MA2MP_SPSY psychomathematics

Faculty of Education
Spring 2014
Extent and Intensity
0/0. 2 credit(s). Type of Completion: k (colloquium).
Teacher(s)
Mgr. Helena Durnová, Ph.D. (lecturer)
Guaranteed by
Mgr. Helena Durnová, Ph.D.
Department of Mathematics – Faculty of Education
Supplier department: Department of Mathematics – Faculty of Education
Timetable
Wed 26. 3. 17:35–20:10 učebna 33, Thu 27. 3. 15:45–16:30 učebna 33, 18:30–20:10 učebna 33
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
Ernst Mach was teaching psychophysics in order to teach the foundations of physics as well as improving the understanding of its genesis and how it is best taught. Prof. em. Martin Černohorský still uses a similar approach. In the same way, psychomathematics uses the foundations of mathematics (philosophy of mathematics, erkenntnis-psychology) in order to lay more consistent conceptual foundations of mathematics as well as of mathematics teaching. The approach is similar to intuitionism in mathematics (e.g. as used by Poincaré, Weyl and Brouwer). The course is organized as a seminar in order to provide the students through their seminar thesis to apply this scientific meta-methodology from Mach to different questions and problems in mathematics teaching. This scientific method is general and thereby applicable to any pedagogic or scientific question or problem. The seminar is explicitly for students of any semester as all basic knowledge requirements are provided in the course. The language will be English, but command of language will not in any way be part of the evaluation and the language will - especially in the beginning - be used slowly and clear with translations of difficult words and ideas into Czech language. The meaning of central concepts are introduced partly non-verbal.
Syllabus
  • The course first lays a consistent and general basis through the central concepts needed for understanding and teaching mathematics. On these, it builds a theoretical framework, which consists of vivid mental representations (Anschauung, sensualism), the economy of thoughts (by gestalts) and the erkenntnis-theory (theory of knowledge) as a meta-reflection level in order to stabilize the learning process. The theoretical framework provides valuable tools for a) understanding mathematics in a consistent way, b) teaching mathematics (and any other topic) in a genetic, i.e. exponential way, c) understanding one's own learning and optimizing it (learning to learn). The students learn to work empirically, i.e. how to distinguish between empiry and metaphysics, between facts and artifacts in teaching as well as in mathematics. Although the course includes theory, it uses a reciprocal process of "practical theory", i.e. of using many practical examples in order to give empirical meanings to the theoretical concepts used. The practical examples will include materials for mathematics teaching (Stern, Montessori, etc.), games, phenomena in-between mathematics and related topics, etc. Through the process, the participants learn to understand their own learning process (as well as that of other learners) as adaptative, transformative and plastic. The examples will include for instance the introduction of the number concept (foundations of arithmetic) as well as the foundations of geometry. They also include higher-level concepts, such as exponential functions, topology, etc. References to the history of pedagogy, mathematics, mathematics teaching and philosophy of science are used as examples, but not as the main focus of the course.
Teaching methods
The course will be taught in blocks. The first block is meant to introduce the theoretical framework, while the second is mainly focused on discussing examples and providing some more in-depth information on specific topics. Depending on practicalities, the second block can be split and added to the first and third block respectively. The third block is used for presenting and discussing the seminar theses.
Assessment methods
The evaluation mainly tries to focus on the process, rather than the end product by each student. What is evaluated is a) attendance, b) participation, c) thesis and d) peer-review of other theses.
Language of instruction
English
Further Comments
Study Materials
The course is also listed under the following terms Spring 2015, Spring 2016, Spring 2017.
  • Enrolment Statistics (Spring 2014, recent)
  • Permalink: https://is.muni.cz/course/ped/spring2014/MA2MP_SPSY