1 / 14

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. Idea/Goal /question Framework Design Outcome /Results Discussion Outlook.

Télécharger la présentation

Some examples for research in mathematics education from own experience

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Some examples for research in mathematics education from own experience Bernd Zimmermann Friedrich-Schiller Yliopisto Jena Turun Yliopisto 27.11.2003

  2. Steps of research • Idea/Goal/question • Framework • Design • Outcome/Results • Discussion • Outlook Prof. Bernd Zimmermann Turun Yliopisto 2003

  3. 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

  4. 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

  5. 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

  6. 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

  7. 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

  8. 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

  9. 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

  10. 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

  11. 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

  12. 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

  13. 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

  14. 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

More Related