1. Using technology to
support mathematics
education and research
Dr. Christian Bokhove
7 June 2017
Loughborough

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
• Lecturer at University of
Southampton
– Maths education
– Technology use
– Large-scale assessment
– Computer Science stuff

3. Disclaimer
• Pondered if I would dive into the detail of one project, or
go ‘wide’ to provide an wide-ranging overview.
• I settled for the latter (in other words: I couldn’t choose,
a consistent theme in my life)
DESIGN RESEARCH, ALGEBRAIC EXPERTISE, FEEDBACK
DIGITAL MATHEMATICAL BOOKS
MENTAL ROTATION SKILLS
COMPUTER SCIENCE TO SUPPORT RESEARCH

4. Using a digital tool to improve students’
algebraic expertise in the Netherlands:
crises, feedback and fading
DESIGN RESEARCH, ALGEBRAIC EXPERTISE, FEEDBACK
DIGITAL MATHEMATICAL BOOKS
MENTAL ROTATION SKILLS
COMPUTER SCIENCE TO SUPPORT RESEARCH

5. Rationale
Algebraic skills
Year 12 students
Netherlands
often
disappointing

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

7. So conceptual understanding and
pattern recognition are important!

8. Use of ICT

9. So can’t we use ICT for acquiring,
practicing and assessing algebraic
expertise?

10. Research Questions:
What is the effect of an intervention on the
development of algebraic expertise, including both
procedural skills and symbol sense?
Which factors predict the resulting algebraic
performance?
Conceptual framework, elements of:
• Symbol sense – basic skills (e.g. Arcavi)
• Formative – summative assessment
(e.g. Black & Wiliam)
• Research on feedback

11. Research set-up
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
Bokhove, C., &Drijvers, P. (2010). Digital tools for algebra education: criteria and
evaluation. International Journal of Computers for Mathematical Learning, 15(1), 45-62. Online first.

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

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

14. Design principles
(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.

15. Crisis-tasks
“students learn a lot from what goes wrong”

16. Feedback: overcoming a crisis
Youtube clips
“but students will not always overcome these if no feedback is provided, and”

17. Feedback: worked examples and hints
IDEAS feedback, webservice with Jeuring et al

18. Fading
“too much of a dependency on feedback needs to be avoided”

19. Significant
predictors higher
posttest score
• Previous knowledge
• Time spent in self-
test and summative-
test modes
• General attitude
towards mathematics
Non-significant
predictors higher
posttest score
• Gender
• Attitude towards ICT
• Total time spent on
module
• More time spent at
home or at school
Multilevel models: predictors
Bokhove, C., & Drijvers, P. (2012). Effects of a digital intervention on the development of algebraic
expertise. Computers & Education, 58(1), 197-208. doi:10.1016/j.compedu.2011.08.010

20. Using technology for maths teaching and learning:
Instructional design, digital books and automated
feedback
DESIGN RESEARCH, ALGEBRAIC EXPERTISE, FEEDBACK
DIGITAL MATHEMATICAL BOOKS
MENTAL ROTATION SKILLS
COMPUTER SCIENCE TO SUPPORT RESEARCH

21. Towards digital textbooks
• Digital textbook: theory, examples,
explanations
• Interactive content (in MC-squared widgets)
• Interactive quizzes (formative assessment,
feedback)
• Integrated workbook

22. Examples
• Apple iBooks
• Great looks
• Limited interaction
• Limited student
management
options

23. FP7 EU project
Designing creative electronic books
for mathematical creativity

24. Aims
• Design and develop a new genre of authorable e-book,
which we call 'the c-book' (c for creative)
– Creative Mathematical Thinking (CMT): fluency, flexibility,
originality, elaboration, (usefulness)
• 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

25. 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
MC-squared platform based on Utrecht
University’s ‘Digital Mathematics
Environment’ (now Numworx).
https://app.dwo.nl/en/student/

26. Authorable

27. Feedback

28. Also geometry

29. Creativity: fluency

30. 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…
Bokhove, C., (in press). Using technology for digital maths textbooks: More than the sum of the parts.
International Journal for Technology in Mathematics Education.

31. 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.
3. The methodology will include a more qualitative
approach based on lesson observations and a quasi-
experimental element.

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

33. Flowchart
http://engasia.soton.ac.uk

34. Training mental
rotation skills to
improve spatial ability
DESIGN RESEARCH, ALGEBRAIC EXPERTISE, FEEDBACK
DIGITAL MATHEMATICAL BOOKS
MENTAL ROTATION SKILLS
COMPUTER SCIENCE TO SUPPORT RESEARCH

35. Aims collaboration Psychology
1. Online digital version of Mental Rotation
Skills measurement instrument.
2. Flexibility in environment to cater for
different conditions (demonstration later on)
as MRS training tool.
3. To eventually see if MRS training
(i) improves MRS, but
(ii) also transfers to other spatial and maths
domains, e.g. wayfinding in mazes.

