Didactics of mathematics - Pedagogická fakulta MU

Didactics of mathematics I R??ena Bla?ková BRNO 2013 Content Preface
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...................... 3 1. Didactics of mathematics and its role in a system of sciences
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1. How we understand the notion didactics of mathematics
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1. Didactics of mathematics particularities
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2. The relationship between mathematics and didactics of mathematics
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3. The relationship between general didactics and didactics of
mathematics 7
2. The aim of didactics of mathematics
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1.2.1 Didactics of mathematics focused on a curriculum content
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1.2.2 Didactics of mathematics focused on pupil´s cognitive processes
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2. Curriculum documents
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1. Framework of educational programme
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2. Aims of the educational area Mathematics and its application
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3. Educational area Mathematics and its application
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4. Educational programme Basic school
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5. Curriculum of basic school mathematics 1979
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6. Mathematics curriculum of the nine-year basic school (ZD?) 1973
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3. Didactical principles
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18
4. Teaching methods
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22
5. Communication
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... 25
6. Creation of basic notions
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1. Notions and their properties
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2. Notions introduction in mathematics
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3. Notions creation
process...................................................................
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7. History of teaching mathematics
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Bibliography and recommended literature
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PREFACE Dear students, the introduced text is dealing with preliminary chapters of
mathematics (math) didactics which are the starting point of thinking about
the possibility of an effective math teaching implementation. It´s meant
for students of a follow-up master study programme for teaching general
educational subjects and math.
The whole text is divided into 7 chapters. Each chapter has its own
aim which should be fulfilled after its study, and you should be able to
answer concept questions which appear at the end of the chapter. Math
didactics study requires an active and independent approach, deals with
special and didactical literature, and with math textbooks. There is still
being solved the problem, how to use theoretical knowledge in a particular
pedagogical job with pupils, and there exists the ceaseless confrontation
of their successfulness. The presented approaches are general, but
teacher´s work with each class and with each individual pupil is
unrepeatable, unique, and requires teacher´s a creative approach. We assume
math knowledge as a necessary theoretical basis of school math,
acquaintance with methods of work at math, pedagogical-psychological
relations of learning and teaching, and mainly a good relationship with
children. The first chapter reflects the relation of math didactics to
individual disciplines it is closely connected with, i.e. the relation to
math and general didactics. The second chapter introduces valid curriculum documents which were
issued by the Ministry of Education, Youth and Sports, and which deal with
teaching math. For the comparison, there are also presented examples of two
documents from the past which show us the approach to math curriculum in
this time. The third and fourth parts pay attention to didactical principles and
teaching methods you already know from your pedagogy and general didactics
study. The aim of these chapters is the implementation of methods and
principles in teaching math. The fifth chapter focuses on various kinds of communication in
teaching math. Apart from a common communication teacher-pupil, it is
necessary in math to acquire other types of it, mainly symbolic and
pictorially illustrative communications. The essential part of the text is the sixth chapter which deals with
forming math notions. The most important thing is a teacher´s approach to
forming each math notion and its properties so as to get right ideas, which
could be enriched in an educational process and which could form an
information system. In the last chapter there is a brief history of math teaching in the
Czech lands. Monitoring both the math teaching development at our schools
and changes of a math content as a school subject, it is very informative for teachers. The text provides
illustrational examples and demonstrations which enable to compare them
with your own approaches to math and its teaching. Study of math didactics is a permanent educational process and it
looks for more effective ways of math teaching at a basic school. I wish
you success and a lot of nice experiences at your study. Author 1. DIDACTICS OF MATHEMATICS AND ITS ROLE IN A SYSTEM OF SCIENCES Aims: While studying this chapter . you'll understand didactics of math tasks
. you´ll be able to characterize the role of didactics of math in a
system of sciences . you´ll be able to understand the importance of math theoretical
ground and its transformation into the system of primary school math
curriculum The guide of study In the first chapter there are presented some approaches for defining
didactics of math and the relationship of math with other science
disciplines it has a close connection with. The relationship between
didactics of math and scientific math is an essential theoretical ground of
school math curriculum. 1. What the term "didactics of math" means It is not possible to use more precise opinion than the one which J.
A. Komenský presented in his book Analytical Didactics (Komenský, 1947):
"Didactics means the ability to teach well. Teaching is an activity which
enables to transfer somebody´s knowledge to somebody else´s one so as to
master it."
The definition of the term "didactics of math" occurs in various
publications mostly with the aim to show its role among scientific
disciplines which are math, pedagogy, and general didactics. Let us mention
some of them.
Dictionary of school math (1981) under the headword "didactics of
math" says: "Didactics of math - it is a boundary scientific discipline
between math and pedagogy which deals with various matters of school math
at all types of schools, i.e. its content and methods how to teach and how
to learn math." P. Kv?to? (1982) understands didactics of math in this way:
"Didactics of math is a scientific discipline which examines relations of
teaching math in accordance with tasks determined by society." B. Novák(2003) says: "Didactics of math is usually considered a
special didactics (subject, possibly branch didactics) in a sense of
educational theory in math. It is a science with its own structure, logic
and the way of thinking. We can distinguish four dimensions in it: content,
pedagogical, psychological, and constructive." Didactics of math is a scientific discipline which solves special
math teaching tasks at individual levels and types of schools. It defines
aims and a content of a math curriculum, it recommends appropriate teaching
methods and procedures, organizational forms of teaching, it takes into
account psychological relations of learning, and provides teaching
technology. At present didactics of math is dealing with the role of a
pupil and a teacher in an educational process, it studies processes which
are going in pupil´s and teacher´s minds during teaching math, solving
problem tasks, and using math in practise. In the past there also appeared titles such as Theory of math
teaching, Math methodology, Math pedagogy. For example J. Mikul?ák (1982)
says: "The aim of Math pedagogy is complex examining of a math education
system, all its elements, interrelations, and relations to didactic and non-
didactic environment of the system." Considering the relationship between math and didactics presents M.
Hejný (1990):
"Term - teaching math - consists of two words. The first word expresses the
subject content, the second one an activity which is carried out by a
teacher. Both math and teaching have their own structure, logic, and the
way of thinking. Between the both fields there is a big difference. Math
works with idealized objects, axiomatically accurately with full
argumentation.
Teaching is dealing with people and each effort to axiomatise the structure
of math methodology leads inevitably to reality violating. In math
methodology similarly as in any other real scientific discipline there
exist phenomena, objects, situations, and examples which are typic