Module EFPM324 for 2019/0
- Overview
- Aims and Learning Outcomes
- Module Content
- Indicative Reading List
- Assessment
Postgraduate Module Descriptor
EFPM324: Technology in Mathematics Education: Shaping Mathematical Knowledge in the 21st Century
This module descriptor refers to the 2019/0 academic year.
Module Aims
The aim of the module is for you to a) learn about how technological affordances impact on shaping mathematical knowledge and understanding, b) based on existing theories, develop your own ways of understanding of theoretical aspects of the teaching and learning of mathematics with technologies c) design and evaluate effective mathematical learning environments with technology for your own teaching contexts.
Specifically the module will enable you to:
explore current technology, affordances and potential in the teaching and learning of mathematics
develop a understanding about how affordances of technologies will impact on shaping learners’ knowledge of mathematical concepts
develop a conceptual and practical understanding of the nature of effective teaching and learning of mathematics with technology
identify the possible impacts of technological innovative teaching
develop skills to design and implement learning activities and units which reflect on theoretical underpinnings of teaching and learning of mathematics with technology
critically evaluate existing research in mathematics education with technology
develop your own pedagogy with technology in mathematics
| On successfully completing the programme you will be able to: | |
|---|---|
| Module-Specific Skills | 1. demonstrate a critical awareness of theoretical perspectives and practical concerns in mathematics education with technology informed by your reading and professional practice; 2. demonstrate the ability to identify affordances of technologies and analyse how learners knowledge of mathematical concepts will be shaped by these affordances; 3. demonstrate the ability to evaluate existing software, to design innovative learning environments with technology and to evaluate critically by utilising relevant theories; |
| Discipline-Specific Skills | 4. identify systematically and evaluate insightfully current research and advanced scholarship relevant to the field of education and educational technology; 5. apply theoretical insights, through critical reflection, to evaluate professional practice with technology; 6. present data and findings in a form appropriate for educational and technological contexts; |
| Personal and Key Skills | 7. demonstrate the ability to identify and critically discuss current issues in education; 8. demonstrate the ability to reflect independently, critically and creatively on professional practice; 9. demonstrate the ability to construct organised, structured, critically reflective and analytic writing; 10. demonstrate the ability to manage time and engagement in the context of masters level study that has a high level of independent study; 11. demonstrate the ability to take the initiative in contributing collaboratively in interactive learning contexts; 12. demonstrate communication skills both oral and written and in on-line contexts. |
Module Content
Syllabus Plan
The module will be delivered through a programme of face-to-face sessions and/or online activities including lectures and seminars, peer presentation, group work, peer discussions and support, interactive activities, and workshop-type sessions to reflect the ILOs.
Supervision of directed and independent work will be through email, moderation of discussion forums and instant messaging/chat programmes. You will use a range of online platforms to support your learning.
Whilst the module’s precise content may vary from year to year, it is envisaged that the syllabus will cover some or all of the following topics:
Introduction: Module introduction and philology; an overview of research in mathematics education with technology; an overview of available technologies; impact of technological affordances on knowledge and understanding.