36. Spatial skills: assumptions
• MRS can be trained.
– Meta-analysis of training studies for spatial skills:
training in mental rotation can lead to stable gains
in MRS (e.g. Uttal et al., 2013)
• MRS predict maths achievement
• Relation MRS and wayfinding
– Predicts orientation and wayfinding (e.g. Nori et
al., 2016), especially in children.
Bokhove, C., & Redhead, E. (2017). Training mental rotation skills to improve spatial ability.
Online proceedings of the BSRLM, 36(3)

37. Methodology
• Lab-based: psychology students. 43 undergraduate
Psychology students from a university in England (majority
female). Collectively, the 43 students made 43×48=2064
assessment items for MRS, and 2×43=86 mazes
• We measure wayfinding before and after.
• 2x2 factorial design. The two conditions are:
– Treatment group. This group will use a combined
assessment and training tool based on a standardized MRS
instrument.
– Control group. Students in the control condition will
complete crossword puzzles similar to those used as filler
tasks in previous research on MRS (e.g. Cherney, 2008).
• JASP 0.8 beta.

38. • Ganis and Kievit (2015),
based on Shepard and
Metzlar (1971)
• Validated mental
rotation stimuli
• 48 sets of two block
buildings with 7 to 11
cubes
• Four arms rotated over
four angles: 0, 50,
100 and 150o
• ‘Same’ and
‘different’
http://openpsychologydata.metajnl.com/article/10.
5334/jopd.ai/

39. Wayfinding
• Instruction cues
• Local cues
• Distal cues

40. • Familiar platform
• Stores correct/incorrect
• Time taken

41. Aim 1: MRS instrument
• Similar behaviour as Ganis and Kievit (2015)
• Differences ‘same’ and ‘different’.

42. Aim 2: Flexible environment

43. Aim 3: improvements
• When controlling for pre-test maze score, MRS duration and
MRS precision, as well as the interaction between MRS
duration and precision there was no statistically significant
difference between control and treatment group on the post-
test maze score.

44. Limitations and further research
• Undergraduate setting. Extending to naturalistic setting end of
June 2017.
• Tension length of treatment and (supposed) effectiveness.
• No interaction in MRS tool (while it does this so nicely!).
Consequences of first wanting baseline.
Bokhove, C., & Redhead, E. (2017). Training mental rotation skills to improve spatial ability.
Online proceedings of the BSRLM, 36(3)
MC-squared platform based on
Utrecht University’s ‘Digital
Mathematics Environment’ (now
Numworx).
https://app.dwo.nl/en/student/

45. Computer Science
to support research
DESIGN RESEARCH, ALGEBRAIC EXPERTISE, FEEDBACK
DIGITAL MATHEMATICAL BOOKS
MENTAL ROTATION SKILLS
COMPUTER SCIENCE TO SUPPORT RESEARCH

46. Text mining
• Inspection reports
• Conventional text
software
• R (topic models and
sentiment analysis)

48. Dynamic Social Network Analysis
• Classroom interaction
• Methodological proof-of-concept for 5 maths
lessons
Bokhove, C. (2016). Exploring classroom interaction with dynamic social network analysis.
International Journal of Research & Method in Education, doi:10.1080/1743727X.2016.1192116

49. • With Bruno Reddy
• Affective measures
– Intrinsic Motivation
– Extrinsic Motivation
– Self-Concept
– Maths Anxiety
– Locus of control
• Predictive power based on psycho-mathematical
profile
• Relationship between knowledge retention and
psycho-mathematical profile
1 2 3 4 5 6 7 8 9 10 11 12
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For more info, see these slides: https://t.co/BYkdeRyT4V

50. Conclusion
• Overview of several former and current projects I am enthusiastic
about.
• Especially like interdisciplinary work
– Maths education and psychology
– Computer science and maths education
DESIGN RESEARCH, ALGEBRAIC EXPERTISE,
FEEDBACK
DIGITAL MATHEMATICAL BOOKS
MENTAL ROTATION SKILLS
COMPUTER SCIENCE TO SUPPORT RESEARCH

51. Thank you
• Contact:
–C.Bokhove@soton.ac.uk
–Twitter: @cbokhove
–www.bokhove.net
• Most papers available somewhere; if
can’t get access just ask.
• I’ll add the references and post on
Slideshare