Research Information System
International Conference on Mathematics and Mathematics Education (ICMME-2018), Ordu, Turkey, 27 - 29 June 2018, pp.639-640
Models are conceptual systems which consist of elements, relations, operations, and rules governing interactions. These systems are expressed using external notation systems, and that are used to construct, describe, or explain the behaviors of other systems so that the other systems can be manipulated or predicted intelligently [1]. Mathematical modelling is defined as a dynamic process which facilitates the ability to see the relationships in everyday life problem, discover and write the relationships between them in mathematical terms, classify, generalize and draw conclusions. As an outcome of this process, a mathematical model is formed to solve real life problems. Furthermore, Mathematical modelling provide an opportunity to describe the problem situation, establish a bridge from real world to mathematical world, manipulate the model to make predictions related to the problem situation, translate the results gathered in mathematical world to real life, and verify the model [1]. During this process, problem solvers share their mathematical thoughts by using and creating representations. In this study it is aimed to explore the mathematical understandings and mathematisation processes that pre-service mathematics teachers used in constructing their models.
DRAFT VERSION International Conference on Mathematics and Mathematics Education (ICMME-2018), Ordu University, Ordu, 27-29 June 2018 639 Pre-Service Mathematics Teachers’ Mathematisation Processes In Modelling Activities Berna Aygün 1 , Demet Baran Bulut2 1 Süleyman Demirel University Education Faculty bernaaygun@sdu.edu.tr 2 Recep Tayyip Erdoğan University Education Faculty demet.baran@erdogan.edu.tr ABSTRACT Models are conceptual systems which consist of elements, relations, operations, and rules governing interactions. These systems are expressed using external notation systems, and that are used to construct, describe, or explain the behaviors of other systems so that the other systems can be manipulated or predicted intelligently [1]. Mathematical modelling is defined as a dynamic process which facilitates the ability to see the relationships in everyday life problem, discover and write the relationships between them in mathematical terms, classify, generalize and draw conclusions. As an outcome of this process, a mathematical model is formed to solve real life problems. Furthermore, Mathematical modelling provide an opportunity to describe the problem situation, establish a bridge from real world to mathematical world, manipulate the model to make predictions related to the problem situation, translate the results gathered in mathematical world to real life, and verify the model [1]. During this process, problem solvers share their mathematical thoughts by using and creating representations. In this study it is aimed to explore the mathematical understandings and mathematisation processes that pre-service mathematics teachers used in constructing their models. This study was conducted in the province of Rize during the 2016-2017 academic year. The sample of the study consisted of 10 group of pre-service teachers in the 4th year of elementary mathematics education programme. The data collection tool utilized in the study was four mathematical modelling activities designed by [2]: Foot Print, Which one is the best seat?, Summer Job Problem, and Jumping Ball. The study employed the case study which is one of the qualitative research approaches. As for data analysis, the descriptive analysis method was utilized. The pre-service teachers’ models in the data collection tool were evaluated in terms of the nature of the problem factors that pre-service teachers chose to consider, the types of transformations they made through the operations they applied, and the representations they used. The frequency values for these solutions evaluated within this scope have been presented in a table. Based on the findings, the pre-service teachers’ solutions of mathematical modelling activities entailing daily life situations were found to be at a moderate mathematical thinking. They used varies representations such as table, graphics, written symbols, formula. They integrated these multiple representations effectively to solve these daily life problems. Furthermore, as creating their model, the pre-service teachers worked with some or all of the problem factors. For instance, in the summer job problem they focused on work load, months, earning money per hour, etc. Preservice teachers’ operations on these factors included variety of operations such as: finding units, using interval quantities, aggregating quantities, using informal measures of rate, etc. Based on these results, various recommendations have been made for further studies.
Key Words: Mathematical Modelling, Mathematical knowledge
REFERENCES [1] Lesh, R., & Doerr, H. In what ways does a models and modeling perspective move beyond constructivism? Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning, and teaching, Mahwah, New Jersey: Lawrence Erlbaum Associates, Inc., (2003), 519-556.
[2] Erbaş, A. K., Çetinkaya, B., Alacacı, C., Çakıroğlu, E., Aydoğan Yenmez, A., Şen Zeytun, A., & Şahin, Z. Lise matematik konuları için günlük hayattan modelleme soruları. Ankara: Türkiye Bilimler Akademisi, (2016).