• Journal of Educational Research in Mathematics
• /
• v.16 no.2
• /
• pp.157-177
• /
• 2006

The concepts of ratio and proportion do not develop in isolation. Rather, they are part of the individual's multiplicative conceptual field, which includes other concepts such as multiplication, division, and rational numbers. The current study attempted to clarify the beginning of this development process. One fourth student, Kyungsu, was encourage to schematize his trial-and-error-based method, which was effective in solving so-called missing-value tasks. This study describes several advancements Kyungsu made during the teaching experiment and analyzes the challenges Kyungsu faced in attempting to schematize his method. Finally, the mathematical knowledge Kyungsu needed to further develop his ratio and proportion concepts is identified. The findings provide additional support for the view that the development of ratio and proportion concepts is embedded within the development of the multiplicative conceptual field.

• Journal of The Korean Association For Science Education
• /
• v.34 no.3
• /
• pp.295-301
• /
• 2014

The purpose of this study is to investigate the difficulties of teachers and students on the unit about 'measuring weight.' In this research, we have acquired data about teachers through survey, interview, and self-reflection journals, at the same time we have collected information on the students through survey, assessment test, and interview. We have extracted the difficulties from analysis with constant comparison method. In addition, we have analysed the curriculum of science and mathematics to know the leaning sequence. The analysis had been checked up by experts in science education. The result of the study is as follows: The difficulties of teachers are from the lack of teachers' descriptive knowledge, disorder of conceptual hierarchy in the curriculum, poor experimental instruments, and low psychomotor skill of students. The difficulties of students are from common misconceptions, opaque concepts, lack of manipulation skill, insufficiency of mathematical ability, difficulty of application of principles to the real situation, and lack of problem-solving ability. In addition, teachers have recognized that students face more difficulties in experiment class, while students think that they face more difficulties in conceptual understanding class.

• School Mathematics
• /
• v.11 no.4
• /
• pp.625-642
• /
• 2009

This paper presents an overview of theories about ethnomathematics to seek for implications for multicultural mathematics education. Initiated by anthropological inquiries into mathematics outside of Europe, research of ethnomathematics has revealed the facets of mathematics as a historicocultural construct of a community. Specifically, it has been shown that mathematics is culturally relative knowledge system situated within a certain communal epistemological norms. This implies that indigenous mathematics, which had traditionally been regarded as primitive and marginal knowledge, is a historicocultural construct whose legitimacy is conferred by the system of the communal epistemological norms. The recognition of the cultural facets in mathematics has faciliated the reconsideration of what is legitimate mathematics. what is mathematical competence, and what teaching and learning mathematics is an about. This paper inquires multicultral discourses of mathematics education that research of ethnomathematics provides and identifies its implications concerning multicultural mathematics education.

• Education of Primary School Mathematics
• /
• v.25 no.4
• /
• pp.297-312
• /
• 2022

Word problems can lead learners to more meaningfully learn mathematics by providing learners with various problem-solving experiences and guiding them to apply mathematical knowledge to the context. This study attempted to provide implications for the textbook writing and teaching and learning process by examining the word problem of elementary mathematics textbooks from the perspective of practical context. The word problem of elementary mathematics textbooks was examined, and elementary mathematics textbooks in the United States and Finland were referenced to find specific alternatives. As a result, when setting an unnatural context or subject to the word problem in elementary mathematics textbooks, artificial numbers were inserted or verbal expressions and illustrations were presented unclearly. In this case, it may be difficult for learners to recognize the context of the word problem as separate from real life or to solve the problem by understanding the content required by the word problem. In the future, it is necessary to organize various types of word problems in practical contexts, such as setting up situations in consideration of learners in textbooks, actively using illustrations and diagrams, and organizing verbal expressions and illustrations more clearly.

