The Effects of Mathematical Problem Solving with Multiple Strategies on the Mathematical Creativity and Attitudes of Students
김서령 Kim¸ Seoryeong , 박만구 Park¸ Mangoo
24(4) 175187, 2021
김서령 Kim¸ Seoryeong , 박만구 Park¸ Mangoo
DOI: JANT Vol.24(No.4) 175187, 2021
The purpose of this study is to investigate the effects of solving multistrategic mathematics problems on mathematical creativity and attitudes of the 6th grade students. For this study, the researchers conducted a survey of forty nine (26 students in experimental group and 23 students in comparative group) 6th graders of S elementary school in Seoul with 19 lessons. The experimental group solved the multistrategic mathematics problems after learning mathematics through mathematical strategies, whereas the group of comparative students were taught general mathematics problem solving. The researchers conducted pre and post isomorphic mathematical creativity and mathematical attitudes of students. They examined the ttest between the pre and post scores of subelements of fluency, flexibility and creativity and attitudes of the students by the iSTATistics. The researchers obtained the following conclusions. First, solving multistrategic mathematics problems has a positive impact on mathematical creativity of the students. After learning solving the multistrategic mathematics problems, the scores of mathematical creativity of the 6th grade elementary students were increased. Second, learning solving the multistrategy mathematics problems impact the interest, value, will and efficacy factors in the mathematical attitudes of the students. However, no significant effect was found in the areas of desire for recognition and motivation. The researchers suggested that, by expanding the academic year and the number of people in the study, it is necessary to verify how mathematics learning through multistrategic mathematics problemsolving affects mathematical creativity and mathematical attitudes, and to verify the effectiveness through longterm research, including qualitative research methods such as indepth interviews and observations of students' solving problems.

An Analysis of the Questions Presented in Chapters of Pattern Area in Elementary School Mathematics
도주원 Do¸ Joowon
24(4) 189202, 2021
도주원 Do¸ Joowon
DOI: JANT Vol.24(No.4) 189202, 2021
The teacher’s questions presented in the problemsolving situation stimulate students' mathematical thinking and lead them to find a solution to the given problem situation. In this research, the types and functions of questions presented in chapters of Pattern area of the 2015 revised elementary school mathematics textbooks were compared and analyzed by grade cluster. Through this, it was attempted to obtain implications for teaching and learning in identifying the characteristics of questions and effectively using the questions when teaching Pattern area. As a result of this research, as grade clsuter increased, the number of questions per lesson presented in Pattern area increased. Frequency of the types of questions in textbooks was found to be high in the order of reasoning questions, factual questions, and open questions in common by grade cluster. In chapters of Pattern area, relatively many questions were presented that serve as functions to help guess, invent, and solve problems or to help mathematical reasoning in the process of finding rules. It can be inferred that these types of questions and their functions are related to the learning content by grade cluster and characteristics of grade cluster. Therefore, the results of this research can contribute to providing a reference material for devising questions when teaching Pattern area and further to the development of teaching and learning in Pattern area.

Analysis of Learning Opportunities Provided in Elapsed Time Instruction: Focusing on Quantitative Objectification
한채린 Han¸ Chaereen
24(4) 203216, 2021
한채린 Han¸ Chaereen
DOI: JANT Vol.24(No.4) 203216, 2021
Seeing the elapsed time as a quantity that can be measured is quite challenging for students while making students see it is also challenging for teachers. Tuning on these challenges, this article reports on what learning opportunities elementary teachers provide when they teach elapsed time focusing on quantitative objectification. I observed three mathematics classrooms where the elapsed time was taught by three elementary teachers and did a narrative analysis on the instructions. All three teachers utilized certain tools to support students access to the elapsed time as a quantity. They appropriated various quantitative attributes of the tool. In the case of the analog clock, one teacher tried to quantification the elapsed time with the number of minute hand’s turning, while the other teacher indicated the distance of minute hand’s moving. One teacher represented the elapsed time with the longitudinal attribute of the time band. Standing on the findings, the didactical implications of various attempts for quantitative objectification of the elapsed time implemented were discussed.

