Mogens Niss

Applied mathematical problem solving, modelling, applications, and links to other subjects — State, trends and issues in mathematics instruction

The paper will consist of three parts. In part I we shall present some background considerations which are necessary as a basis for what follows. We shall try to clarify some basic concepts and notions, and we shall collect the most important arguments (and related goals) in favour of problem solving, modelling and applications to other subjects in mathematics instruction. In the main part II we shall review the present state, recent trends, and prospective lines of development, both in empirical or theoretical research and in the practice of mathematics instruction and mathematics education, concerning (applied) problem solving, modelling, applications and relations to other subjects. In particular, we shall identify and discuss four major trends: a widened spectrum of arguments, an increased globality, an increased unification, and an extended use of computers. In the final part III we shall comment upon some important issues and problems related to our topic.

Modelling and Applications in Mathematics Education

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Goals of Mathematics Teaching

This chapter attempts to analyse the justification and the goals of mathematics education from both theoretical and historical perspectives. Methodological issues related to the identification and reconstruction of the justification and the goals of mathematics education are discussed as well.

Issues and Problems of Research on the Teaching and Learning of Applications and Modelling

In the past three decades, international activity in the area of applications and modelling has focused mainly on the goals for and the implementation of these components in mathematics curricula at various levels. More specifically, attention has concentrated on the very plea for including these components in mathematics education and on matters pertaining to the design of curricula, the provision of materials, and on the presentation of cases and of ways to organise assessment. Relatively little emphasis has been given to research in this area, and the research actually conducted has been rather scattered as far as themes and foci are concerned. In my lecture I shall attempt to identify, characterise, and to some extent review, existing research on the teaching and learning of applications and modelling. Moreover, some reflections on possible causes for the relative scarcity of such research will be offered. I shall finally attempt to indicate issues and themes on which research on applications and modelling is missing and needed, and to discuss potential methodological and politico-practical problems such research may encounter.

Applications and modelling in the mathematics curriculum — state and trends

This article presents a survey of post‐war development and present states and trends in the role of applications and modelling in mathematics curricula at all levels. Characteristic phases in the development of elementary and post‐elementary curricula respectively are identified. The present situation is described as a period of movement, investigation and experimentation, with the following predominant features. (a) Applications and modelling are being secured a footing in more and more curricula, but considerable variety exists. There are differences between countries with central and countries with local curriculum authorities; (b) the distance between ‘the front’ and ‘the main‐stream’ of applications and modelling in mathematics curricula is great. The article finishes by addressing a few key problems. There is a need for a more balanced view of applications and modelling than is usually seen. What are the barriers to applications and modelling obtaining a reasonable position in curricula, and how may...

Cases of Assessment in Mathematics Education

Introduction M. Niss. Mathematics Assessment in the Spanish Educational System L. Rico. Major Issues in Assessing Mathematics Performance at 16+ Level: A Caribbean Perspective D.R. Broomes, J.A. Halliday. Assessment in Mathematics Education in the Arab Countries M. Jurdak. Issues in Mathematics Assessment in the United States J.A. Dossey, J.A. Swafford. Assessment in the Context of Mathematics Instruction Reform: The Design of Assessment in the QUASAR Project E.A. Silver, S. Lane. Assessment in Mathematics Education: Developments in Philosophy and Practice in the United Kingdom M. Brown. The School Mathematics Project: some Secondary Assessment Initiatives in England C. Little. The Teaching/Learning Process and Assessment Practice: Two Intertwined Sides of Mathematics Education L. Bazzini. Types of Problems and How Students in Norway solve Them G. Gjone. Assessment of Primary and Lower Secondary Mathematics in Denmark H.N. Jensen. Assessment in Upper Secondary Mathematics in Denmark K. Hermann, B. Hirsberg. Assessment of Examinations in the Netherlands W. Kleijne, H. Schuring. New Developments in Senior Secondary Assessment in Australia M. Stephens, R. Money. Assessment in an Innovative Curriculum Project for Mathematics in Grades 7-9 in Portugal L. Cunha Leal, P. Abrantes. Educational Assessment in Mathematics Teaching: Applied Research in China Wei Chao-Qun, Zhang Hui. The Practice and Study of Evaluating Mathematics Teaching in China Cheng Zemin, Lu Shaozheng. Assessment in Mathematics vwithin the International Baccalaureate R.K. Sweetnam. Index.

Teaching of Mathematical Modelling and Applications

Presents a resume of the papers presented at the 4th International Conference on the Teaching of Mathematical Modelling and Applications. It presents a distillation of the experience, views and ideas of leading researchers, lecturers and teachers in the field.

Assessment in Mathematics Education and Its Effects: An Introduction

The present book, Investigations into Assessment in Mathematics Education, is one of two studies resulting from an ICMI Study Conference on Assessment in Mathematics Education and Its Effects. The book which is published in the series of ICMI Studies under the general editorship of the President and Secretary of ICMI is closely related to another study resulting from the same conference: Cases of Assessment in Mathematics Education (Niss, 1992). The two books, although originating from the same sources and having the same editor, emphasize different aspects of assessment in mathematics education and can be read independently of one another. While the present book is devoted to critically analyzing general and principal aspects of assessment, the other study presents and discusses cases of assessment that have been implemented in actual practice. Naturally, the content of either book is enriched by the materials and perspectives provided by the other one.

Modeling a Crucial Aspect of Students’ Mathematical Modeling

Through the use of three mathematical examples, our study explores the origins of students abilities to model (a) the process in which students acquire the ability to both model and learn transferable modeling abilities across modeling activities, and (b) the way in which the modeling cycle should be characterized. We conclude by suggesting that philosophical issues are present in understanding how the modeling ability emerges in students who have never modelled. This is linked to efforts to find activities and methods that will enable better modeling capabilities to be learned.

Classroom Activities and the Teacher

In this section we discuss a broad range of classroom activities, and of teaching style, that are required to produce the benefits that modeling can provide to the student learning mathematics. We discuss support for teachers and the shortage of good modeling tasks that need to be developed into effective curriculum materials.