Han Hyuk Cho , Dong Jo Shin , Ahn Sun Woo

DOI: Vol.16(No.1) 1-13, 2012

This paper explores gifted students` reasoning abilities. Three tests were developed in order to assess and analyze their reasoning abilities building on previous research on covariational reasoning. Giving consideration to the arising problems in the tests, we constructed a LOGO-based JavaMAL microworld environment which engages students in an active learning environment. This environment was designed by applying ``instrumental approach`` in microworld. Based upon the post test results, the role of activity in microworld environment as ``instrument mediated activity`` is also discussed.

JavaMAL microworld, covariational reasoning, instrument mediated activity, artifact, sign

Chun Chor Litwin Cheng

DOI: Vol.16(No.1) 15-29, 2012

One of the important aims in mathematics education is to enhance mathematical thinking for students. And students posing questions is a vital process in mathematical thinking as it is part of the reasoning and communication of their learning. This paper investigates how students develop their mathematical thinking through working on tasks in fractions and posing their own questions after successfully solved the problems. The teaching was conducted in primary five classes and the results showed that students` reasoning is related to their analogy with what previously learned. Also, posing their problems after solving the problem not only helps students to understand the structure of the problem, it also helps students to explore on different routes in solving the problem and extend their learning content.

mathematical thinking

Patkin, Dorit

DOI: Vol.16(No.1) 31-50, 2012

The present study explored whether the implementation of focused activities (intervention programme) can enhance 22 pre-service mathematics teachers` proficiency in solid geometry thinking level as well as change for the better their feelings in this discipline. Over a period of 6 weeks the pre-service teachers participated in activities and diversified experiences with 3D shapes, using illustration aids and actual experience of building 3D shapes in relation to the various spatial thinking levels. The research objectives were to investigate whether the intervention programme, comprising task-oriented activities of solid geometry, enhance mathematics pre-service teachers` mastery of their geometric thinking levels as well as examine their feelings towards this discipline before and after the intervention programme. The findings illustrate that learners` levels of geometric thinking can be promoted, entailing control on higher thinking levels as well as a more positive attitude towards this field.

Van Hiele theory, Level of thinking in solid geometry, 3D shapes, pre-service mathematics teachers, reflection

Tak Wah Wong , Yiu Chi Lai

DOI: Vol.16(No.1) 51-66, 2012

This study investigated the impact of entry level of mathematics subject knowledge on student teachers` mathematics pedagogical content knowledge development and performance in mathematics teaching practice. The sample consisted of 24 mathematics student teachers, 12 of whom passed A-Level mathematics and 12 of whom only passed O-level mathematics. They were all studying in a 4-year bachelor of education (Honours/ Primary) programme; they were either majoring or minoring in mathematics. Results showed that student teachers` entry-level mathematics subject knowledge is not related to their mathematics pedagogical content knowledge development or their mathematics teaching performance. These findings may lead society to consider whether student teachers who have passed O-level mathematics are already eligible to be trained as professional primary mathematics teachers. As a consequence, this study raises the issues of how to develop student teachers` mathematics pedagogical content knowledge and whether we need to restructure our bachelor of education (Primary) programmes` curriculum in teacher professionalism.

entry Level of mathematics subject knowledge, mathematics pedagogical content knowledge, mathematics teaching performance

Changsri, Narumon , Inprasitha, Maitree , Pattanajk, Auijit

DOI: Vol.16(No.1) 67-77, 2012

This study aimed to explore teachers` perceived beliefs regarding teaching practice in the context of three-year Professional Development Project (ProDev) implementing lesson study incorporating Open Approach. The data were collected through questionnaire distributing to the teachers in three schools. Qualitative data were collected through participatory observation on teaching practice and interviewing members of lesson study team. The findings revealed that teacher`s perceived beliefs regarding teaching practice could be categorized into three categories according to 3 phases of lesson study as the followings: 1) Perceived beliefs related to collaboratively designing research lessons 2) Perceived beliefs related to collaboratively observing their friend teaching the re-search lesson 3) Perceived beliefs related to collaboratively doing post-discussion or reflection on the activities of the two phases.

Professional Development Project, ProDev, teachers` perceived beliefs, teaching practice, Lesson study, open approach

Han Hyuk Cho , Ji Yoon Lee , Hyo Myung Lee

DOI: Vol.16(No.1) 79-90, 2012

This research investigated if the embodied symbol using a turtle metaphor in a mi-croworld environment works as a cognitive tool to mediate the learning of combinatorics. It was found that students were able to not only count the number of cases systematically by using the embodied symbols in a situated problem regarding Permutation and Combination, but also find the rules and infer a concept of Combination through the activities manipulating the symbols. Therefore, we concluded that the embodied symbol, as a bridge that connects learners` concrete experiences with abstract mathematical concepts, can be applied to introduction of various mathematical concepts as well as a combinatorics concept.

combinatorics, embodied, symbols, mediation, bridge, microworld