• Education of Primary School Mathematics
• /
• v.11 no.1
• /
• pp.59-74
• /
• 2008

Mathematical knowledge is not exact definition but the supposition. Considering the nature of mathematics, realization of mathematics teaching which pursues critical thinking and rationality would be our problems. Accordingly, I set the subject of this study whether learning of constructivist discussion, which induces reflective thinking through communicating with others by expression with language of mathematical thinking in discussion, is effective against attitude on Mathematics and Mathematics achievement and study themes are as follows; A. Is learning of constructivist discussion effective against attitude on Mathematics? A-1. Is there any difference of self-conception on the subject between experimental group applied to learning of constructivist discussion and comparative group? A-2. Is there any difference of attitude on the subject between experimental group applied to learning of constructivist discussion and comparative group? A-3. Is there any difference of learning habits on the subject between experimental group applied to learning of constructivist discussion and comparative group? B. Is learning of constructivist discussion effective against mathematics achievement? The objects of study are 30 children of one class in the third grade of elementary school in Seoul for experimental group, and another one class with 30 children is comparative group. Study results and conclusion based on those results are as follows; First, students make reflective thinking through communication each other, therefore, instructor should create discussion environment for communication to express and form their mathematical thinking. Next, adaptability in student's mathematics activities and mathematical ideas should be permissible, and those should become divergent thinking. However, this study analyzed comparative results from only two each class having enrollment of thirty in the third grade. Accordingly, results from students in various grades and environment that are required to get more significant conclusion statistically.

• Education of Primary School Mathematics
• /
• v.22 no.1
• /
• pp.49-64
• /
• 2019

The purpose of the study was to examine the current status of prospective elementary school teachers' mathematical beliefs. 339 future elementary school teachers majoring in mathematics education from 4 universities participated in the study. The questionnaire used in the TEDS-M(Tatto et al., 2008) was translated into Korean for the purpose of the study. The researchers analyzed the pre-service elementary teachers' beliefs about the nature of mathematics and about mathematics learning. Also, the results of the survey was analyzed by various aspects. To determine differences between the groups, one-way analysis of variance was used. To check the relationship between beliefs about the nature of mathematics and about the mathematics learning, correlation analysis was used. The results of the study revealed that the pre-service elementary teachers tends to believe that the nature of mathematics as 'process of inquiry' rather than 'rules and procedures' which is a view that mathematics as ready-made knowledge. In addition, the pre-service elementary teachers tend to consider 'active learning' as desirable aspects in mathematics teaching-learning practice, while 'teacher's direction' was not. We found that there were statistically significant correlation between 'process of inquiry' and 'active learning' and between 'rules and procedures' and 'teacher direction'. On the basis of these results, more extensive and multifaced research on mathematical beliefs should be needed to design curriculum and plan lessons for future teachers.

• Journal of Educational Research in Mathematics
• /
• v.9 no.2
• /
• pp.383-404
• /
• 1999

This study began with an epistemological question about the nature of mathematical cognition in relation to the learner's activity. Therefore, by examining Piaget's 'reflective abstraction' theory which can be an answer to the question, we tried to get suggestions which can be given to the mathematical education in practice. 'Reflective abstraction' is formed through the coordination of the epistmmic subject's action while 'empirical abstraction' is formed by the characters of observable concrete object. The reason Piaget distinguished these two kinds of abstraction is that the foundation for the peculiar objectivity and inevitability can be taken from the coordination of the action which is shared by all the epistemic subjects. Moreover, because the mechanism of reflective abstraction, unlike empirical abstraction, does not construct a new operation by simply changing the result of the previous construction, but is forming re-construction which includes the structure previously constructed as a special case, the system which is developed by this mechanism is able to have reasonability constantly. The mechanism of the re-construction of the intellectual system through the reflective abstraction can be explained as continuous spiral alternance between the two complementary processes, 'reflechissement' and 'reflexion'; reflechissement is that the action moves to the higher level through the process of 'int riorisation' and 'thematisation'; reflexion is a process of 'equilibration'between the assimilation and the accomodation of the unbalance caused by the movement of the level. The operational learning principle of the theorists like Aebli who intended to embody Piaget's operational constructivism, attempts to explain the construction of the operation through 'internalization' of the action, but does not sufficiently emphasize the integration of the structure through the 'coordination' of the action and the ensuing discontinuous evolvement of learning level. Thus, based on the examination on the essential characteristic of the reflective abstraction and the mechanism, this study presents the principles of teaching and learning as following; $\circled1$ the principle of the operational interpretation of knowledge, $\circled2$ the principle of the structural interpretation of the operation, $\circled3$ the principle of int riorisation, $\circled4$ the principle of th matisation, $\circled5$ the principle of coordination, reflexion, and integration, $\circled6$ the principle of the discontinuous evolvement of learning level.

