Peter Gøtze, Cohort 5
The role of teacher students mathematical modelling skills
and democratic competencies when working with real world
use of mathematics in the classroom.
Keywords: Teacher students - critical citizenship - mathematical modelling - societal debates
Background for project
Many important discussions in society include the use of mathematical modelling at some level of
the argumentation. Climate debates, debates about risks and benefits related to construction of new
power plants and oil rigs and debates about government investments in infrastructure are all
examples of debates where results of simulations of mathematical models might (more or less
explicitly) occur as part of an argumentation for a position. These are also examples of debates
where consequences of decisions have a large influence on the everyday life of many people.
The ability as a citizen to participate in discussions like these can be viewed as parts of critical
citizenship and part of an overall democratic competency. In Schooling for democracy Henry Giroux
argues that schools needs to educate students to become critical citizens who can challenge and
believe that their actions make a difference in society (Giroux as referenced in Skovsmose,1992).i
Both mathematical modelling and more generally the ability to apply mathematics in real life
contexts are focus points of the curriculum in many countries in Europe and the rest of the world
(Eurydice,2011). Understanding how future mathematics teachers at primary and lover secondary
level are able to participate in activities surrounding the debate of such questions, gives an important
insight into the capabilities of the individuals educating students to become the critical citizens of
tomorrow.
Aim of study
The project outlined here is a qualitative study on how teacher students at the master level in
Norway approach class room activities based on authentic problems from society. Thus the study
seeks to investigate how teacher students approach real world situations as they are reformulated to
a class room setting. An important part of the study will be to identify how such a reformulation can
be done authentically such that the teacher students are get an actual possibility to apply their
democratical as well as mathematical skillset. The students approaches to activities, along with their
arguments and reflections during the activities, will be investigated in order to characterize their use
of critical citizenship and mathematical skills.
Characterization of authentic activities in the study
The study will focus on including activities that can be characterized as being authentic_. That is the
activities are true in their representation of the complexity of the real world context, including their
portrayal of uses of mathematical modelling in these contexts. Determining how activities
constructed for the study can best be constructed as to be authentic will be part of the investigation
undertaken in the research literature review stage of the project.
The activities will be constructed in a way that will include possibilities for teacher students to apply
their critical citizenship_, to work with mathematical modelling and ICT_ methods. Classroom activities
that focus on fostering student work in these three areas will be termed as Critical ICT Modelling
activities, abbreviated CICTM activities.
Mathematical modelling in education and the role of ICT in education has been central focus points
in educational research studies for many years. The ICTMA_ community has produced a number of
monumental studies on modelling in education e.g.. (Niss, Blum and Galbraith, 2007), while ICT was a
primary focus of the 17th ICMI study (Hoyles, Lagrange, 2010). There also exists a large body of
research on critical citizenship in mathematics education. A literature review of existing research that
falls within the intersection of these three themes will be a first step for this study. This will be done
in order to be able to construct class room activities that support the aim of the study, and also in
order to find analytical tools that can help to interpret the data produced during teacher student
participation in these activities.
Motivation for studying CICTM activities
The focus put on critical citizenship, ICT and modelling in the authentic activities is done for several
reasons. Real world debates are complex situations where many forms of arguments can be found
including mathematical and technically founded arguments. The complexity of the problems that are
debated often foster complex models and large amounts of data. Professional modelers in these
situation rely on ICT methods to a large extent in the modelling process. Thus, if one is to
authentically represent the background for arguments made in such a debate in a class room activity,
a presentation of the modelling process and (ICT) tools used in this process might naturally be
included.
The societal debates sketched out above also include laymen arguments as well as mathematical and
technical arguments. Including elements surrounding critical citizenship as in the real world
discussions could therefore also be considered a natural element in an authentic portrait of debates.
