An analysis of understanding of prospective elementary teachers on students’ strategies for fraction tasks with number lines
김정원 Kim Jeongwon
61(3) 375396, 2022
김정원 Kim Jeongwon
DOI: JANT Vol.61(No.3) 375396, 2022
With the importance for teachers of understanding students’ strategies and providing appropriate feedback to their students, the purpose of this study is to analyze how prospective elementary teachers interpret and respond students’ strategies for fraction tasks with number lines. The findings from analysis of 64 prospective teachers’ responses were as follow. First, the prospective teachers in general could identify the students’ understanding and errors based on their strategies, however, some prospective teachers overgeneralized students’ mathematical thinking at a superficial level. Second, the prospective teachers could pose diverse tasks or activities for revising the students’ errors, while some prospective teachers tried to correct students’ errors by using only the area models. Based on these results, this study suggests for prospective teachers to have opportunities to understand elementary students’ diverse problem strategies and to consider teaching methods with different fraction models.

Mathematics education experts’ perception of information literacy in mathematics education
김은현 Kim Eun Hyun , 김래영 Kim Rae Young
61(3) 397417, 2022
김은현 Kim Eun Hyun , 김래영 Kim Rae Young
DOI: JANT Vol.61(No.3) 397417, 2022
The purpose of this study is to discuss information literacy in mathematics education by comparatively analyzing mathematics education experts’ perception of information processing and information literacy in mathematics education. We collected mathematics education experts’ opinions using the modified Delphi method and focus group interviews, then analyzed their responses with an analytic framework through a constant comparative method. Even though we used different methods, we could compare their perceptions under the common themes. The findings are in threefolds. First, most experts focused only on the use of technological tools or statistics as a way of developing information literacy. In addition, even though mathematics education experts recognize the need for information literacy in mathematics education, their definition and meaning of information literacy somehow varied. Secondly, teachers as practitioners emphasized social competency which could be developed through information literacy. Thirdly, they asked for concrete and systematic plans for school practice in order to well develop information literacy in schools. Even though there were some differences in their perception of information literacy in mathematics education in terms of their prior experiences and background, it is very meaningful that there were commonalities among their perceptions which would allow us to find the ways of developing information literacy in mathematics education.

Mathematising process analysis of linear function concept based on Freudenthal’s didactical phenomenology
김은숙 Kim Eun Suk , 조완영 Cho Wan Young
61(3) 419439, 2022
김은숙 Kim Eun Suk , 조완영 Cho Wan Young
DOI: JANT Vol.61(No.3) 419439, 2022
This study is based on Freudenthal’s mathmatising process and the didactical phenomenology of linear function concept, I have described and examined the process in which students represent the constant rate of change into tables, graphs and equations and, in this way, how they construct mental objects and essence of the linear function concept. The students used the proportionality as composite units, when they represented the phenomenon with constant rate of change into tables. When representing in graphs, all but one student represented it into a line. There were differences among the students in the level they were using the given conditions, covariation perspective, and corresponding rules when formulating equations. The students compared the relationship between two variables in a multiplicative way, and under the guidance of teachers they reached to the understanding that its relationship becomes a constant. Moreover, they could construct mental objects of a constant rate of change, understanding the situation where the relationship between time difference and distance difference becomes one value, namely speed. The students had difficulties in connecting the rate of change with the inclination of a line. The students constructed the essence (concept) of linear functions, after building and organizing the image that the rate of change is constant, the graph is linear, and the equation is formulated as y=ax+b (a: inclination, b: intercept).

A case study on the quadratic function problem solving process of middle school students with different unit coordination stages
이진아 Lee Jin Ah , 이수진 Lee Soo Jin
61(3) 441456, 2022
이진아 Lee Jin Ah , 이수진 Lee Soo Jin
DOI: JANT Vol.61(No.3) 441456, 2022
The purpose of the current study is to report a part of our larger project whose focus is to understand a relationship between students’ units coordination and K12 school mathematics. In particular, in this paper we report how students who exhibit distinct levels of units coordinations used their knowledge of proportion to solve quadratic function problems of the form y = ax^{2} . To this end, three 7th grade students all of whom assimiliated whole number problem situations with three levels of units but showed different levels for fraction problems were chosen. We carried out clinical interviews not only to understand their ability to coordinate units but to understand their problem solving process of proportion and the quadratic function problems. The analysis suggest that their abilities to coordinate units influenced their ways to solving proportion problems, and in turn influenced their ways to solve the specific form of quadratic functions. We have finalized our study by discussing how students’ ability to construct and coordinate units, their proportion knowledge, and their knowledge associated with expressing the specific type of quadractic functions could be related.

