Creativity and  Mathematics Education  July 15 - 19, 1999  in Muenster, Germany

About 80 experts in mathematics education from more than 20 countries presented their ideas and experiences and discussed the above questions.
 
 
 

The conference has come to an end. The participants will have returned to their homes by now, the local organizers have finished cleaning up the place of venue, so now there is time to take a look back to those five days when the conference took place.    What was so special about this conference? Well, when going to a conference you would expect to have lectures and posters, a lot to listen to and a lot to read through. But, thinking of fifty people leaning back in their seats and listening to some lecturer talking on creativity would have been a contradiction, wouldn´t it ?  So the idea of this conference was different: It was to overcome this passivity by asking people to prepare their presentations in such a way that the audience takes part actively.  It was no surprise then that the type of presentation that dominated the conference were workshops. Workshops where participants could make and explore materials designed for classroom use: Paper folding, computers, strategy games, maths and arts, etc., each accompagnied by a thorough theoretical framework. Unusual also were mathematical problems presented on posters, or „Challenges“ as we called them. Challenges they were indeed, perhaps not so much for pupils for which they were primarily designed but for the well trained (or shall we say „overtrained“ ?) mathematicians. So fascinated many of them were that instead of accepting solutions they preferred to continue working on them on their way home. Then there were stalls with materials for hands-on experiences, so called „Activity Displays“ on solid geometry in primary grades, or computer software on graph theory, or plastic material for sphere geometry, or ... The idea of active participation was so present that in many of the more traditional lecturetype presentations, too, the audience had the opportunity of trying materials as well.         Photographs by Monika Schwarze The principle of active participation extended to the social events, too, that accompagnied the days of conference. „Make your own salad“ was the motto during the barbecue on the first evening when the newly arrived participants formed groups for preparing food and get to know each other. „Make your way to the watercastles“ : Though all were on a preorganized bus tour, this tour to typical Westphalian places required quite some activity as well as the weather wasn´t typical Westphalian at all. Warm it was, warm indeed.  Muenster has shown itself from its brightest side, not only in terms of sunshine. The conference on „Creativity and Mathematics Education“ that it was host to, seemed a promising start for further international activities on this topic. And there will be further activities, as you will notice when you read through to the end of this document.    Guido Pinkernell  P.S. You might want to read a report on this conference in german, written by Monika Schwarze. For this, click on Ka's Geometriepage: Tagungen, LFB, Kolloquien für Mathematik

 

In the following you will find . . .  Results of the Conference  Survey Proceedings  Survey Program Structure in Muenster  Address of the Conference Secretariat

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Results of the Conference
 

Proceedings

The proceedings (304 pages) were distributed to the participants at the beginning of the conference with the complete papers of almost all contributions. Additional copies were available till the end of 1999 at the conference secretariat.  Now they are sold out. But we have produced an electronic version of those papers which were available in an electronic format, details see Proceedings.

Discussion Groups

 In the discussions on the last day of the conference we concentrated on three aspects:

• Challenges
• Activity Displays
• Next Steps?

More than 25 challenging questions or problems were printed in the proceedings and put on display during the conference. The conference participants were asked to find solutions. Several solutions were discussed. But basically there was the opinion not to discuss or to publish solutions of  challenges. Some participants preferred to continue working on the solutions on their way home. Others claimed that a challenge no longer will be a challenge if the solution already is known. We then discussed what characterizes a "challenge" and what the role of a challenge in mathematics teaching could be. There was a general agreement that the value of a challenge not only is a question of the content and the question itself but also of the abilities of the person who is confronted with this problem or question. "Challenges" in mathematics education seem to stimulate or to promote creativity.
 

Activity Displays
(Presider: John Mason)

The presentation of  posters was more than a written text only. There were posters fascinating all our senses, provoking curiosity already by a distant view, encouraging visitors to play, to manipulate, to discover, ... In the discussion we pointed out the necessity of the process of "doing" something. This is a process of "seeding", similar as in the workshops. Posters should be developed by the children in the classroom. Investing energy and social forces are important.
 