Critical review of existing theories: Instrumentation theory and instrumental genesis; Affordance theory; cKc model for describing mathematical knowledge with technology;; Discussion how affordances of technology will shape learners’ understanding
Evaluations of existing software; evaluations of TouchCount (iPad), Dynamic geometry software (DGS) and Tinkerplots; Digital textbooks and web-based learning environments such as WisWeb http://www.fi.uu.nl/wisweb/en/; designing mathematical rich learning environment;
Pedagogical issues in technology; teaching approaches and interventions with technology; dragging modalities of DGS and task design; online discussion tools in mathematics; dialogic approach with technology
Reflection of practice and future perspective: use of technologies in classroom; evaluation of teaching; identifying issues of teaching with technology in future
Learning and Teaching
This table provides an overview of how your hours of study for this module are allocated:
| Scheduled Learning and Teaching Activities | Guided independent study | Placement / study abroad |
|---|---|---|
| 10 | 290 |
...and this table provides a more detailed breakdown of the hours allocated to various study activities:
| Category | Hours of study time | Description |
|---|---|---|
| Scheduled Learning and Teaching | 10 | Face-to-face four x 2.5 hours sessions including lectures, seminars and tutorials (Blended) with equivalent on-line provision for distance students (Distance) |
| Guided independent study | 20 | Online-based learning , e.g. undertaking pre-session reading, reading session notes, watching videos, posting notes on Hive and so on. |
| Guided independent study | 70 | Directed reading related to topics discussed in the module |
| Guided independent study | 20 | Preparing group presentations |
| Guided independent study | 20 | Writing blog entries |
| Guided independent study | 20 | Planning and implementing designed activities, analysing your own practice |
| Guided independent study | 10 | Evaluating existing mathematical software |
| Guided independent study | 10 | Field work including classroom observations and implementing teaching |
| Guided independent study | 100 | Preparation for assignments, further independent readings |
| Guided independent study | 20 | Contributions to online discussions and commenting on peer blogs. |
Online Resources
This module has online resources available via ELE (the Exeter Learning Environment).
Mathematics Education Journals
Educational Studies in Mathematics: http://www.springer.com/education+%26+language/mathematics+education/journal/10649
Journal of Mathematical Behavior: http://www.journals.elsevier.com/the-journal-of-mathematical-behavior/
Research in Mathematics Education: http://www.tandfonline.com/toc/rrme20/current#.UwTPrHkc2jM
ZDM: http://www.springer.com/education+%26+language/mathematics+education/journal/11858
Mathematical thinking and learning: http://www.tandfonline.com/toc/hmtl20/current
ERME proceedings: http://www.mathematik.uni-dortmund.de/~erme/index.php?slab=proceedings
Technology, Knowledge and Learning: http://link.springer.com/journal/10758
Other Learning Resources
European Society for Research in Mathematics Education: http://www.mathematik.uni-dortmund.de/~erme/
David Tall Academic homepage: http://homepages.warwick.ac.uk/staff/David.Tall/
How this Module is Assessed
In the tables below, you will see reference to 'ILO's. An ILO is an Intended Learning Outcome - see Aims and Learning Outcomes for details of the ILOs for this module.
Formative Assessment
A formative assessment is designed to give you feedback on your understanding of the module content but it will not count towards your mark for the module.
| Form of assessment | Size of the assessment (eg length / duration) | ILOs assessed | Feedback method |
|---|---|---|---|
| Video/online presentation of critical reflections of reading & practice | 10-15 minutes presentation/edited video | 1, 2, 4, 5, 7-12 | Written peer assessment and tutor feedback |
| Constructive comments/discussion on presentations/videos from peers | No fixed word length | 1-12 | Written peer assessment and tutor feedback |
Summative Assessment
A summative assessment counts towards your mark for the module. The table below tells you what percentage of your mark will come from which type of assessment.
| Coursework | Written exams | Practical exams |
|---|---|---|
| 100 | 0 | 0 |
...and this table provides further details on the summative assessments for this module.
| Form of assessment | % of credit | Size of the assessment (eg length / duration) | ILOs assessed | Feedback method |
|---|---|---|---|---|
| Critical evaluation of learning environments with technology and how they influence on shaping students mathematical understanding | 75 | 6000 words | 1, 2, 4, 5, 7-12 | Written summative feedback |
| Designing a lesson / activity plan with digital learning environments with critical annotations | 15 | 1000 words | 1, 3, 4, 6, 7-12 | Written summative feedback |
| Contributions to online discussions | 10 | 500 words equivalent | 1-12 | Written summative feedback |
Re-assessment
Re-assessment takes place when the summative assessment has not been completed by the original deadline, and the student has been allowed to refer or defer it to a later date (this only happens following certain criteria and is always subject to exam board approval). For obvious reasons, re-assessments cannot be the same as the original assessment and so these alternatives are set. In cases where the form of assessment is the same, the content will nevertheless be different.
