• Education of Primary School Mathematics
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• v.24 no.4
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• pp.189-202
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• 2021

The teacher's questions presented in the problem-solving 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.

• Journal of Elementary Mathematics Education in Korea
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• v.14 no.2
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• pp.441-463
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• 2010

This study purposes to examine the learning achievements, attitude and reactions of elementary school students in fifth grade in mathematics after inducing to use of learning-notebook on mathematics. To achieve the purpose, this study focuses on the following matters. First, we develop the ways to write thoughts and activities in solving problems on learning-notebook for elementary school student in fifth grade. Second, we analyze the effects of the students' learning achievements after applying the ways to them in every mathematics learning activities at home and in school, etc. Third, this study examine the attitudes and reactions of the students toward mathematics after observing the learning activities and interviewing them. The results are summarized as follows. First, using learning-notebook helps to improve the performance of students. The average point of the final examination went up to 90.67 while the average of the first level test was 70.75. And almost each student's result have improved. Second, the interviews with the students show that they feel sense of accomplishment, their mathematical attitude has changed to be positive, and they've actively participated in class by using the learning-notebook. The students felt confidence and achievement and they were more interested in studying mathematics when they use the learning-notebook. Further, the students used the notes in doing their homework and at home studying. Finally, the learning-notebook had a good influence on the relationships between students and teachers. Moreover, learning-notebook serves as a medium that connects teacher and student's work.

• School Mathematics
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• v.17 no.2
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• pp.203-222
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• 2015

This study analyzed the classroom discourse between teacher and students based on the Mehan(1979a)'s theory to examine the characteristics of the classroom discourse between teacher and students in high school statistics class. The results of this study on the structure of class showed that the statistics class in this study adopted knowledge transmission-oriented teacher-led class in which the framework of introductiondevelopment- arrangement, which is Mehan's basic 3 stages, is clearly represented. The results of examining I-R-E sequence showed that $I_T-R_T$ structure, in which the teacher asks questions and the teacher talks about the answer, frequently appeared. And the statistics class in this study was monological class in which students hardly participated. Through these results of this study, it was found that teacher should form the statistical context, in which students can participate in discourse, and build discourse learning community and induce argumentational discourse through metaprocess elicitation.

• School Mathematics
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• v.5 no.1
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• pp.115-133
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• 2003

Investigation of the students' mathematical misconceptions is very important for improvement in the school mathematics teach]ng and basis of curriculum. In this study, we categorize second-grade middle school students' misconceptions on the learning of linear function and make a comparative study of the error-remedial effect of students' collaborative learning vs explanatory leaching. We also investigate how to change and advance students' self-diagnosis and treatment of the milton ceptions through the collaborative learning about linear function. The result of the study shows that there are three main kinds of students' misconceptions in algebraic setting like this: (1) linear function misconception in relation with number concept, (2) misconception of the variables, (3) tenacity of specific perspective. Types of misconception in graphical setting are classified into misconception of graph Interpretation and prediction and that of variables as the objects of function. Two different remedies have a distinctive effect on treatment of the students' misconception under the each category. We also find that a misconception can develop into a correct conception as a result of interaction with other students.

• School Mathematics
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• v.10 no.1
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• pp.1-22
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• 2008

The purpose of this study is to search the effective teaching-learning program by considering how affect on formation of linear function using Excel. This study was based on qualitative case study. The teaching experiment using Excel executed with five 8th graders' students for second research content. Teaching experiment was performed for two classes. Collecting the data was conducted via observations and interviews with students. The data include audio and video recording of the students' work, students' worksheets and detailed field notes. The conclusions drawn from teaching experiment are as follows: First, when students explored relevancy content of function in Excel environment, formation of concept of function was facilitated by experiencing operation of algebraic formulas, tables and graphs. We could infer that formation of concept was effected by conjecture activity and iterative process of feedback through Excel environment. Second, the students explored the changes very interestingly making algebraic formulas and presenting tables and graphs. The students were familiarized with observation on algebraic formulas, graphs and tables concurrently. Also, they tried to look for general rules through inductive observation. According to this study, we noticed that exploration teaming environment using Excel could supplement paper-and-pencil environment.

