Representation Systems of Building Blocks in Logobased Microworld
Ji Yoon Lee , Han Hyuk Cho , Min Ho Song , Hwa Kyung Kim
15(1) 114, 2011
Ji Yoon Lee , Han Hyuk Cho , Min Ho Song , Hwa Kyung Kim
DOI: JANT Vol.15(No.1) 114, 2011
Logo has influenced many researchers and learners for the past decades as a 2D turtle geometry environment in the perspective of constructionism. Logo uses the metaphor of ``playing turtle`` that is intrinsic, local and procedural. We, then, design an environment in which the metaphor of ``playing turtle`` is applied to construct 3D objects, and we figure out ways to represent 3D objects in terms action symbols and 3D building blocks. For this purpose, design three kinds of representation systems, and asked students make various 3D artifacts using various representation systems. We briefly introduce the results of our investigation into students` cognitive burden when they use those representation systems, and discuss the future application measures and the design principles of Logobased 3D microworld.

On the Design of Logobased Educational Microworld Environment
Han Hyuk Cho , Min Ho Song , Ji Yoon Lee , Hwa Kyung Kim
15(1) 1530, 2011
Han Hyuk Cho , Min Ho Song , Ji Yoon Lee , Hwa Kyung Kim
DOI: JANT Vol.15(No.1) 1530, 2011
We study to design educational Logobased microworld environment equipped with 3D construction capability, 3D manipulation, and webbased communication. Extending the turtle metaphor of 2D Logo, we design simple and intuitive symbolic re presentation system that can create several turtle objects and operations. We also present various mathematization ctivities applying the turtle objects and suggest the way to make good use of them in mathematics education. In our microworld environment, the symbolic representations constructing the turtle objects can be used for webbased collaborative learning, communication, and assessments.

Mathematical Problem Solving for Everyone: A Design Experiment
Quek Khiok Seng , Dindyal Jaguthsing , Toh Tin Lam , Leong Yew Hoong , Tay Eng Guan
15(1) 3144, 2011
Quek Khiok Seng , Dindyal Jaguthsing , Toh Tin Lam , Leong Yew Hoong , Tay Eng Guan
DOI: JANT Vol.15(No.1) 3144, 2011
An impetus for reviving research in mathematical problem solving is the recent advance in methodological thinking, namely, the design experiment ([Gorard, S. (2004). Combining methods in educational research. Maidenhead, England: Open University Press.]; [Schoenfeld, A. H. (2009). Bridging the cultures of educational research and design. Educational Designer. 1(2). http://www.educationaldesigner.org/ed/volume1/issue2/]). This methodological approach supports a "redesign" of contextual elements to fulfil the overarching objective of making mathematical problem solving available to all students of mathematics. In problem solving, components critical to successful design in one setting that may be adapted to suit another setting include curriculum design, assessment strategy, teacher capacity, and instructional resources. In this paper, we describe the implementation, over three years, of a problem solving module into the main mathematics curriculum of an Integrated Programme school in Singapore which had sufficient autonomy to tailorfit curriculum to their students.

Mathematical Thinking through Different Representations and Analogy
Cheng Chun Chor Litwin
15(1) 4557, 2011
Cheng Chun Chor Litwin
DOI: JANT Vol.15(No.1) 4557, 2011
Mathematical thinking is a core element in mathematics education and classroom learning. This paper wish to investigate how primary four (grade 4) students develop their mathematical thinking through working on tasks in multiplication where greatest products of multiplication are required. The tasks include the format of many digit times one digit, 2 digits times 2 digits up to 3 digits times 3 digits. It is found that the process of mathematical thinking of students depends on their own representation in obtaining the product. And the solution is obtained through a pattern/analogy and "pattern plus analogy" process. This specific learning process provides data for understanding structure and mapping in problem solving. The result shows that analogy allows successful extension of solution structure in the tasks.

Reconsidering the Category Framework for Describing Mathematics Teachers` Values
Chih Yeuan Wang
15(1) 5968, 2011
Chih Yeuan Wang
DOI: JANT Vol.15(No.1) 5968, 2011
This paper proposes a modified category framework derived from VAMP and VIMT projects for describing teachers` mathematical and pedagogical values, and examines the dialectical relations between values awareness/willingness and teaching, based on case studies of student teachers of secondary mathematics from a followup project of VIMT. The preliminary results show that student teachers would teach certain values depending on the awareness of values priority, willingness to teach, their teaching capabilities and classroom conditions. So, mathematics teacher educators should provide relevant courses to facilitate student teachers to be aware of their implicit values and be willing to enact these values, and to empower student teachers with the knowledge and experiences to teach the values.

Development of a Mathematical Creativity Test for Bengali Medium School Students
Roy Avijit
15(1) 6979, 2011
Roy Avijit
DOI: JANT Vol.15(No.1) 6979, 2011
Based on the work of Haylock (cf. [Haylock, D. W. (1987). A framework for assessing mathematical creativity in schoolchildren. Educ. Stud. Math. 18(1), 5974]) a mathematical creativity test containing items of two categories overcoming fixation and divergent thinking has been developed for Bengali medium school students with sample size 262. The items measuring divergent thinking are found highly internally consistent and there is a significant correlation between overcoming fixation and divergent thinking. Study of the factorial validity of the test by Thursstone`s centroid method gives satisfactory result. Validity coefficient of the test with teachers` rating, alpha reliability and testretest reliability of the test are also found satisfactory.

Exploring Level Descriptors of Geometrical Thinking
Srichompoo Somkuan , Inprasitha Maitree , Sangaroon Kiat
15(1) 8191, 2011
Srichompoo Somkuan , Inprasitha Maitree , Sangaroon Kiat
DOI: JANT Vol.15(No.1) 8191, 2011
The aim of this study was to explore the grade 13 students` geometrical thinking level descriptors based on van Hiele level descriptors. The data were collected through collection of geometric curriculum materials such as indicators and learning standards in Basic Education Core Curriculum and mathematics textbook for grades 13. The findings were found that 1) Inconsistency between descriptors appeared on mathematics curriculum and Thai mathematics textbooks. 2) Using topics on textbooks as criterion for exploring 5 of 7 descriptors appeared on Thai mathematics textbook indicated geometrical thinking levels based on van Hiele`s model merely level 0 (Visualization) across textbooks for grades 13.

Just Maybe the Problem Lies in Reading the Pictorial Model
Patton Barba
15(1) 93104, 2011
Patton Barba
DOI: JANT Vol.15(No.1) 93104, 2011
Sixtyfour EC6 teacher candidates were asked to elaborate on the method they used when interrupting seven mathematical pictorial models. The instrument used was research designed but modeled after a 4th grade released state tests. This study was conducted in the southern part of the United States. A panel of experts worked with the researcher to determine the most appropriate initial approach to interrupting the mathematical pictorial model. The pictorial models examined such concepts as measurement, place value and time. Since the questions were on a 4th grade level, it was expected that the teacher candidates would score 100%, however, this was not the case. The results will be given in the paper as each question is discussed. The results of the survey are being used to develop teaching modules for teacher candidates in mathematics methodology classes.
