Presentation for the Asian Centre for Mathematics Education at East China Normal University, 2018/10/2, 14:00-15:00. NB. References not included.

1. Using technology for maths
teaching and learning: instructional
design, digital books and
automated feedback
Asian Centre for Mathematics Education
East China Normal University
2018/10/2 14:00-15:00

2. Who am I?
• Dr. Christian Bokhove
• From 1998-2012 teacher maths, computer science, head of
ICT secondary school Netherlands
• National projects Maths & ICT at Freudenthal Instituut,
Utrecht University
• PhD 2011 under Prof. Jan van Maanen and prof. Paul Drijvers
• Associate Professor at University
of Southampton
– Maths education
– Technology use
– Large-scale assessment
(TIMSS, PISA)

3. Technology use: mixed results
• OECD report
• Ma overview
http://www.keepeek.com/Digital-Asset-Management/oecd/education/students-computers-and-
learning_9789264239555-en#.V8wy2jV5-aU

4. https://www.nber.org/papers/w23744

5. “experimental evidence suggests that giving a
child a computer may have limited impacts on
learning outcomes, but generally improves
computer proficiency and other cognitive
outcomes.”

6. “From our review, computer-assisted learning and
behavioral interventions emerge as two areas that show
considerable promise. Especially when equipped with a
feature of personalization, computer-assisted learning
can be quite effective in helping students learn,
particularly with math.”
For example:
“a fairly low-intensity online program that provides
students with immediate feedback on math homework
was found to have an effect size of 0.18 standard
deviations”

7. SOME EXAMPLES OF PROJECTS

8. Part of PhD
Algebraic skills
Year 12 students
Netherlands
often
disappointing

9. But even when rewriting
skills are OK…
…many things can go wrong

10. So conceptual knowledge and
pattern recognition are important!

11. Could the use of technology
help improve such algebraic skills?

12. Study in four rounds….
Rnd Focus Target N
Pre What software, what
characteristics?
Experts
1 Could it work? 1-to-1s,
qualitative
N=5
2 In what way can it
work?
2 classes in 1
school
N=31
3 Does it work? 9 schools,
quantitative
N=324

13. Student can choose own strategy...

14. Equations: in-between steps, multiple
strategies allowed

15. (i) students learn a lot from what goes wrong,
(ii) but students will not always overcome these if
no feedback is provided, and
(iii) that too much of a dependency on feedback
needs to be avoided, as summative assessment
typically does not provide feedback.
These three challenges are addressed by principles
for crises, feedback and fading, respectively.

16. Crisis-tasks
“students learn a lot from what goes wrong”
“Failure is, in a sense, the highway to success” –
(Probably not) Keats

17. Feedback: overcoming a crisis
Screencast clips
“but students will not always overcome these if no feedback is provided”

18. Feedback: worked examples and hints

19. Fading
“too much of a dependency on feedback needs to be avoided”
A lot of feedback A little bit less
feedback
No feedback

20. BUT THIS WAS ONLY ONE TOOL….

21. Towards digital textbooks
• Digital textbook: theory, examples,
explanations
• Interactive content (in different small
applications)
• Interactive quizzes (formative assessment,
feedback)
• Integrated workbook

22. European project:
MC-squared

23. 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

24. The
environme
nt 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
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

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

26. Feedback

27. More feedback
http://is.gd/kheng5

28. NOW WE WANTED TO GO EVEN
FURTHER…

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

30. This time we
took a real
textbook

31. And we
made two
sections with
geometry
into digital
textbooks

32. Demo

33. Digitalbooks
33

34. 35

35. BUT IT WASN’T ENOUGH TO JUST HAVE
DIGITAL TEXTBOOKS. THE CONTENT
HAD TO BE GOOD AS WELL…

36. For example by integrating solid
mathematics education principles

39. By using underpinning literature…
Fan, L., & Bokhove,
C. (2014). Rethinking the
role of algorithms in school
mathematics: a conceptual
model with focus on
cognitive
development. ZDM:
International Journal on
Mathematics
Education, 46(3), 481-492.
DOI: 10.1007/s11858-014-
0590-2

40. Core
content
Design
principles
Digital
layer

41. • D: Digital layer
– Different tools
– Integrated design (paper book AND digital book)
• Pr: Design principles
– Instructional design (eg feedback)
– Maths education (eg representations)
Now we ‘just’ need enough core content (Cc) to
cover the secondary mathematics curriculum…
Cc
Pr
Dl

42. Towards a School Mathematics Project 2.0

43. Brief history of SMP
• From the 1960s to the 1990s, the School Mathematics
Project (SMP) was an iconic project in English
mathematics education (Thwaites, 2012; Wikipedia,
2017).
• Originated at the University of Southampton and
created a ground-breaking textbook series that was
used in the majority of mathematics classrooms in
England throughout the 1970s and 1980s
• Combined expertise of both the Mathematics and
Education departments in the University of
Southampton, collaborating fruitfully with numerous
schools and teachers nationally.

44. Decline
• Changes to how exam boards were organised
meant a decline in its popularity.
• Textbooks not always used widely. Why not
(contrast with my experience in the
Netherlands).
• ..but now

45. ..but now
• Return of the SMP archives and copyright to the
university
• Renewed interest of schools and government into
high quality textbooks (Department for
Education, 2015),
• Opportunities for digital books (e.g. Bokhove &
Drijvers, 2012; Bokhove, 2017)
Can we revive these quality resources and
transform SMP into an SMP 2.0.

46. Digitise the archive

47. Conclusion
• Lots of experience with appropriate use of
technology.
• Use lots of mathematics education principles
for the design.
• Our aim is now to digitise core content from
the old SMP books and use as basis for 5 years
of secondary school content.
• Also in different languages. Result: paper AND
digital books for 11-16 yr olds.
Cc
Pr
Dl

48. Thank you
• Contact:
–C.Bokhove@soton.ac.uk
–Wechat: ChristianBokhove
–www.bokhove.net
• Most papers available somewhere; if
can’t get access just ask me.