IPC Panel:  Successful Steps into a Creative Future
Panelists: Noel Geoghegan, Wilfried Herget, William Higginson, Frantisek Kurina, John Mason, Hartwig Meissner, Shangzhi Wang

There was a broad consensus about the importance of this conference.  Creativity seems to be something incompatible with mathematics teaching. The traditional style of working in the mathematics classroom seems not to allow many creative ideas. Thus creativity is far too less developed in the classroom teaching. It is a tremendous problem for the whole community of mathematics educators when we realize how the enthusiasm of young children for mathematics disappears step by step when they get older. To help developing creative ideas a discussion started what "creativity" might mean. After getting a long list of necessary "indicators" (of abilities, social aspects and "human" aspects) the discussion ended with the agreement not to continue into that direction: "Creativity" is a highly complex phenomenon. We should not provoke the impression that creativity can be described as a  long list of isolated items nor that such a list may help to identify or to develop creative ideas.

How to continue? Hartwig Meissner (Muenster, Germany) and Hathleen Heid  (Pensylvania State University, USA) will be the Chief Organizers of the Topic Study Group TSG 16 at ICME 9 in JAPAN (July 30 -Aug. 6, 2000) with the title "Creativity in Mathematics Education and the Education of Gifted Students". William Higginson (Queen's University Kingston, Canada) will be one of the Associate Organizers for this TSG 16. We will have two  90 minutes sessions on Tue (Aug 1) and Wed (Aug 2). One session shall concentrate on "Creativity". To prepare that session Jerry Goldin, John Mason, Bill Higginson, Noel Geoghegan and Hartwig Meissner met at one night during the Muenster conference to develop first suggestions and they presented their ideas to the Muenster participants. The suggestion is to have at the ICME session a well prepared state-of-the-art review on the following main aspects of creativity:

• Creative Environments (includes also theoretical, psychological, social, ...  components)
• "Creative" Mathematics (what does that mean, projects, examples, problems, ...)
• The Impact of Teachers
• The Needs of the Learners

All participants from the Muenster conference, all readers of these lines and all other interested colleagues are encouraged to give further suggestions and/or to send short papers to the Organizers of TSG 16 to describe activities they might be able to contribute to the two ICME sessions.
 

Addendum from March 2001:  ICME was very successful. New activities are planned. There was a general agreement that also after ICME 9 there should be further conferences on creativity and mathematics education. It was suggested that in the year 2001 such a conference should be organized in North America. For more details see http://wwwmath.uni-muenster.de/math/inst/didaktik/u/meissne/WWW/TSG16c.htm

 
 

Survey Proceedings

We list the table of contents of the complete proceedings, but sorry, they are sold out. Thus we have produced an electronic version of all those papers which were available electronically. These papers are printed in red. Just click on the part you are interested in and you will get this part as a WORD document. Please select then from this WORD document the titles you are interested in.

Table of Contents of the Conference Proceedings
 

I. INTRODUCTION	page
Organisation of the Conference	2
Aims of the Conference	3
Preface	11
Welcome greetings from the Lord Mayor	15
rußwort von der Bezirksregierung Münster                                                                                                                                                                  .	16

 

II. CONFERENCE   PAPERS   IN   ENGLISH
Part I, please click here (You will get then all titles in red as a WORD document)
1. Workshops	page
Introduction	18
Ford, Marilyn Sue/Usnick, Virginia: Problem solving as a creative activity	20
Herget, Wilfried: Good estimating and hardly calculating –  one problem, but many solutions	25
Higginson, William/Colgan, Lynda: The joy of X: Helping prospective teachers see the creative potential of mathematics: Contextual remarks for a workshop	28
Kokol-Voljc, Vlasta/Sheffield, Linda Jensen: Creating geometry on  the TI-92	32
Mason, John: Student-constructed-examples	38
Meissner, Hartwig: Creative use of calculators	39
Reitberger, Wolfgang: Stimulation of creative thinking by solving with learning materials – priority: instruction in small groups	45
Sheffield, Linda Jensen: When the problem is solved the creativity has just begun	51
Teeguarden, Janet E.: Math-art in the elementary classroom	57
Usnick, Virginia/Ford, Marilyn Sue: Connecting mathematics and  art	63
Wollring, Bernd: Examples and working environments for the geometry of paper folding in the primary grades	68

 

