Effect of Mathematical Modeling on Students
Students’ beliefs and attitudes toward mathematics affect their cognitive involvement in the learning process determining to a great extent the amount and quality of acquired knowledge. The formulation of these beliefs and attitudes is mainly attributed to students’ experiences in the mathematics class. This thesis reports of a case study in which a model-eliciting activity was chosen as a teaching approach which could invite students to mathematical activities different from what they were used to.
This research study was built around a short teaching intervention in a Greek high school and was designed to reveal the relevance of mathematics to real life and the social character of mathematics through open-ended activities, group work and a student-centered teaching approach. Two classes in grade 9 participated in the study, one as a control and the other as an experimental group, in order to explore whether and in what ways a mathematical modeling experience could influence students’ beliefs and attitudes toward mathematics.
Results showed no significant differences between the groups which could be attributed to the intervention. However, indicators were found to support that such activities can have positive results on various aspects of the teaching and learning in the mathematics classroom; that is low-achievers seemed to engage more in the mathematics lesson. Also the teacher of the class was inspired to include group work in his teaching methods after observing students’ enthusiasm during the intervention.
The idea for this research study stems from my own experience in different stages of the Greek mathematics education system: young people are taught mathematics in an authoritarian and traditional1 way. As a result they tend to think of mathematics as too formal, too boring and too useless for their life outside school grounds (OECD PISA, 2004; Schoenfeld, 1985). Such beliefs and attitudes toward of mathematics influence students’ motivation in learning mathematics in school and study the discipline further at university. Furthermore, students’ beliefs and attitudes often become an obstacle in their cognitive involvement with mathematics (de Abreu et al., 1997; Boaler, 1999). In an effort to improve students’ beliefs and attitudes regarding mathematics and increase their interest in the discipline, alternative teaching approaches, which promise to offer different experiences to students, could offer a solution. My study follows this rationale in the context of a Greek high school. With a short intervention on mathematical modeling, I explored the effect of a modeling experience on students’ beliefs and attitudes toward mathematics.
Compulsory education in Greece begins with children at the age of five and includes one year of pre-primary education, six years of primary education and three years of lower secondary education. Post-compulsory secondary education includes two types of schools, namely the mainstream senior high school of three years and vocational schools (Greek Ministry of National Education and Religious Affairs, n.d.). According to surveys of the Greek Ministry of Education, 95% of the teenagers at the age of 15 in Greece attend junior high school while 77% of students attending upper secondary education visit mainstream high schools (Eurydice, 2009; Eurydice, 2007/8).
In the last two years of mainstream high schools students are obliged to choose a specialized stream: theoretic, scientific or technological. Admission to university is based on the school grade of the final year in senior high school and grades on six subjects of the national level examinations that take place at the end of high school (Eurydice, 2009). Mathematics is always a part of the national examinations although the level of mathematical knowledge examined depends on the student’s stream. Finally, books for every school subject are provided by the ministry and are, therefore, common in all schools of the same type.
In the last decades the Greek government has engaged in a series of reforms in order to upgrade the educational system in the country. In 2003 a new curriculum was introduced, which revised the aims of compulsory education and introduced ideas of student-centered teaching and learning, an interdisciplinary approach towards knowledge, and meta-cognitive skills (Eurydice, 2007/8). Regarding mathematics the aims of the new curriculum are to “help pupils develop structured and critical thinking abilities and improve their reasoning abilities of analysis, abstraction and generalization” and to “stimulate their initiative, creative imagination and freethinking” (Pedagogical Institute, 2003a, p.127). Emphasis is also put on the relevance of mathematics to real life and the development of students’ “communication skills as well as a positive attitude towards co-operation and initiative taking” (Pedagogical Institute, 2003b, p.10).
Although it may seem that mathematical modeling activities would fit well in this new curriculum for school mathematics, no such activities are included in the books used in the three years of junior high school. When word problems are placed in an everyday life context, this is always a pseudo-real context where the situation is simplified to serve only as an application of algorithms and procedures rather than of analysis and interpretation skills.