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Seminar University of Loughborough: Using technology to support mathematics education and research

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I WILL ADD THE REFERENCES IN DUE TIME

Christian received his PhD in 2011 at Utrecht University and is lecturer at the University of Southampton. In this talk Christian will present a wide spectrum of research initiatives that all involve the use of technology to support mathematics education itself and research into mathematics education. It will cover (i) design principles for algebra software, with an emphasis on automated feedback, (ii) the evolution from fragmented technology to coherent digital books, (iii) the use of technology to measure and develop Mental Rotation Skills, and (iv) the use of computer science techniques to study the development of mathematics education policy.

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Seminar University of Loughborough: Using technology to support mathematics education and research

  1. 1. Using technology to support mathematics education and research Dr. Christian Bokhove 7 June 2017 Loughborough
  2. 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. 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. 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. 5. Rationale Algebraic skills Year 12 students Netherlands often disappointing
  6. 6. But even when rewriting skills are OK… …many things can go wrong
  7. 7. So conceptual understanding and pattern recognition are important!
  8. 8. Use of ICT
  9. 9. So can’t we use ICT for acquiring, practicing and assessing algebraic expertise?
  10. 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. 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. 12. Equations: in-between steps, multiple strategies allowed
  13. 13. Store student results, and use these as a teacher to study misconceptions and for starting classroom discussions students
  14. 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. 15. Crisis-tasks “students learn a lot from what goes wrong”
  16. 16. Feedback: overcoming a crisis Youtube clips “but students will not always overcome these if no feedback is provided, and”
  17. 17. Feedback: worked examples and hints IDEAS feedback, webservice with Jeuring et al
  18. 18. Fading “too much of a dependency on feedback needs to be avoided”
  19. 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. 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. 21. Towards digital textbooks • Digital textbook: theory, examples, explanations • Interactive content (in MC-squared widgets) • Interactive quizzes (formative assessment, feedback) • Integrated workbook
  22. 22. Examples • Apple iBooks • Great looks • Limited interaction • Limited student management options
  23. 23. FP7 EU project Designing creative electronic books for mathematical creativity
  24. 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. 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. 26. Authorable
  27. 27. Feedback
  28. 28. Also geometry
  29. 29. Creativity: fluency
  30. 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. 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. 32. This could be a geogebra widget but perhaps not necessary. More important is feedback.
  33. 33. Flowchart http://engasia.soton.ac.uk
  34. 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. 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. 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. 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. 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. 39. Wayfinding • Instruction cues • Local cues • Distal cues
  40. 40. • Familiar platform • Stores correct/incorrect • Time taken
  41. 41. Aim 1: MRS instrument • Similar behaviour as Ganis and Kievit (2015) • Differences ‘same’ and ‘different’.
  42. 42. Aim 2: Flexible environment
  43. 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. 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. 45. Computer Science to support research DESIGN RESEARCH, ALGEBRAIC EXPERTISE, FEEDBACK DIGITAL MATHEMATICAL BOOKS MENTAL ROTATION SKILLS COMPUTER SCIENCE TO SUPPORT RESEARCH
  46. 46. Text mining • Inspection reports • Conventional text software • R (topic models and sentiment analysis)
  47. 47. 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
  48. 48. • 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 1 2 3 4 5 6 7 8 9 10 11 12 For more info, see these slides: https://t.co/BYkdeRyT4V
  49. 49. 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
  50. 50. 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

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