About This Course
In this course we’d like to show, that mathematics can be interesting, nice and easy to understand. We show strategies to develop mathematical skills and abilities through visualization. You can learn some theoretical background in problem solving, examples of visual communication and maths lessons in lower and upper secondary school (video and discussion), optical illusions and the psychology of seeing, how it can help the development of thinking abilities, spatial abilities, examples of useful kits for teaching mathematics (Zometool, origami, tangram, logical games and puzzles, etc.), connection between visual arts and mathematics – some artists, whose artistry is rich in mathematical objects, patterns, computer graphic softwares (e.g. GeoGebra).There is a webpage vismath.ektf.hu (external link), where you can find lectures and presentations dealing with the above mentioned topics – the lecturers are from various fields and countries: there are mathematicians, artists, psychologists, teachers of higher education, researchers among them, from Finland, Belgium, Austria, Hungary and Serbia. There are also good practices, how to implement these methods in maths lessons, made by Serbian Mathematics teachers. You can join our Summer University lectures, held in Eger, 2013, and in Belgrade, 2014 through videos. You can get an insight into the programmes and workshops seeing the photo gallery. The participants can learn these methods by reading the slideshows of the workshops and presentations. You can also find useful links on the webpage for further information.
You can apply for the course by writing an application letter to the course instructor Ilona Téglási (email@example.com). Some basic information needed for application: name, country, institute, status(student/teacher), major studies, language competences, e-mail address, motivation letter. For this e-course we use the Moodle system, which has been developed especially for educational purpose, easy and comfortable to work with. If you haven’t met Moodle before, you can find many information about it on https://docs.moodle.org/27/en/About_Moodle (external link) . During the course you’ll have the chance to get acquainted with other participants, share ideas, make questions, comments through a forum.
After the course, the participant will be able to
- understand the importance of visuality in teaching mathematics.
- see the connections between mathematics and visual arts.
- use the visualization in own teaching practise.
- understand the importance of motivation through arts in maths education.
- work out and try out models, which use visuality in different fields of teaching mathematics.
- collect evidence of the effect of the teaching approach and the research question.
- How can visuality and visual arts be used in different fields of Mathematics?
- Which are the ways of visualizing different topics (not only geometry) in the teaching practise?
- How can visualization help the pupils understanding mathematical objects, procedures deeper?
Content / schedule
- week 1 Introduction: the course instructor and the participants introduce themselves through forum
- week 2 Problem solving in mathematics (some theoretical background in problem solving strategies).
week 3-4 Examples of visual communication and maths lessons in lower and upper secondary school (lesson plan, video and discussion through forum).
week 5 Optical illusions and the psychology of seeing, role in development of thinking abilities.
week 6 Spatial abilities and their evaluation – tests and tools.
week 7 Visualizing algebraic expressions.
week 8 Examples of useful kits for teaching mathematics (Zometool, origami, tangram, logical games ...) Planning models for teaching a regular topic in math curriculum.
week 9 Visual arts and mathematics – some artists, whose artistry is rich in mathematical objects, patterns.
week 10-11 Computer graphic softwares. Planning implementation for teaching a regular topic in maths curriculum.
week 12-13 Finalizing and uploading models, lesson plans and results. Discussion via forum, final evaluation.
- Studying strategies to develop mathematical abilities, didactical approaches.
Discussing the example lessons.
Finding the common points in mathematics and visual arts through experiences.
Planning or choosing a model/kit for teaching.
Piloting the model in maths teaching practice.
Collecting evidence concerning the effect of the research questions.
Shared reflection by continuous discussions via Moodle forum.
Evaluation and assessment criteria
- The participants has to plan a visual model to a special topic in Mathematics!
The participants has to write lesson plans (at least 2) using the learned teaching methods!
Implement the plan into practice – if possible!
Essay or test on effectiveness of the planned lesson – questionary for the pupils or school test.
The participants should take part in discussions with other participants through forum on Moodle.
The lesson plans and models will be evaluated according to methodological aspects, general mathematics curriculum.
Jerome Bruner: The Process of Education (Harvard University Press, 1976)
Jerome Bruner: The Culture of Education (Harvard University Press, 1997)
N. C. Presmeg, C. Bergsten: Preference for Visual methods: An International Study (in: Proceedings of the 19th International Conference for the Psychology of Mathematics Education, Recife, Brazil, 1995)
Solano, N. C. Presmeg: Visualization as a Relation of Images (in: Proceedings of the 19th International Conference for the Psychology of Mathematics Education, Recife, Brazil, 1995)
N. Presmeg: Research on Visualization in Learning ans Teaching Mathematics (in: Handbook of Research on the Psychology of Mathematics Education – Past, Present, Future eds: Angel Guttiérrez, Paolo Boero, PME 1976-2006)
Tom Lowrie: The Influence of Visual Representations on Mathematical Problem Solving and Numeracy Performance (in: 24th Annual MERGA Conference, Sydney, 2001)