Misconceptions about Density of Decimals: Insights from Indonesian Pre-Service Teachers (original) (raw)
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Misconceptions about density of decimals: insights from Indonesian pre-service teachers’ work
Extensive studies have documented various difficulties with, and misconceptions about, decimal numeration across different levels of education. This paper reports on pre-service teachers' misconceptions about the density of decimals. Written test data from 140 Indonesian pre-service teachers, observation of group and classroom discussions provided evidence of pre-service teachers' difficulties in grasping the density notion of decimals. This research was situated in a teacher education university in Yogyakarta, Indonesia. Incorrect analogies resulting from over generalization of knowledge about whole numbers and fractions were identified. Teaching ideas to resolve these difficulties and challenges in resolving pre-service teachers' misconceptions are discussed. Evidence from this research indicates that it is possible to remove misconceptions about density of decimals.
Preservice Teachers' Knowledge of Difficulties in Decimal Numeration
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In this study we investigated preservice elementary school teachers' content knowledge and pedagogical content knowledge of decimal numeration. The preservice teachers completed a decimal comparison test, marked items they thought would be difficult for students, and explained why. Only about 80 percent of the sample tested as experts, indicating that a significant proportion of preservice teachers have inadequate content knowledge of decimals. Confusion about the size of decimals in relation to zero was a significant and unexpected difficulty, leading to concerns about the fragmentary nature of the preservice teachers' knowledge. Most preservice teachers were aware of longer-is-larger misconceptions in students, but had little awareness of shorter-is-larger misconceptions. Preservice teachers' explanations for the reasons students might have difficulty demonstrated that many are good at identifying features that make comparisons difficult but less able to explain why these cause trouble. Results point to the need for teacher education to emphasise content knowledge that integrates different aspects of number knowledge, and pedagogical content knowledge that includes a thorough understanding of common difficulties.
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This study investigated whether new teaching resources and minimal support could help teachers make a difference to children's understanding of decimal numeration. Three schools were offered resources and a professional development session specifically to address the common misconceptions children have about decimal numbers. One school agreed to participate, and four teachers were supplied with the resources. Use of the resources was unexpectedly low, but teachers who used them achieved an educationally and statistically significant improvement in decimal understanding, indicating that a small amount of deliberate attention to decimal concepts can make a difference.
Mathematics Education Across Cultures: Proceedings of the 42nd Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, 2020
Researchers, who have studied the understanding of the density property in the set of decimal numbers, have shown that the student uses the property of the discrete of natural numbers to solve tasks related to density. So, a restructuring of concepts is necessary, that is, a conceptual change from "the discrete" to "the dense". This report presents evidence from ten pre-service teachers from Mexico City that this change can initiate through the implementation of a didactic sequence. The pre-service teachers managed to visualize that a decimal number can be found in an interval. Consequently, they were able to conceive an infinity. However, several of them persisted with the idea of the existence of a successor in the set of decimal numbers.
This paper discussed and analysed the growth of one pre-service teachers' knowledge about decimals and fractions during a teaching experiment. Evidence of her progress is based on responses to written test and interview questions. This case shows with probing questions and appropriate teaching ideas, it is possible for a pre-service teacher with initially weak and fragmented knowledge about decimals and fractions to develop a meaningful knowledge about decimals and fractions. The stronger conceptual base provided by use of a concrete representation of decimals enabled Vivi to move away from reliance on memorised facts and rules and towards conceptually based explanations of ideas. The fact that knowledge for teaching mathematics must go well beyond knowledge about mathematical content is now well established. The seminal notion of Pedagogical Content Knowledge (PCK) coined by Shulman (1986) has been accepted as the common currency in teacher education to refer to knowledge which...
International Conference on Elementary Education, 2021
Textbooks are still used as the main learning resource used by teachers in school. The book must provide content that is very supportive in helping students to achieve understanding related to a topic. This study aims to analyze how decimal material is studied in mathematics textbooks published by the Ministry of Education and Culture of the Republic of Indonesia. The analysis focuses on the content and presentation of math problems available in books. This study uses a qualitative approach with analytical methods. Research findings show that the decimal material focuses more on procedural knowledge than on trying to deepen conceptual understanding. The problems in the book are dominated by problems that only reveal procedural knowledge. There are no questions that reveal representation skill, reasoning, and conceptual understanding. Based on this research, it appears that teachers should make more efforts to find learning resources that more supportive of success in learning mathematics. Because the success of learning mathematics can be seen from the development of mathematical proficiency, not only in computational or numerical skills.
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