The purpose of this research is to formulate or devise a design concept form didaktis algebra and... more The purpose of this research is to formulate or devise a design concept form didaktis algebra and its elements as well as perform operations on algebraic forms based on the learning obstacles that have plagued previous learning students. The design used as learning trajectory of thinking arithmetic to algebraic thinking, researchers call it with pre-algebra. Learning obstacles which will be tested in this study i.e. ontogenic obstacle, didactical obstacle and epistemological obstacle. From the results of the analysis, the researchers offer an expected learning design can minimize barriers to learning (learning obstacles). Design didaktis offered based on the results of such research are compiled based on didactical design research with stages starting from the granting of initial concept in arithmetic, trajectory (liaison), namely the stage of pre-algebra, then the concept of the end (final concept) algebraic formally.
The equal sign seems to be interpreted differently by students depending on the learning experien... more 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.
Abstrak. Penelitian ini dilatarbelakangi oleh banyaknya siswa SMP yang mengalami hambatan belajar... more Abstrak. Penelitian ini dilatarbelakangi oleh banyaknya siswa SMP yang mengalami hambatan belajar (learning obstacle) pada saat mempelajari aljabar. Penelitian desain didaktis (didactial design research) digunakan dalam penelitian ini yang diawali dengan studi pendahuluan untuk mendapatkan data learning obstacle di enam kelas pada tiga SMP dengan kluster yang berbeda-beda. Tujuan dari penelitian ini yaitu menghasilkan suatu desain pembelajaran yang diharapkan dapat meminimalkan learning obstacles yang ditemukan. Terdapat tiga kategori learning obstacle yang ditemukan yaitu ontogenic obstacle, didactical obstacle, dan epistemological obstacle sebelum bahan ajar dibuat. Desain didaktis yang ditawarkan berdasarkan hasil studi pendahuluan tersebut disusun dengan tahapan dimulai dari pemberian konsep awal secara aritmatika, trajectory (penghubung) yaitu tahap pra-aljabar, kemudian konsep akhir aljabar secara formal. Hasil dari penelitian ini merupakan hasil uji coba terbatas kepada 28 si...
This paper reports an investigation of students' understanding of the concept of factorizatio... more 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 eq...
The equal sign seems to be interpreted differently by students depending on the learning experien... more 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 ...
Penelitian ini adalah penelitian kualitatif deskriptif. Ketika belajar matematika SD, matematika ... more Penelitian ini adalah penelitian kualitatif deskriptif. Ketika belajar matematika SD, matematika masih berorientasi pada perhitungan (aritmatika). Simbol-simbol yang digunakan dalam aritmatika adalah angka-angka yang dengan langsung dapat dibayangkan seberapa besarnya, atau paling tidak siswa dapat mengenalinya sebagai suatu bilangan tertentu. Ketika belajar aljabar, siswa mulai mengalami perubahan yang signifikan dalam proses berpikir yaitu dari berpikir aritmatik menjadi berpikir aljabar (abstrak). Bagi kebanyakan guru, mengajar aljabar dengan cara biasa adalah mudah. Diberikan contoh suatu bentuk aljabar, definisi, kemudian memperkenalkan unsur-unsurnya. Baik contoh maupun langkah-langkah mengajar yang dilakukan sama dengan yang terdapat dalam buku paket matematika yang digunakan dalam proses belajar-mengajar matematika di kelas.
The purpose of this research is to formulate or devise a design concept form didaktis algebra and... more The purpose of this research is to formulate or devise a design concept form didaktis algebra and its elements as well as perform operations on algebraic forms based on the learning obstacles that have plagued previous learning students. The design used as learning trajectory of thinking arithmetic to algebraic thinking, researchers call it with pre-algebra. Learning obstacles which will be tested in this study i.e. ontogenic obstacle, didactical obstacle and epistemological obstacle. From the results of the analysis, the researchers offer an expected learning design can minimize barriers to learning (learning obstacles). Design didaktis offered based on the results of such research are compiled based on didactical design research with stages starting from the granting of initial concept in arithmetic, trajectory (liaison), namely the stage of pre-algebra, then the concept of the end (final concept) algebraic formally.
This paper reports an investigation of students’ understanding of distributive law used to facili... more 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 t...
The teacher as an educator plays an important role in the process of forming a concept image of s... more The teacher as an educator plays an important role in the process of forming a concept image of students about the equal sign in learning mathematics. Teachers must have an equal sign meaning in accordance with the capacity, learning experience, and knowledge which is a source for them to compile a certain didactic design. The didactic design that has been compiled becomes a learning environment that triggers students' mental perceptions and actions so that a concept image of the equal sign is formed. This study aims to explore teachers' understanding and confirm that the concept image formed by these students may be the impact of the learning process with didactic designs that have been compiled by the teacher. The investigation was conducted qualitatively using a case study approach involving 6 teachers and 55 elementary and middle school students. The data collection methods included teacher questionnaires and interviews with two selected teachers, as well as students answering a series of questions then six students were deliberately selected to be interviewed based on their responses. The results show that the teachers' concept images about the equal sign are generally difficult to say that they already have a well-developed relational view, in addition, they lack the knowledge and skills to identify, anticipate, reduce, or correct students' misconceptions about the equal sign. As a result, the majority of students do not have a concept image about the equal sign that matches the scientific conception that should be.
