Summary:
The affective domain and its connection with learning and studying of
Mathematics, as it comes from the international and Greek literature, is of
great
interest for the research in Mathematics Education. In our inquiry, we studied
students’ beliefs and attitudes concerning Mathematics of 10th, 11th and 12th
grade (16,
17, 18 years old), and their ways and strategies of studying and learning
Mathematics.
We focused, especially, on the factors which contribute in students’ beliefs and
attitudes formation and development. Our interest has been focused similarly on
the
investigation of three other important variables: Students’ fear for
Mathematics and
reasons that invoke it, students’ intention to choose Mathematics as an
optional course
of studies and students’ interest-stability about Mathematics, during their
studies at
lyceum. We, also, investigated if there is any correlation among students’
beliefs and
attitudes concerning Mathematics, their ways and strategies of studying and
their
mathematical achievement.
Our research was realized into two stages: In the first one, a pilot study was
accomplished, aimed on one hand at the testing of the Questionnaire, in order to
correct it and give it an appropriate form. On the other hand to trace, if they
existed,
any studying patterns of the students. In the second stage our main study was
carried
out. The Questionnaire was administered to a random sample of 1645 students of a
random sample of schools (General public lyceums, General private lyceums,
Technical public lyceums), in Attica county of Greece. Our data had been
collected,
were statistically elaborated using two statistical packages: The Statistical
Package for
the Social Sciences (spss) and the M-plus statistical package (statistical
analysis with
latent variables). We used Factor Analysis (spss) to identify twelve factors of
students’ beliefs, attitudes, studying methods and strategies about
Mathematics. We
confirmed these factors and their structure, using Confirmatory Factor Analysis
(Mplus).
Pearson correlation coefficient (spss) and Path Analysis (M- plus) helped us to
discover various relationships and connections of the traced factors and to be
led to
very useful conclusions, concerning the connection between students’ beliefs and
attitudes, and understanding of Mathematics. Using Pearson correlation
coefficient,
we discovered some relationship between the factors traced above, fear for
Mathematics, students’ intention to choose Mathematics, students’
interest-stability
about Mathematics, students’ self-concepts, students’ spending time for studying
Mathematics, and Mathematical achievement. We, also, identified reasons for
which,
according to students’ declare, they are afraid or not of Mathematics, they
would
choose or not Mathematics as a free course and we traced some differences or
similarities for these variables among students, according to gender, social and
economical surrounding, and age.
Further analysis, by using the statistical methods of analysis of variance
(anova) and multivariate analysis of variance (manova), helped us to trace some
differences or similarities for the factors we identified, concerning students’
beliefs
and attitudes towards Mathematics, among students, relatively to educational
district,
school category (general public, general private, technical public), class,
studying
direction (theoretical, positive, technological) and gender. We concluded that
students’ affective domain is mainly influenced and shaped by category of
school,
class, studying direction and gender.
We, finally, identified some distinct groups of students, relatively to their
beliefs and attitudes about the nature and utility of Mathematics, students’
perceptions
about their teachers’ teaching practice of Mathematics and the methods and
strategies
for studying, they follow. The most interesting categorization is that
concerning
methods and strategies of studying. We identified the following three groups:
Utilitarian, who study enough to pass the exams and they are led to flat
understanding
and low mathematical achievement. Exploratory I, who may reach first level of
understanding, which means that they understand the successive steps of a
proof, or a
problem solution and stop there, without any other extension. These students may
succeed high mathematical achievement. Exploratory II, who may reach second
level
of understanding, which means that they go further, posing searching questions
and
thinking again on the deductive steps and methods (reflection), which have been
followed. These students may succeed high mathematical achievement and probably
some of them to be future researchers.
One of the main conclusions of our investigation is that students’ positive
beliefs and attitudes towards Mathematics are strongly connected with high
mathematical achievement. For this reason mathematics teachers and anyone who
has
a position of responsibility in Mathematics education, must help students to
develop
positive beliefs and attitudes towards Mathematics. Doing so, they will
contribute to
Mathematics education improvement.
