• School Mathematics
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• v.19 no.2
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• pp.289-317
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• 2017

This study aims to explore how Korean middle-school mathematics textbooks on functions provide students an opportunity-to-learn [OTL]. For this purpose, we investigate 3 textbooks in terms of mathematics content and practice, the level of cognitive demands of mathematical tasks, types of student responses, types of context-based tasks, and connections among the tasks. The findings from the data analysis suggest as follows: a) an opportunity-to-learn to connect procedures to functional concepts and new ideas of functions to the existing one is very limited; b) the textbooks seem to provide students an OTL to understand functions as definitions, rules and conventions and to experience repeatedly procedural executions through worked examples and mathematics tasks; c) students may not experience to explain their own ideas/thinking by using mathematical sentence or justify their own cognitive processes; and d) students can be exposed to get a sense of mathematics as a set of fragmented and isolated facts or procedures, rather than to encourage to expand and deepen their understanding of functions.

• Journal of Elementary Mathematics Education in Korea
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• v.12 no.2
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• pp.125-148
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• 2008

The purpose of this study was to analyze concretely and minutely a primary factor of deciding attitude of learning mathematics of elementary school students, grope a solution for negative attitude of learning mathematics with researching a difference between major factors by achievement in mathematics, and examine a suggestion in forming positive attitude of learning mathematics. The results of this study is as follows. First, elementary school students decided whether they liked or disliked mathematics, depending on not only characteristics of mathematics, but also teacher's teaching mathematics with interest and fun, or teacher's teaching tediously and difficultly. Second, negative attitude toward mathematics exam of elementary school students was influenced by parents' meddling for exam and negative attitude toward result of exam more than uneasiness by exam itself. Third, as private education for elementary school students becomes more popular, the learning mathematics out of school can be an important factor to decide attitude of learning mathematics of students on several sides such as teacher, teaching method, method of presenting task, and so on as much as mathematics class in school, and characteristics of mathematics. Fourth, students demanded silent and concentrative atmosphere in studying to have positive attitude of learning mathematics. Fifth, as the result of examining major factors that form attitude of teaming mathematics of groups by achievement in mathematics, there was considerable difference in each group. Students in a group of ‘upper’ and ‘lower’ disliked parents' meddling and rebuke, but it didn't change greatly their attitude toward mathematics exam. However a group of ‘middle’ showed the greatest uneasiness toward an exam, and they reacted sensitively to parent's rebuke, scolding, learning environment, and so on.

• Communications of Mathematical Education
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• v.13 no.1
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• pp.107-127
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• 2002

본 연구는 유아기 교수-학습 방법에 대한 기초 이론과 수학교육에서의 교수-학습 방법에 대한 제안들을 근거로 유아에게 적절하고도 효과적인 수학 교수-학습 방법은 무엇인지를 알아보는 것이다. 이를 구성주의에 근거한 상호적 접근과 교수-학습을 위한 기타 제안들 그리고 활동중심의 통합적 접근으로 나누어 그 이론적 기초와 구체적인 적용방법에 대해 자세히 살펴보았다. 구성주의에 근거한 상호적 접근은 Piaget와 Vygotsky의 견해와 인지적 도제모형, 상황적 교수 모형, 그리고 인지적 유연성 이론의 세 가지를 포함하였고, 기타 제안들에는 NCTM, NAEYC, Schweinhart Perlmutter, Bloom & Burrell, 그리고 Althouse의 견해를 포함하였다. 그리고 활동중심의 통합적 접근은 수학적 개념 중심의 활동 통합교육과 활동 중심의 수학 통합교육으로 나누어 Web을 구성하고 적용하는 과정을 알아보았다.

• Communications of Mathematical Education
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• v.9
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• pp.227-239
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• 1999

영재교육의 이론적 근거를 제시한 연구물이 국내에는 그다지 많지 않다. 뿐만 아니라 지금 한국과학재단에서 지원하고 있는 전국의 9개 대학 과학영재교육센터 역시 실천적인 차원의 활동을 벗어나지 못하고 있다. 외국의 대학부설 연구소들이 30년 이상 이와 같은 연구와 서비스를 지속적으로 실천해오고 있는 사례들을 우리는 쉽게 찾을 수 있다는 점을 거울 삼아 모처럼 마련된 국가적 차원의 지원을 토대로 그 바람직한 실천과 연구를 위한 방안을 다음과 같이 제시해본다. 첫째, 질적 연구의 집적에 힘써야 한다. 영재교육이라는 특수한 상황을 전제로 할 때는 더구나 그렇듯이 일반화를 전제로 한 양적 연구보다는, 사례연구와 같은 질적 연구물들의 집적에 노력을 아끼지 말아야할 것이다. 둘째, 교수-학습 활동은 활동이론과 구성주의 이론의 적절한 조화가 요망된다. 구성주의 이론에 입각한 교수-학습 활동의 모습을 단적으로 말하자면, 학습자 자신이 주어진 문제 상황에서의 탐구를 통하여, ‘구체적인 것에서 추상적인 것으로’ 나아가 스스로 지식을 구성하는 것이다. 그러나, 활동이론에 입각한 교수-학습 활동의 요지는 활동은 정말로 전형적인 활동에 국한하고 나머지는 교사의 설명에 의해 학습자들이 ‘추상적인 것에서 구체적인 것으로의 소급’이 가능하도록 하는 것이다. 완전히 정반대의 주장을 하는 것 같으면서도 일면 그 타당성들을 갖고 있는 것으로 볼 수 있다. 셋째, 학제적 ${\cdot}$ 통합적 연구가 절실하다. 연구의 측면에서 수학반 아동과 과학반 아동들의 활동상의 차이점이나 유사점 등에 대한 질적 연구를 시도해보는 것은 매우 의미있는 일이 될 것이다.

