• Research in Mathematical Education
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• v.20 no.1
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• pp.11-19
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• 2016

Investigating students' lived mathematical experiences presents dual challenges for the researcher. On the one hand, we must respect that students' experiences are not directly accessible to us and are likely very different from our own experiences. On the other hand, we might not want to rely upon the students' own characterizations of what constitutes mathematics because these characterizations could be limited to the formal products students learn in school. I suggest a characterization of mathematics as objectified action, which would lead the researcher to focus on students' operations-mental actions organized as objects within structures so that they can be acted upon. Teachers' and researchers' models of these operations and structures can be used as a launching point for understanding students' experiences of mathematics. Teaching experiments and clinical interviews provide a means for the teacher-researcher to infer students' available operations and structures on the basis of their physical activity (including verbalizations) and to begin harmonizing with their mathematical experience.

• Journal of Educational Research in Mathematics
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• v.13 no.1
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• pp.25-55
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• 2003

In the school mathematics, the negative numbers have been instructed by means of intuitive models(concrete situation models, number line model, colour counter model), inductive-extrapolation approach, and the formal approach using the inverse operation relations. These instructions on the negative numbers have caused students to have the difficulty in understanding especially why the rules of signs hold. It is due to the fact that those models are complicated, inconsistent, and incomplete. So, students usually should memorize the sign rules. In this study we studied on the didactical phenomenology of the negative numbers as a foundational study for the improvement of teaching negative numbers. First, we analysed the formal nature of the negative numbers and the cognitive obstructions which have showed up in the historic-genetic process of them. Second, we investigated what the middle school students know about the negative numbers and their operations, which they have learned according to the current national curriculum. The results showed that the degree they understand the reasons why the sign rules hold was low Third, we instructed the middle school students about the negative number and its operations using the formal approach as Freudenthal suggest ed. And we investigated whether students understand the formal approach or not. And we analysed the validity of the new teaching method of the negative numbers. The results showed that students didn't understand the formal approach well. And finally we discussed the directions for improving the instruction of the negative numbers on the ground of these didactical phenomenological analysis.

• Communications of Mathematical Education
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• v.26 no.1
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• pp.71-84
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• 2012

The purpose of this study is to analyze some Korean elementary pre-service teachers' Mathematical Knowledge for Teaching(MKT) and compare the results with those obtained by Kwon, Nam, & Kim(2009), so that we can provide some suggestions to improve education of elementary mathematics subject at Korean teachers colleges. For this purpose, we selected the MKT items on number and operations which were adapted for Korean in-service teachers by Kwon et al. The survey consisting of those items was administered to 88 Korean elementary pre-service teachers at teachers college, J University. The results are the following: First, the respondents, elementary pre-service teachers, showed that they already had a sufficient amount of Content Knowledge(CK) on number and operations, but that their level of Knowledge of Content and Students(KCS) was insufficient. This means we need to strengthen our students' KCS in education of elementary mathematics subject at our teachers colleges. Second, there was a strong correlation, in both CK and KCS, of item difficulty felt by the respondents with that by the Kwon et al's in-service teachers. Third, although the respondents valued the MKT items more than the above-mentioned elementary in-service teachers, about 70% of them said the items were never learned at their college. Furthermore, they had different opinions on some of the items from their counterparts'. The suggestions we get here are we need to first consider the results in improving education of elementary mathematics subject at our teachers colleges and second develop MKT items suitable for the situation of Korean schools and curriculums in order to obtain exact estimations of Korean elementary pre-service teachers' MKT.

• Journal of Educational Research in Mathematics
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• v.26 no.4
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• pp.683-700
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• 2016

The traditional teaching-learning in mathematics, which pursue only one correct answer, should be reexamined to cope with an age of uncertainty. In this research, Perry's epistemological development scheme was noticed as a theoretical approach to diagnose problems of dualistic mathematics lessons and to search solutions of the problems. And Design-Based Research method was adopted, We developed the epistemological development scheme through considering Perry's theory and related studies, scaffoldings and teaching-learning to enhance students' epistemological positions in mathematics. Based on these discussions we designed teaching experiment about operations with negative numbers, and analyzed its didactic implications.

• Journal of Korean Home Economics Education Association
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• v.14 no.2
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• pp.1-14
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• 2002

The goal of the study is to find the necessary measures to facilitate a desirable Technology and Home Economics curriculum by reflecting the Perception and needs of the teachers from the perspective of the curriculum content. professionalism of the teacher realistic operations of the school . and the administration of the school system. The results obtained from the research are as follows : 1) The background knowledge and characteristics of the two curriculums are different. and in addition there is a negative perception due to the fact that it is hard to facilitate a class with just one teacher. 2) The issues that were most serious to teachers were professionalism of the teacher. qualification of the teachers. and teaching method. Also the teachers lacked in confidence in teaching and the curriculum itself. 3) In regards to qualifications of the teacher the teachers requested that teachers should have single qualification in 'Technology(or Home Economics)'or dual qualifications in both 'Technology' and 'Home Economics'. As for teaching methodology responded that from the teacher and student perspective the teaching should be divided whereas from the school's perspective the responsibility should be Put on a single teacher. 4) Teachers responded that from the perspective of the teacher, parent or student Technology and Home Economics should be separated into two subjects.

