• Communications of Mathematical Education
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• v.32 no.3
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• pp.363-383
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• 2018

The subject of 'Mathematical Task Inquiry' was introduced newly in the curriculum revised in 2015. The subject is dealt with after completing the subject of 'mathematics' to be dealt with in the tenth grade. Its main content is comprised of the understanding and learning of the purpose and procedure of inquiry task and of study ethics, and its educational goal is to enforce the prior mathematical knowledge and to obtain the ability to select interesting topics that combine mathematics with other subjects. However the textbook of the subject does not exist, and teachers should handle with the subject with responsibility for their own ways. Because of this reason, this study is to develop an instruction model on project(task) inquiry model and materials. Namely, according to the model, students is guided to select and decide the subject of the task, and develop the task for themselves, solve it with peers in cooperation, and announce the solution and their feelings. During those students' exploration and activities, the role of teachers is to guide students to complete their work. By the way, in order to develop more creative tasks that is appropriate to their academic and cognitive level, this study conducted the experimentation for the subject of 9 students (6 girls and 3 boys), who are scheduled to advance to the 11 grade of J high school located in G domestic. The experimentation was consisted of three class and after the third class, the semi-structured interview was conducted immediately for the students.

• Journal of the Korean School Mathematics Society
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• v.12 no.2
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• pp.309-325
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• 2009

The purpose of the study was to investigate the differences between Korean mathematics textbooks and CPMP textbooks in the view of conceptual network, structure of mathematical contents, instructional design, and teaching and learning environment to explore the implications for mathematics education in Korea. According to the results, Korean textbooks emphasized the mathematical structures and conceptual network, on the other hand, CPMP textbooks focused on making connections between mathematical concepts and corresponding real life situations as well as mathematical structures. And generalizing mathematical concepts at the symbolic level was very important objective in Korean textbooks, but in the CPMP textbooks, investigating mathematical ideas and solving problems in diverse contexts including real- life situations were considered very important. Teachers using Korean textbooks preferred an explanatory teaching method with the use of concrete manipulatives and student worksheet, however, teachers using CPMP textbooks emphasized collaborative group activities to communicate mathematical ideas and encouraged students to use graphing calculators when they explore mathematical concepts and solve problems.

• Journal of Elementary Mathematics Education in Korea
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• v.18 no.1
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• pp.105-122
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• 2014

In this paper, fraction division algorithms in Korean elementary mathematics textbooks are analyzed as a part of the groundwork to improve teaching methods for fraction division algorithms. There are seemingly six fraction division algorithms in ${\ll}Math\;5-2{\gg}$, ${\ll}Math\;6-1{\gg}$ textbooks according to the 2006 curriculum. Four of them are standard algorithms which show the multiplication by the reciprocal of the divisors modally. Two non-standard algorithms are independent algorithms, and they have weakness in that the integration to the algorithms 8 is not easy. There is a need to reconsider the introduction of the algorithm 4 in that it is difficult to think algorithm 4 is more efficient than algorithm 3. Because (natural number)${\div}$(natural number)=(natural number)${\times}$(the reciprocal of a natural number) is dealt with in algorithm 2, it can be considered to change algorithm 7 to algorithm 2 alike. In textbooks, by converting fraction division expressions into fraction multiplication expressions through indirect methods, the principles of calculation which guarantee the algorithms are explained. Method of using the transitivity, method of using the models such as number bars or rectangles, method of using the equivalence are those. Direct conversion from fraction division expression to fraction multiplication expression by handling the expression is possible, too, but this is beyond the scope of the curriculum. In textbook, when dealing with (natural number)${\div}$(proper fraction) and converting natural numbers to improper fractions, converting natural numbers to proper fractions is used, but it has been never treated officially.

• Journal of Elementary Mathematics Education in Korea
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• v.14 no.1
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• pp.43-64
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• 2010

This study aimed to foster the learning abilities of mathematics, that is, along with the formation of a sure mathematical concept, extending the powers of doing mathematics, and bringing the creativities for 3rd grade elementary school children. In order to achieve these objects, we have executed mathematical classes for two consecutive hours of 16 times using the teaching model of [Learning contents in textbook]$\rightarrow$[The first problem Posing]$\rightarrow$[Problem solving to childrens' posing some problems]$\rightarrow$[Advanced problem posing] to 3rd grade school children during the first semester of 2009. In this paper, we analyzed problems that are made by children focusing on the four fundamental rules +, -, ${\times}$, $\div$ of arithmetic, with the view points of problem's completion, fluencies, flexibilities, buildings of concept, originalities and using materials. As a result of the comparative analysis of the first problems and advanced problems made by the children, the first problems were revealed to be rather better in of problem's completion and fluencies. And the flexibilities were improved in the division and multiplication classes carried on. Setting up the experimental and comparative class, we compared to the scholastic achievement of two classes for the beginning and end in the first semester. In the result, the former was improved in the scholastic achievement more than the latter.

