mavrikis, Noss, Hoyles, and Geraniou 2012)
a combination of bespoke software, lesson activities
and teachers’ professional development is needed to
support wider student access to technology in
mathematics (Hoyles et al 2013, Clark-Wilson et al
2014)
transformative change in teaching practices takes
time (Even & Loewenberg Ball, 2009)
The national context
National
Curriculum
(Dept. and
of Ed.
2013).
‘62.new
Carefully
chosen
practical activities
resources,
including
computer
software,
have two principal
increased
school
autonomy.
benefits:
aid conceptual
understanding
and make
somethey
funded
professional
development
learning more interesting. Too few of the schools used
support
for
mathematics
National
Centre
for
these resources well.’
Excellence in the Teaching of Mathematics.
Office
for market
Standards
Education
(2012)
open
forinschool
improvement
services.
technology enhanced learning is just one of
many priorities that schools could choose to
address.
The geographical reach
258 teachers in 124
schools across England
(over 7000 students).
6 Cornerstone Maths
networks
expanding group of PD
‘multipliers’
8
But scaling is not just
‘more schools’…
Products:
More schools
More professional networks
Improved student
attainment
More whole departments
involved
Wider use of materials
(more classes within
schools)
More teachers within
departments involved
Processes:
web based curricular activity
system
teacher community
localised PD offer (school clusters
becoming networks)
school devised evaluation
approaches
school based PD offer
embedding in local schemes of
work
development of multipliers
Project phases
Planning Phase 1 (Jun-Jul 2011)
Phase 1 (Jul – Dec 2011) – Pilot phase (unit 1)
Phase 2 (Jan – Jul 2012) – Pilot phase (unit 2)
Phase 3 (Dec 2012 – Nov 2014) – Ongoing
(re)design cycles with ‘Design’ schools
alongside scaling to 100+ ‘Focus’ schools
Sustainability beyond Dec 2014… …and scaling
nationally…
10
The vision
The Cornerstone Maths units
Unit 1 – linear functions
Unit 2 – geometric similarity
Unit 3 – patterns and expressions
The curriculum units
Unit of work (2-4 weeks)
Teacher guide
Explicit mathematical progression, technical
support, pedagogic guidance
Students’
individual work
(workbook)
Students’
collaborative work
(f2f and online)
embedded webbased software
Linear functions
Context: Developing games for mobile phones:
using mathematics to analyse and create simulated
motion games.
Design principles:
•
•
•
dynamic simulation and linking between
representations
drive the simulation from the graph or the
function
show/hide representations, as appropriate
Big mathematical ideas
Context: Let’s work on a game with
robots. We need to set up the
mathematics to make our robots
move at different speeds.
14
•
Coordinating algebraic, graphical, and tabular
representations
•
y= mx+c as a model of constant velocity motion
– the meaning of m and c in the motion context
•
Velocity as speed with direction and average
velocity
However
We have many years of research evidence that
highlights how dynamic maths technology in the
students’ hands brings about new challenges for
teachers…
the mathematics is different…
the pedagogy is different…
(see Hoyles and Lagrange 2009, Clark-Wilson, Robutti and
Sinclair 2014)
Design principles:
the professional development
no ‘one size fits all’ – teachers are not a
homogeneous group.
sustained – initial one-day face-to-face
followed by weeks/months/years…
blended – face to face, synchronous and
asynchronous online, ongoing online
communication.
teachers adopt different roles.
The PD process
Before PD
• pre task – getting
instrumented
• online support for
pre-task (video
walkthrough of
software)
• optional webinar
support
Face to face
PD
(one-day)
• hands-on access
to the technology
• deep discussion of
the mathematics
• planning for
classroom
adaptation
• introduction to
online community
During
teaching
• some classroom
support visits
• asynchronous
forum discussions
• other teachers’
resources
• webinars on key
themes
• online surveys
After
teaching
• webinars on key
themes
• online survey
(evaluation)
• [..more active
involvement in
community]
e-Learning elements
completing a pre-PD task (email and
online)
‘joining’ the (online) project community
participating in the (online) project
community
participating in webinars
responding to online project surveys
pre-PD task (email and online)
Task designed to give teachers a ‘pre-PD’
experience with the software
Sent to the teachers 2 weeks in advance
Access to a narrated video walkthrough (via
DropBox)
Optional webinar arranged – no teachers
attended this!
the online community
joining the community
making a first post to the forum
accessing resources
contributing resources
beginning a forum thread
project webinars
project online surveys
Was the CM curriculum unit implemented in
the classroom?
How was the CM curriculum unit
implemented? (choice of class? choice of
technology? pathway through the unit?)
Were teachers positive about the materials?
Would they use them again?
How did teachers engage with the project
community?
