• The Mathematical Education
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• v.40 no.2
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• pp.335-343
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• 2001

Algebra is important part of mathematics education. Recent days, many mathematics educators emphasize on real world situation. Form real situation, pupils make sense of concepts, and mathematize it by reflective thinking. After that they formalize the concepts in abstract. For example, operation in numbers develops these course. Operation in natural number is an arithmetic, but operation on real number is algebra. Transition from arithmetic to algebra has the cutting point in representing the concepts to mathematics sign system. In this note, we see the cognitive tendency of 10th grade about operation of real number, their cutting point of transition from arithmetic to algebra, and show some methods of helping pupils.

• The Mathematical Education
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• v.53 no.1
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• pp.93-110
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• 2014

Algebra deals with so general properties about number system that it is called as 'generalized arithmetic'. Observing students' activities in algebra classes, however, we can discover that recognition of the generality in algebraic proofs is not so easy. One of these difficulties seems to be caused by variables which play an important role in algebraic proofs. Many studies show that students have experienced some difficulties in recognizing the meaning and the role of variables in algebraic proofs. For example, the confusion between 2m+2n=2(m+n) and 2n+2n=4n means that students misunderstand independent/dependent variation of variables. This misunderstanding naturally has effects on understanding of the meaning of proofs. Furthermore, students also have a difficulty in making a transition from algebraic proof to numerical cases which have the same structure as the proof. This study investigates whether middle school students can recognize dependent generality and make a transition from proofs to numerical cases. The result shows that the participants of this study have a difficulty in both of them. Based on the result, this study also includes didactical implications for teaching the generality of algebraic proofs.

• Journal of Educational Research in Mathematics
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• v.17 no.2
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• pp.91-109
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• 2007

This study deals with the problem of transition from arithmetic to algebra and the relationship between elementary and secondary school mathematics for systems of linear equations. In elementary school, activity for solving word problems related to systems of linear equations in two variables falls broadly into using two strategies: Guess and check and making a table. In secondary school, those problems are solved algebraically, for example, by solving systems of equations using the technique of elimination. The analysis of mathematics textbooks shows that there is no link between strategies of elementary school mathematics and secondary school mathematics. We devised an alternative way to reinforce link between elementary and secondary school mathematics for systems of linear equations. Drawing a diagram can be introduced as a strategy solving word problems related to systems of linear equations in two variables in elementary school. Moreover it is closely related to the idea of the technique of elimination of secondary school mathematics. It may be a critical juncture of elementary-secondary school mathematics in the case of systems of linear equations in two variables.

• Journal of Educational Research in Mathematics
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• v.10 no.1
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• pp.85-102
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• 2000

The concept of variables is central to mathematics teaching and learning in junior and senior high school. Understanding the concept provides the basis for the transition from arithmetic to algebra and necessary for the meaningful use of all advanced mathematics. Despite the importance of the concept, however, much has been written in the last decade concerning students' difficulties with the concept. This Thesis is based on research to investigate the hypothesis that LOGO programming will contribute to 6th grader' learning of variables. The aim of the research were to; .investigate practice on pupils' understanding of variables before the activity with a computer; .identify functions of LOGO programming in pupils' using and understanding of variable symbols, variable domain and the relationship between two variable dependent expressions during the activity using a computer; .investigate the influence of pupils' mathematical belief on understanding and using variables. The research consisted predominantly of a case study of 6 pupils' discourse and activities concerning variable during their abnormal lessons and interviews with researcher. The data collected for this study included video recordings of the pupils'work with their spoken language.