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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.

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- 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.

- 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.