The introduction of algebra : comparative studies of textbooks in Finland, Norway, Sweden and USA
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This master thesis is a comparative analysis of textbooks from four different countries, Finland, Norway, Sweden and USA (California), concerning the introduction of algebra. The topic for this research was inspired and initiated in connection with the international project VIDEOMAT, which I have been involved with since its planning phase. Following the design of this project, two mathematics textbooks of two consecutive grades from the four different countries have been analyzed. The focus in these has been the 60 first tasks presented in the algebraic chapters. The review of literature includes a look at the origins of algebra from a didactical perspective. This was found to be helpful for the understanding of the diverging and extensive material on modern algebra. In a problem solving context, algebra evolved and contributed to the field of mathematics a powerful symbolic language, which has opened many doors for new developments. The flip side of this in education is that students can no longer make further progress in mathematics without adopting fluency in this language. However, it has proven to be a great obstacle to countless of students. The abstract nature of this language is exemplified by the variable which always has the same representation in form of a letter, but has multiple meanings depending on the context in which it is found. This calls for a need to provide students with varied and meaningful experiences in algebra. The aim of identifying the qualities of the introductory tasks and different perspectives of algebra reflected in the textbooks required the development of an original coding system. This has been generated inductively, were the initial stage was a descriptive set of codes that has developed and was finalized in the internet based research program Dedoose. The review of literature played a formative role in this process. The study shows that the introductory tasks presented in the textbooks often have a purpose of developing technical skills necessary for work with algebra. An example of this are tasks focusing the sequences of operations, which prepare the students for equation solving. There was also found to be an emphasis on the equal sign as an attempt to deal with the misconception of using it as an operational sign. Only one textbook was found to present introductory tasks that provide a natural progression into the use of algebraic symbols embedded in meaning. This was done through the use of patterns which also have a motivational element for the learning of algebra. The frequent presence of tasks aimed at developing skills in interpretation and formulations of expressions and equations indicates a focus on algebra as a language early in the algebraic chapters. The implications of this study are that opportunities for varied and meaningful experiences in algebra can be provided through tasks focusing the topics of problem solving, patterns and geometry.
Masteroppgave i matematikkdidaktikk- Universitetet i Agder, 2012