• Education of Primary School Mathematics
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• v.17 no.3
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• pp.205-230
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• 2014

New teaching and learning theory on various aspects about class is needed to implement education which reflects constructivism, ideally. For an ideal learner-centered mathematics class, tangible and intangible elements related to education(view of knowledge, view of leaner, teacher's role, evaluation, the form of class, learning, teaching material, etc.) should be integrated from a constructive perspective and especially, teaching material has to be premised on that learners have intellectual abilities to construct knowledge themselves, and reflect integrity of knowledge, diversity and others, and contain open attributes. In addition to this, teaching material should have characteristics different from those when objective epistemology applies, so there is a need to analyze whether teaching material has those characteristics. For this, this study compared and analyzed <1. Three-Digit Numbers> which belongs to the domain of numbers and operations out of the units of mathematics(3) textbook of the 2009 revised curriculum for the first and second grade that first introduced story-telling, and <3. Understanding of Place Values> for the second grade of constructive math class used in the U.S.

• The Mathematical Education
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• v.47 no.4
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• pp.519-543
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• 2008

The study has been conducted with 29 children from 4th to 6th grades to realize how they understand addition, subtraction, multiplication, and division of whole numbers, and how their understanding influences solving of one-step word problems. Children's understanding of operations was categorized into "adding" and "combination" for additions, "taking away" and "comparison" for subtractions, "equal groups," "rectangular arrange," "ratio," and "Cartesian product" for multiplications, and "sharing," "measuring," "comparison," "ratio," "multiplicative inverse," and "repeated subtraction" for divisions. Overall, additions were mostly understood additions as "adding"(86.2%), subtractions as "taking away"(86.2%), multiplications as "equal groups"(100%), and divisions as "sharing"(82.8%). This result consisted with the Fischbein's intuitive models except for additions. Most children tended to solve the word problems based on their conceptual structure of the four arithmetic operations. Even though their conceptual structure of arithmetic operations helps to better solve problems, this tendency resulted in wrong solutions when problem situations were not related to their conceptual structure. Children in the same category of understanding for each operations showed some common features while solving the word problems. As children's understanding of operations significantly influences their solutions to word problems, they needs to be exposed to many different problem situations of the four arithmetic operations. Furthermore, the focus of teaching needs to be the meaning of each operations rather than computational algorithm.

• Education of Primary School Mathematics
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• v.22 no.2
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• pp.129-147
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• 2019

Because of the various concepts and meanings of fractions and the difficulty of learning, studies to improve the teaching methods of fraction have been carried out. Particularly, because there are various methods of teaching depending on the type of fractions or the models or methods used for problem solving in fraction operations, many researches have been implemented. In this study, I analyzed the fractional operations of CCSSM-CA and its U.S. textbooks. It was CCSSM-CA revised and presented in California and the textbooks of Houghton Mifflin Harcourt Publishing Co., which reflect the content and direction of CCSSM-CA. As a result of the analysis, although the grades presented in CCSSM-CA and Korean textbooks were consistent in the addition and subtraction of fractions, there are the features of expressing fractions by the sum of fractions with the same denominator or unit fraction and the evaluation of the appropriateness of the answer. In the multiplication and division of fractions, there is a difference in the presentation according to the grades. There are the features of the comparison the results of products based on the number of factor, presenting the division including the unit fractions at first, and suggesting the solving of division problems using various ways.

• Journal of Elementary Mathematics Education in Korea
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• v.13 no.1
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• pp.17-30
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• 2009

This paper is about the basic skills of four operations in numbers and operations areas from step 1 to step 3 in elementary mathematics. Here are the results of the evaluation. First, addition and subtraction take the largest time. The average difficulty rate in operations area is 91.2%. Most students understand the contents of textbook well. Specifically, students easily understand the step 1. However, subtraction has lower difficulty rate than addition. Also, three mixed computation, calculation in horizontal, and rounding(rounding down) are difficult areas for students. The contents of step 2 are fully understood. However, lots of mistakes are found in the process of rounding(rounding down), and sentence problems are thought as difficult. Second, the multiplication is first starting in the step 2-Ga. The unit 'Multiplication 99' takes 13 hours, the longest. The difficulty rate in this unit is 89.4%, students understand well. However, students are influenced by addition and subtraction errors in the process of multiplication, and have difficulty in changing the sentence problem to multiplication expression. Third, the division, which starts in step 3-Ga, has 89.9% of difficulty rate. Students well understand. Result of this paper: most of students understand well four operations, but accurate concept, the relationship between multiplication and division, specific instructions in teaching principles of division calculation and sentence problems are in need. Setting the amount of the contents and difficulty rate in understanding are depends on every school's situation, so suggesting universal standard is really hard. However, studying more objects broadly and specific study will be helpful to suggest proper contents and effective teaching.

• The Journal of the Korea Contents Association
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• v.15 no.2
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• pp.520-528
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• 2015

This study is intended to find out pre-service teachers' perceptions of effective teaching behaviors. 89 pre-service teachers observed teaching demonstrations of each other and rated the degree of importance of teaching behaviors and their own performance level. It was found that Class Operations received the highest score in both the importance and performance levels, followed by Lesson Organizations and Verbal Expressions. However, they considered Gesture and Clothing as well as Facial Expressions and Gaze less important. The results of t-tests showed that the differences between the importance and performance levels for all five areas were statistically significant. The results of importance-performance analysis indicated that Verbal Expressions, Eye Contacts, Time Control, and Emphasis on Important Contents are the factors which need to be improved for effective teaching.