Newly educated mathematics teachers in Norway are expected to poses a solid mathematical skill set
as well as a solid foundation in ICT methods. Teacher students at the masters level should therefore
be expected to have a foundation in mathematics and ICT methods that would allow them to
approach mathematical modelling and ICT aspects of CICTM activities_. Furthermore teachers are
expected to teach students how to apply mathematical abilities to various types of problems. It is
therefore natural to expect that teachers might readily be able to apply their own mathematical
abilities, ICT skills and critical citizenship when participating in CICTM activities. In regards to the
study the interesting questions then become how the teacher students skill sets, mathematical as
well as critical competencies become apparent in the CICTM activities.
Research Questions
How do teacher students use their mathematical and critical competencies in CICTM activities?
What type of arguments and abilities do they use in CICTM activities?
How do teacher students reflect on their use of competencies and own arguments when
reflecting on their participation in the CICTM activities?
How do the teacher students refer to CICTM activities they have previously been involved in
when participating in other CICTM activities?
The final research question refers to the situation that the teacher students being studied are
exposed to various CICTM activities during the study.
Method
The data material for the study will be collected during three seminar sessions at a masters level
course in educational theory of mathematics at the teacher education at Bergen University College in
the spring of 2015. The course is a 6 seminar specialization course for teacher students, who will be
teaching students from 5th to 10th grade in primary school. The title of the course is »specialization
in didactics of mathematics«.
Two lecturers will be teaching the course, and both are active researchers in education research in
mathematics with backgrounds as mathematical modellers. In a collaboration with the two lecturers
of the course and the Phd student, CICTM activities will be constructed for three of the seminar
sessions which cover the subject of mathematical modelling. The three seminars will thematically
cover themes such as ›What is a mathematical model?‹ › Examples of various types of models and
their use in society‹, ›Didactical motivations for including mathematical modelling in education‹ and
›ICT and modelling‹. The constructed CICTM activities will be introduced to the students by the
lecturers and activities will be observed and documented by the PhD student.
The teacher students participation in CICTM activities during the three seminar sessions, and
classroom discussions surrounding these activities will be recorded on video. Elements of the
students activities involving computers will also be screen recorded.
Video recordings of classroom and computer activity will subsequently be coded. The preliminary
coding strategy is to base the coding on a classification of teachers arguments according to
Skovsmose's characterization of levels of reflection as described in Skovsmose 1992.
References
Eurydice 2011. Mathematics education in Europe: common challenges and National Policies.
Brussels: The European Union. Education, Audiovisual and Culture Executive Agency. Available at:
http://eacea.ec.europa.eu/education/eurydice/documents/thematic_reports/132EN.pdf [Accessed
21-12-2013]
Blomhøj, Morten, Kjeldsen, Tinne Hoff. 2010. Learning mathematics through modelling – the case of
the integral concept. In: The First Sourcebook on Nordic Research in Mathematics Education. B.
Sriraman, L. Haapasalo, B. D. Søndergaard, G. Palsdottir, and S. Goodchild (Eds.). Information Age
Publishing
Hoyles, Celia, Lagrange Jean-Baptiste. 2010. Mathematics Education and Technology-Rethinking the
Terrain The 17th ICMI Study, eds. Hoyles, C., Lagrange J.-B.. Springer
Niss, Mogens, Werner Blum and Peter Galbraith. 2007. Introduction. In: Modelling and Applications
in Mathematics Education. The 14th ICMI study, eds. Werner, B., P. Galbraith, P. L. Henn & M. Niss.
Springer.
Skovsmose, Ole. 1992. Democratic competence and reflective knowing in mathematics. For the
Learning of Mathematics, 2-11.
Skovsmose, Ole. 2008. Critical Mathematics Education for the Future. In: ICME-10 Proceedings:
proceedings of the 10th International Congress on Mathematical Education. Ed. Mogens Niss.
IMFUFA, Roskilde University.
Vos, Pauline. 2011. What is “Authentic” in the Teaching and Learning of Mathematical
Modelling?.Trends in Teaching and Learning of Mathematical Modelling- ICTMA 14. Eds. Kaiser,
Gabrielle, Werner Blum, Rita Borromeo Ferri and Gloria Stillman. Springer Netherlands.