• The Mathematical Education
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• v.42 no.3
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• pp.295-302
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• 2003

The purpose of this study is to make more reliable researches on the tendency of shirking from the mathematics by including those of the students in the other country, and there are a series of researches such as 'math-camp to raise the mathematical tendency of the students who make little progress in the study', 'establishment of factors causing the shirking tendency from the mathematics and development of the analyzing instruments for it' and 'study on the preference to each category of the school mathematics.' For this purpose, I used a test developed by the shirking tendency research team. I compared the average score and standard deviation between the Korean and the Australian students. As for the average score, that of the Australian elementary school students is about one point higher than the Korean students, and there was no remarkable difference in the deviation. Comparing the math-shirking tendency of the two groups, they show higher shirking tendency in the aspects of emotional and mathematical recognition that belong to the psychological and environmental sphere. And, as for an extent of association in difficulties according to each school grades, its degree of the Australian students is comparatively lower than that of the Korean students, therefore, the shirking tendency of the Australian students is intermediate level whereas that of the Korean students is the lowest. They show us a peculiar result in teacher factor. It is noteworthy in that the Korean students show a positive reaction in that factor, however, the Australian students show a comparatively weak reaction. It might be caused by a cultural difference. I also have compared the accumulated percentage according to each shirking tendency factors. It will not only be very efficient for teachers to establish a teaching plan but also a good data to understand the shirking tendency of each student. This will be a very good data for the planners of teaching policy to remedy the causes of shirking tendency. And, it will also be used effectively to write a new textbook. It has been uncommon that a psychological test is used in the research for the improvement of teaching and learning mathematics. In this aspect, I am sure that this study including the preceding research will be a good in studying the shirking tendency factors by using a psychological test. I believe that this research will be a help to grasp the outline of the shirking tendency and I will have to try continuously to make it be a reasonable and reliable study.

• Education of Primary School Mathematics
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• v.19 no.1
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• pp.1-18
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• 2016

Patterns are of great significance to develop algebraic thinking of elementary students. This study analyzed teaching methods of patterns in current elementary mathematics textbook series in terms of three main activities related to pattern generalization (i.e., analyzing the structure of patterns, investigating the relationship between two variables, and reasoning and representing the generalized rules). The results of this study showed that such activities to analyze the structure of patterns are not explicitly considered in the textbooks, whereas those to explore the relationship between two variables in a pattern are emphasized throughout all grade levels using function table. The activities to reason and represent the generalized rules of patterns are dealt in a way both for lower grade students to use informal representations and for upper grade students to employ formal representations with expressions or symbols. The results of this study also illustrated that patterns in the textbooks are treated rather as a separate strand than as something connected to other content strands. This paper closes with several implications to teach patterns in a way to foster early algebraic thinking of elementary school students.

• Journal of Science Education
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• v.36 no.2
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• pp.381-393
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• 2012

This study was analyzed that what kind of elements for STEAM, except scientific commonsense, are contained in 2009 revised chemistry textbooks I for high school students. So first, elements of STEAM in textbooks were examined by following three sections; by publishing company, each unit and area of textbook. For reference, new sub-elements of STEAM were set because existing elements of STEAM is incongruent with current textbooks. As a result, most chemistry textbooks included elements of STEAM properly for inter-related learning with the other fields. Every textbook had its unique learning methods for utilizing elements of STEAM and they were unified as one way. Depending on textbooks, learning methods were little bit different from the others. Also, detailed elements of STEAM contained in textbooks were classified just 14 types. And they were even focused on a few elements according to sort of textbook. Thus, it seemed that there was a certain limitation of current education of STEAM in chemistry Field. By the unit, according to the curriculum, contained elements of STEAM were different. Almost all elements of STEAM were located in I section. Consequently, it is difficult to include elements of STEAM if mathematics or history were not existed in curriculum. Lastly, by the area, most of all elements of STEAM were included in reference section. Almost all elements of STEAM were focused on art and culture. Thus, STEAM was used for utilization about chemical knowledge in substance. Otherwise, convergence training for approach method was not enough in chemical knowledge.

