• Communications of Mathematical Education
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• v.31 no.3
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• pp.331-347
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• 2017

The purpose of this study is to develop a sample chapter of mathematics textbook at the first middle school according to the model of supporting learners' self-directed learning. The self-directed learning is a learning strategy to develop learner's ability to solve unstructured problems by himself or herself. Basically, the textbook should included learning objectives distinctively. Second textbook should consist of some appropriate method for learners to learn content. Third, it suggests some plans to utilize learning strategies of this model effectively when authors or developers develop textbooks in future. Based on those condition, it is also requested that the sample chapter of the textbook be develop in order to study interestingly as well as to implement self-directed study, and content materials using mixed diverse subjects would be included in the chapter. Furthermore, the sample chapter which is suitable to the semester of managing self-directed learning middle school would be developed. For this purpose, in this study the 'Plane shapes' was selected dealt with in the first middle school. The sample chapter is developed at first by the researchers and then revised and completed through the checking from the professionalists two times.

• The Mathematical Education
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• v.58 no.3
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• pp.403-422
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• 2019

As the informal graph was introduced newly in the area of function in middle school mathematics curriculum revised in 2015, ten publishing company became to have a concern on how to represent the graph content uniquely and newly. At this time, it may be meaningful and useful to compare and analyze the content of the graph unit shown on each textbook published by publishing companies. To accomplish this, on fundamentally the basis of diverse prior researches this study tried to select the elements of expression and interpretation of the graph and establish an analytic frameworks of expression and interpretation of the graph respectively. This study executed the frequency analysis and cross analysis by textbook system, textbook, and the number of the graph drawn on a coordinate plane on the representation and interpretation of the graph. As a result, the textbook contains more items on interpretation than the representation of the graph, and students showed a learning effect on the graph unit but showed a neutral response to the impact of learning. This basic and essential paper shed light on developing the practical and more creative textbook which has diversity and characteristic respectively, while adjusting the scope of the elements of the graph's representations and interpretations and providing proper level and quality content.

• Journal for History of Mathematics
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• v.24 no.3
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• pp.145-163
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• 2011

This study sets the cut points of affective achievement scores based on the criteria referenced assessment. The modified Angoff method is applied to the standardized mathematics affect inventory which had validity and reliability. The cut points are set for 6 factors i.e. learning directivity, self control, anxiety, interest, cognizing value and confidence. As the results, among percentages of factor that middle school 2nd grade students in Korea achieved, the proportion of cognizing value is the highest. And there are no difference of the proportions as for gender, differentiated instruction, and region.

• Journal of Educational Research in Mathematics
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• v.17 no.4
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• pp.453-475
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• 2007

School algebra starts with introducing algebraic expressions which have been one of the cognitive obstacles to the students in the transfer from arithmetic to algebra. In the recent studies on the teaching school algebra, algebraic thinking is getting much more attention together with algebraic expressions. In this paper, we examined the processes of the transfer from arithmetic to algebra and ways for teaching early algebra through algebraic thinking factors. Issues about algebraic thinking have continued since 1980's. But the theoretic foundations for algebraic thinking have not been founded in the previous studies. In this paper, we analyzed the algebraic thinking in school algebra from historico-genetic, epistemological, and symbolic-linguistic points of view, and identified algebraic thinking factors, i.e. the principle of permanence of formal laws, the concept of variable, quantitative reasoning, algebraic interpretation - constructing algebraic expressions, trans formational reasoning - changing algebraic expressions, operational senses - operating algebraic expressions, substitution, etc. We also identified these algebraic thinking factors through analyzing mathematics textbooks of elementary and middle school, and showed the middle school students' low achievement relating to these factors through the algebraic thinking ability test. Based upon these analyses, we argued that the readiness for algebra learning should be made through the processes including algebraic thinking factors in the elementary school and that the transfer from arithmetic to algebra should be accomplished naturally through the pre-algebra course. And we searched for alternative ways to improve algebra curriculums, emphasizing algebraic thinking factors. In summary, we identified the problems of school algebra relating to the transfer from arithmetic to algebra with the problem of teaching algebraic thinking and analyzed the algebraic thinking factors of school algebra, and searched for alternative ways for improving the transfer from arithmetic to algebra and the teaching of early algebra.

• Journal of Educational Research in Mathematics
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• v.24 no.3
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• pp.359-374
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• 2014

Students' difficulties and errors in relation to mathematical proofs are worth while to say one of the dilemmas in mathematics education. The potential elements of their difficulty are scattered over the process of proving in geometry as well as algebra. This study aims to investigate whether middle school students understand the context of algebraic proof including literal expressions. We applied 24 third-grade middle school students a test item which shows a proof including a literal expression and missing the conclusion. Over the half of them responded wrong answers based on only the literal expression without considering its context. Three of them were interviewed individually to show their thinking. As a result, we could find some characteristics of their thinking including the perspective on proof as checking the validity of algebraic expression and the gap between proving and understanding of proof etc. From these, we also discussed about several didactical implications.

