Uppeldi og menntun - 01.01.2012, Page 95

Uppeldi og menntUn/icelandic JoUrnal of edUcation 21(1) 2012 95
friðrik diego og kristín halla Jónsdóttir
Pre-service training of mathematics teachers with respect
to conceptual understanding and constructivism
aBstraCt
The participants in this study were twelve undergraduate students majoring in
mathematics education at the university level in Iceland. The purpose of the study
was to evaluate whether their pre-service training was sufficiently oriented towards
strengthening the students’ conceptual understanding in mathematics as well as
their problem solving ability and analytical skills. The study was aimed at answering
the question whether the students’ preparation in mathematics was solid enough
to enhance their competence to work as professional schoolteachers in the spirit of
constructivism.
A short overview of constructivism in mathematics teaching is provided and, in
order to show the constantly growing emphasis that this theory has been given in the
Icelandic educational system, a brief overview is included of the curricular changes
in mathematics for the past few decades in Iceland. It is pointed out that both the
1999 and the 2007 official curricula explicitly state the importance of problem solving
and present a discussion on what it means to understand a mathematical concept.
The growing emphasis on constructivism in mathematics teaching is also clearly
witnessed in recently published mathematics textbooks for Icelandic primary schools.
The paper contains a short discussion on the importance of problem solving in
connection with constructivism in mathematics teaching. In the second half of the
20th century problem solving was one of the key issues of mathematics as a field of
study. In the skill of problem solving as well as in the theory of constructivism the
questioning mind of the student is paramount.
The evaluation of the students’ preparation was based on observations of their
tackling five given mathematical problems, interviews with the students about
the problems and the students’ written solutions. The evaluation was based on the
following research questions put forward in the study: 1) Do the students understand
the problem well enough to realize how they should solve it? 2) Do the students use
analytical skills in trying to solve the problem? 3) Do the students analyze the problem
they are working on and show a questioning mind? Do the students try to see the
problem in a wider perspective? 4) Can students be encouraged to analyze further a
problem they have already solved?
To shed light on why the above research questions were chosen by the researchers,
there is a brief mention of two reports on competency in mathematics teaching and
one research article addressing the same subject. One of these reports is an official
Danish report and the other an official American report. The research article describes
an Icelandic study on how successfully the pre-service education of teachers promotes
their overall competency.