• Research in Mathematical Education
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• v.21 no.1
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• pp.35-46
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• 2018

In this perspective paper, we present seven elements of the appropriate educator mindset for teaching in the constructivist elementary mathematics classroom. The elements include supporting students as they construct their own understanding, eliminating deficit view of slow learners, setting new understanding and growth as the learning objective, providing opportunities to co-construct meaning with peers, using student contributions as the source of curricular material, encouraging all students to participate in learning, and providing instruction not bounded by time. In our struggles to provide authentic, inclusive elementary classrooms, we hope that our discussion of the educator mindset can increase discourse on constructivism from philosophy to practice in the community of mathematics education and policy makers.

• Research in Mathematical Education
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• v.25 no.2
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• pp.117-133
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• 2022

Examining ways to interact with students in small groups is an important topic for researchers to understand. Existing studies pertaining to the topic have not shed light on knowing why teachers interact with students in small groups the way they do. Given that teacher identity shapes teaching practices, this study explores how teacher identity shapes teachers' interaction with students in small groups. Working with two beginning teachers, I conducted four interviews to collect the data related to reasons behind their interactions with students in small groups in the interview. I analyzed the interview transcripts using a thematic analysis. I found that one teacher's teacher identity was related to her personal experiences as a child and a learner and another teacher's teacher identity was related to her view of teachers' roles as a teacher. I provide discussion and implications of this study.

• Communications of the Korean Mathematical Society
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• v.38 no.4
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• pp.1309-1320
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• 2023

Let f : X → Y be a map between simply connected CW-complexes of finite type with X finite. In this paper, we prove that the rational cohomology of mapping spaces map(X, Y ; f) contains a polynomial algebra over a generator of degree N, where N = max{i, π_i(Y)⊗ℚ ≠ 0} is an even number. Moreover, we are interested in determining the rational homotopy type of map(𝕊ⁿ, ℂP^m; f) and we deduce its rational cohomology as a consequence. The paper ends with a brief discussion about the realization problem of mapping spaces.

• East Asian mathematical journal
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• v.39 no.4
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• pp.437-454
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• 2023

The core of the change in the era of the 4th industrial revolution is the change in the base of 'digital technology'. These changes are incomparably large and are expected to have a more important impact on our lives than ever before. One of the major inflection points in the transition to the digital era is the education field, and IT technology has become an essential element in the educational field. Accordingly, this study examines domestic research trends related to the educational environment based on digital technology. Then, we would like to provide implications for the establishment of a digital-based educational environment that will change in the future. To this end, Semantic network analysis has been conducted to quantitatively structure text data obtained from studies related to digital technology in the field of mathematics education over the past 10 years, and the discussion will continue based on the results.

• School Mathematics
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• v.13 no.3
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• pp.423-446
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• 2011

In school mathematics, concepts of definite integral and integration by substitution have mathematical connection with introduction of probability density function, expectation of continuous random variable, and standardization of normal distribution. However, we have difficulty in finding mathematical connection between integration and continuous probability distribution in the curriculum manual, 13 kinds of 'Basic Calculus and Statistics' and 10 kinds of 'Integration and Statistics' authorized textbooks, and activity books applied to the revised curriculum. Therefore, the purpose of this study is to provide a teaching method connected with mathematical concepts of integral in regard to three concepts in continuous probability distribution chapter-introduction of probability density function, expectation of continuous random variable, and standardization of normal distribution. To find mathematical connection between these three concepts and integral, we analyze a survey of student, the revised curriculum manual, authorized textbooks, and activity books as well as 13 domestic and 22 international statistics (or probability) books. Developed teaching method was applied to actual classes after discussion with a professional group. Through these steps, we propose the result by making suggestions to revise curriculum or change the contents of textbook.

• Journal of Educational Research in Mathematics
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• v.14 no.3
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• pp.221-237
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• 2004

This research analyzed mathematical discourse of the students in an RME-based differential equations course at a university in order to investigate the social transformation of the students' conceptual model of differential equations. The analysis focused on the change in the students' use of conceptual metaphor for differential equations and pedagogical factors promoting the change. The analysis shows that discrete and quantitative conceptual model was prevalent in the beginning of the semester However, continuous and qualitative conceptual model emerged through the negotiation of mathematical meaning based on the inquiry of context problems. The participation in the project class has a positive impact on the extension of the students' conceptual model of differential equations and increases the fluency of the students' problem solving in differential equations. Moreover, this paper provides a discussion to identify the pedagogical factors Involved with the transformation of the students' conceptual model. The discussion highlights the sociocultural aspect of teaching and learning of mathematics and provides implications to improve teaching of mathematics in school.

• 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.

• The Mathematical Education
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• v.55 no.3
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• pp.251-279
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• 2016

There are many studies on 'how' students solve mathematical problems, but few of them sufficiently explained 'why' they have to solve the problems in their own different ways. As quantitative reasoning is the basis for algebraic reasoning, to scrutinize a student's way of dealing with quantities in a problem situation is critical for understanding why the student has to solve it in such a way. From our teaching experiments with two ninth-grade students, we found that emergences of a certain level of covariational reasoning were highly consistent across different types of problems within each participating student. They conceived the given problem situations at different levels of covariation and constructed their own quantity-structures. It led them to solve the problems with the resources accessible to their structures only, and never reconciled with the other's solving strategies even after having reflection and discussion on their solutions. It indicates that their own structure of quantities constrained the whole process of problem solving and they could not discard the structures. Based on the results, we argue that teachers, in order to provide practical supports for students' problem solving, need to focus on the students' way of covariational reasoning of problem situations.

• Communications of Mathematical Education
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• v.29 no.4
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• pp.661-685
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• 2015

This study is to search for a program of professional development of mathematics teachers on the viewpoint of content knowledge of mathematics. To do this, we select algebraic subject as content knowledge for solution of polynomials and develop material for group study based on selected subject. We supply the developed material to teachers and discuss the possibility of application and the acceptability of it. For discussion, we collect data through tests and questionnaire. Through analysing the data, we obtain the positive result.

• Journal of Elementary Mathematics Education in Korea
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• v.18 no.3
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• pp.493-504
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• 2014

Some problems of elementary mathematics textbook applying storytelling continue to be suggested since implementing it in mathematics instruction. The paper looks into concrete problems. First problem is the lack of mathematics education experts studying storytelling in the field. Second problem is that a variety of materials including storytelling need to be used in the process of developing instruction materials. Third problem is that storytelling needs to include integration of various mathematical knowledge. Fourth problem is that it is needed to develop making storytelling focused on mathematical concepts. Fifth problem is that there is no appropriate lessen plan necessary for instruction applying storytelling. Sixth problem is that storytelling inducts intrinsic motivation as well as extrinsic motivation. Final problem is the sources of story need to be diverse. It is expected that storytelling reflecting those aspects is developed.