57 research outputs found
The Assessment of Students’ Cognitive Conflict by Using Student’s Cognitive Map in Solving Mathematics Problem
Full text linkKnowing students’ cognitive conflict when solving mathematical problems is important. We can explore some misconceptions and mistakes made by the students in constructing mathematical concepts. The aim of this study is to assess students’ cognitive conflict by using the students’ cognitive map. This is a qualitative study that conducted on one 6th grader student of SD Wahid Hasyim Malang. Based on our exploration by using students’ cognitive map, it was found that the cognitive conflict occured as a result of conflict between the students’ concept with facts/result of the concept. Keywords : cognitive conflict, cognitive ma
Fostering Indonesian Prospective Mathematics Teachers' Geometry Proof Competence
Full text linkIt is widely accepted that comprehending and constructing mathematical proof is an essential topic at any level of mathematics education, including higher education. Prospective mathematics teachers (PMTs) learn mathematical proof in university because proof competence could help them understand and explain mathematical concepts to their students when they are a high school teacher. From a small-scale observational study at a university in Malang, Indonesia, I learned that most students faced difficulties understanding and constructing mathematical proof. This situation motivated me to investigate and improve PMTs’ proof competence.For that purpose, I designed a course and investigated how this course supported PMTs in developing proof competence in geometry. My findings indicated that the course supported PMTs in developing their proof competence, particularly in conjecturing, which is a precursor activity of proving, and their understanding and construction of proof. A quasi-experimental study showed that students achieved better results than in the regular course. The designed learning trajectory can inform curriculum designers about effective teaching strategies for geometrical proof, particularly in an early stage at Indonesian universities. I recommend that in the future, PMTs at all Indonesian universities should acquire not only the content knowledge of mathematical proofs (on which this study focused) but also the pedagogical content knowledge. Following this study, proof should be promoted in Indonesian secondary schools, along with guidance for teachers about implementation in their classrooms
SUPPORTING STUDENTS’ REASONING THROUGH INTRODUCING FRACTIONS AS PART-WHOLE AND MEASURE MEANING
No full textOne of reasons why fractions are a topic which many students find difficult to learn is that there exist many rules calculating with fractions. Some previous researcher confirmed that the problem which students encounter in learning fraction operations is not firmly connected to concrete experiences. Primary school curricula in Indonesia introduce fractions in class III and by class V, students are expected to learn many operastions on fractions. In fact, many students in class V have some misconceptions or misunderstandings about the concepts. For instance, they would say that ¼ is more than 1/3 and ½ + 2/3 = 3/5. In addition, most textbooks used by students contain basically many procedures, they learn fractions mechanically without any conceptual grasp. Moreover the textbooks use only part-whole interpretation as a way to introduce a fractions, it is not enough in facilitating students’ reasoning in the context of task of comparing, finding equivalent fractions and operating fractions. In this paper, we describe data/informations colected during facilitating student in learning fractions using methode combining the part-whole and measure interpretation of fractions. We also will show examples of students’ reasoning indicating teaching fractions using the combination migh prove to be better methode in supporting students’ reasoning about fractions.
Key words: reasoning, fractions, part-whole, measur
Understanding geometric proofs: scaffolding pre-service mathematics teacher students through dynamic geometry system (dgs) and flow-chart proof
Full text linkInternational audienceThe objective of this paper is to discuss the pedagogic potential that is offered by the use of a flow-chart proof with open problems and a Dynamic Geometry System in understanding geometric proofs by pre-service mathematics student teachers at an Indonesian university. Based on a literature review, we discuss aspects and levels of understanding of geometric proof and how to assess students’ understanding of the structure of deductive proofs, and how the use of a Digital Geometry System may support students’ understanding of geometric terms and statements, including definitions, postulates, and theorems. The pedagogic focus consists of exploiting the semiotic potential of a DGS, especially the use of GeoGebra tools that may function as tools of semiotic mediation to understand the geometry statements and the scaffolding potential of flow-chart proof with open problems in identifying the structure of deductive geometry proofs
ELICITING MATHEMATICAL THINKING OF STUDENTS IN ADDITION OF FRACTIONS THROUGH REALISTIC MATHEMATICS EDUCATION
No full text
Supporting Student’s Thinking In Addition Of Fraction From Informal To More Formal Using Measuring Context
No full textOne of reasons why fractions are a topic which many students find difficult to learn is that there exist many rules calculating with fractions. In addition, students have been trained for the skills and should have mastered such procedures even they do not ‘understand’. Some previous researcher confirmed that the problem which students encounter in learning fraction operations is not firmly connected to concrete experiences. For this reason, a set of measuring context was designed to provide concrete experiences in supporting students’ reasoning in addition of fractions, because the concept of fractional number was derived from measuring. In the present study we used design research as a reference research to investigate students’ mathematical progress in addition of fractions. In particular, using retrospective analysis to analyze data of fourth graders’ performance on addition of fractions, we implemented some instructional activities by using measuring activities and contexts to provide opportunities students use students’ own strategies and models. The emergent modeling (i.e. a bar model) played an important role in the shift of students reasoning from concrete experiences (informal) in the situational level towards more formal mathematical concept of addition of fractions. We discuss these findings taking into consideration the context in which the study was conducted and we provide implications for the teaching of fractions and suggestions for further research.
Key word: measuring context, addition of fractions, design research, emergent modelin
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