• Research in Mathematical Education
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• v.15 no.1
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• pp.1-14
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• 2011

Logo has influenced many researchers and learners for the past decades as a 20 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 Logo-based 3D microworld.

• School Mathematics
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• v.18 no.2
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• pp.323-348
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• 2016

The 2009 revised national mathematics curriculum have inserted mathematical 'linking cube' activities in the 6th grade math classes to improve students' spatial problem solving abilities and communication skills. However, we found that it was hard for teachers to teach problem solving and communication skills due to the absence of mathematical way of representing linking cubes in the classroom. In this paper, we propose 3D 'turtle representation system' as teaching and learning tools for linking cube activities. After using turtle representation system for linking cube activities, teachers responded that turtle representation system is a valuable problem solving and communication tools for the linking cube mathematics classes. We conclude that turtle representation system is a well designed teaching and learning tools for linking cube activities, and there are lots of educational meanings in the 3D turtle representation system.

• Research in Mathematical Education
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• v.15 no.1
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• pp.15-30
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• 2011

We study to design educational Logo-based microworld environment equipped with 3D construction capability, 3D manipulation, and web-based communication. Extending the turtle metaphor of 2D Logo, we design simple and intuitive symbolic representation system that can create several turtle objects and operations. We also present various mathematization activities 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 web-based collaborative learning, communication, and assessments.

• Research in Mathematical Education
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• v.18 no.4
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• pp.273-288
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• 2014

In recent years, coding education has been globally emphasized and the Free Semester System will be executed to the public schools in Korea from 2016. With the introduction of the Free Semester System and the rising demand of Computational Thinking (CT) capacity, this research aims to design 'learning environment' in which learners can design and construct mathematical objects through computers and print them out through 3D printers. Furthermore, it will design learning mathematics by constructing the figurate number patterns from 'soma cubes' in the playing context and connecting those to algebraic and combinatorial patterns, which will allow students to experience mathematical connectivity. It is expected that the activities of designing figurate number patterns suggested in this research will not only strengthen CT capacity in relation to mathematical thinking but also serve as a meaningful program for the Free Semester System in terms of career experience as 3D printers can be widely used.