• Journal of Educational Research in Mathematics
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• v.16 no.4
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• pp.273-295
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• 2006

It is the purpose of this study to help computational estimation study to settle down in effective teaching method through analysis how students are understanding computational estimation and what occurs using computational estimation in actual life problem situations. I set 3 cases to accomplish these purposes. (1) How students are understanding computational estimation? (2) How students' computational estimation ability is in applying actual life problem situation? (3) What is students' different attitudes in an actual life problem situation before studying computational estimation and after? To accomplish tile purpose, I chose 6 third grade students and taught 'Computational estimation using actual life problem situation' and analyzed students computational estimation processing. Then I arranged the computational estimation processing in an actual life problem situation and differences between the before and tile after. As a result, I obtained the followings. (1) Need of estimation: Every students could recognize the need of estimation with experiencing an actual life problem situation. (2) Choosing the order of decimals: Students could choose appropriate order of decimals according to an actual life problem situations. (3) Using strategy: They usually use rounding strategy and quite often use special number and compatible number strategy.

• Communications of Mathematical Education
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• v.8
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• pp.121-135
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• 1999

본 연구는 초등학교 수학의 연산 영역에 있어서, 문제설정활동의 두 가지 방법(문제꾸미기, 문제만들기) 중 어느 방법이 4학년 아동의 수학적 문제해결력에 더 효과적인지 알아보고, 아동의 학습능력수준과 성별에 따라 수학적 문제해결력의 신장에 더 유용한 문제설정방법을 찾아보는데 그 목적이 있었다. 그 결과 '문제꾸미기'에 의한 문제설정방법이 학습 수준이 상 ${\cdot}$중위 집단에서 유용한 방법이며, 문제해결력 요소 중 문제구성력과 전략적용력을 신장시킬 수 있다는 방법이라는 것을 알 수 있었고 남녀성별에 따른 유의미한 차이는 없었다. 이런 연구 결과로 주어진 문제를 조건과 내용을 바꾸는 다소 쉬운 문제설정 방법보다는 어떤 상황만 제시하고 그 상황 속에서 문제를 만들어보는 문제꾸미기의 문제설정 방법이 문제해결력의 신장에 도움이 됨을 알 수 있었다.

• Journal of the Korean School Mathematics Society
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• v.13 no.4
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• pp.635-653
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• 2010

The purpose of this article is to investigate the relationship between children's goals and activities in terms of continuity and transformation of their learning through interactions between learners and practices across settings. By observing children's activities across settings and tasks and interviewing the children, I found that the continuity and transformation in learning are developed in the relationship between changing individuals and changing social context. In this process, social interaction with others plays an important role in changing their goals and strategies. The results imply that appropriate tasks and teachers' guidance are crucial to facilitate students' learning across settings.

• School Mathematics
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• v.18 no.4
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• pp.773-791
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• 2016

Teacher noticing ability has been considered as one of important elements influencing a quality of teaching. Noticing is closely related to teachers' in the moment decision making in a class, and teachers notice things as they create and interact with their classroom setting. Mathematics teachers as an expert should notice students' mathematics learning during a class. The aim of this study was to analyze how mathematics teacher's pre-noticing activity that the teacher anticipated students' typical strategies and difficulties in learning targeted mathematics knowledge and prepared appropriate responses worked in practice. As a result, the teacher conducted three types of noticing in her classes: noticing shaping students' understanding by using students' misconceptions or errors; noticing creating students' learning opportunities based on their prior knowledge; noticing improving students' informal reasoning. This study concluded with discussion about the positive effect of teacher's pre-noticing activity on her actual noticing in practice, as well as implications for teacher education.

• Journal of Elementary Mathematics Education in Korea
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• v.13 no.2
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• pp.141-161
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• 2009

Mathematical Communication ability can be more developed through sharing thoughts with others. Therefore when we instruct students in math, it is very important for teachers to provide them with opportunity to communicate mathematically. So this study provided open-ended problems in small-group collaborative learning. And we analyzed students' mathematical communication focused on the student's level of understanding. Furthermore, to improve students' mathematical communication ability, this study tries to attract the factors that we should consider the exact date for inserting the open-ended problems into a course of math and the student's level of understanding for selecting suitable open-ended problems.

• Journal of the Korean School Mathematics Society
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• v.9 no.3
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• pp.265-286
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• 2006

Given that less attention has been paid to teachers than students in mathematics education, this study attempted to provide theoretical foundations to understand better mathematics teacher learning and teaching practice in transition. First, this paper summarized three conceptions of teacher learning on the basis of the relationships of knowledge and practice followed by several implications to mathematics teacher education. Second, this paper provided a brief overview of cognition as situated, social, and distributed. This paper then explored new implications and issues about mathematics teacher learning that the overview brought to light. It is expected for teacher educators and researchers to participate in rich discussion of many implicit issues about teacher learning that this paper begins to raise.