• Journal of the Korean School Mathematics Society
• /
• v.15 no.4
• /
• pp.719-745
• /
• 2012

This research is a study on student's understanding fundamental conception of mathematical curriculum, especially in geometry domain. The goal of researching is to analyze student's wrong conception about that domain and get the mathematical teaching method. We developed various questions of descriptive assessment. Then we set up the term, procedure of research for the understanding student's knowledge of geometry. And we figured out the student's understanding extent through analysing questions of descriptive assessment in geometry. In this research, we concluded that most of students are having difficulty with defining the fundamental conception of mathematics, especially in geometry. Almost all the students defined the fundamental conceptions of mathematics obscurely and sometimes even missed indispensable properties. Prior to this study, we couldn't identify this problem. Here are some suggestions. First, take time to reflect on your previous mathematics method. And then compile some well-selected questions of descriptive assessment that tell us more about student's understanding in geometry.

• Journal of Educational Research in Mathematics
• /
• v.27 no.1
• /
• pp.113-135
• /
• 2017

The purpose of the research was to develop an analysis framework for Korean mathematics textbooks from a critical mathematics education perspective. For this, we conducted a comprehensive literature review regarding critical theory, critical education, and critical mathematics education. Based on the literature review, we derived a preliminary framework for textbook analysis. To validate the preliminary framework delphi survey was carried out twice with 21 expert panelists in the field of mathematics education and multicultural education. The first delphi survey was conducted with open-ended questions to investigate diverse opinions regarding educational goals, contents, and teaching methods of critical mathematics education. The second delphi survey was conducted with Likert-type scale and it was analyzed using Mean, Contents Validity Ratio, Degree of Consensus. As the result of the whole research procedures, the final analysis framework was developed consisting of four categories: classical knowledge, community knowledge, communicative knowledge, and political knowledge. A development of the analysis framework from a critical mathematics education perspective could give a significant impact on the mathematics curriculum or mathematic teacher education in the Korea and a meaningful initial step for the effort of practicing critical mathematics education. It is expected that this study could not only incite consideration for the better mathematics education but also expand the prospect of research and practice in mathematics education. This study would provide a new paradigm of future mathematics education with which to teach and guide students to become members of world civil society with mathematical power and critical competency.

• Communications of Mathematical Education
• /
• v.34 no.2
• /
• pp.179-200
• /
• 2020

The study investigates how two different methods of peer tutoring impact academic achievement and student affect in a high school mathematics class. The two methods include the one-on-one non-reciprocal peer tutoring and the one-on-four interactive peer-tutoring method. We looked into students' cognitive gains and their affect toward mathematics after students had experienced peer tutoring for six weeks. Further, we analyzed student responses in a survey about peer tutoring activities. A finding is that the two methods produced no statistically significant difference in both cognitive gains and student affect toward mathematics. As students expressed views about their peer tutoring experiences, their comments, however, revealed the multifaceted aspects of peer tutoring in the classroom setting. In turn, this supports the use of diverse peer tutoring methods especially when the teacher makes incremental changes in teaching practices to improve student learning. Findings also indicate that appropriate peer tutoring experiences have the potential to create intellectually safe learning environments with high student engagement. This underscores the benefit of designing and implementing diverse peer tutoring methods that are effective in engaging students in learning and increasing the opportunity to learn and create knowledge with peers.