This paper outlines the development of a project supported by the Scottish Government with the aim of promoting the development of mathematical thinking in the primary classroom. This was developed in collaboration with teachers and local authorities in North East Scotland during 2011-12 within the context of the Scottish Curriculum for Excellence reform. The project was set up within a design based research framework, which aimed to promote classroom-based action research on the part of participants and also research by the university researchers into the process of curriculum development. The teachers (n=24) were all involved in a jointly developed Masters course based on a blended learning approach within an open and flexible learning environment. This project was designed as a classic example of an “Open Collective Cycle” model of a professional learning community (Hudson, 2012; Huberman, 1995). Findings from the research study in relation to the teachers’ experience are reported in Hudson et al. (2015), which highlight the way the course had a transformational and emancipatory impact on these teachers concerning their levels of confidence and competence in relation to teaching mathematics. An example of the impact on student learning is reported in Hudson (2015a) based on one teacher-researcher’s action research project involving the development of a topic-based approach to teaching and learning mathematics. Findings from this study highlight the ways in which the children actively engaged in the class activity and also how the topic-based approach made the mathematics more widely accessible and led to an evolution in the development of mathematical thinking for all. Policy implications point towards the value of the Mathematics Specialist Teacher (MaST) approach in England, which informed the development of this project. In conclusion the paper outlines a potential approach to uncovering and documenting further impact on teachers and pupils involved in this and subsequent courses. References Hudson, B., Henderson, S. and Hudson, A., (2015) Developing Mathematical Thinking in the Primary Classroom: Liberating Teachers and Students as Learners of Mathematics, Journal of Curriculum Studies, Vol. 47, Issue 3, 374-398. http://dx.doi.org/10.1080/00220272.2014.979233 Hudson, B. (2015a) Butterflies and Moths in the Amazon: Developing Mathematical Thinking through the Rainforest, Education and Didactique, Vol. 9, Issue 1. (In press) Hudson, B. (2012) Aiming for e-Learning Sustainability: Transforming Conceptions of Teachers’ Professional e-Learning, Educational Technology, 52, 2, 30-34. Huberman, M. (1995) Networks that Alter Teaching: Conceptualizations, Exchanges and Experiments, Teachers and Teaching: Theory and Practice, 1, 2, 193-211.

1. 1
Building research and development
partnerships between schools and Higher
Education
Brian Hudson,
University of Sussex
Sheila Henderson and Alison Hudson
University of Dundee
TEPE 2015
University of Dundee
15 May 2015

2. 2
Structure of presentation
 Background context to the DMTPC project
 Design of the Masters course of study and approach to
support for the professional learning community
 Research design, research questions and methods
 Findings and reflections
 Policy implications
 Impact potential

3. 3
Developing Mathematical Thinking in the
Primary Classroom (DMTPC) Project
 Funded by the Scottish
Government (2010-12)
 ‘Curriculum for Excellence’
Partnership development of a
Masters level course for
teachers
 Technology enhanced blended
learning approach.
 Piloted with a group of 24
practising primary teachers
from Dundee, Fife, Angus and
Perth & Kinross LEAs.

4. 4
Design of the course of study
19 September 2011 Online module opens
24 September 2011 Workshop 1 10:00 – 16:00
26 October 2011 Twilight session 1 16:30 – 19:30
7 December 2011 Twilight session 2 16:30 – 19:30
4 February 2012 Workshop 2 10:00 – 16:00
23 April 2012 Assignment submission

5. 5
Outline structure: three key questions, key
texts and an action research project
 Key questions
 What is mathematics?
 What is mathematical thinking?
 What is good mathematics teaching?
 Key texts
 Joe Boaler (2009) The Elephant in the Classroom
 John Mason et al. (2010) Thinking Mathematically – it’s
OK to get stuck!
 Action research plan and project as the module
assignment

6. Open Collective Cycle
6

7. Teachers’ responses to reading “The
Elephant in the Classroom’
 Very powerful responses to reading Jo Boaler’s book:
 The elephant, or the common idea that is extremely
harmful to children, is the belief that success in
mathematics is a sign of general intelligence and that some
people can do maths and some can’t … In many maths
classrooms a very narrow subject is taught to children, that
is nothing like the maths of the world or the maths that
mathematicians use. This narrow subject involves copying
methods that teachers demonstrate and reproducing them
accurately over and over again … this narrow subject is not
mathematics, it is a strange mutated version of the subject
that is taught in schools.
7

8. 8
Design research framework

9. 9
Research questions
1. What are the teachers’ perceptions concerning their levels
of confidence and competence in relation to teaching
mathematics?
2. What are the teachers’ perceptions concerning their
attitudes and beliefs in relation to mathematics as a
subject?
3. What are the teachers’ expectations of the impact on pupil
learning arising from this course of study?
4. How do these perceptions and expectations change as a
result of participating in this course of study?

