The Mathematical Education

Issue: Vol.60 No.1

Semiotic mediation through technology: The case of fraction reasoning 여승현 Yeo Sheunghyun 60(1) 1-19, 2021 Semiotic mediation through technology: The case of fraction reasoning 여승현 Yeo Sheunghyun DOI: JANT Vol.60(No.1) 1-19, 2021 This study investigates students’ conceptions of fractions from a measurement approach while providing a technological environment designed to support students’ understanding of the relationships between quantities and adjustable units. 13 third-graders participated in this study and they were involved in a series of measurement tasks through task-based interviews. The tasks were devised to investigate the relationship between units and quantity through manipulations. Screencasting videos were collected including verbal explanations and manipulations. Drawing upon the theory of semiotic mediation, students’ constructed concepts during interviews were coded as mathematical words and visual mediators to identify conceptual profiles using a fine-grained analysis. Two students changed their strategies to solve the tasks were selected as a representative case of the two profiles: from guessing to recursive partitioning; from using random units to making a relation to the given unit. Dragging mathematical objects plays a critical role to mediate and formulate fraction understandings such as unitizing and partitioning. In addition, static and dynamic representations influence the development of unit concepts in measurement situations. The findings will contribute to the field’s understanding of how students come to understand the concept of fraction as measure and the role of technology, which result in a theory-driven, empirically-tested set of tasks that can be used to introduce fractions as an alternative way.
Teachers’ understanding of the definition of rational exponent 신보미 Shin Bomi 60(1) 21-39, 2021 Teachers’ understanding of the definition of rational exponent 신보미 Shin Bomi DOI: JANT Vol.60(No.1) 21-39, 2021 The aim of this study was to deduce implications of the growth of mathematics teachers’ specialty for effective instruction about the formulae of exponentiation with rational exponents by analyzing teachers' understanding of the definition of rational exponent. In order to accomplish the aim, this study ascertained the nature of the definition of rational exponent through examining previous literature and established specific research questions with reference to the results of the examination. A questionnaire regarding the nature of the definition was developed in order to solve the questions and was taken to 50 in-service high school teachers. By analysing the data from the written responses by the teachers, this study delineated four characteristics of the teachers’ understanding with regard to the definition of rational exponent. Firstly, the teachers did not explicitly use the condition of the bases with rational exponents while proving f’(x)=rx^r-1. Secondly, few teachers explained the reason why the bases with rational exponents must be positive. Thirdly, there were some teachers who misunderstood the formulae of exponentiation with rational exponents. Lastly, the majority of teachers thought that (-8)^1/3 equals to -2. Additionally, several issues were discussed related to teacher education for enhancing teachers’ knowledge about the definition, features of effective instruction on the formulae of exponentiation and improvement points to explanation methods about the definition and formulae on the current high school textbooks.
The effects of peer tutoring on the mathematics learning achievements and affective domain by meta-analysis 조창호 Jo Chang Ho , 최송희 Choi Song-hee , 김동중 Kim Dong-joong 60(1) 41-59, 2021 The effects of peer tutoring on the mathematics learning achievements and affective domain by meta-analysis 조창호 Jo Chang Ho , 최송희 Choi Song-hee , 김동중 Kim Dong-joong DOI: JANT Vol.60(No.1) 41-59, 2021 The purpose of this study is to synthesize a comprehensive and general conclusion about the effects of mathematics classes using peer tutoring on the cognitive (mathematics learning achievement) and affective domains. For this purpose, a total of 61 individual studies were meta-analyzed in this study to calculate the effect size, measuring the strength of the relationship between mathematics classes using peer tutoring and either the cognitive or affective domain. As a result of this study, it was confirmed that mathematics classes using peer tutoring generally have a medium effect size in both cognitive and affective domains. Also, it was found that level of school, type of student, learning location, class time, tutor education or prior training are significant variables that affect the impact of mathematics classes using peer tutoring on the cognitive and affective domains. These results suggest specific ideas on how to design and operate peer tutoring in school mathematics classes on the basis of different variables.
