Research in Mathematical Education

Issue: Vol.18 No.1

Prospective Teachers` Understanding of the Constant π andtheir Knowledge of How to Prove its Constant Nature through the Concept of Linearity Leung K C Issic 18(1) 1-29, 2014 Prospective Teachers` Understanding of the Constant π andtheir Knowledge of How to Prove its Constant Nature through the Concept of Linearity Leung K C Issic DOI: JANT Vol.18(No.1) 1-29, 2014 When taught the precise definition of π, students may be simply asked to memorize its approximate value without developing a rigorous understanding of the underlying reason of why it is a constant. Measuring the circumferences and diameters of various circles and calculating their ratios might just represent an attempt to verify that π has an approximate value of 3.14, and will not necessarily result in an adequate understanding about the constant or formally proves that it is a constant. In this study, we aim to investigate prospective teachers` conceptual understanding of π, and as a constant and whether they can provide a proof of its constant property. The findings show that prospective teachers lack a holistic understanding of the constant nature of π, and reveal how they teach students about this property in an inappropriate approach through a proving activity. We conclude our findings with a suggestion on how to improve the situation
Investigating Arithmetic Mean, Harmonic Mean, and Average Speed through Dynamic Visual Representations Vui Tran 18(1) 31-40, 2014 Investigating Arithmetic Mean, Harmonic Mean, and Average Speed through Dynamic Visual Representations Vui Tran DOI: JANT Vol.18(No.1) 31-40, 2014 Working with dynamic visual representations can help students-with-computer discover new mathematical ideas. Students translate among multiple representations as a strategy to investigate non-routine problems to explore possible solutions in mathematics classrooms. In this paper, we use the area models as new representations for our secondary students to investigate three problems related to the average speed of a particle. Students show their ideas in the process of investigating arithmetic mean, harmonic mean, and average speed through their created dynamic figures. These figures really utilize dynamic geometry software.
An Investigation of the Visual-Mental Capability of Pre- and In-Service Mathematics Teachers: A Tale of Two Cones and One Cube Barkai Ruthi , Patkin Dorit 18(1) 41-54, 2014 An Investigation of the Visual-Mental Capability of Pre- and In-Service Mathematics Teachers: A Tale of Two Cones and One Cube Barkai Ruthi , Patkin Dorit DOI: JANT Vol.18(No.1) 41-54, 2014 This study investigated the visual-mental capabilityof pre-service and in-service mathematics teachers as well as academicians making a career change to mathematics teachers with regard to manipulations of two geometric shapes (from 2- to 3-dimensional). Moreover, it investigated whether there are differences between the visual-mental capabilityof these participant groups. Findings illustrate that most of the participants demonstrate an adequate visual capability relating to the task dealing with a cube. Conversely, very low percentage of participants manifested a visual-mental capability in a task requiring the identification of a solid resulting from rotation of a square page, whose diagonal serves as the rotation axis. The study indicates that learners` high visual view should be developed in order to enhancetheir visual-mental capability.
Examination of Prospective Teachers` Perceptions on Ma-thematical Concepts and Their Potential Teaching Strate-gies Ji Eun Lee 18(1) 55-74, 2014 Examination of Prospective Teachers` Perceptions on Ma-thematical Concepts and Their Potential Teaching Strate-gies Ji Eun Lee DOI: JANT Vol.18(No.1) 55-74, 2014 This study examined the potential teaching strategies of prospective elementary teachers and their perceptions of the procedural/conceptual nature of examples. Fifty-four prospective teachers participated in this study, engaging in two-phase tasks. Analysis of data indicated that:(a) Overall, the participants` perceptions were geared toward putting emphasis on conceptual understanding rather than procedural understanding; but(b) Generally, procedure-oriented strategies were more frequently incorporated in participants` potential teaching plans. This implied that participants` preconceived ideas regarding math examples were not always reliable indicators of their potential teaching strategies. Implications and suggestions for mathematics teacher preparation are discussed.
How to Develop a Scale Measuring an Affective Construct in Mathematics Education Research Do Hyoung Ryang 18(1) 75-87, 2014 How to Develop a Scale Measuring an Affective Construct in Mathematics Education Research Do Hyoung Ryang DOI: JANT Vol.18(No.1) 75-87, 2014 It is central to use a scale to measure a person`s level of a construct in mathematics education research. This article explains a practical process through which a researcher rapidly can develop an instrument to measure the construct. The process includes research questioning, reviewing the literature, framing a background theory, treating the data, and reviewing the instrument. The statistical treatment of data includes normality analysis, item-total correlation analysis, reliability analysis, and factor analysis. A virtual example is given for better understanding of the process.