This document discusses international comparisons of mathematics education based on assessments like TIMSS and PISA. It summarizes differences in curricula, instructional time, and technology use between high-performing countries like Hong Kong and Japan and England. It then describes the enGasia project which involves designing digital mathematics textbooks to compare geometry education internationally and implement them in classrooms. Interactive features and opportunities for feedback in the digital textbooks are demonstrated.

2. • Dr. Christian Bokhove
• From 1998-2012 teacher maths, computer
science, head of ICT secondary school NL
• National projects maths+ict at Freudenthal
Instituut, Utrecht University
• Lecturer at University of
Southampton
– Maths education
– Technology use
– Large-scale assessment

3. In England more and more people are
looking towards Asia because of their
excellent scores on international maths
assessments like TIMSS and PISA. It,
however, is not easy to unpick ‘what
works’ and ‘what doesn’t work’. This
seminar draws from previous research
and the current ‘enGasia’ project to:

4. Rationale
• enGasia project, studying geometry education in
international perspective
• Differences in curricula between countries
• Existing international comparisons like TIMSS and PISA
• Recently published paper ‘Opportunity to Learn’

5. Internal comparisons: IEA & OECD
“The International Association for
the Evaluation of Educational
Achievement (IEA) is an
independent, international
cooperative of national research
institutions and governmental
research agencies. It conducts large-
scale comparative studies of
educational achievement and other
aspects of education.”
“The mission of the Organisation
for Economic Co-operation and
Development (OECD) is to promote
policies that will improve the
economic and social well-being of
people around the world.”

6. TIMSS 2011 results
6

7. 7

8. SES and achievement (TIMSS)
Country SES MATHS SE GEOM SE
Hong Kong,
SAR 9.83 585.6 3.8 597.4 4.3
Japan 10.75 569.8 2.6 585.8 3.5
England 10.71 506.8 5.5 497.9 5.7
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9. Country mean content coverage (TIMSS)
Country
OTL_co
ntent_c
overage
ccNumb
er
ccAlge
bra
ccGeo
metry ccData
Hong Kong,
SAR 81.48 99.11 85.86 79.86 61.08
Japan 89.37 98.58 91.29 93.13 74.47
England 82.81 96.33 73.64 76.67 84.59
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10. Country curriculum coverage (TIMSS)
10
Country
cNumb
er
cAlgebr
a
cGeo
metry cData cAll
Hong Kong,
SAR 1 0.8 0.67 0.33 0.7
Japan 1 1 1 1 1
England 1 0.8 1 1 0.95

11. Mathematics instructional time

12. Teachers prepared for geometry?

13. TIMSS 2011 ICT use

14. Types of technology
(Not official taxonomy ;-)
• Exploratory tools
• One-way, two-way
• Practice tools
• Feedback
I’m going to say a bit more on:
• Previous research with the Digital Mathematics
Environment
• Interactive e-textbooks?

15. • International Conference on Mathematics
Textbook Research and Development 2014. Strand
on e-Textbooks and technology.
From Prof. Yerushalmy’s talk

16. Examples
• Apple iBooks
• Great looks
• Limited interaction
• Limited student
management
options
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17. Integrated in c-books

18. Aims
• Design and develop a new genre of authorable e-book, which we call
'the c-book' (c for creative)
– Creative Mathematical Thinking (CMT)
• Initiate a ‘Community of Interest’ (CoI) (Fischer, 2001)
– A community of interest consists of several stakeholders from
various ‘Communities of Practice’ (Wenger, 1998).
– England, Spain, Greece, France
– Within these teachers who co-design and use resources for
teaching, can contribute to their own professional development
(e.g., Jaworski, 2006).
– Social Creativity, Boundary objects
• UK CoI: learning analytics

19. The
environment
stores
student
work.
Separate
‘schools’ can
have several
classes.
This is the ‘edit’ mode of the
environment : this c-book is
about planets
c-books can have several pages:
each circle indicates a page.
Other options are available as
well
C-book pages can have
random elements, like
random values.
Pages consist of ‘widgets’, which can
range from simple text to
simulations (here: Cinderella). Some
widgets can give automatic feedback.
The MC-squared project aims aims to design and develop a new genre of
creative, authorable e-book, which the project calls 'the c-book
http://www.mc2-project.eu
The project aims to harness the structure of a
CoI to stimulate social creativity (SC) and
creative mathematical thinking (CMT). In the
UK CoI we are treating CMT in problem-posing
and solving as entailing the indicators fluency,
flexibility, originality, elaboration, and

20. Store student results, and use these as a
teacher to study misconceptions and for
starting classroom discussions

21. Authorable

22. Feedback

23. HTML5 player

24. Also geometry (more later…)

25. Technology-added value of the c-books
• Creative and interactive activities made by designers
(creative process authoring)
• Collaboration within CoI between designers, teachers and
computer scientists. Feeds into DA component (see later
section)
• Interactivity: feedback design
• More than one widget factories used
• All student data stored
• Sum is more than the parts…

26. Digital Mathematics Environment
JAVA/HTML5 disclaimer
•Demo: http://app.dwo.nl/en/teacher/ login as guest
•Secondary education
– Algebra, Geometry, Statistics, Number
•Undergraduate
•DME widget list

27. Environments
• MC-squared environment
– This is where we will do most of the work
– After that it will be transferred to the DME
• enGasia DME environment
• Chinese and Japanese DME versions
– might have to be done offline with notepad

29. enGasia project
1. Compare geometry education in England, Japan
and Hong Kong → some shown now.
2. two digital resources (electronic books) will be
designed. They are then implemented in
classrooms in those countries → technology
shown, now demo.
3. The methodology will include a more qualitative
approach based on lesson observations and a
quasi-experimental element.

31. The design process
• Multiple widgets
• Some work ‘in the backend’ (e.g. feedback)

32. This could be a geogebra
widget but perhaps not
necessary. More
important is feedback.

33. I replicated the
image in
geogebra (points
are fixed, they
could be ‘free’).
Also feedback
plus layout.

34. Demo

36. Try out geometry books
DESKTOP: http://is.gd/mc2dme
•Transformations
•Meaningful lines
TABLET: http://is.gd/mc2tablet
(UNDER DEVELOPMENT)
•Transformations
•Meaningful lines

37. Author your own
• If you want you can try and make your own book

38. Thank you
• Questions/comments?
• More information:
C.Bokhove@soton.ac.uk
• http:/blog.soton.ac.uk/engasia
• Twitter: @cbokhove
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