• Journal of the Korean School Mathematics Society
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• v.22 no.3
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• pp.221-240
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• 2019

The purpose of this study is to suggest Reciprocal Peer Tutoring(RPT) for mathematics underachieving students as one way of the instructional strategies to supplement their lack of mathematics learning and to provide them with successful experiences in learning mathematics. We defined underachieving student in mathematics as the student whose mathematics achievement was high or middle level in the middle school but became lower in high school. Four mathematics underachievers voluntarily participated in this study. We examined the effects and roles of RPT by focusing on their positive change in the affective domain. RPT was conducted for about three months, including pre-training, pretest, and posttest. As the results of this research, RPT has generally made positive changes in the affective domain of underachieving mathematics students. Although four students did not show the same pattern of change and the sub-elements of positive change were different for each student, RPT provided opportunities for 4 all students to experience positive change.

• Communications of Mathematical Education
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• v.19 no.2 s.22
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• pp.417-434
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• 2005

본 연구에서 문제제기 수업이 수학학습에 미치는 효과를 알아보기 위하여 문제제기 수업과 기존의 교사 주도식 수업방식에서 문제해결력과 수학적 창의력에 대한 효과를 분석하였다. 중학교 3학년 학생을 대상으로 28주 동안 문제제기 수업을 실시하여 수업을 한 후, 문제해결력 검사지와 수학적 창의력 검사지를 평가한 결과는 다음과 같다. 첫째, 문제제기 수업을 활용한 수업방식이 기존의 교사 주도식 수업방식에 비해 문제해결력 신장에 효과가 있는 것으로 나타났다. 둘째, 문제제기 수업이 교사 주도식 수업에 비해 수학적 창의력 신장에 효과가 있는 것으로 나타났고, 특히 수학적 창의력 하위 요소 중 유창성과 융통성 신장에 효과가 있었다. 따라서 문제해결력 신장과 수학적 창의력 신장을 위해서 학교수업에서 문제제기 수업 활동의 도입을 제언한다.

• The Journal of Korean Association of Computer Education
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• v.4 no.1
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• pp.99-107
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• 2001

One of the main objects of geometry in mathematics education is to improve students' geometric intuition capability and logical reasoning capability based on them. A visual element related to intuition plays an important role in teaching and learning of geometry. Therefore, in this research, we focus on the development of multimedia title available to dynamic operation about visual elements and verify of effect of its application. This title for the learning of "the Pythagorean theorem and its practical use" in the third grade of middle school is designed and implemented by an authoring tool, Toolbook. And it enables learners to study mathematics individually and can be applied to the educational field, too. And we taught two groups, the applied group and the compared one of the second grade of middle school and surveyed Questions and evaluated study achievement. We calculated study achievement of two groups on t-test using SPSS. As the result, we knew that the applied group is higher than the compared one in the study achievement and provision of dynamic operation possibility on visual elements make students know very high learning effect and help improvement of intelligent capability.

• Communications of Mathematical Education
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• v.33 no.4
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• pp.425-444
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• 2019

Comparing to the U.S. mathematics textbooks, this study examines the opportunity to learn statistical processes represented in mathematics textbooks reflecting 2015 revised curriculum. Analyzing four different kinds of Korean middle school mathematics textbooks and two kinds of corresponding U.S. textbooks for seventh graders, we found that the tasks dealing with all the phases of statistical processes were found only in the U.S. textbooks while not even one task in such a case was not observed in the Korean textbooks. To make matters worse, the proportion of the tasks dealing with only one phase of statistical processes was 93.3% of all the tasks in Korean textbooks. In terms of types of tasks, the types of tasks were very homogeneous in Korean textbooks, usually Types FPR or PR while more various types of tasks were found in the U.S. textbooks such as Types FRI, PRI, FR, or RI. In views of features of each phase in statistical processes, Korean textbooks heavily focused only on some particular statistical behaviors such as 'formulating a problem', 'collecting data', 'transforming data', and 'analyzing a part of data.' The findings of this study provide meaningful implications for improving statistics education and developing mathematics textbooks to enhance students' statistical thinking and problem-solving ability.

• School Mathematics
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• v.6 no.4
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• pp.325-344
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• 2004

This study was carried out to investigate effects of the mindmap note-taking for the formation of the mathematical concepts structure and the matjematical creativity. Two classes were randomly chosen for this study from the third grade students of a middle school located in a medium size city. Thirty one lecture hours of the mindmap note-taking on the quadratic equation and functions were administered to the experimental class of 41 students, while same lecture hours of the ordinary instruction on the same contents were administered to the control class of 40 students. It was shown from this experiment that there ware significant evidences of improvement both in the formation of students' mathematical concepts structure and mathematical creativity through the mindmap note-taking lecture. Hence, the mindmap note-taking lecture is suggested for the improvement in the formation of student's mathematical concepts structure and mathematical creativity.