10. 10
Methods and data sources
 Pre-trial survey of the teachers’ perceptions (n=26)
 Pre-trial interviews with a sample of participants (n=4)
 Post-trial interviews with a sample of participants (n=4)
 Post-trial survey of the teachers’ perceptions (n=15)
 Action research reports from teachers (n=10)
 Online discussion forum

11. Findings from the research study
 Highlight the way the course had a transformational and
emancipatory impact on these teachers concerning their
levels of confidence and competence in relation to teaching
mathematics.
 They also highlight ways in which the ‘framing’ of particular
aspects of the curriculum had an oppressive impact on
learners in the ways that suppressed creativity and limited
the exercise of learner autonomy.
 Furthermore, they highlight the ways in which a number of
these teachers had experienced mathematics as a school
subject in very negative ways, involving high levels of
‘symbolic violence’ and of being ‘labelled’.
 Hudson, Henderson and Hudson (2015)
11

12. Findings from one teacher’s action research
study involving a topic based approach
 Findings from this study
highlight the ways in which
the children actively
engaged in the class
activity and also how the
topic-based approach
made the mathematics
more widely accessible and
led to an evolution in the
development of
mathematical thinking for
all.
 (Hudson, 2015a)
12
John’s drawings of the River Amazon (left)
and the River Tay (right)

13. Reflections on the nature of school
mathematics
 The key readings challenged widely held views about the
nature of mathematics and provided support for the
development of active and participatory teaching methods.
 Boaler (2009) refers to a narrow subject which involves
copying methods that teachers demonstrate and
reproducing them over and over again which she argues is
not mathematics but rather which is “a strange mutated
version of the subject” that is taught in schools.
 This process of ‘mutation’ reflects the process of didactic
transposition, which changes the mathematical knowledge
profoundly and leads to the epistemic quality of the subject
becoming degraded.
13

14. Reflections on the nature of school
mathematics
 We describe this mutated or degraded version of
mathematics as mathematical fundamentalism and as
being of low epistemic quality. It is characterised by a view
of maths as infallible, authoritarian, dogmatic, absolutist,
irrefutable and certain and which involves rule following of
strict procedures and right or wrong answers.
 We contrast this with mathematical fallibilism and high
epistemic quality involving a view of maths as fallible,
refutable and uncertain and which promotes critical
thinking, creative reasoning, the generation of multiple
solutions and learning from errors and mistakes.
 Hudson, Henderson and Hudson (2015)
14

15. Reflections on the nature of the joint activity
in the professional learning community
 Essentially this provided an opportunity for the course
participants to engage in a collective process of didactic
analysis.
 The course experience invoked very powerful responses
amongst this group of teachers. In particular there was a
strong sense of empathy developed with Boaler’s (2009)
challenge to the idea that some people can do maths and
that others can’t. There was also a strong association with
Boaler’s ideas of ‘mutated mathematics’.
 Subsequent discussions reflected a strong sense of
questioning of purpose in terms of the What and Why
questions of didactical analysis.
 Hudson (2015b) 15

16. Policy implications in relation to
Mathematics Specialist Teachers
 Policy implications point towards the value of the
Mathematics Specialist Teacher (MaST) approach in
England, which informed the development of this project.
 The recommendation made in the Williams Review report
(2008) was that ‘there should be at least one Mathematics
Specialist in each primary school, in post within 10 years,
with deep mathematical subject and pedagogical
knowledge, making appropriate arrangements for small and
rural schools.’
 Independent Review of Mathematics Teaching in Early Years Settings
and Primary Schools in England by Sir Peter Williams in 2008
16

17. Policy implications in relation to support for
professional learning communities
 This project clearly demonstrated the value of an ‘Open
Collective Cycle’ model of professional learning community
“in which clusters of schools work collaboratively on
curriculum design and development projects together with
external resource people who might be from universities
and resource centres such as museums, science centres or
art galleries, for example.” (Huberman, 1995)
 The project also clearly demonstrated the potential of
Technology Enhanced Learning for creating the conditions
for an open, participatory and connected learning
community engaged in joint activity with the common
purpose of developing mathematical thinking in the Primary
classroom.
17

18. Exploring the potential for uncovering and
documenting research impact
 Potential approaches to uncovering and documenting
further impact on teachers and pupils involved in this and
subsequent courses.
 Impact is defined as an effect on, change or benefit to the
economy, society, culture, public policy or service, health,
the environment or quality of life, beyond academia.
 Impact is evaluated according to its ‘reach and significance’
(REF 2014)
 For discussion.
18

19. 19
References (i)
 Boaler, J. (2009) The Elephant in the Classroom. London:
Souvenir Press Ltd.
 Hudson, B., Henderson, S. and Hudson, A., (2015) Developing
Mathematical Thinking in the Primary Classroom: Liberating
Teachers and Students as Learners of Mathematics, Journal of
Curriculum Studies, Vol. 47, Issue 3, 374-398.
http://dx.doi.org/10.1080/00220272.2014.979233
 Hudson, B. (2015a) Butterflies and Moths in the Amazon:
Developing Mathematical Thinking through the Rainforest,
Education and Didactique, Vol. 9, Issue 1. (In press)

20. References (ii)
 Hudson, B. (2015b) Epistemology and Methodology of Curriculum:
Didactics. In D. Wyse, L. Hayward and J. Pandya (Eds.) SAGE
Handbook of Curriculum, Pedagogy and Assessment, Sage
Publications. (In press)
 Hudson, B. (2012) Aiming for e-Learning Sustainability:
Transforming Conceptions of Teachers’ Professional e-Learning,
Educational Technology, 52, 2, 30-34.
 Huberman, M. (1995) Networks that Alter Teaching:
Conceptualizations, Exchanges and Experiments, Teachers and
Teaching: Theory and Practice, 1, 2, 193-211.
 Mason, J., Burton, L. and Stacey, K. (2010) Thinking
Mathematically, Harlow: Prentice Hall.
20

21. 21
Thank you for your attention
Further detail about
Developing Mathematical Thinking in the Primary Classroom
is available at:
http://blog.dundee.ac.uk/mathematical-thinking/
To access these slides go to:
http://www.slideshare.net/brianghudson