| Original form of assessment | Form of re-assessment | ILOs re-assessed | Timescale for re-assessment |
|---|---|---|---|
| Critical evaluation of learning environments with technology (6000 words | Critical evaluation of learning environments with technology (6000 words) | 1, 2, 4, 5, 7-12 | 6 weeks |
| Designing a lesson / activity plan with digital learning environments with critical annotations (1000 words) | Designing digital learning environments with critical annotation (1000 words) | 1, 3, 4, 6, 7-12 | 6 weeks |
| Contributions to online discussions | Reflection on online discussion experience (500 words) | 1-12 | 6 weeks |
Re-assessment notes
If students are referred/deferred with regard to their contributions to the online discussions, then they will be asked to submit written reflections on their experience of online learning in this module (max. 500 words)
Indicative Reading List
This reading list is indicative - i.e. it provides an idea of texts that may be useful to you on this module, but it is not considered to be a confirmed or compulsory reading list for this module.
Artigue, M. (2002). Learning mathematics in a CAS environment: The genesis of a reflection about instrumentation and the dialectics between technical and conceptual work. International Journal of Computers for Mathematical Learning, 7(3), 245-274.
Balacheff, N., & Gaudin, N. (2003). Conceptual framework. In S. Soury-Lavergne (Ed.), Baghera Assessment Project: Designing a hybrid and emergent educational society (pp. 3–22). Grenoble, France: Laboratoire Leibniz-IMAG.
English, L. D. (Ed.). (2010). Handbook of international research in mathematics education. Routledge.
Gutiérrez, A., & Boero, P. (Eds.). (2006). Handbook of research on the psychology of mathematics education: Past, present and future. Sense publishers.
Hoyles, C. (2009). Mathematics education and technology: rethinking the terrain. New York, NY: Springer.
Hyde, Rosalyn and Edwards, Julie-Ann (eds.) (2013) Mentoring mathematics teachers: supporting and inspiring pre-service and newly qualified teachers, Abingdon, GB, Routledge
Jones, K. (2000). Providing a foundation for deductive reasoning: students' interpretations when using Dynamic Geometry software and their evolving mathematical explanations. Educational studies in mathematics, 44(1-2), 55-85.
Kazak, S., Wegerif, R., & Fujita, T. (2013). I get it now!. Stimulating insights about probability through talk and technology. Mathematics Teaching, 235, 29-32.
Kelly, A. E., & Lesh, R. A. (Eds.). (2012). Handbook of research design in mathematics and science education. Routledge.
Leung, A., Chan, Y. C., & Lopez-Real, F. (2006). Instrumental genesis in dynamic geometry environments. In Proceedings of the ICMI 17 Study Conference: Technology Revisited, Part 2 (pp. 346–353). Hanoi, Vietnam.
Sfard, A. (2008). Thinking as communicating: Human development, the growth of discourses, and mathematizing. Cambridge, England: Cambridge University Press.
Sinclair, N., & Yurita, V. (2008). To be or to become: How dynamic geometry changes discourse. Research in Mathematics Education, 10(2), 135-150.
Stylianou, D. A., Blanton, M. L., & Knuth, E. J. (Eds.). (2009). Teaching and learning proof across the grades: A K-16 perspective. Routledge.
Trouche, L. (2004). Managing the complexity of human/machine interactions in computerized learning environments: Guiding students’ command process through instrumental orchestrations. International Journal of Computers for Mathematical Learning, 9(3), 281-307.
Watson, A., Jones, K., & Pratt, D. (2013). Key Ideas in Teaching Mathematics: Research-based guidance for ages 9-19. Oxford University Press.
Wegerif. R. (2007) Dialogic, Educational and Technology: Resourcing the Space of Learning. New York: Springer-Verlag
Wegerif. R. (2013) Dialogic: Education for the Internet Age, Routledge.
