In the United Kingdom, many students struggle in their transition from secondary school mathematics to undergraduate mathematics. It is not always possible to remediate deficiencies in mathematical knowledge within a school setting. At the same time, we know that Intelligent Tutoring Systems can aid students in acquiring, practicing, and assessing mathematical content. In this paper, we will present interactive workbooks created at our institution, that cover units of study from the secondary A-level mathematics curriculum, comprising a series of technical expositions and a modular collection of quizzes. Each quiz addresses content equivalent of at most two classroom lessons and features automated feedback bespoke to the students’ (algebraic or numeric) input. The ‘digital books’ make use of a Computer Algebra System to provide automated feedback. The development of the books is a collaborative process in a ‘Community of Interest’ with local secondary teachers, developers recruited from local departments, and the Southampton Education School. An iterative design-based research approach was adopted for the development, with multiple opportunities for feedback and improvement. After initial prototyping, a teacher focus group will attend a follow-up session where they are invited to review the materials and to make suggestions or requests before implementing them with their students later in the year. We present preliminary reflections on the results of our reflective design-based process, and discuss how this process contributes to both better digital books and research insights.

1. CREATING INTERACTIVE DIGITAL
BOOKS FOR THE TRANSITION FROM
SECONDARY TO UNDERGRADUATE
MATHEMATICS
CADGME
12 September 2023
Dr Christian Bokhove
Professor in Mathematics Education
Southampton Education School
University of Southampton

2. Prof Christian Bokhove Dr Ben Davies

3. Context: challenging transition
• Students’ transition from
secondary to university
mathematics
(e.g., Gueudet, 2008)
Free 60-page book
A-level degree (16-18y)
Undergraduate maths
at a research-
intensive university

4. SMP materials
• From the 1960s to 90s, the School Mathematics
Project (SMP) was iconic in English
mathematics education originating at the
University of Southampton (Thwaites, 2012).
• Textbooks with strong teacher input.
• In the 80-90s the majority of English schools
used SMP.
• But after exam board reforms popularity went
down. Last series appeared around 2002.
• The charity gave all the copyrights back to us.
1000s of books, >10 different languages as well.
• This provides enormous opportunities.

5. So, we have….
• Ready-made high quality instructional materials for almost
every topic 8-18 yr olds. This should not be
underestimated, because development time for this is
enormous.
• The content includes specific books with A-level content.
• Knowledge and skills about the opportunities for digital
books, which include interaction and feedback (e.g.
Bokhove & Drijvers, 2012; Bokhove, 2017), as Intelligent
Tutoring Systems (Kulik & Fletcher, 2016).
This project brings these three things together.

6. This project
• Collaborative development of three workbooks, on content
selected in consultation with >10 local teachers, and colleagues
from the Department of Mathematics (Community of Interest,
Fisher).
• Adopted an iterative design-based research approach to
development, with multiple opportunities for feedback and
improvement.
• Interactive elements of the workbook will be implemented using
STACK (System for Teaching and Assessment using a Computer
algebra kernel).
Iterations of systematic design cycles
(Plomp, 2013)

7. Software - STACK
• STACK is an open-source online assessment system for
mathematics and STEM, designed by Chris Sangwin
(Edinburgh) and colleagues. It is available for Moodle,
ILIAS and as an integration through LTI.
• Features include:
• Algebraic answers.
• Separate validation and assessment
• Randomisation
• Language support
• Open source
• Specific feedback
• Part of the quiz module.
• See https://stack-assessment.org/

8. Outcomes
• Three interactive workbooks in Moodle..
• Each covers one unit of study from the A-level
mathematics curriculum and will comprise instructional
materials (SMP) and a collection of quizzes.
• Each quiz features automated feedback bespoke to the
students’ (algebraic or numeric) input. Storing student
results.
• These features are created in co-creation with teachers.
For example, teacher and student input for feedback
design (i.e. Bokhove, 2010).
• After that, use with students,
and analyse these data.  ongoing

10. Teachers chose from the book

15. Randomisation

16. Worked example

17. Feedback

18. • Question text
• General feedback
• Question note
• Possible answers
• Potential response tree – can be quite elaborate.
• “Choose any two points you found above and try to derive
the equation for the line.”
• If it is easier, you can try to get the equation in the form
(y=mx+c) first and then rearrange to the required form.”

19. Further thoughts
• Expand the statistical methods with the data – already
use classical test theory and IRT, but also include
sequence analysis and learning analytics methods.
• This server also used by maths who don’t mind that these
are called ‘quizzes’ – however, we prefer they are part of
‘digital books’ – own server.
• Further use students, analyse these data.  ongoing
• The technology to do this has been around for a few
decades e.g. Mavrikis’ Wallis, STACK, DME and many
other platforms. Maybe the combination of AI and existing
computer algebra systems (WolframAlpha, Maxima) will
give the field an impulse.

20. THANK YOU
QUESTIONS
Christian Bokhove Dr Ben Davies

21. Selected references
Gueudet, G. (2008). Investigating the secondary–tertiary transition. Educational studies in
mathematics, 67(3), 237-254. https://doi.org/10.1007/s10649-007-9100-6
Bokhove, C. (2010). Implementing Feedback in a Digital Tool for Symbol Sense. International
Journal for Technology in Mathematics Education, 17(3), 121-126.
Bokhove, C. (2017). Using Technology for Digital Mathematics Textbooks: More than the Sum
of the Parts. International Journal for Technology in Mathematics Education, 24(3), 107-114.
Bokhove, C., & Drijvers, P. (2012). Effects of a digital intervention on the development of
algebraic expertise. Computers & Education, 58(1), 197–208.
https://doi.org/10.1016/j.compedu.2011.08.010
Kulik, J. A., & Fletcher, J. D. (2016). Effectiveness of intelligent tutoring systems: a meta-
analytic review. Review of educational research, 86(1), 42-78.
https://doi.org/10.3102/0034654315581420
Plomp, T. (2013). Educational design research. Part A: An introduction. SLO. Retrieved from
https://slo.nl/publish/pages/4474/educational-design-research-part-a.pdf
Thwaites, B. (2012). The School Mathematics Project. Exeter: Short Run Press Limited.