Towards mathematical literacy in the 21st century : perspectives from Indonesia

The notion of mathematical literacy advocated by PISA (OECD, 2006) offers a broader conception for assessing mathematical competences and processes with the main focus on the relevant use of mathematics in life. This notion of mathematical literacy is closely connected to the notion of mathematical modelling whereby mathematics is put to solving real world problems. Indonesia has participated as a partner country in PISA since 2000. The PISA trends in mathematics from 2003 to 2009 revealed unsatisfactory mathematical literacy among 15-year-old students from Indonesia who lagged behind the average of OCED countries. In this paper, exemplary cases will be discussed to examine and promote mathematical literacy at teacher education level. Lesson ideas and instruments were adapted from PISA 2006 released items. The potential of such tasks will be discussed based on case studies of implementing these instruments with samples of pre-service teachers in Yogyakarta.&nbsp; <br /

Modelling the cooling of coffee : insights from a preliminary study in Indonesia

This paper discusses an attempt to examine pre-service teachers&rsquo; mathematical modelling skills. A modelling project investigating relationships between temperature and time in the process of cooling of coffee was chosen. The analysis was based on group written reports of the cooling of coffee project and observation of classroom discussion. Findings showed that pre-service teachers were able to model the process of cooling of coffee as a decreasing exponential function. Difficulties with interpretation of the constant rate of cooling and reinterpretation of mathematical model were identified

Exercising sociomathematical norms in classroom discourse about data representation : insights from one case study of a grade 6 lesson in Indonesia

This paper examines a research study to foster mathematical discourse about data representations among Indonesian students. It was situated in the context of implementing an Indonesian version of Realistic Mathematics Education, labelled as PMRI, in primary schools. A case study of one lesson involving Grade 6 students on the choice of data representations in Yogyakarta will be discussed. The analysis focused on the enacted social norms and sociomathematical norms during a wholeclass discussion and their impacts on students&rsquo; knowledge of data representations. The need for constant effort to enact these norms in classroom mathematical discourse is highlighted

Growth of pre-service teachers’ knowledge and teaching ideas about decimals and fractions : The case of Vivi

This paper discussed and analysed the growth of one pre-service teachers&rsquo; knowledge about decimals and fractions during a teaching experiment. Evidence of&nbsp;her progress is based on responses to written test and interview questions. This&nbsp;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&nbsp;of decimals enabled Vivi to move away from reliance on memorised facts and rules and towards conceptually based explanations of ideas

COUNTEREXAMPLES: CHALLENGES FACED BY ELEMENTARY STUDENTS WHEN TESTING A CONJECTURE ABOUT THE RELATIONSHIP BETWEEN PERIMETER AND AREA

One pedagogical approach to challenge a persistent misconception is to get students to test a conjecture whereby they are confronted with the misconception. A common misconception about a ‘direct linear relationship’ between area and perimeter is well-documented. In this study, Year 4-6 students were presented with a conjecture that a rectangle with a larger perimeter will always have a larger area. Eighty-two (82) students’ written responses from three elementary schools in Victoria, Australia were analyzed. The findings revealed that Year 4-6 students could find multiple examples to support the conjecture but they struggled to find counterexamples to refute the conjecture. The findings underscored the importance of developing elementary school students’ capacity to construct counterexamples and recognize that it is sufficient to offer one counterexample in refuting a conjecture about all cases. Implications for ­teaching practice to support investigating and testing a conjecture are discussed

Year 3/4 children\u27s forms of justification

Engaging children in justifying, forming conjectures and generalising is critical to develop their mathematical reasoning. Previous studies have revealed limited opportunities for primary school children to justify their thinking, form conjectures and generalise in mathematics lessons. Forms of justification of Year3/4 children from three schools in Victoria, Australia will be examined. Evidence from children\u27s written explanations and their verbal explanations captured in video recordings revealed that some children employed sophisticated mathamatical ideas in their justifications. The value of making children\u27s reasoning explicit through written explanations and verbal communications is highlighted

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&rsquo; 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&rsquo; 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&rsquo; misconceptions are discussed. Evidence from this research indicates that it is possible to remove misconceptions about density of decimals