Findings: face-to-face PD
Teachers evaluate the face-to-face
I'd love alldevelopment
the extra reading,
professional
eventwebinars,
very highly in
video's,
however
in all honestly
withthe
a full
terms ofetc,
their
‘preparedness
to teach’
timetable
curriculumI won't
units. have the time to dedicate to
reading
and
researching,
so
any
help/support
Teachers ask for further support on: formative
needs to be something
I can for
do in
less than 2
assessment
(58%), adapting
Special
Educational Needsminutes.
(57%) (n=166).
Only 8% ask for webinars!
Findings: Online community
Despite regular posts and uploads by the LKL
Project Team, the NCETM Community did not
become the vibrant ‘teacher-owned’ online
Community as was originally hoped.
57% of teachers reported that they had
accessed the NCETM Community in relation to
their teaching of Unit 1 (n=110).
Findings: Online community
Teachers’ reported uses of the NCETM Community
% of teachers
(n=63)
To keep up to date with the project news
52%
To read questions or comments by the community
83%
To post questions or comments to the community
22%
To access the electronic version of the Teacher Guide
38%
To access the electronic version of the Pupil Workbook
37%
To upload resources for other teachers to access
3%
To download resources created by other teachers
11%
Findings: Online community
The 49 teachers who did not report any use of
the NCETM Community cited the most common
reasons as:
not enough time;
forgetting that it existed;
not feeling the need to;
not encountering any problems.
Findings: Project webinars
very limited take-up of the webinars that were
organised by the LKL Project Team to respond
to teachers’ requests for more support on
differentiating the Unit for pupils with
SEN/EAL and ideas to support formative
assessment.
Only 22 teachers participated in at least one
webinar.
Ongoing tensions
Increases participation and collaboration BUT the temporary
Online
nature of the project limits the time frame for its usefulness
forum
As a frequent
social network and forum user, I really
should have made better use of the community teachers evaluate this highly BUT very few
Webinars
even to theParticipating
point
of
encouraging others to use it.
teachers attend
Perhaps I may have tried more if I thought it was
EXPECTED
me rather than REQUESTED? (I need a
An essential element at the beginning BUT how to sustain
face
to face of
overfor
timethings like that!) If this were the
good 'rocket'
community
case, maybe others would have made better use too
Online
portal
Used by some teachers in a pragmatic way BUT how to
develop a more contributory/critical use
Future research
The impact of the various blended learning
approaches adopted within different
Cornerstone Maths networks
Deeper research into the nature of teachers’
development of knowledge – and the impact
of this on evolving classroom practices
Continued research into the design of the PD
‘toolkit’ – in collaboration with multipliers.
Nuffield Foundation Project
A 2-year project from Dec 2014 that aims to
research the impact on key stage 3 teachers
mathematical knowledge and practices – as they
engage with the CM units of work.
7 new networks (pairs of teachers from 15
schools) will be established
schools will be recruited in spring 2015
will produce a PD toolkit that will be
disseminated nationally
Project aims
The project will use teachers’ classroom experiences of
the Cornerstone Maths curriculum units to learn more
about:
how teachers develop a deeper understanding of the
curriculum topics to enable them to teach for
‘mastery’;
how teachers develop their classroom pedagogies
when the students are more active in the dynamic
exploration of the underlying maths.
References
Clark-Wilson, Alison, Hoyles, Celia, Noss, Richard, Vahey, Phil, & Roschelle, Jeremy. (2015).
Scaling a technology-based innovation: Windows on the evolution of mathematics teachers'
practices. ZDM Mathematics Education, 47(1). doi: 10.1007/s11858-014-0635-6
Clark-Wilson, Alison, Robutti, Ornella, & Sinclair, Nathalie. (2014). The Mathematics Teacher
in the Digital Era: An International Perspective on Technology Focused Professional Development
(Vol. 2). Dordrecht: Springer.
Department of Education. (2013). National Curriculum in England. Mathematics
programmes of study: key stage 3. London: Department of Education.
Hoyles, Celia, & Lagrange, Jean Baptiste (Eds.). (2009). Mathematics Education and
Technology - Rethinking the Terrain: The 17th ICMI Study. Berlin: Springer.
Even, Ruhama, & Loewenberg Ball, Deborah (Eds.). (2009). The professional education and
development of teachers of mathematics: The 11th ICMI study. Berlin: Springer.
Mavrikis, Manolis, Noss, Richard, Hoyles, Celia, & Geraniou, Eirini. (2012). Sowing the seeds
of algebraic generalisation: designing epistemic affordances for an intelligent microworld Journal
of Computer Assisted Learning, 29(1), 68-84.
Office for Standards in Education. (2012). Mathematics: Made to measure. London:
Department for Children, Schools and Families.
Blended learning and e-learning
support within the Cornerstone
Maths Project
Alison Clark-Wilson
a.clark-wilson@ioe.ac.uk