Research in Mathematical Education

Issue: Vol.6 No.1

Relationships Between Teacher`s Knowledge of School Mathematics and their Views of Mathematics Learning and Instructional Practice : A Case Study of Taiwan Hsin Mei E. Huang 6(1) 1-27, 2002 Relationships Between Teacher`s Knowledge of School Mathematics and their Views of Mathematics Learning and Instructional Practice : A Case Study of Taiwan Hsin Mei E. Huang DOI: JANT Vol.6(No.1) 1-27, 2002 This study explored teachers (n = 219) from northern, central, southern and eastern Taiwan concerning their views about children`s learning difficulties, mathematical instruction and school mathematics curricular. Results showed that teachers` mathematics knowledge or their instruction methods had no significant influence on their views of children`s learning difficulties. Even though teachers indicated that understanding of abstract mathematical concepts was the most prominent difficulty for children, they tended to employ direct instruction rather than constructive and cooperative problem solving in their teaching. However, teachers` views of children`s learning difficulties did influence their instructional practice. Results from in-dept interviews revealed that there were some obstacles that prevented teachers from putting constructiveism perspectives of instruction into teaching practice. Further investigation is needed to develop a better understanding of epistemology and learning psychology as well as to help teachers create constructive learning situations.
Children`s Representations of Numbers Man Goo Park 6(1) 29-38, 2002 Children`s Representations of Numbers Man Goo Park DOI: JANT Vol.6(No.1) 29-38, 2002 The purpose of this paper was to examine early numerical representations between American and Korean children. Fifty-five first graders (35 Korean and 20 American) participated in the study. According to the findings of the current study, the author concluded that the Korean children had a stronger conception of base ten representations of numbers than that of the American children. The Korean children used various strategic reasoning such as decomposition and recomposition on the basis of base 10 structure to solve addition and subtraction problems effectively. However, the author cannot conclude that language differences would be the largest factor that would make Korean children salient in the representations of base ten structures.
An Elementary Teacher`s Practical Knowledge of Using Mathematical Tasks for Promoting Students` Understanding and Discourse Cheong Soo Cho 6(1) 39-51, 2002 An Elementary Teacher`s Practical Knowledge of Using Mathematical Tasks for Promoting Students` Understanding and Discourse Cheong Soo Cho DOI: JANT Vol.6(No.1) 39-51, 2002 This study described an elementary teacher`s practical knowledge of selecting and using mathematical tasks for promoting students` understanding and discourse. The informant of this ethnographic inquiry was a third grade teacher and has 10 years of teaching experience. According to the analysis of multiple data sources, this study showed that based on his beliefs about the development of understanding of mathematics and discourse, he continually employed two different types of tasks: open-ended tasks and tasks from students` mistakes and comments during discourse. Teachers` practical knowledge of teaching mathematics and the classroom norms for students` understanding and discourse are suggested to be given attention for further research on this area.
Tools for the Acquisition of Graphing Ability : Real - Time Graphing Technology Oh Nam Kwon 6(1) 53-63, 2002 Tools for the Acquisition of Graphing Ability : Real - Time Graphing Technology Oh Nam Kwon DOI: JANT Vol.6(No.1) 53-63, 2002 This study investigates the impact of Calculator-Based Ranger (CBR) activities in the performance of middle school students` graphing abilities of physical phenomena. Two issues about CBR activities on graphing abilities were addressed in this study; (1) the effect of CBR activities on graphing abilities, and (2) the influence of instructional styles on students` graphing abilities. Following the use of CBR activities, students` graphing abilities were significantly more developed in three components-interpreting, modeling, and transforming. Significant differences were found in students` achievement depending on instructional styles related to differentiation, which is closely connected to transforming distance-time graphs to velocity-time graphs. The findings of this study indicate that CBR activities may enhance students in constructing appropriate webs of related concepts and ability to qualitatively interpret graphs. Using collaborative CBR activities to introduce and explore graphing of physical phenomena is, therefore, recommended for inclusion in the secondary mathematics curriculum.
A Review of Mathematics Education Reform in the United States : Ideal , Practice , and Implication Jeong Suk Pang 6(1) 65-80, 2002 A Review of Mathematics Education Reform in the United States : Ideal , Practice , and Implication Jeong Suk Pang DOI: JANT Vol.6(No.1) 65-80, 2002 The current reform recommendations in the United States have been widely recognized but the outcomes with regard to the teaching practice in the classroom were evaluated as ineffective to foster students` mathematical learning. Given this, this paper reviews the current mathematics education reform in terms of the typical and the recommended teaching practices. An analysis of influences of theoretical perspectives is then provided as an attempt to explore the underpinnings that implicitly motivate the current reform movement. This paper then identifies the difficulties in implementing reform ideals. Building on the review and the analysis, this paper finally provides implications of reconceptualizing mathematics instruction in the current reform era.
Impact of Hand - Held Technology for Understanding Linear Equations and Graphs Oh Nam Kwon 6(1) 81-96, 2002 Impact of Hand - Held Technology for Understanding Linear Equations and Graphs Oh Nam Kwon DOI: JANT Vol.6(No.1) 81-96, 2002 This article describes a research project that examined the impact of hand-held technology on students` understanding linear equations and graphs in multiple representations. The results indicated that students in the graphing-approach classes were significantly better at the components of interpreting. No significant differences between the graphing-approach and traditional classes were found for translation, modeling, and algebraic skills. Further, students in the graphing-approach classes showed significant improvements in their attitudes toward mathematics and technology, were less anxious about mathematics, and rated their class as more interesting and valuable.
On Radar Surveillance in Statistical Perspective for the Classroom Sung Sook Kim , G. Daniel Kim 6(1) 97-106, 2002 On Radar Surveillance in Statistical Perspective for the Classroom Sung Sook Kim , G. Daniel Kim DOI: JANT Vol.6(No.1) 97-106, 2002 Educators have found that the concept of randomness is often misunderstood by students. Chance recently pointed out that students should be introduced to the concept of randomness through the use of simulations. In this article, we studied various aspects of the probability distribution of a linear random path in a circle and introduce some related simulations to guide student exploration and discovery. Consider a random line segment that crosses a circle with a certain radius. Perhaps it can be considered to be a path that an airplane shows up and flies into a random direction in a monitor. What is the expected amount of flying distance through the monitor, and the expected variation? Are we monitoring what we see scientifically? This article studies the probability distribution and some related aspects of a linear random path within a circular monitor. Some simulative activity is also introduced which can be used in a statistics or probability classes.