• School Mathematics
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• v.13 no.4
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• pp.581-598
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• 2011

Given the growing agreement that algebra should be taught in the early stage of the curriculum, considerable studies have been conducted with regard to early algebra in the elementary school. However, there has been lack of research on how to organize mathematic lessons to develop of algebraic reasoning ability of the elementary school students. This research attempted to gain specific and practical information on effective algebraic teaching and learning in the elementary school. An exploratory qualitative case study was conducted to the fourth graders. This paper focused on the associative law of the multiplication. This paper showed what kinds of activities a teacher may organize following three steps: (a) focus on the properties of numbers and operations in specific situations, (b) discovery of the properties of numbers and operations with many examples, and (c) generalization of the properties of numbers and operations in arbitrary situations. Given the steps, this paper included an analysis on how the students developed their algebraic reasoning. This study provides implications on the important factors that lead to the development of algebraic reasoning ability for elementary students.

• Journal for History of Mathematics
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• v.28 no.3
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• pp.151-164
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• 2015

The purpose of this paper is to develop a teaching and learning material integrated two subjects Pythagorean theorem and Fibonacci numbers. Traditionally the former subject belongs to geometry area and the latter is in algebra area. In this work we integrate these two issues and make a discovery method to generate infinitely many Pythagorean numbers by means of Fibonacci numbers. We have used this article as a teaching and learning material for a science high school and found that it is very appropriate for those students in advanced geometry and number theory courses.

• Journal of Educational Research in Mathematics
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• v.10 no.1
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• pp.85-102
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• 2000

The concept of variables is central to mathematics teaching and learning in junior and senior high school. Understanding the concept provides the basis for the transition from arithmetic to algebra and necessary for the meaningful use of all advanced mathematics. Despite the importance of the concept, however, much has been written in the last decade concerning students' difficulties with the concept. This Thesis is based on research to investigate the hypothesis that LOGO programming will contribute to 6th grader' learning of variables. The aim of the research were to; .investigate practice on pupils' understanding of variables before the activity with a computer; .identify functions of LOGO programming in pupils' using and understanding of variable symbols, variable domain and the relationship between two variable dependent expressions during the activity using a computer; .investigate the influence of pupils' mathematical belief on understanding and using variables. The research consisted predominantly of a case study of 6 pupils' discourse and activities concerning variable during their abnormal lessons and interviews with researcher. The data collected for this study included video recordings of the pupils'work with their spoken language.

• Journal of the Korean School Mathematics Society
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• v.22 no.1
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• pp.81-94
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• 2019

The purpose of this study is to investigate the meaning of CAS(Computer Algebra System) using in mathematics teaching and learning, and the change of the theory of mathematics teaching and learning caused by introduction of CAS. Especially, when CAS was introduced, some categories of assessment items were examined, and alternative assessment directions were presented and the implications of them were discussed.

• Communications of Mathematical Education
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• v.28 no.1
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• pp.65-79
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• 2014

The present study seeks to provide an easy path to differential perceptions of students at the upper high school level by applying a story telling method and also, characteristically, to earn some time for class discussion by reducing learning time for simple calculational procedure through Computer Algebra System(CAS) tools. This study offers a clear example of storytelling textbooks through Sage. Hence, the study aims at enabling students who have practiced contents with Sage tools to deal with diverse and complicated calculation problems, if they learn to build up mathematical formulas for those problems.

• School Mathematics
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• v.16 no.4
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• pp.803-825
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• 2014

From the early stages of learning algebra, literal symbols are used to represent algebraic objects such as variables and parameters. The concept of parameters contains both indeterminacy and fixity resulting in confusion and errors in understanding. The purpose of this research is to compare the beginners of algebra and pre-service teachers who completed secondary mathematics education in terms of understanding this paradoxical nature of parameters. We recruited 35 middle school students in eight grade and 73 pre-service teachers enrolled in a undergraduate course at one university. Using them we conducted a survey on the perception of the nature of parameters asking if one considers parameters suggested in a problem as variables or constants. We analyzed the collected data using the mixed method of qualitative and quantitative approaches. From the analysis results, we identified several difficulties in understanding of parameters from both groups. Especially, our statistical analysis revealed that the proportions of subjects with limited understanding of the concept of parameters do not differ much in two groups. This suggests that learning algebra in secondary mathematics education does not improve the understanding of the nature of parameters significantly.

• Journal of Educational Research in Mathematics
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• v.15 no.2
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• pp.215-232
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• 2005

Computer algebra system (CAS) calculators are becoming increasingly common in schools and universities. While Hey offer quite sophisticated mathematical capability to teachers and students, it is not clear at present how they may best be employed. In particular their integration into students' learning and problem-solving remains an issue. In this paper we address this issue through the lens of a study that considered the introduction of the TI-89 CAS calculator to students about to enter university. We describe a number of different aspects of the partnership they formed with the calculator as they began the process of instrumentation of the CAS in their learning.

• Journal of the Korean School Mathematics Society
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• v.7 no.2
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• pp.99-116
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• 2004

This study investigates the concept of irrational number which middle school students begin to learn for the first time in their learning mathematics. Further, this explores how that concept is being taught, how much students understand that concept and things that students have difficulty in understanding relating to the concept of irrational number. Thus we try to figure out how the concept of irrational number should be taught for the most effective students' understanding. Thus, we want to provide some suggestions for teaching and learning irrationals numbers.

• Journal for History of Mathematics
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• v.20 no.3
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• pp.105-126
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• 2007

The present paper considers how to teach mathematical concepts. In particular, we aim to a balanced, unified achievement for three elements of concept loaming such as concept understanding, computation and application through one's mathematical intuition. In order to do this, we classify concepts into three patterns, that is, intuitive concepts, logical concepts and formal concepts. Such classification is based on three kinds of philosophy of mathematics : intuitionism, logicism, fomalism. We provide a concrete, practical investigation with important nine concepts in theory of vectors from the viewpoint of three patterns of concepts. As a consequence, we suggest certain solutions for an effective concept learning in teaching theory of vectors.

• Journal of the Institute of Convergence Signal Processing
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• v.14 no.1
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• pp.57-61
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• 2013

A hybrid genetic algorithm based learning method for the morphological neural networks (MNN) is proposed. The morphological neural networks are based on max-plus algebra, therefore, it is difficult to optimize the coefficients of MNN by the learning method with derivative operations. In order to solve the difficulty, a hybrid genetic algorithm based learning method to optimize the coefficients of MNN is used. Through the image compression/reconstruction experiment using test images extracted from standard image database(SIDBA), it is confirmed that the quality of the reconstructed images obtained by the proposed method is better than that obtained by the conventional neural networks.