Part II, please click here  (You will get then all titles in red as a WORD document)
2. Project Presentations	page
Introduction	74
Bankov, Kiril: Extracurricular work & mathematics competitions	75
Colgan, Lynda: (Re)Learning & teaching through the eyes of a child: Reflections on a pre-service elementary mathematics education course	77
Gelfman, Emanuila/Demidova, Ljudmila: The role of school-texts in developing students’ creative initiative	82
Geoghegan, Noel/Reynolds, Anne/Lillard, Eileen: A grade-two teacher’s incorporation of children’s creativity to effectuate problem-centered learning with constructivist and systems theories in mathematics education	89
Peter-Koop, Andrea: Open real-world problems in the elementary mathematics classroom	95
Schindler, Monika/Simeonov, Emil: Early mathematical education – A course with 4 to 6 year-olds	101

 

Part III, please click here  (You will get then all titles in red as a WORD document)
3.  Reports on Experiences	page
Introduction	107
Caglar, Mehmet/Dogancioglu, Ülkü/Ersoy, Yasar: Pupils‘ math journal: Dancing with Numbers	108
Copes, Larry/Lewis, Joan: Creating meaning about discrete mathematics through investigations	114
Fan Liming: Multimedia technology, mathematics problem solving and the development of students‘ creativity	119
Garmann, Rosemary: Two measurement projects	125
Hospesova, Alena: Creativity and classroom communication	129
Kurina, Frantisek: Geometry and creativity	133
Löffler, Rainer: A drawing template for mathematics teaching	137
Mueller-Philipp, Susanne: Daddy Cube and his kids	138
Nolte, Marianne: Are elementary school pupils already able toperform creatively substantial bricks of knowledge? – A report on first striking findings from working with smallergroups of highly gifted and motivated elementary school pupils aged 8-10	142
Oleinik, Tatyana/Volkova, Oksana: Development of creative activity using technologies	146
Safuanov, Ildar: Mathematical fights as the way of fostering mathematical talents	150
Schumann, Heinz: Computer aided solution of open ended problems in spatial geometry	154
Semadeni, Zbigniew: Special problems for willing children	155
Ticha, Marie: On students’ creativity in grasping situations	159
Vasarhelyi, Eva: Combination of traditional and computer based tools as a strategy for problem solving	163
Vinogradova, Natalya V.: The way to develop school children’s creative abilities through the probability problems	167

 

Part IV, please click here  (You will get then all titles in red as a WORD document)
4. Activity Displays	page
Introduction	170
Kajikawa, Yuji/Uehara, Shimon: Teaching by the level of achievement on matrices-calculation	171
Lenart, Istvan: Experiments in comparative geometry on plane and sphere	173
Lewis, Joan/Copes, Larry: Learning discrete mathematics through investigations with the GrafPad software	175
Meissner, Hartwig: Invent your own solids	177
Perkkilä, Päivi : A didactic analysis of two series of mathematics books at the first and the second grade of the comprehensive school	179
Teeguarden, Janet E.: Math-art activities	181
5. Challenges
Introduction	183
Bankov, Kiril: Points on a circle	184
Herget, Wilfried: Creating numbers	184
Higginson, William: Ratios	185
Kurina, Frantisek: Ten challenges	185
Mason, John: Four challenges	187
Meissner, Hartwig: Eight challenges	188
Chumak, Alexandr: Symbolism and algorithmization for the teaching of fundamentals of geometry	191
Hospesova, Alena: Classroom interaction, teachers’ education	192
Kurina, Frantisek: Creativity – obstacles and possibilities	192
6.  Exhibitions
Introduction	194
Caglar, Mehmet/Dogancioglu, Ülkü/Ersoy, Yasar: School math  journal: Dancing with numbers	195
König, Gerhard: Databases: A gateway to literature in mathematics education research – the case mathematical creativity	197
Meissner, Hartwig: Mathematics in our environment (video display)	199
Meissner, Hartwig: Mathematics from the storyteller	201

 