• School Mathematics
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• v.15 no.2
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• pp.481-501
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• 2013

The purpose of this study is to review the role of dragging in dynamic geometry environments. Dragging is a kind of dynamic representations that dynamically change geometric figures and enable to search invariances of figures and relationships among them. In this study dragging in dynamic geometry environments is divided by three perspectives: dynamic representations, instrumented actions, and affordance. Following this review, six conclusions are suggested for future research and for teaching and learning geometry in school geometry as well: students' epistemological change of basic geometry concepts by dragging, the possibilities to converting paper-and-pencil geometry into experimental mathematics, the role of dragging between conjecturing and proving, geometry learning process according to the instrumental genesis perspective, patterns of communication or discourse generated by dragging, and the role of measuring function as an affordance of DGS.

• Journal of Elementary Mathematics Education in Korea
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• v.17 no.2
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• pp.207-223
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• 2013

Teachers unfold a series of timeless mathematical symbols such as 5+2=7 in time by verbalizing the symbols in classrooms. A number sentence 5+2=7 is read in Korean as '5 더하기 2는(five plus two) 7과(seven) 같다(equals). Unlike in English, 5+2 and 7 are read first before the equal sign in Korean. This sequence of reading in Korean conflicts with the conventional linguistic sequence of writing from left to right. Ways of resolving the discrepancy between reading and writing sequences can make a difference students' understanding of the equal sign. Students would be in danger of perceiving the equal sign as an operational symbol, if a teacher resolves the discrepancy by subordinating reading sequence to linguistic convention of writing. This way of resolving results in the undesired phenomenon of changing the reading expressions in Korean elementary math textbook which represent relational notion of the equal sign into other reading expressions that represent operational notion of it. For understanding of relational notion of the equal sign, the discrepancy should be resolved by changing writing sequence in accordance with reading sequence. In addition, teaching of verbalizing the equal sign should be integrated with teaching of verbalizing inequality signs.

• School Mathematics
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• v.14 no.3
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• pp.331-355
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• 2012

All the method used in teaching the ellipse was to have students draw the points which have the same sum of distances from the two points so that they can confirm the shapes of the ellipse before showing them the definition of ellipse. In this process, students would not get an opportunity to think or make the definition of ellipse for themselves. This deductive way can hinder students from having clear understanding of why such definition was made. This paper introduces a method of defining the ellipse based on the similarity between a circle and an ellipse, leading into the equation. This method is possible by introducing Analytic Geometry taught in current school mathematics and Transformation Geometry. By doing so, this paper will discuss a fundamental understanding about the ellipse and the feature of the ellipse expandable by intuition. Furthermore this paper will also show various advantages which can be given by defining the ellipse in Transformation Geometry.

• School Mathematics
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• v.18 no.3
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• pp.647-666
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• 2016

This study investigates pre-service teacher's understanding of the concept and representations of irrational numbers. We classified the representations of irrational numbers into six categories; non-fraction, decimal, symbolic, geometric, point on a number line, approximation representation. The results of this study are as follows. First, pre-service teachers couldn't relate non-fractional definition and incommensurability of irrational numbers. Secondly, we observed the centralization tendency on symbolic representation and the little attention to other representations. Thirdly, pre-service teachers had more difficulty moving between symbolic representation and point on a number line representation of ${\pi}$ than that of $\sqrt{5}$ We suggested the concept of irrational numbers should be learned in relation to various representations of irrational numbers.

• School Mathematics
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• v.19 no.3
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• pp.571-591
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• 2017

The purpose of this study is to understand the characteristics of mathematical discourse about the length in the class that learns the length of the curve defined by definite integral. For this purpose, this study examined the discourse about length by paying attention to the usage of the word 'length' in the class participants based on the communicative approach. As a result of the research, it was confirmed that the word 'length' is used in three usages - colloquial, operational, and structural usage - in the process of communicating with the discourse participants. Particularly, each participant did not recognize the difference even though they used different usage words, and this resulted in ineffective communication. This study emphasizes the fact that the difference in usage of words used by participants reduces the effectiveness of communication. However, if discourse participants pay attention to the differences of these usages and recognize that there are different discourses, this study suggests that meta - level learning can be possible by overcoming communication discontinuities and resolving conflicts.