16-May-2012  (HM)

Homepage Hartwig Meissner                             

 



   









...3...		 Prof. Dr. Hartwig Meissner 
Westfaelische Wilhelms-Universitaet 
Einsteinstr. 62 
D-48149 Muenster (Germany) 

Tel.: +49 (0251) 32 43 81
Fax: +49 (0251) 83 38350
E-mail: meissne@uni-muenster.de 

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There was a last update for the pages below in Nov. 2007

Vita

Research

Special research field "Learning and Understanding Mathematics": How do we learn mathematics, how can we help the learner, which are the obstacles? Which will be the impact of learning software, which will be the role of calculators and computers? What does "understanding" mean, which mathematics for whom and why, mathematics in your environment, mathematics in the ivory tower, creativity and mathematics education, consequences for curriculae and teacher training, consequences for the classroom teaching, developing and evaluating of new teaching units, ... . You will get more information upon specific topics by clicking on research fields and interest areas. Publications see for example

Teacher Education

Preservice for teachers in primary schools and junior high schools (age of children: 6-16 years) in mathematics and didactics of mathematics, including practical exercises or investigations (with evaluation) in schools. Special seminars and projects to combine theory with practice. Publications see for example

International Cooperation

International Memberships

Research Fields and Interest Areas, Part I

          In this Part I the list of topics basically was prepared till about 1995. After that time only a few small updates were added. All references in Part I are in English, but in the German homepage version you will find additional references written in German.
          Since the topics mentioned here are not that much isolated to each other as the numeration system seems to indicate we also will add a Part II below with a more open structure. 
  1. Calculators in Mathematics Education (TIM Projects). Numerous empirical studies about the use of calculators in primary schools and junior highschools. Summary of the results in about 30 TIM-Reports (in German). See also Meissner, H.: Examples How to Use the Calculator to Become Independent from It. In: "Proceedings of the International Symposium in Osaka Kyoiku University", Osaka Japan 1986 (translated also into Japanese and Chinese) and Meissner, H./Fraser, R./Mohyla, J.(Eds.): The Role of Technology - Theme Group 3: Report. Publications Unit South Australian College of Advanced Education 1986
  2. Computers and Problem Solving, advantages by an algorithmic thinking? E. g. see Kienel, E.: Datenverarbeitung und die algorithmische Methode im Mathematikunterricht. Dissertation Muenster 1977
  3. Computers in Mathematics Education. The impact of computers on the traditional curriculum. Which will be mathematics curriculum for the next century? See also Meissner, H.: The Art to Compute. In: Journal of the Cultural History of Mathematics, Vol. 3-1, p. 21-27, Kurofune Press Japan 1993
  4. Software to Learn Mathematics. Analysis and evaluation schemes. E. g. see Meissner, H.: Software for Learning Mathematics. In: Proceedings of the International Conference on Mathematics Education, History of Mathematics and Cultural History of Mathematics & Informatics. Beijing China 1998. There  is a separate Webpage (in German) summarizing our results from testing software to learn mathematics.
  5. Guess and Test. Which is the role of guess and test in daily life situations? Are there consequences for the learning of mathematics? E. g. see Meissner, H.: How Do Students Proceed in Problem Solving. In: "Proceedings of the Sixth International Conference for the Psychology of Mathematical Education", p. 80-84, Antwerpen Belgien 1982
  6. One-Way-Principle. This is a method how to use calculators or computers as a tool to develop and test a thesis upon possible solutions of a problem. E. g. see Meissner, H.: Problem Solving with the One Way Principle. In: "Proceedings of the Third International Conference for the Psychology of Mathematics Education", p. 157-159, Warwick England 1979
  7. What does "Understanding" mean? Following the ideas from Richard Skemp we distiguish "instrumental understanding", relational understanding" and "communicable understanding". More details see e. g. Meissner, H.: How to prove relational understanding. In: "Proceedings of the Seventh International Conference for the Psychology of Mathematics Education", p. 76-81, Jerusalem Israel 1983
  8. Early Number Concept. Investigations in Kindergartens. Analysis of developments, impact of calculators in primary schools. E. g. see Meissner, H.: Kindergartner's Conception of Numbers. In: "Proceedings of the 11th International Conference for the Psychology of Mathematics Education", Vol. II, p. 361-367, Montreal Canada 1987. See also Lange, B.: Zahlbegriff und Zahlgefühl. Lit-Verlag, Münster 1984 (Dissertation)
  9. We Build a Village. Teaching unit for geometry in primary schools. E. g. see Meissner, H./Mueller-Philipp, S.: Geometry: We build a village. In: "The Student Confronted by Mathematics". Proceedings of ICSIMT 44, p. 241-252 (Ed. A.I. Weinzweig), University of Illinois, Chicago 1992
  10. Mathematics in Your Environment. Teaching units for primary schools, consequences for teacher preservice courses. E. g. see Meissner, H.: Teacher Training and Research in Mathematics Education. In: "Proceedings of the Third Five Countries Conference on Mathematics Education", p. 18-28, Beijing China 1990
  11. Teaching Fractions. An international study about different approaches how to teach fractions. See Schrage, K. P.: Bruchrechnung international - Eine Bestandsaufnahme in vier Ländern. Dissertation Münster 1988
  12. Teaching Percentages. Teaching unit using the percentage key of simple calculators and the One-Way-Principle to develop a percentage feeling by guess-and-test procedures. E. g. see Meissner, H.: The Effect of the Early Use of Calculators on the Acquisition of Number Concepts and Skills. In: "Proceedings of the Fourth International Congress on Mathematical Education", p. 605-606, Birkhäuser Boston 1983
  13. Pre-Algebra. Cognitive processes in learning and understanding algebra. Examples to bridge the gap between instrumental and relational understanding. See Sauer, M.: "Algebra können" - was heißt das. In: Beiträge zum Mathematikunterricht 1997. Verlag Franzbecker, Hildesheim 1997
  14. Teaching Functions. Using the computer and the One-Way-Principle to develop a function feeling between "term" and "graph" without the use of "tables". See Mueller-Philipp, S.: Der Funktionsbegriff im Mathematikunterricht. Waxmann Münster/New York 1994 (Dissertation) and Meissner, H.: Teaching Functions. In: "Proceedings of the Seventeenth International Conference for the Psychology of Mathematics Education", Vol. II, p. 89-96, Tsukuba Japan 1993
  15. Teacher Students as Researchers to conduct empirical research studies for the benefit of both, of teachers and researchers. See Meissner, H.: Teacher Students as Researchers. In: "European Research Conference on the Psychology of Mathematics Education", p. 50-53, Osnabrück 1995
  16. Videos and Teacher Training. Taping teaching lessons, interviews or producing video spots on topic themes. E. g. see Meissner, H.: Geometry: Learning by Doing. In: "Proceedings of SEMT - International Symposium on Elementary Mathematics Teaching", p. 24-27, Prague Czech Republic 1995
  17. Creativity in Mathematics Education. How to promote the creativity of our children? How to further our gifted students? How to stimulate our teachers? How to enrich mathematics education with challenging activities? E. g. see Meissner, H., Grassmann, M., and Mueller-Phillip, S. (Eds.): Proceedings of the International Conference "Creativity and Mathematics Education". There  also is a separate Webpage summarizing up to date activities in the field of creativity and the education of gifted students in mathematics education.