III. TAGUNGSBEITRÄGE   IN   DEUTSCH
1. Workshops	page
Vorbemerkung	203
Herget, Wilfried: Gut geschätzt und kaum gerechnet – eine Frage, viele Wege, viele Antworten	205
Kokol-Voljc, Vlasta/Sheffield, Linda Jensen: Geometrie mit TI-92 betreiben	208
Meißner, Hartwig: Kreativer Taschenrechner-Einsatz	214
Reitberger, Wolfgang: Anregung zum kreativen Denken durch Lern mittel zum Lösen von Problemen – Schwerpunkt Unterricht in kleinen Gruppen	220
Strecker, Christian: Das kreative Potential von Schülerfehlern erkennen und nutzen	226
Wollring, Bernd: Beispiele und Arbeitsumgebungen zur Papierfaltgeometrie im mathematischen Anfangsunterricht	229
2. Projekt-Präsentationen
Vorbemerkung	235
König-Wienand, Anette: Einmaleins einmal anders – Darstellung und Reflexion einer handlungs- und problemorientierten Unterrichtskonzeption zur Erforschung der 100 Einmaleinsaufgaben auf eigenen Wegen	236
Verboom, Lilo: Lebendiges Rechnen mit ANNA-Zahlen, PAPA-Zahlen und anderen Zahlenmustern	237
3. Erfahrungsberichte
Vorbemerkung	243
Köhler, Hartmut: Kreativitätsförderung – allererst eine Frage der Lehrereinstellung	244
Löffler, Rainer: Zeichenschablone für den Mathematikunterricht	248
Müller-Philipp, Susanne: Papa Würfel und seine Kinder	254
Nolte, Marianne: Ist schon Grundschülern kreatives Produzieren von mathematisch substantiellen Wissensbausteinen möglich? – Ein Bericht über erste Erkenntnisse aus der Arbeit mit Kleingruppen von besonders begabten und motivierten 8 bis 10-jährigen Grundschulkindern	258
Riede, Heidrun: Begabtenförderung zugunsten der Schwächeren	262
Schumann, Heinz: Computerunterstütztes Lösen offener raumgeometrischer Aufgaben	266
Vasarhelyi, Eva: Paralleler Einsatz von traditionellen Anschauungsmitteln und Computeranimationen als Strategie für Problemlösen	270
4. Aktiv-Poster
Vorbemerkung	274
Lenart, Istvan: Vergleichende Experimente in der Geometrie in der Ebene und auf der Kugel	275
Löffler, Rainer: Zeichenschablone für Mathematik	277
Meißner, Hartwig: Geometrische Körper selbst erfinden	279
5. Knobelaufgaben
Vorbemerkung	281
Herget, Wilfried: Zahlen erzeugen	282
Kurina, Frantisek: Zehn Knobelaufgaben	282
Mason, John: Vier Knobelaufgaben	284
Meißner, Hartwig: Acht Knobelaufgaben	286
6. Ausstellungen
Vorbemerkung	289
König, Gerhard: Nutzung elektronischer Fachinformation in der Mathematikdidaktik	290
Meißner, Hartwig: Mathematik in unserer Umgebung (Video)	292
Meißner, Hartwig: Mathematik vom Märchenerzähler	294
IV. SUMMARY
Results of the Conference	296
Addresses of the Authors	298
List of Participants	303

 
 

Survey Program Structure in Muenster

                        Thursday, July 15
14:30                Opening Ceremony
16:00 - 17:30    Project Presentations and Experience Reports
19:00 - 23:00    Get-Together-Party

             Friday, July 16
09:00 - 12:30    Workshops, Project Presentations and Experience Reports
14:00 - 15:00    Workshops, Project Presentations and Experience Reports
15:20 - 15:50    Exhibitions + Challenges + Activity Displays (the authors will be present)
16:00 - 17:00    Workshops, Project Presentations and Experience Reports
18:00                Reception by the Lord Mayor of the City of Muenster

             Saturday, July 17
09:00 - 12:30    Workshops, Project Presentations and Experience Reports
14:00 - 16:30    Workshops, Project Presentations and Experience Reports
16:50 - 17:20    Exhibitions + Challenges + Activity Displays (the authors will be present)
17:30 - 18:30    Happy Hour

             Sunday, July 18
09:00 - 12:00   Workshops, Project Presentations and Experience Reports
13:30 - 23:00   Excursion to 2 Watercastles, Tecklenburg, Dinner in a Westphalian cottage

             Monday, July 19
09:00 - 10:00    Panel upon the Challenges
10:10 - 11:10    Discussion Group Activity Displays
11:30 - 12:30    IPC Panel: Successful Steps into a Creative Future
12:30 - 12:45    Closing Ceremony
 
 

Address of the Conference Secretariat

(Please use e-mail or fax if possible)
email: meissne@uni-muenster.de     or     cfische@math.uni-muenster.de
Fax: +49 251 83 32718     or     +49 251 83 38350
Postal mail:
Dr. Hartwig Meissner - Universitaet - Fb. Mathematik - Einsteinstr. 62 - D-48149 Muenster - Germany