The document summarizes a presentation on integrating 21st century learning in mathematics classrooms using the Bridge21 model. It discusses: 1) The Bridge21 model which uses group work, technology, and realistic contexts to teach mathematics through investigation and problem-solving. 2) Examples of activities developed by teachers following Bridge21 principles, such as using technology to measure heights or simulating betting odds. 3) Benefits reported by teachers including changing beliefs about their role and increased student engagement, as well as barriers like time constraints.

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Teachers’ Experiences of the Integration of 21st
Century Learning in the Mathematics Classroom
the Bridge21 Model in Action
Author: Dr Aibhín Bray Presented by: Professor Brendan Tangney
Email: brayai@tcd.ie slideshare.net/tangney/csedu16-maths
Date: April 2016
Trinity College Dublin, The University of Dublin
Bibliography
• Anderson, T. and J. Shattuck, Design-Based Research: A Decade of Progress in Education
Research? Educational Researcher, 2012. 41(1): p. 16-25.
• Freudenthal, H. (1991). Revisiting mathematics education: China lectures (Vol. 9).
Dordrecht/Boston/London:Springer.
• Puentedura, R., The SAMR model: Background and exemplars. Retrieved June, 2012. 24:
p. 2013.
• Conneely, C., Girvan, C., Lawlor, J., Tangney, B., An Exploratory Case Study into the
Adaption of the Bridge21 Model for 21st Century Learning in Irish Classrooms, in
editor(s) Butler, D., Marshall, K., Leahy, M., Shaping our Future: How the lessons of the
past can shape educational transformation, Dublin, Liffey Press. 2015, pp 348-381.
• Lawlor J., Marshall K., Tangney B., Bridge21 – Exploring the potential to foster intrinsic
student motivation through a team-based, technology mediated learning model,
Technology, Pedagogy and Education, 2015, 1-20
http://dx.doi.org/10.1080/1475939X.2015.1023828

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Publications
• Bray A., Tangney B., "Enhancing Student Engagement through the Affordances of Mobile
Technology: A 21st Century Learning Perspective on Realistic Mathematics Education",
Mathematics Education Research Journal. 2015. 1 -25 DOI 10.1007/s13394-015-0158-7
• Bray, A,. Oldham, E. & Tangney, B. Technology-Mediated Realistic Mathematics Education And The
Bridge21 Model: A Teaching Experiment. Proceedings of the Ninth Conference of the European
Society for Research in Mathematics Education (CERME9). February (2015). pp. 2487 – 2494,
Prague, Czech Republic.
• Tangney B., Bray A., Oldham E., Realistic Mathematics Education, Mobile Technology & The
Bridge21 Model For 21st Century Learning – A Perfect Storm, in Mobile Learning and Mathematics:
Foundations, Design, and Case Studies, Crompton H., & Traxler J., (Eds) Routledge, 2015, pp 96-
105.
• Bray, A., & Tangney, B. (2014). Barbie Bungee Jumping, Technology and Contextual Learning of
Mathematics. 6th International Conference on Computer Supported Education (CSEDU), 206 -
213.
• Bray, A. Oldham, E. & Tangney, B., The Human Catapult and Other Stories – 11th International
Conference on Technology in Maths Teaching, Italy, July 2013, pp77-83.
• Bray, A., & Tangney, B., Mathematics, Technology Interventions and Pedagogy - Seeing the Wood
From the Trees, 5th International Conference on Computer Supported Education, Aachen,
Germany, May, 2013, pp57-63.
Trinity College Dublin, The University of Dublin
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Irish Secondary School Education
Year 1
•Age ~13 –Junior Cylce
Year 2
•Age ~14 –Junior Cycle
Year 3
•Age ~ 15 –Junior Cycle
•State Examination – Junior Certificate
Year 4
•Age ~16 –Transition Year – flexibilty in curriculum
Year 5
•Age ~17 –Senior Cycle
Year 6
•Age ~ 18 –Senior Cylce
•HIGH STAKES STATE EXAMINATION
•Grades are sole requirement for entry to 3rd level

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Beliefs - ICT in the Classroom
Trinity College Dublin, The University of Dublin
21 C Teaching & Learning Requires a Move to
TRANSFORMARTION Layers in the SAMR Model of
Technology Adoption
(Puentedura 2012)

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Trinity College Dublin, The University of Dublin
Educational
system/context
Teacher professional
development and pre-
service education
Evidence base
Develop activities
& design principles
Train students
Model of
21st
T&L
What is needed
to bring about
Transformation
Trinity College Dublin, The University of Dublin
Educational
system/context
Teacher professional
development and pre-
service education
Evidence base
Develop activities
& design principles
Train students
Model of
21st
T&L
Bridge21
Longitudinal
Design Based Research
Initiative in Trinity
College Dublin
(Anderson 2012)

