ebook ebooks e-book e-books downloaden bei MyEbooks.ch downloaden

Challenging Mathematics In and Beyond the Classroom The 16th ICMI Study

:	Peter J. Taylor, Edward J. Barbeau
:	Edward J. Barbeau, Peter J. Taylor
:	Challenging Mathematics In and Beyond the Classroom The 16th ICMI Study
:	Springer-Verlag
:	9780387096032
:	1
:	CHF 132.60
:

:	Schulpädagogik, Didaktik, Methodik
:	English

:	337
:	Wasserzeichen/DRM
:	PC/MAC/eReader/Tablet
:	PDF

In the mid 1980s, the International Commission on Mathematical Instruction (ICMI) inaugurated a series of studies in mathematics education by comm- sioning one on the influence of technology and informatics on mathematics and its teaching. These studies are designed to thoroughly explore topics of c- temporary interest, by gathering together a group of experts who prepare a Study Volume that provides a considered assessment of the current state and a guide to further developments. Studies have embraced a range of issues, some central, such as the teaching of algebra, some closely related, such as the impact of history and psychology, and some looking at mathematics education from a particular perspective, such as cultural differences between East and West. These studies have been commissioned at the rate of about one per year. Once the ICMI Executive decides on the topic, one or two chairs are selected and then, in consultation with them, an International Program Committee (IPC) of about 12 experts is formed. The IPC then meets and prepares a Discussion Document that sets forth the issues and invites interested parties to submit papers. These papers are the basis for invitations to a Study Conference, at which the various dimensions of the topic are explored and a book, the Study Volume, is sketched out. The book is then put together in collaboration, mainly using electronic communication. The entire process typically takes about six years.

	Preface	6
	References	7
	School years	7
	Contents	9
	The Authors	11
	Introduction	14
	0.1 Challenging: a human activity	14
	0.2 Challenges and education	16
	0.3 Debilitating and enabling challenges	18
	0.4 What is a challenge?	18
	References	22
	Challenging Problems: Mathematical Contents and Sources	23
	1.1 Introduction	23
	1.2 Challenges within the regular classroom regime	24
	1.2.1 Challenge from observation	26
	1.2.2 Challenge from a textbook problem	27
	1.2.3 Increasing fluency with fractions	28
	1.2.4 Engaging with algebra	29
	1.2.5 Pedagogies to help development	31
	1.2.6 Combinatorics	31
	1.2.7 Geometry	32
	1.2.8 Other settings for school challenges	34
	1.3 Challenges in popular culture	38
	1.3.1 Another schoolyard problem	40
	1.3.2 A Russian problem	40
	1.3.3 The Microsoft problem	41
	1.3.4 A problem from children s literature	42
	1.3.5 A probabilistic element	43
	1.3.6 Concluding comments	43
	1.4 Challenges from inclusive and other teacher-supported contests	43
	1.4.1 Diophantine equations	44
	1.4.2 Pigeonhole principle	45
	1.4.3 Discrete optimization and graph theory	46
	1.4.4 Cases	47
	1.4.5 Proof by contradiction	47
	1.4.6 Enumeration	48
	1.4.7 Invariance	49
	1.4.8 Inverse thinking	49
	1.4.9 Coloring problems	50
	1.4.10 Concluding comments	51
	1.5 Challenges from Olympiad contests: Students independent of classroom teacher	51
	1.6 Content and context	57
	1.6.1 Three groups of requirements for assignments	57
	1.6.2 Challenges in classrooms: identifying patterns in their appearance	59
	1.6.3 The psychology of the art of writing problems as a research problem	60
	1.6.4 Using different areas of mathematics in different contexts	60
	1.6.5 The structure of problems and the form of their presentation as a means of responding to context and transforming it	61
	1.6.6 The issue of mathematics teacher education	61
	1.6.7 Conclusion	62
	References	62
	Challenges Beyond the Classroom-Sources and Organizational Issues	64
	2.1 Introduction	64
	2.1.2 Working as individuals and in teams	66
	2.1.2 Involvement of teachers	66
	2.2 Environments for challenging mathematics	66
	2.2.1 Mathematics competitions	68
	2.2.1.1 Inclusive competitions	70
	2.2.1.2 Different types of competition	71
	2.2.1.3 Some general comments	74
	2.2.2 Mathematics journals, books and other published materials (including Internet)	75
	2.2.3 Research-like activities, conferences, mathematics festivals	77
	2.2.3.1 Jugend Forscht (youth quests), Germany and Switzerland	78
	2.2.3.2 Research Science Institute (RSI), USA	78
	2.2.3.3 High School Students Institute for Mathematics and Informatics, Bulgaria	79
	2.2.3.4 Mathematics festivals, Iran	80
	2.2.4 Mathematical exhibitions	80
	2.2.4.1 Historical background	81
	2.2.4.2 Examples of exhibitions	83
	2.2.5 Mathematics houses	86
	2.2.6 Mathematics lectures	87
	2.2.7 Mentoring mathematical minds	88
	2.2.8 Mathematics camps, summer schools	88
	2.2.8.1 International Mathematics Tournament of Towns summer camp	89
	2.2.8.2 International mathematics kangaroo summer camps	89
	2.2.8.3 Summer School Festival UM+	89
	2.2.8.4 The Canadian seminar	89
	2.2.8.5 Isfahan summer camps	90
	2.2.8.6 The Institute for Advanced Study in USA	90
	2.2.9 Correspondence programs	90
	2.2.10 Web sites	93
	2.2.11 Public lectures, columns in newspapers, magazines, movies, books, general purpose journals	93
	2.2.12 Math days, open houses, promotional events for school students at universities	94
	2.2.13 Mathematics fairs	94
	2.2.13.1 Canadian Andy Liu model	95
	2.2.13.2 A mathematical house for younger children (Years 1 to 5)	95
	2.2.13.3 Mathematics day at universities	95
	2.2.13.4 Long night of mathematics at the high school, Karlsruhe	96
	2.2.13.5 India	96
	2.2.14 Mathematical quizzes	96
	2.2.14.1 The mathematical organization Archimedes	97
	2.3 Concluding remarks: challenging infrastructure-a powerful motivational factor	97
	2.4 Appendix	98
	2.4.1 Iran: what is a Mathematics House?	99
	2.4.1.1 History	99
	2.4.1.2 Audiences	100
	2.4.1.3 Activities	100
	2.4.1.4 Activities for high school students	101
	2.4.1.5 Activities for university students	101
	2.4.1.6 Activities for teachers	101
	2.4.1.7 Other activities	102
	2.4.1.8 Library	102
	2.4.1.9 Laboratories	102
	2.4.1.10 Achievements	102
	2.4.2 Serbia: the mathematics organization Archimedes	103
	2.4.2.1 Activities	103
	2.4.2.2 Lessons learned	104