###
Volume 38 (June 2006) Number 3
##
**ZDM**
###
Zentralblatt für Didaktik der Mathematik
Articles • Electronic-Only Publication • ISSN 1615-679X
** ABSTRACTS**
*(Full texts are available to subscribers
only)*
**
Enhancing the image of
mathematics by association with simple pleasures from real **
world contexts
Robyn Pierce (Australia) and Kaye Stacey (Australia) ##
Those who market
people or products choose their images very carefully. They create positive
associations in the public’s mind by photographing their clients with sporting
heroes or national icons. In this paper we present a variety of evidence to
show that a major and overlooked reason for teachers’ use and choice of real
world problems is to take advantage of this ‘halo effect’ to improve students’
attitude towards learning mathematics. Analysis of interviews, reports, and
results of a brief survey from teachers of middle secondary school classes
indicate that they place a very high priority on positive attitudes and hence
both choose and enhance real world problems to promote students’ affective
engagement through simple pleasures. Pleasant sensory stimuli, generally
non-cognitive and peripheral to the situation to be modelled, are used to
promote a positive view of mathematics. This is a good strategy for creating
enjoyable and memorable lessons, but there is a danger that it may override more
substantive learning goals.
Full text (PDF)
**
****Mathematical
modelling as a tool for the connection of school mathematics**
Fco. Javier García (Spain), Josep Gascón (Spain), Luisa Ruiz Higueras (Spain)
Marianna Bosch(Spain)
*We start introducing some aspects of the theoretical
framework: the Anthropological Theory of Didactics (ATD). Then, we consider on
the research domain commonly known as “modelling and applications” and briefly
describe its evolution using the ATD as an analytical tool. We propose a
reformulation of the modelling processes from the point of view of the ATD,
which is useful to identify new educational phenomena and to propose and
tackle new research problems. Finally, we focus on the problem of the
connection of school mathematics. The reformulation of the modelling processes
emerges as a didactic tool to tackle this research problem. We work on the
problem of the articulation of the study of functional relationships in
Secondary Education and present a teaching proposal designed to reduce the
disconnection in the study of functional relationships in Spanish Secondary
Education.*
Full text (PDF)
**
****
Modeling conceptions revisited**
Bharath Sriraman (USA) and Richard Lesh (USA)
The previous issue of ZDM raised several fundamental
issues on the role of modeling in the school curricula at micro and macro levels
In this paper we complement the approaches described there by discussing some of
the issues and the barriers to the implementation of mathematical modeling in
school curricula raised there from the perspective of the on going work of the
models and modeling research group. In doing so we stress the need for critical
literacy as well as the need to initiate a new research agenda based on the fact
that we are now living in a fundamentally different world in which reality is
characterized by complex systems. This may very well require us to go beyond
conventional notions of modeling.
Full text (PDF)
**Teachers’ ways of listening and
responding to students’ emerging mathematical models**
Helen M. Doerr (USA)
In this paper, I present the results of case study of
practice of four experienced secondary teachers as they engaged their students
in the initial development of mathematical models for exponential growth. The
study focuses on two related aspects of their practices: (a) when, how and to
what extent they saw and interpreted students' ways of thinking about
exponential functions and (b) how they responded to the students’ thinking in
their classroom practice. Through an analysis of the teachers' actions in the
classroom, I describe the teachers' developing knowledge when using modeling
tasks with secondary students. The analysis suggests that there is considerable
variation in the approaches that teachers take in listening to and responding to
students' emerging mathematical models. Having a well-developed schema for how
students might approach the task enabled one teacher to press students to
express, evaluate, and revise their emerging models of exponential growth.
Implications for the knowledge needed to teach mathematics through modeling are
discussed.
Full text (PDF)
**
****
**__Functions: a modelling tool in mathematics
and science__
Claus Michelsen (Denmark)
It is
difficult for the students to transfer concepts, ideas and procedures learned in
mathematics to a new and unanticipated situation in science. An alternative to
this traditional transfer method stresses the importance of modelling activities
in an interdisciplinary context between mathematics and science. In the paper we
introduce a modelling approach to the concept of function in upper secondary
school is introduced. We discuss pedagogical and didactical issues concerning
the interplay between mathematics and science. The discussion is crystallized
into a didactical model for interdisciplinary instruction in mathematics and
science. The model is considered as an iterative movement with two phases: (1)
the horizontal linking of the subjects: Situations from science are
embedded in contexts which are mathematized by the students, (2) the vertical
structuring in the subjects: The conceptual anchoring of the students’
constructs from the horizontal linking in the systematic and framework of
mathematics and science respectively.
Full text (PDF)
**
****
****Simple thinking using complex math vs.
complex thinking using simple math**
Steffen M. Iversen (Denmark) and Christine J. Larson (USA)
Traditional mathematics assessments often fail to identify students who can
powerfully and effectively apply mathematics to real-world problems, and many
students who excel on traditional assessments often struggle to implement their
mathematical knowledge in real-world settings (Lesh & Sriraman, 2005a). This
study employs multi-tier design-based research methodologies to explore this
phenomenon from a models and modeling perspective. At the researcher level, a
Model Eliciting Activity (MEA) was developed as a means to measure student
performance on a complex real-world task. Student performance data on this
activity and on traditional pre- and post-tests were collected from
approximately 200 students enrolled in a second semester calculus course in the
Science and Engineering department of the University of Southern Denmark during
the winter of 2005. The researchers then used the student solutions to the MEA
to develop tools for capturing and assessing the strengths and weaknesses of the
mathematical models present in these solutions. Performance on the MEA, pre-
and post-test were then analyzed both quantitatively and qualitatively to
identify trends in the subgroups corresponding to those described by Lesh and
Sriraman.
Full text (PDF)
In
this paper, I outline a socio-critical perspective of modelling in mathematics
education and discuss implications for the analysis of students’ activities at
the micro level. In particular, a discursive perspective is presented with
contributions from discursive psychology. Recent studies and classroom examples
are taken into consideration.
Full text
(PDF)
**
A global survey of international
perspectives on modelling in mathematics education **
Gabriele Kaiser (Germany), Bharath Sriraman (USA)
In
this article we survey the current debate on modelling and describe different
perspectives on this debate. We relate these perspectives with earlier
perspectives and show similarities and differences between these different
approaches.
Full text
(PDF) |