The purpose of this research is to formulate or devise a design concept form didaktis algebra and... more The purpose of this research is to formulate or devise a design concept form didaktis algebra and its elements as well as perform operations on algebraic forms based on the learning obstacles that have plagued previous learning students. The design used as learning trajectory of thinking arithmetic to algebraic thinking, researchers call it with pre-algebra. Learning obstacles which will be tested in this study i.e. ontogenic obstacle, didactical obstacle and epistemological obstacle. From the results of the analysis, the researchers offer an expected learning design can minimize barriers to learning (learning obstacles). Design didaktis offered based on the results of such research are compiled based on didactical design research with stages starting from the granting of initial concept in arithmetic, trajectory (liaison), namely the stage of pre-algebra, then the concept of the end (final concept) algebraic formally.
The equal sign seems to be interpreted differently by students depending on the learning experien... more 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.
Abstrak. Penelitian ini dilatarbelakangi oleh banyaknya siswa SMP yang mengalami hambatan belajar... more Abstrak. Penelitian ini dilatarbelakangi oleh banyaknya siswa SMP yang mengalami hambatan belajar (learning obstacle) pada saat mempelajari aljabar. Penelitian desain didaktis (didactial design research) digunakan dalam penelitian ini yang diawali dengan studi pendahuluan untuk mendapatkan data learning obstacle di enam kelas pada tiga SMP dengan kluster yang berbeda-beda. Tujuan dari penelitian ini yaitu menghasilkan suatu desain pembelajaran yang diharapkan dapat meminimalkan learning obstacles yang ditemukan. Terdapat tiga kategori learning obstacle yang ditemukan yaitu ontogenic obstacle, didactical obstacle, dan epistemological obstacle sebelum bahan ajar dibuat. Desain didaktis yang ditawarkan berdasarkan hasil studi pendahuluan tersebut disusun dengan tahapan dimulai dari pemberian konsep awal secara aritmatika, trajectory (penghubung) yaitu tahap pra-aljabar, kemudian konsep akhir aljabar secara formal. Hasil dari penelitian ini merupakan hasil uji coba terbatas kepada 28 si...
This paper reports an investigation of students' understanding of the concept of factorizatio... more 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 eq...
The equal sign seems to be interpreted differently by students depending on the learning experien... more 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 ...
Penelitian ini adalah penelitian kualitatif deskriptif. Ketika belajar matematika SD, matematika ... more Penelitian ini adalah penelitian kualitatif deskriptif. Ketika belajar matematika SD, matematika masih berorientasi pada perhitungan (aritmatika). Simbol-simbol yang digunakan dalam aritmatika adalah angka-angka yang dengan langsung dapat dibayangkan seberapa besarnya, atau paling tidak siswa dapat mengenalinya sebagai suatu bilangan tertentu. Ketika belajar aljabar, siswa mulai mengalami perubahan yang signifikan dalam proses berpikir yaitu dari berpikir aritmatik menjadi berpikir aljabar (abstrak). Bagi kebanyakan guru, mengajar aljabar dengan cara biasa adalah mudah. Diberikan contoh suatu bentuk aljabar, definisi, kemudian memperkenalkan unsur-unsurnya. Baik contoh maupun langkah-langkah mengajar yang dilakukan sama dengan yang terdapat dalam buku paket matematika yang digunakan dalam proses belajar-mengajar matematika di kelas.
The purpose of this research is to formulate or devise a design concept form didaktis algebra and... more The purpose of this research is to formulate or devise a design concept form didaktis algebra and its elements as well as perform operations on algebraic forms based on the learning obstacles that have plagued previous learning students. The design used as learning trajectory of thinking arithmetic to algebraic thinking, researchers call it with pre-algebra. Learning obstacles which will be tested in this study i.e. ontogenic obstacle, didactical obstacle and epistemological obstacle. From the results of the analysis, the researchers offer an expected learning design can minimize barriers to learning (learning obstacles). Design didaktis offered based on the results of such research are compiled based on didactical design research with stages starting from the granting of initial concept in arithmetic, trajectory (liaison), namely the stage of pre-algebra, then the concept of the end (final concept) algebraic formally.
This paper reports an investigation of students’ understanding of distributive law used to facili... more 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 t...
The teacher as an educator plays an important role in the process of forming a concept image of s... more The teacher as an educator plays an important role in the process of forming a concept image of students about the equal sign in learning mathematics. Teachers must have an equal sign meaning in accordance with the capacity, learning experience, and knowledge which is a source for them to compile a certain didactic design. The didactic design that has been compiled becomes a learning environment that triggers students' mental perceptions and actions so that a concept image of the equal sign is formed. This study aims to explore teachers' understanding and confirm that the concept image formed by these students may be the impact of the learning process with didactic designs that have been compiled by the teacher. The investigation was conducted qualitatively using a case study approach involving 6 teachers and 55 elementary and middle school students. The data collection methods included teacher questionnaires and interviews with two selected teachers, as well as students answering a series of questions then six students were deliberately selected to be interviewed based on their responses. The results show that the teachers' concept images about the equal sign are generally difficult to say that they already have a well-developed relational view, in addition, they lack the knowledge and skills to identify, anticipate, reduce, or correct students' misconceptions about the equal sign. As a result, the majority of students do not have a concept image about the equal sign that matches the scientific conception that should be.
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