Effects of Flipped Learning through EBSmath on Mathematics Learning and Mathematical Dispositions
오혜진 Oh¸ Hyejin , 박성선 Park¸ Sungsun
24(4) 217231, 2021
오혜진 Oh¸ Hyejin , 박성선 Park¸ Sungsun
DOI: JANT Vol.24(No.4) 217231, 2021
The purpose of this study was to investigate the effects of flipped learning through EBSmath on Students’ ‘rate and ratio’ learning. By increasing demands for change in education, an innovative teaching and learning paradigm, ‘Flipped Learning’, has been presented and drawing attentions. In South Korea, Flipped Learning is also highly recognized for its effectiveness by many scholars and various media. However, this innovative learning model has limitations in application and expansion due to the excessive burden of class preparation of teachers.
As remote learning becomes more active, it would be possible to overcome the limitations of Filliped learning by using the platform provided by the Korea Educational Broadcasting System (EBS). EBSmath is an online learning module that is designed to assist students’ selfdirected learning. Thus, EBSmath would reduce teachers’ burden to prepare mathematics classes for the application of Flipped Learning; and led to students’ better understanding of mathematical concepts and problem solving.
In this study, the effect of Flipped Learning through EBSmath on learning ‘rate and ratio’ was investigated. In order to scrutinize the effects of flipped learning, students’ achievement and mathematical disposition were examined and analyzed. Students’ achievement, specifically, was divided into two subcategories: concept understanding and problem solving.
As a result, Flipped learning through EBSmath had a positive effect on students’ ‘rate and ratio’ problem solving. In addition, a statistically significant change was identified in the ‘willingness’, which is subdomain of students’ mathematical disposition.

Analysis for Triangles in Elementary School Curriculum and Textbook: Focusing on the Instructional Teaching and Learning Elements of 2D Shapes
권미선 Kwon¸ Misun
24(4) 233246, 2021
권미선 Kwon¸ Misun
DOI: JANT Vol.24(No.4) 233246, 2021
Twodimensional shapes have a great influence on elementary school students' learning and are closely related to other content areas. Therefore, in this study, The Teaching and Learning Elements that should be taught in twodimensional shapes were extracted from the literature. It also was analyzed that revised mathematics textbooks in the year 2015 were properly implemented with the teaching and learning elements. As a result of the analysis, in the case of Understanding The Concept, the activities in the textbooks are not able to recognize 2D shapes which are focusing on shapes of the actual object. In the case of Classifying twodimensional shapes according to the Criteria, the classification criteria were presented differently from what was learned in the previous course. In the aspect of Applying the Concept, the activities in order to Discuss twodimensional shapes were not sufficient. Lastly, in view of the fact the 2015 revised curriculum is not considered with the relationship between twodimensional shapes. For that reason, the following Knowing Relationships parts are insufficiently presented; Understanding the Relationship Between shapes through Definitions and Properties, Identifying the relationship between shapes throughout classification activities, and Discussing the relationship between shapes. Based on the analysis result of twodimensional shapes, it is suggested that the finding of this research helps to enlarge the teaching methodology of triangles and provide educational perspectives for development in other shape areas.

An Analysis of Example Spaces Constructed by Students in Learning the Area of a Trapezoid based on Dienes’ Theory of Learning Mathematics
오민영 Oh¸ Min Young , 김남균 Kim¸ Nam Gyun
24(4) 247264, 2021
오민영 Oh¸ Min Young , 김남균 Kim¸ Nam Gyun
DOI: JANT Vol.24(No.4) 247264, 2021
The area of a trapezoid is an important concept to develop mathematical thinking and competency, but many students tend to understand the formula for the area of a trapezoid instrumentally. A clue to solving these problems could be found in Dienes’ theory of learning mathematics and Watson and Mason’ concept of example spaces. The purpose of this study is to obtain implications for the teaching and learning of the area of the trapezoid. This study analyzed the example spaces constructed by students in learning the area of a trapezoid based on Dienes’ theory of learning mathematics. As a result of the analysis, the example spaces for each stage of math learning constructed by the students were a trapezoidal variation example spaces in the play stage, a common representation example spaces in the comparisonrepresentation stage, and a trapezoidal area formula example spaces in the symbolizationformalization stage. The type, generation, extent, and relevance of examples constituting example spaces were analyzed, and the structure of the example spaces was presented as a map. This study also analyzed general examples, special examples, conventional examples of example spaces, and discussed how to utilize examples and example spaces in teaching and learning the area of a trapezoid. Through this study, it was found that it is appropriate to apply Dienes’ theory of learning mathematics to learning the are of a trapezoid, and this study can be a model for learning the area of the trapezoid.