• Communications of Mathematical Education
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• v.30 no.3
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• pp.393-418
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• 2016

Theory and fundamentals of mathematics consist mostly of proposition form. Activities by research of the proposition which leads to determine the true or false, justify the true propositions and refute with counterexample improve logical reasoning skills of students in emphases on mathematics education. Also, utilizing of counterexamples in school mathematics combines mathematical knowledge through the process of finding a counterexample, help the concept study and increase the critical thinking. These effects have been found through previous research. But many studies say that the learners have difficulty in generating counterexamples for false propositions and materials have not been developed a lot for the counterexample utilizing that can be applied in schools. So, this study analyzed the current textbook and examined the use of counterexamples and developed educational materials for counterexamples that can be applied at schools. That materials consisted of making true & false propositions and students was divided into three groups of academic achievement level. And then this study looked at the change of the students' thinking after counterexample classes. As a study result, in all three groups was showed a positive change in the cognitive domain and affective domain. Especially, in top-level group was mainly showed a positive change in the cognitive domain, in upper-middle group was mainly showed in the cognitive and the affective domain, in the sub-group was mainly found a positive change in the affective domain. Also in this study shows that the class that makes true or false propositions in education of utilizing counterexample, made students understand a given proposition, pay attention to easily overlooked condition, carefully observe symbol sign and change thinking of cognitive domain helping concept learning regardless of academic achievement levels of learners. Also, that class gave positive affect to affective domain that increase interest in the proposition and gain confidence about proposition.

• Journal of Educational Research in Mathematics
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• v.23 no.2
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• pp.135-152
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• 2013

The purpose of this study is to navigate to the desired direction for the figure of number line through the extensive analysis of number line in middle school textbooks and literatures. For the efficient achievement of this purpose, three research questions were posed as follows: First, we compare the figures of number line in textbooks of Korea and other countries. Korean math textbooks mark the arrow on both sides of number line. But, however, coordinate plane was marked with arrow on only positive direction of number line. In contrast, the majority of secondary school textbooks in several foreign countries has the arrow only on positive direction. Second, the change in the figure of number line has been analyzed historically from two perspectives. From the first to 2007-revised curriculum, math textbooks of Korea were analyzed. Since the 6th curriculum, the number of textbooks with arrows on both sides has increased sharply. That is, textbooks with one arrow almost have disappeared. It is strange that any explanation for this abrupt change can't be found. The following analysis was also performed on published foreign literatures since Descartes. There was no arrow in the early figures of number line. But after 19th century, number lines with one arrow have begun to appear. Third, based on the previous study, we propose a reasonable way for the figure of number line. In fact, we claim that, in terms of linguistic symbols, the number line should be with only one arrow on positive side.

• Journal of Educational Research in Mathematics
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• v.15 no.3
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• pp.251-272
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• 2005

Given that cognitive demands of mathematical tasks can be changed during instruction, this study attempts to provide a detailed description to explore how tasks are set up and implemented in the classroom and what are the classroom-based factors. As an exploratory and qualitative case study, 4 of six-grade classrooms where high-level tasks on ratio and proportion were used were videotaped and analyzed with regard to the patterns emerged during the task setup and implementation. With regard to 16 tasks, four kinds of Patterns emerged: (a) maintenance of high-level cognitive demands (7 tasks), (b) decline into the procedure without connection to the meaning (1 task), (c) decline into unsystematic exploration (2 tasks), and (d) decline into not-sufficient exploration (6 tasks), which means that the only partial meaning of a given task is addressed. The 4th pattern is particularly significant, mainly because previous studies have not identified. Contributing factors to this pattern include private-learning without reasonable explanation, well-performed model presented at the beginning of a lesson, and mathematical concepts which are not clear in the textbook. On the one hand, factors associated with the maintenance of high-level cognitive demands include Improvising a task based on students' for knowledge, scaffolding of students' thinking, encouraging students to justify and explain their reasoning, using group-activity appropriately, and rethinking the solution processes. On the other hand, factors associated with the decline of high-level cognitive demands include too much or too little time, inappropriateness of a task for given students, little interest in high-level thinking process, and emphasis on the correct answer in place of its meaning. These factors may urge teachers to be sensitive of what should be focused during their teaching practices to keep the high-level cognitive demands. To emphasize, cognitive demands are fixed neither by the task nor by the teacher. So, we need to study them in the process of teaching and learning.