Research Fields and Interest Areas, Part II

          We will not continue to describe our research fields and interest areas similar to a structure given in Part I. Instead we concentrate only on a few clusters. We hope this "open approach" will allow the reader more individually to select the wanted information. There also will be a shift from the German language to the English language. We therefore will have only one big list of references, for technical reasons split up into the three successive parts References 1 (till 1992), References 2 (1992 - 2003), and References 3 (starting 2002). 
  1. Mental Processes. Analyzing mental or cognitive aspects of learning mathematics we must be aware that we only can observe or assess or interpret external, observable performances like gestures, oral comments, writings, discussions, interactions with a computer or with the teacher or with peers or other activities, etc. We must interpret performances because we cannot see or evaluate directly the related mental activities, processes, conceptual frames, etc. To distinguish more consciously the external representations or performances from the "related" internal representations or internal mental processes we will use for the latter the German word Vorstellungen. A Vorstellung is an individual concept image, it is the personal internal mental repre­sen­tation of objects, of processes, of relations and functions, etc. A Vorstellung is part of the cognitive structure of the individual. A Vorstellung in this sense is simi­lar to a cognitive net, a frame, a script or a micro world. Each learner has his/her own individual Vorstel­lungen. – An important goal in mathematics education is to develop powerful mathematical Vorstellungen. In our research we concentrated on analyzing the development of spatial abilities, number sense, paper & pencil skills, proportionality, percentage feeling, and concept of functions. And we also analyzed mental processes when working with calculators or computers. How develop these Vorstellungen, how do they change? Which are the processes in the head of the learner? What happens consciously, what unconsciously? For more details see References 3. 
  2. Teacher Pre- and Inservice. An important aspect is to combine the theoretical knowledge with practical experiences. Preservice and inservice teachers became members of our research projects for investigations in the class room. For details and examples we refer to the three lists of References (see projects JUMBO, DORF, TIM, Percentages, …).
  3. Creativity. Young children are very creative. Getting older they lose their creativity, why? We argue we need more creativity in mathematics education and organized in 1999 in Muenster the first International Congress on Creativity in Mathematics Education. Meanwhile many colleagues got interested, we refer to our specific web page Creativity.
  4. Calculators and Computers. The first German school book already was antiquated when it appeared (Meißner, H.: Datenverarbeitung und Informatik, Ehrenwirth Verlag KG München 1971). And since then the development of new mathematics curricula dramatically runs behind the development of new technologies. In our investigations we concentrated on the mental processes when the learners use these technologies. Especially we observed (conscious or unconscious) guess and test activities and we developed a specific teaching method (One-Way-Principle) to use calculators or computers. For more details see the three lists of References and  two web pages on calculator projects: TIM-Projects (in Muenster) and International Investigations. 
  5. Arithmetic in Primary Schools. Using calculators or computers in upper grades is quite usual, but calculators in primary grades? Here in most countries the use of calculators just is forbidden and we still teach paper & pencil algorithms as if there would no calculators exist. We waste more than 100 hours of class room lessons to teach skills which will not be used any longer after leaving the school. To discuss this anachronism we refer to the Internet-Forum and to some papers in the list of  References 3.

References

          Now there is only one single List of References, for technical reasons split up into the three successive parts References 1 (till 1992), References 2 (1992 - 2003), and References 3 (starting 2002). Most of the papers since about 1992 are available electronically, just klick in the appropriate list of references.    

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