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ELEMENTARY SCHOOL TEACHERS' FACILITATION OF MATH TALK
J. Colen,Y. S. Colen,J. H. Kim 장전수학회 2015 Proceedings of the Jangjeon mathematical society Vol.18 No.4
This paper presents an ethnographical approach to documenting two elementary school teachers’ facilitation of math talk. The described math talk moves afford a community of learners frequent opportunities to articulate their mathematical reasoning and to assess their peers’ conjectures and conclusions. In short, these moves are not unguided, aimless discourses. The vignettes and examples of the classroom discussions among the students and teachers illustrate: (1) the utilized math talk moves, (2) how the teachers, integrating the math talk moves, interconnected mathematical concepts, and (3) what knowledge the teachers drew upon to probe for student understanding and to scaffold mathematical learning.
( Yong S. Colen ),( Jung Colen ) 한국수학교육학회 2021 수학교육연구 Vol.24 No.1
For elementary school children, learning the standard multiplication algorithm with accuracy, clarity, consistency, and efficiency is a daunting task. Nonetheless, what should be our expectation in procedural fluency, for example, in finding the product of 25 and 37 among fifth grade students? Collectively, has the mathematics education community emphasized the value of conceptual understanding to the detriment of procedural fluency? In addition to examining these questions, we survey multiplication algorithms throughout history and in textbooks and reconceptualize the standard multiplication algorithm by using a new tool called the Multiplication Aid Template.
Teaching Moves for Students’ Mathematical Proficiencies in Multiplication Lessons
( Jung Colen ),( Sheunghyun Yeo ),( Nayoung Kwon ),( Hoyun Cho ),( Jinho Kim ) 한국수학교육학회 2021 수학교육연구 Vol.24 No.4
In this paper, we report the types of teaching moves a mathematics teacher educator attempted in his teaching of third-grade students at an urban elementary school in South Korea over two months. We analyze the lesson videos to find the patterns of teaching moves and speculate the link between the teaching and students’ mathematical proficiencies recommended in the Common Core State Standards for Mathematical Practices. Closely related teaching moves to the students’ development of a certain mathematical proficiency would imply the exemplary practices that teachers―both inservice and preservice teachers―can implement in their classrooms.
Elementary School Teachers’ Beliefs of the Common Core State Standards for Mathematical Practice
( Jung Colen ) 한국수학교육학회 2019 수학교육연구 Vol.22 No.1
Pennsylvania is one of the states that adopted the Common Core State Standards for Mathematics (CCSSM) and crafted its own standards (The PA Core State Standards). Pennsylvania teachers are required to have a clear understanding of the PA Core Standards. It is timely and appropriate to study Pennsylvania teachers’ beliefs, as the standards have been adopted and implemented for several years since the revision of the PA Core Standards (2014). This study examined how eight western Pennsylvania elementary school teachers’ beliefs about teaching and learning mathematics related to the SMP. To this end, I conducted an in-depth interview with each participating teacher. The in-depth interviews featured the teachers’ overarching mathematical instructional goals and their productive beliefs. Furthermore, I linked these beliefs with the CCSSM Standards for Mathematical Practice (SMP).
An Introduction to the Edumatrix Set and Its Didactic Capabilities
( Mikhail Semenov ),( Yong S. Colen ),( Jung Colen ),( Antony Pardala ) 한국수학교육학회 2020 수학교육연구 Vol.23 No.1
Learning through “recreational mathematics” has become a meaningful outlet to children of all ages. The Edumatrix set is a didactic tool for the development of logical and abstract reasoning among students. In this paper, we provide several illustrative exercises involving Edumatrix that teachers can utilize in their classrooms. We formulate students’ expected learning outcomes by aligning each exercise to the CCSSM content standards as well as examining which Standards for Mathematical Practices (SMP) our proposed exercises promote.
Sande, Denise,Colen, Gecernir,dos Santos, Gabriel Franco,Ferraz, Vany Perpetua,Takahashi, Jacqueline Aparecida 한국식품과학회 2018 Food Science and Biotechnology Vol.27 No.2
Hydrolysis of vegetable oils (Olive, corn, peanut, sesame, flaxseed, soy, canola, garlic, sunflower, almond, castor bean oils) and beef marrow bone oil by Colletotrichum gloeosporioides lipase was studied. The enzyme was capable of generating free fatty acids from all oils tested. The higher hydrolytic activity of the enzyme was towards olive (18.0 IU) and soybean (17.8 IU) oils. The average percentage of essential fatty acids generated from hydrolysis of the oils was 32.92% of omega 9 (as oleic acid C18:1), 26.24% of omega 6 (linoleic C18:2), and 5.86% of omega 3 (such as ${\alpha}$-linolenic acid C18:3). Comparison between chromatographic profile of the oils and its enzymatic hydrolysate showed a good equivalence, stressing the applicability of these vegetable substrates under the action of lipase from C. gloeosporioides produce essential fatty acids, being more efficient production of ${\alpha}$-linolenic acid from flaxseed oil, linoleic acid from sunflower oil, and oleic acid from olive.
Denise Sande,Gecernir Colen,Gabriel Franco dos Santos,Vany Perpe´tua Ferraz,Jacqueline Aparecida Takahashi 한국식품과학회 2018 Food Science and Biotechnology Vol.27 No.2
Hydrolysis of vegetable oils (Olive, corn, peanut, sesame, flaxseed, soy, canola, garlic, sunflower, almond, castor bean oils) and beef marrow bone oil by Colletotrichum gloeosporioides lipase was studied. The enzyme was capable of generating free fatty acids from all oils tested. The higher hydrolytic activity of the enzyme was towards olive (18.0 IU) and soybean (17.8 IU) oils. The average percentage of essential fatty acids generated from hydrolysis of the oils was 32.92% of omega 9 (as oleic acid C18:1), 26.24% of omega 6 (linoleic C18:2), and 5.86% of omega 3 (such as a-linolenic acid C18:3). Comparison between chromatographic profile of the oils and its enzymatic hydrolysate showed a good equivalence, stressing the applicability of these vegetable substrates under the action of lipase from C. gloeosporioides produce essential fatty acids, being more efficient production of alinolenic acid from flaxseed oil, linoleic acid from sunflower oil, and oleic acid from olive.
Mathematics Teacher Educators’ Collective Noticing on Microteaching
( Na Young Kwon ),( Jung Colen ),( Sheunghyun Yeo ),( Hoyun Cho ),( Jinho Kim ) 한국수학교육학회 2023 수학교육연구 Vol.26 No.4
This article explores how mathematics teacher educators (MTEs) engaged in collaborative inquiry into the microteaching experiences of preservice teachers (PSTs), ultimately developing a noticing framework through collective MTE inquiry. We delve into the specifics of what MTEs notice focusing on three emerging categories of noticing on PST’s microteaching videos―lesson structure, task quality, and teaching practices. Each category, along with MTEs’ noticing within these components, is elaborated through vignettes. This approach positions MTEs’ noticing as a crucial element in the overarching vision to enhance the teaching practices of PSTs.