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Some examples for research in mathematics education from own experience. Bernd Zimmermann Friedrich-Schiller Yliopisto Jena Turun Yliopisto 27.11.2003. Steps of research. Idea/Goal /question Framework Design Outcome /Results Discussion Outlook.

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some examples for research in mathematics education from own experience

Some examples for research in mathematics education from own experience

Bernd Zimmermann

Friedrich-Schiller Yliopisto Jena

Turun Yliopisto 27.11.2003

steps of research
Steps of research
  • Idea/Goal/question
  • Framework
  • Design
  • Outcome/Results
  • Discussion
  • Outlook

Prof. Bernd Zimmermann Turun Yliopisto 2003

analyzing problem solving processes bz diss 1977
Analyzing problem solving processes (BZ Diss. 1977)
  • Idea/goal: Lüer/Dörner; searching for a basic rhythm of thinking connected with problems from incidence geometry
  • Design: exploratory study; developing a complex category-system, describing activities with respect to 12 activities/aspects, sequential analysis
  • Outcome: also a basic rhythm, two types of problem solvers, advantage and disadvantage of perception

Prof. Bernd Zimmermann Turun Yliopisto 2003

trends in german mathematics education
Trends in German Mathematics Education
  • Idea/goal: Constituting sound basis for research (in m.e.)
  • Design: development of categories constituting a trend: general goals; view on math, learning and teaching of maths, on research. Analysis of literature.
  • Outcome: elementarization, operatoric approach; genetic; “Bourbakism”; application; problem-oriented; computer oriented: Framework for development of questionnaire for teachers

Prof. Bernd Zimmermann Turun Yliopisto 2003

beliefs of students and teachers
Beliefs of students and teachers
  • Idea/goal: Getting information about initial and boundary conditions of (math) instruction
  • Design: development of questionnaires for pupils and teachers by using trend analysis and further literature.
  • Outcome: Teachers: different clusters (e. g. Bourbaki-c.; problem.-or.-c., conventional c.). Pupils: often correspondence to attitudes of their teachers; explanations of teachers are most important, also for gender-differences.

Prof. Bernd Zimmermann Turun Yliopisto 2003

history of mathematical heuristics
History of mathematical heuristics
  • Idea/goal: What kind of thinking methods (heuristics) proved to be most successful within 5000 years? What kind of typical difficulties occurred across time? (Invariants)
  • Design: Analysis of relevant (original) literature with respect to thinking methods and their outcome.
  • Outcome: Heuristics: successive approximation, working backwards, analogy, atomistic methods. Use/application first implicitly; later on explicitly.

Prof. Bernd Zimmermann Turun Yliopisto 2003

changing patterns in the history of mathematical beliefs
Changing patterns in the history of mathematical beliefs
  • Idea/goal: (1) Searching for motivating and stimulating activities involved in creating new maths. (2) To what extent these activities were involved in local (mathematical) beliefs?
  • Design: Analysis of literature. Rating the amount of importance.
  • Outcome: Eight important activities. Different profiles of beliefs at different times and for different cultures, supported by a “web-representation”.

Prof. Bernd Zimmermann Turun Yliopisto 2003

studies of primary school children who are potentially mathematically gifted k pnick 1997
Studies of primary school children, who are potentially mathematically gifted (Käpnick 1997)
  • Idea/goal: (1) Development of a conceptual system for mathematically gifted pupils. (2) To search for different profiles of mathematically giftedness
  • Design: Analysis of literature. Empirical study by using cluster analysis.
  • Outcome: (1) Conceptual system for giftedness (2) Test for identification (3) Different profiles of mathematically giftedness.

Prof. Bernd Zimmermann Turun Yliopisto 2003

slide9
Different profiles of giftedness in mathematics – attempts to improve differentiation with respect to styles of thinking (Rehlich 1995)
  • Idea/goal: To get more information about different profiles of mathematical giftedness by use of a computerprogram
  • Design: (1) conceptual framework (2) program (3) subjects explore problem modeled by computer
  • Outcome: Different profiles of mathematical giftedness.

Prof. Bernd Zimmermann Turun Yliopisto 2003

evaluation of the quality of mathematical problem solving processes by computer support rehlich
Evaluation of the quality of mathematical problem solving processes by computer support (Rehlich)
  • Idea/goal: Evaluate problem solving processes by support of a computer program
  • Design: (1) conceptual framework (2) program (ready) (3) select appropriate problems
  • Outcome: standardized process analysis.

Prof. Bernd Zimmermann Turun Yliopisto 2003

analyzing turning points and changes in mathematical problem solving processes heinrich 2003
Analyzing turning points and changes in mathematical problem solving processes (Heinrich 2003)
  • Idea/goal: To characterize situations of change in problem solving situations
  • Design: (1) Development of a sound theoretical framework (2) Selection of a representative problems (3) Problem solving sessions in small groups (4) Categorize, classify and analyze different situations of change
  • Outcome: Classification of situations of change; possible use for instruction

Prof. Bernd Zimmermann Turun Yliopisto 2003

slide12
Teacher students sensitivity for the complexity (sfc) of problem oriented (mathematics) instruction(Fritzlar 2003)
  • Idea/goal: Constructing an instrument to measure students sfc.
  • Design:. (1) Development of a sound theoretical framework concerning sensitivity for complexity of p.o.m.i. (2) Selection of a representative problem and gaining experience/material by teaching 50 classes (3) Development of a computer program (4) Development of a category system for sfc. (5) Analyzing students ps behavior when using this computer scenario
  • Outcome: (1) Programm (2) Category system (3) Determination of the sfc of a sample of 20 teacher students.

Prof. Bernd Zimmermann Turun Yliopisto 2003

slide13

Ordering and multimodality in thinking processes of mathematically gifted pupils: sequential and topological properties of cognitive microstates (Seidel 2001)

  • Idea/goal: To get brain-physiological evidence for giftedness related to (1) effective entropy-reduction and (2) flexibility in changing the mode of representation
  • Design: (1) sample of gifted students (2) set of problems (3)analyzing problemsolving processes by using EEG and appropriate software for evaluation
  • Outcome: Support of the aforementioned hypothesis.

Prof. Bernd Zimmermann Turun Yliopisto 2003

future research e g analyzing problem solving processes in mathematically gifted pupils
Future research: e.g. analyzing problem solving processes in (mathematically) gifted pupils?
  • Idea/goal: Analyze problem solving behavior of gifted students
  • Design: ??
  • Outcome: ??
  • Your suggestions?

Prof. Bernd Zimmermann Turun Yliopisto 2003