Course Details

1. Describe and explain the main recent domains in the research for the teaching and learning of mathematics at education.
2. Present the stages for the development of mathematical thinking and justify the cognitive obstacles pupils encounter concerning different mathematical concepts by using the neopiagetian perspective.
3. Construct and design teaching plans for every mathematical concept and reconstruct mathematical units in order to be taught by using more recent teaching tools.
4. Present the different dimensions of the metacognition and explain its relation with the self-regulatory performance during problem solving.
5. Analyse students’ mistakes, misunderstandings and misconceptions depending on philosophical, epistemological, psychological and teaching factors that influence learning propose ways for encountering those situations.

Description and explanation of the 5 basic units for the teaching of mathematics. Study of the curriculum (the concepts of exploration, investigation and enrichment). The most emphasis at the teaching of mathematics.

The basic theories for learning (constructivism and cognitive psychology). Piagetian and neo- piagetian theories. Cognitive obstacles, intuitive rules and misconceptions.

Cognitive styles, mathematical models and the multiple representation flexibility.

Metacognition and mathematical thinking. Self-representation and self-regulation. Self-regulatory strategies and the problem solving procedure. The use of mathematical model for self-regulation.

The stages of the development of creative thinking in mathematics.

The affective domain in mathematics.

• Campell, J. (2005). Handbook of mathematical cognition. New York: Psychology Press.
• Ernest, P., Greer, B. & Sriraman, B. (2009). Critical issues in mathematics education. Montana Mathematics Enthusiast

• Haners, J. et al. (1999). Teaching and learning thinking skills. Netherlands: Swets & Zeitlinger.
• Lampert, M. (2001). Teaching problems and problems of teaching. New Hoven: Yale University Press.
• Βοσνιάδου, Σ. (1995). Η ψυχολογία των μαθηματικών. Αθήνα: Gutenberg.

The taught part of course is delivered to the students by means of lectures, conducted with the help of computer presentations. Lecture notes and presentations are available through the web for students to use in combination with the textbooks. In many cases students have to work collaboratively in order to think critically and creatively, communicate with each other and present a group work.