This paper reports an investigation of students’ understanding of distributive law used to facilitate students’ awareness of ‘the equations is an equivalent expression’ where each equation can be replaced by an equivalent equation. This study used a cross-sectional approach by distributing a questionnaire to participants as many as 53 junior high school students where 45% were male students and 55% were female students who were selected using purposive sampling techniques. The instrument used in this study was a questionnaire written in Indonesian that contains five statements about distributive law, one question that is “when is the statement true?” and three answer choices. The results showed that the use of students’ understanding of operations in understanding distributive law can be grouped into three levels, namely level 1 (pre-structural), level 2 (a combination of uni-structural and multi-structural) where level 2 is a transitional stage (ie stage pre-algebra) from level 1 to level 3 (a combination of relational and abstract expanded). Students who have been proficient in using distributive law in arithmetic, still have difficulty in applying it to algebraic manipulation. One of the causes of this difficulty is the lack of students’ understanding of the equal sign as a sign of equality. In addition, the absence of parentheses also seems to be a stumbling block for students in recognizing distributive law. The reason for expanding the notion of the equal sign by using distributive property is to provide a foundation for their operation sense construction so as to provide further meaning for equations in algebra and minimize student difficulties in learning school algebra.
The equal sign seems to be interpreted differently by students depending on the learning experiences they have had in the early grades. In fact, the interpretation of the equal sign as a relational symbol does not seem easy or fast for many students to understand. This study aims to explore how students from elementary school to college students describe their understanding of the equal sign. The Qualitative Comparative Analysis can be used to analyze several cases in complex situations so that it fits the purpose of this study. The process of collecting data through the method of written assignments, semi-structured interviews, and documentation was carried out in one time period. This study involved 30 participants in Bandung, Indonesia. The results show that although there are substantial differences in viewing the equal sign, there are similarities in terms of dependence on computational methods in drawing conclusions. This is related to how their experience of number sentences in lower grades places more emphasis on rules than on the meaning of concepts.
This paper reports an investigation of students' understanding of the concept of factorization in algebraic forms learned in secondary school. A total of 31 grade 8th junior high school students were selected by purposive sampling technique as respondents in this case study research. The case study approach is considered in accordance with the objectives of this study, namely obtaining in-depth knowledge of student problems, knowing the causes of these problems, and efforts that can be made to help overcome them. Methods of collecting data using written tests, interviews, and documentation. Data analysis techniques include data reduction, data presentation, and drawing conclusions. The results showed that there was a misunderstanding of students' concepts about the concept of factorization in algebraic forms so that they experienced difficulties in "algebraic manipulation". One of the causes of these difficulties is the lack of students' understanding of the equals sign as a sign of equality. The principle of mathematical equivalence serves as the main link between arithmetic and algebra. The operation transformation and the meaning of the equals sign in arithmetic as equality can underlie "algebraic manipulation".
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