Pre-service teachers’ errors and difficulties in task modification focusing on cognitive demand 강향임 Kang Hyangim , 최은아 Choi Eunah 60(1) 61-76, 2021 Pre-service teachers’ errors and difficulties in task modification focusing on cognitive demand 강향임 Kang Hyangim , 최은아 Choi Eunah DOI: JANT Vol.60(No.1) 61-76, 2021 The purpose of this study is to analyze the errors and difficulties which pre-service secondary teachers shows during the task modification in consideration of the cognitive demand and to provide significant implications to the pre-service teacher education program related to the modification of the mathematical tasks. In the pursuit of this purpose, tasks were selected from perpendicular bisector units and 24 pre-service teachers were asked to modify the tasks to higher and lower level tasks. After the modification activities, opportunities for reflection and modification were provided. The findings from analysis are as follows. Pre-service teachers had a difficulty to distinguish between PNC tasks and PWC tasks. Also, We identified the interference phenomena that pre-service teachers depended on the apparent elements of the task. Pre-service teachers showed a tendency to overlook the learning objectives and learning hierarchy during the task modification, and to focus on some types of task modification. However, pre-service teachers were able to have meaningful learning opportunities and extend the category of tools to technology including Geogebra through self-reflection and correction activities on task modification. The above results were summed up and we presented the implications to the task modification program in the pre-service secondary teacher education.
The characteristics of lesson design prepared by pre-service teachers according to the structural changes of lesson design template 이선영 Lee Seon Young , 한선영 Han Sunyoung 60(1) 77-110, 2021 The characteristics of lesson design prepared by pre-service teachers according to the structural changes of lesson design template 이선영 Lee Seon Young , 한선영 Han Sunyoung DOI: JANT Vol.60(No.1) 77-110, 2021 In this study, a student participation-centered class based on student mathematical thinking as a the meaningful subject was called a student thinking-based math class. And as a way to support these classes, I paid attention to lesson design. For student thinking-based mathematics classes, it is necessary not only to anticipate student thinking and teacher feedback, but also to plan in advance how to properly arrange and connect expected student responses. The student thinking-based lesson design template proposed in this study is a modified three-step(introduction, main topic, summary) lesson design template. The reason for revising the existing design template is that it has limitation that it cannot focus on mathematical thinking. Using the conceptual framework of student thinking-based mathematics lesson as a lens, the difference between the three-step lesson design prepared by pre-service teachers and the students’ thinking-based lesson design prepared by the same pre-service teachers was analyzed. As a result of planning lessons using the student thinking-based lesson design, more attention was paid to the cognitive and social engagement of students. In addition, emphasis was placed in the role of teachers as formative facilitator. This study is of significant in that it recognizes the importance of classes focusing on students’ mathematical thinking and provides tools to plan math classes based on students’ thinking.
Investigating mathematics teachers’ understanding of and intention to use textbooks 조수현 Cho Soohyun , 김구연 Kim Gooyeon 60(1) 111-131, 2021 Investigating mathematics teachers’ understanding of and intention to use textbooks 조수현 Cho Soohyun , 김구연 Kim Gooyeon DOI: JANT Vol.60(No.1) 111-131, 2021 This study aims to investigate how secondary mathematics teachers understand and intend to use textbooks for their mathematics instruction. For this purpose, we developed a set of survey items in order to unpack what the teachers understand the mathematical tasks suggested in the textbooks in terms of the levels of cognitive demand and how they intended to use the tasks in the textbooks for their teaching. Twenty-five teachers participated in the survey. The data from the survey were analyzed. The findings from the data analysis suggested as follows: a) the teachers seemed to closely follow textbooks without attempting to modify the tasks, even when the teachers consider it is necessary to modify textbook tasks to high-level tasks, b) the teachers seemed to be unstable in regards that they admitted themselves very competent for modifying tasks for developing students’ mathematical thinking but, at the same time, they were uncomfortable with transforming tasks into cognitively demanding tasks that promote students’ mathematical understanding, and c) the teachers appeared to consider textbooks as significant criteria in conducting tests including midterm and final exam. In conclusion, the teachers seemed to intend to follow closely the contents and sequence of mathematics textbooks in their mathematics classrooms.