Modelling and Applications in Mathematics Education: The 14th ICMI Study

ISBN-13: 9781489992499 / Angielski / Miękka / 2014 / 523 str.

Peter L Galbraith;Hans-Wolfgang Henn;Mogens Niss

Opis

Among the themes that have been central to mathematics education dur- ing the last 30 years are those of mathematical modelling and applications of mathematics to extra-mathematical fields. More generally we refer to these as relations between mathematics and the extra-mathematical world (some- times also called the -real world-) or preferably, according to Henry PoUak, the -rest of the world-. That applications and modelling have been important themes in mathematics education can be inferred from the wealth of litera- ture on these topics, including material generated from a multitude of na- tional and international conferences. In particular let us mention firstly the ICMEs (the International Congresses on Mathematical Education), with their regular working or topic groups and lectures on applications and modelling; and secondly the series of ICTMAs (the International Conferences on the Teaching of Mathematical Modelling and Applications) which have been held biennially since 1983. Their Proceedings and Survey Lectures, have addressed the state-of-the-art at the relevant time, and contain many exam- ples, studies, conceptual contributions and resources involving relations between the real world and mathematics, for all levels of the educational system. In curricula and textbooks we find today many more references to real world phenomena and problems than, say, twenty years ago.

Spis treści

Plenaries.- Less Chalk, Less Words, Less Symbols ... More Objects, More Context, More Actions.- What’s all the Fuss about Competencies?.- A Theory of Mathematical Modelling in Technological Settings.- What Knowledge Do Teachers Need for Teaching Mathematics Through Applications and Modelling?.- Beyond the Low Hanging Fruit.- Modelling for Life: Mathematics and Children’s Experience.- Modelling in Lower Secondary Mathematics Classroom — Problems and Opportunities.- Mathematical Modelling — a Conversation with Henry Pollak.- Issues in Applications and Modelling.- Epistemology and Modelling — Overview.- Modelling Body Motion: an Approach to Functions Using Measuring Instruments.- Emergent Modelling as a Precursor to Mathematical Modelling.- Proving and Modelling.- A Developmental Approach for Supporting the Epistemology of Modeling.- What is Distinctive in (Our Views about) Models & Modelling Perspectives on Mathematics Problem Solving, Learning, and Teaching?.- Everyday Instruments: On the Use of Mathematics.- Authenticity and Goals — Overview.- How to Replace Word Problems with Activities of Realistic Mathematical Modelling.- The Relevance of Modelling and Applications: Relevant to Whom and for What Purpose?.- Features and Impact of the Authenticity of Applied Mathematical School Tasks.- Elementary Modelling in Mathematics Lessons: The Interplay Between “Real-World” Knowledge and “Mathematical Structures”.- Modelling Competencies — Overview.- Levels of Modelling Competencies.- Modelling Both Complexity and Abstraction: A Paradox?.- Studying and Remedying Students’ Modelling Competencies: Routine Behaviour or Adaptive Expertise.- Assessing the “Phases” of Mathematical Modelling.- The Arithmetic Operations as Mathematical Models.- Applications and Modelling for Mathematics — Overview.- The Roles of Modelling in Learning Mathematics.- Developing Mathematical Literacy.- Classroom Activities and the Teacher.- Uses of Technologies in Learning Mathematics through Modelling.- Modelling Pedagogy — Overview.- Mathematical Modelling in High School Mathematics: Teachers’ Thinking and Practice.- Mathematical Modelling in Teacher Education — Necessity or Unnecessarily.- Building Concepts and Conceptions in Technology-Based Open Learning Environments.- Towards a Wider Implementation of Mathematical Modelling at Upper Secondary and Tertiary Levels.- How Might we Share Models Through Cooperative Mathematical Modelling? Focus on Situations Based on Individual Experiences.- Implementation and Practice — Overview.- Some Conditions for Modelling to Exist in Mathematics Classrooms.- Picture (Im)Perfect Mathematics!.- Learning Mathematical Modelling — From the Perspective of Probability and Statistics Education.- Considering Workplace Activity from a Mathematical Modelling Perspective.- Assessment and Evaluation - Overview.- Modelling Based Project Examination.- Mathematical Modelling and Applications: Ability and Competence Frameworks.- “To Model, or to Let Them Model?” That is the Question!.- Modelling and Applications in Pisa.- Assessment of Applied Mathematics and Modelling: Using a Laboratory-Like Environment.- Educational Levels.- Modelling and Applications in Primary Education.- Possibilities for, and Obstacles to Teaching Applications and Modelling in the Lower Secondary Levels.- Upper Secondary Perspectives on Applications and Modelling.- Teaching Applications and Modelling at Tertiary Level.- Modelling in Teacher Education.- Cases in Applications and Modelling.- Moving the Context of Modelling to the Forefront: Preservice Teachers’ Investigations of Equity in Testing.- Modelling in Ontario: Success in Moving Along the Continuum.- Implementation Case Study: Sustaining Curriculum Change.- Mathematical Modelling of Social Issues in School Mathematics in South Africa.

O autorze

Prof. Dr. Hans-Wolfgang Henn lehrt Mathematik und ihre Didaktik an der Universität Dortmund. Nach mehrjähriger Forschungstätigkeit in der Algebraischen Zahlentheorie und Algebraischen Geometrie war er ab 1979 Gymnasiallehrer und von 1989-1999 Fachleiter für Mathematik.

Blurb

The overall goal of Modelling and Applications in Mathematics Education is to provide a comprehensive overview of the state-of-the-art in the field of modelling and applications in mathematics education. Key issues are dealt with, among which are the following:

Epistemology and the relationships between mathematics and the "rest of the world"; the meaning of mathematical modelling and its process components; the respect in which the distinction between pure mathematics and applications of mathematics make sense

Authenticity and Goals dealing with modelling and applications in mathematics teaching; appropriate balance between modelling activities and other mathematical activities; the role that authentic problem situations play in modelling and applications activities

Modelling Competencies: characterizing how a student's modelling competency can be characterized; identifiable sub-competencies, and the ways they constitute a general modelling competency; developing competency over time

Mathematical Competencies: identifying the most important mathematical competencies that students should acquire, and how modelling and applications activities can contribute toward building up these competencies; the meaning of "Mathematical Literacy" in relation to modelling

Modelling Pedagogy: appropriate pedagogical principles and strategies for the development of modelling courses and their teaching; the role of technology in the teaching of modelling and applications

Implementation and Practice: the role of modelling and applications in everyday mathematics teaching; major impediments and obstacles; advancing the use of modelling examples in everyday classrooms; documenting successful implementation of modelling in mathematics teaching

Assessment and Evaluation: assessment modes that capture the essential components of modelling competency; modes available for modelling and applications courses and curricula; appropriate strategies to implement new assessment and evaluation modes in practice

The contributing authors are eminent members of the mathematics education community. Modelling and Applications in Mathematics Education will be of special interest to mathematics educators, teacher educators, researchers, education administrators, curriculum developers and student teachers.