Research trends of mathematics textbooks: An analysis of the journal articles published from 1963 to 2021
방정숙 Pang Jeong Suk , 오민영 Oh Min Young
61(3) 457476, 2022
방정숙 Pang Jeong Suk , 오민영 Oh Min Young
DOI: JANT Vol.61(No.3) 457476, 2022
Mathematics textbooks as the main resources to support mathematical teaching and learning are used importantly in Korean lessons. Although the scope of mathematics textbook research has been expanded and the research has increased, few studies have analyzed the overall trends of mathematics textbook research in Korea. This study analyzes the overall trends of textbook research on 418 papers pertinent to mathematics textbooks published in domestic mathematics education journals. The results of this study showed that the proportion of textbook analysis research was the highest, followed by textbook use and textbook development research in order. There were more textbook studies at the elementary school level than at the middle or high school levels. Regarding textbook analysis studies, the most frequent topic was to analyze how specific mathematical concepts were presented in textbooks. Regarding textbook use studies, many studies asked both teachers and students to review the appropriateness of textbooks under development or analyzed the perception and use of specific activities of textbooks based on a survey. Regarding textbook development studies, the most popular topics included the directions and examples of new development, such as storytellingbased or electronic textbooks. This paper finally presented implications for textbook research in light of the domestic mathematics education context and the international mathematics textbook research trends.

Adults’ perception of mathematics: A narrative analysis of their experiences in and out of school
조은영 Cho Eun Young , 김래영 Kim Rae Young
61(3) 477497, 2022
조은영 Cho Eun Young , 김래영 Kim Rae Young
DOI: JANT Vol.61(No.3) 477497, 2022
The rapidly changing world calls for reform in mathematics education from lifelong learning perspectives. This study examines adults’ perception of mathematics by reflecting on their experiences of mathematics in and out of school in order to understand what the current needs of adults are. With the two questions: “what experiences do participants have during their learning of mathematics in schools?” and “how do they perceive mathematics in their current life?”, we analyzed the semistructured interviews with 10 adults who have different sociocultural backgrounds using narrative inquiry methodology.
As a result, participants tended to accept school mathematics as simply a technique for solving computational problems, and when they had not known the usefulness of mathematical knowledge, they experienced frustration with mathematics in the process of learning mathematics. After formal education, participants recognized mathematics as the basic computation skill inherent in everyday life, the furniture of their mind, and the ability to efficiently express, think, and judge various situations and solve problems. Results show that adults internalized school education to clearly understand the role of mathematics in their lives, and they were using mathematics efficiently in their lives. Accordingly, there was a need to see school education and adult education on a continuum, and the need to conceptualize the mathematical abilities required for adults as mathematical literacy.

A comparative analysis on ratio and rate in elementary mathematics textbooks of Korea and Singapore
이지영 Lee Jiyoung , 서은미 Seo Eunmi
61(3) 499519, 2022
이지영 Lee Jiyoung , 서은미 Seo Eunmi
DOI: JANT Vol.61(No.3) 499519, 2022
Ratio and rate are key topics in the area of ‘Patterns’, but there are various perspectives on them. This study compared and analyzed the perspectives of Korean and Singaporean mathematics textbooks on ratio and rate, and explored how teaching and learning methods develop according to each perspective in terms of quantitative reasoning. To this end, we reorganized the analysis criteria based on some studies, and analyzed the textbooks of the two countries in relation to context, relationship, and representation. The results of the study are as follows. Regarding the context, there were differences in the situations, types of units and use of units of the problems presented in textbooks. In terms of relationship, there were differences in the types of two quantities and relationship of quantities. Lastly, there were differences in the representation of ratio and rate. Through these results, we found that elementary mathematics textbooks in Korea and Singapore take different perspectives on ratio and rate. In particular, the perspective taken by Korean textbooks on ratio and rate had unique points different from that of other previous studies. Considering this Korean perspective, we suggested some implications that could help improve textbooks related to ratio and rate and teach them meaningfully.