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Trinity College Dublin, The University of Dublin
Educational
system/context
Teacher professional
development and pre-
service education
Evidence base
Develop activities
& design principles
Train students
Model of
21st
T&L
Presentation Focus
(Realistic) Maths Education
Bridge21 Model of 21sT&L
Realistic Education Maths Activities
Postgraduate Teacher Professional Development Programme
Activities Developed by Teachers
Trinity College Dublin, The University of Dublin
The Bridge21 Pedagogical Model
(Lawlor et al 2105,
Conneely et al 2015)

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Trinity College Dublin, The University of Dublin
Bridge21 Model of Groupwork
Trinity College Dublin, The University of Dublin
Bridge21 Activity Model
Set-Up: Ice breaker and teams
Warm Up: Divergent thinking activity
Investigate: Explanation of the problem
context.
Plan: Group planning.
Create: Exploration with resources.
– In the field.
– In the classroom.
Create: Modelling and Calculation:
– Analysis and Synthesis.
Present: Competition and/or Presentations.
Reflect: Reflection and Discussion.

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Sample Bridge21 Math Activities
Trinity College Dublin, The University of Dublin
Plinko
Build a board
Excel & Tracker
Simulation Design the betting
odds for a game

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Trinity College Dublin, The University of Dublin
Maths Activity Design Principles
1. Activities should follow a 21CL model such as Bridge21: they should be collaborative and
team-based in accordance with a socially constructivist approach to learning.
2. They should make use of a variety of technologies (digital and traditional) suited to the
task, in particular, non-specialist mobile technology such as smartphones and digital
cameras that students have to hand. Emphasis should be placed on the transformative,
as well as the computational, capabilities of the technology.
3. Task design should prioritise guided-discovery, involving problem-solving, investigation
and sense-making, and a move from concrete to abstract concepts. Tasks should be
open-ended, allowing for different trajectories and solutions; they should have a “low-
floor” and “high-ceiling”, such that all students will be able to engage meaningfully with
the problem, with the potential for more interested/able students to push its
boundaries.
4. The context of the problem, and the learning experience, should be interesting and
immersive/real, adapting the environment and class routine as appropriate;
5. Presentation, competition and reflection can be used for assessment purposes.
(Bray & Tangney 2015)
Trinity College Dublin, The University of Dublin
Focus of This Study
As part of their assessed work in a postgraduate certificate in 21st
teaching & learning practicing teachers were asked to design and
implement learning activities according to the design principles
outlined.
Research Aims:
1. To explore the experiences of teachers in the creation and
implementation of such activities, with particular emphasis on their
perceived barriers to, and benefits of, the approach.
2. To explore the teachers’ perceptions of their students’ experiences
with the activities.

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Methodology
Exploratory Case Study
Participants:
15 post-primary teachers
Data:
Written reflections (for assessment)
Qualitative Methods:
Constant Comparative Analysis
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The Activities
• 11 distinct activities (some in-school collaboration)
• Lower secondary school students (aged between 11 and 16 years)
• Activities were focused on primarily on the mathematical area of
functions, in realistic contexts.

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Sample Activity
Multimedia presentation by a participating teacher, for assessment.
Trinity College Dublin, The University of Dublin
Other Activities Developed By Teachers
• A helium balloon and technology was used to find the measure of certain
heights around our school.
• Students will be asking themselves “how fast am I running?”.
• Working in groups of five members, students are tasked with comparing the
speed of the shortest and tallest members of their group over a specified
distance.
• The students will be asked to plot the quadratic function for the flight of their
shot in a football crossbar challenge.
• Given an advertisement for a party hire company, the students are
encouraged to use GeoGebra to explore different combinations of tables etc.
to get the best value for money.
• The students will undertake a study to determine if the speed of the ball
affects the chances of scoring goal.

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Findings - Benefits to teachers
• Changes in Beliefs
• Change in role from transmitter of information to facilitator of
learning
“After trying this, my eyes have been
opened to the possibilities of covering
the curriculum, but by changing the
setting of the learning, you can teach
a lot more effectively to an audience
who are stimulated and engaged.”
“I decided to tell the students of how this was as much of a
learning curve to me as it was to them. This was because I really
did feel that they would lose confidence in me if they felt that I
was trying to teach them rather than facilitate them. This seemed
to empower them as they felt that even though I wasn’t part of
their team, I was learning and teaching with them.”
Trinity College Dublin, The University of Dublin
Findings - Benefits to Students
• Development of Key Skills
• Other Outcomes

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Findings – Barriers to the Approach
1. Time Constraints
Most significant barrier
2. Technical Issues:
1. Access at school level
2. Small “hitches”
3. Small number of issues around teamwork
Having a longer block of time would
have been more productive, having to
stop after 40 minutes and then pick up
again a day or two later was inconsistent
Trinity College Dublin, The University of Dublin
Findings – In Conclusion
Consistency in the use of this approach has the potential to lead to
very positive outcomes.
I have worked with this particular class group on two other 21st
Century Teaching and Learning Assignments. Their development
throughout the course of the year has been astounding. The flair
with which they now competently and confidently use technology
to gather and analyse information, and present their findings is
very impressive. This project was a thoroughly enriching
experience for both the students and teachers assisting them.