• School Mathematics
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• v.9 no.1
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• pp.45-64
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• 2007

The primary purposes of this study were to investigate how sixth graders would react to the types of tasks with regard to the comprehension of graphs and what differences might be among the kinds of graphs, and to raise issues about instructional methods of graphs. A descriptive study through pencil-and-paper tests was conducted. The tests consisted of 48 questions with 4 types of tasks (reading the data, reading between the data, reading beyond the data, and understanding the situations) and 6 kinds of graphs. The conclusions drawn from the results obtained in this study were as follows: First, it is necessary to foster the ability of interpreting the data and understanding the situation in graphs as well as that of reading the data and finding out the relationships in the data. Second, it is informative for teachers to know students' difficulties and thinking processes. Third, in order to develop understanding of graphs, it is important that students solve different types of tasks beyond simple question-answer tasks. Fourth, teachers need to pay attention to teach fundamental factors such as reading the data with regard to line graphs and stem-and-leaf plots Finally, graph type and task type interact to determine graph-comprehension performance. Therefore, both learning all kinds of graphs and being familiar with multiple types of tasks are important.

• School Mathematics
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• v.9 no.1
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• pp.29-44
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• 2007

The aim of statistics education is to enhance statistical thinking. Variability is the key components of statistical thinking. The research has been reviewed preceding research about variability of data. Proceeding from what has been considered above, this research developed learning materials that investigated the concept of variability as it relates to Freudenthal's context by having students sort a particular context. The research is executed the case study evidently aimed at Junior High School 3rd Grade Student's Understanding of Variability. The study of variability in data can be an important start to reach a testing of statistical hypothesis; students reduce data and draw graphs by relating probability distribution to relative frequency and normal distribution. Thus, this study offers basic materials into developing both contents and methods of education need to consider with this sense of purpose held by students to achieve this goal.

• Journal of Educational Research in Mathematics
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• v.24 no.2
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• pp.125-143
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• 2014

In this study, we analyzed a mathematical discussion in the Calculus II course of the Gifted Science Academy and individual interviews to determine the relationship between cognitive conflicts and commognitive conflicts. The mathematical discussion began with a question from a student who seemed to have a cognitive conflict about the osculating plane of a space curve. The results indicated that the commognitive conflicts were resolved by ritualizing and using the socially constructed knowledge, but cognitive conflicts were not resolved. Furthermore, we found that the cause of the cognitive conflict resulted from the student's imperfect analogical reasoning and the reflective discourse about it could be a learning opportunity for overcoming the conflict. These findings imply that cognitive conflicts can trigger the appearance of commognitive conflicts, but the elimination of commognitive conflicts does not imply that cognitive conflicts are resolved.

• Journal of Educational Research in Mathematics
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• v.24 no.2
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• pp.103-124
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• 2014

The process of analogical reasoning can be conventionally summarized in five steps : Representation, Access, Mapping, Adaptation, Learning. The purpose of this study is to develop more detailed model for reason of analogies considering the distinct characteristics of the mathematical education based on the process of analogical reasoning which is already established. Ultimately, This model is designed to facilitate students to use analogical reasoning more productively. The process of developing model is divided into three steps. The frist step is to draft a hypothetical model by looking into historical example of Leonhard Euler(1707-1783), who was the great mathematician of any age and discovered mathematical knowledge through analogical reasoning. The second step is to modify and complement the model to reflect the characteristics of students' thinking response that proves and links analogically between the law of cosines and the Pythagorean theorem. The third and final step is to draw pedagogical implications from the analysis of the result of an experiment.

• Journal of Elementary Mathematics Education in Korea
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• v.11 no.1
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• pp.23-42
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• 2007

Learners who have taken learner-centered instruction is expected to construct conceptually mathematical knowledge which is. If so, they can have some ability to solve problems they are confronted with in the first time. To know this, First graders who have been in learner-centered instruction during 1 school year was given 7+52+186 which usually appears in the national curriculum for 3rd grade. According to the results, most of them have constructed the logic necessary to solve the given problem to them, and actually solve it. From this, it can be concluded that first, even though learners are 1st graders they can construct mathematical knowledge abstractly, second, they can apply it to the new problem, and third consequently they can got a good score in a achievement test.

• Journal of Educational Research in Mathematics
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• v.22 no.2
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• pp.137-162
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• 2012

Learning graphical representations for statistical data requires understanding of the context related to measurement in statistical investigation since the choice of representation and the features of the selected graph to represent the data are determined by the purpose and context of data collection and the types of the data collected. This study investigated whether middle school students can think critically about measurement and scales integrating contextual knowledge and statistical knowledge. According to our results, the students lacked critical thinking related to measurement process of data and scales of graphical representations. In particular, the students had a tendency not to question upon information provided from data and graphs. They also lacked competence to critique data and graphs and to make a flexible judgement in light of context including statistical purpose.

• Journal of Educational Research in Mathematics
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• v.18 no.1
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• pp.25-50
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• 2008

Several previous studies suggested that simulation could be a main didactic instrument in overcoming misconception and probability modeling. However, they have not described enough how to reorganize probability knowledge as knowledge to be taught in a curriculum using simulation. The purpose of this study is to identify the theoretical knowledge needed in developing a didactic transposition method of probability knowledge using simulation. The theoretical knowledge needed to develop this method was specified as follows : pseudo-contextualization/pseudo-personalization, and pseudo-decontextualization/pseudo-deper-sonalization according to the introductory purposes of simulation. As a result, this study developed a local instruction theory and an hypothetical learning trajectory for overcoming misconceptions and modeling situations respectively. This study summed up educational intention, which was designed to transform probability knowledge into didactic according to the introductory purposes of simulation, into curriculum, lesson plans, and experimental teaching materials to present didactic ideas for new probability education programs in the high school probability curriculum.

• School Mathematics
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• v.18 no.1
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• pp.127-141
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• 2016

This study analyzes modes related to use of graph representation that appears to solve high school students quadratic function problem based on the graph using modes of Chauvat. It was examined the extent of understanding of the quadratic function of students through the flexibility of the representation of the Bannister (2014) from the analysis. As a result, the graph representation mode in which a high school students are mainly used is a nomographic specific mode, when using operational mode, it was found to be an error. The flexibility of Bannister(2014) that were classified to the use of representation from the point of view of the object and the process in the understanding of the function was constrained operation does not occur between the two representations in understanding the function in the process of perspective. Based on these results, the teaching on use graph representation for the students in classroom is required and the study of teaching and learning methods can understand the function from various perspectives is needed.

• School Mathematics
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• v.18 no.1
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• pp.159-173
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• 2016

In real educational field, there are cases that concrete problematic situations are introduced after abstract concepts are taught on the contrary to process that abstract from concrete contexts. In other words, there are cases that abstract knowledge has to be concreted. Freudenthal expresses this situation to antidogmatical inversion and indicates negative opinion. However, it is open to doubt that every class situation can proceed to abstract that begins from concrete situations or concrete materials. This study has done a comparative analysis in difference of mathematical thinking between a process that builds abstract context after being abstracted from concrete materials and that concretes abstract concepts to concrete situations and attempts to examine educational implication. For this, this study analyzed the mathematical thinking in the abstract process of concrete materials by manipulating AiC analysis tools. Based on the AiC analysis tools, this study analyzed mathematical thinking in the concrete process of abstract concept by using the way this researcher came up with. This study results that these two processes have opposite learning flow each other and significant mathematical thinking can be induced from concrete process of abstract knowledge as well as abstraction of concrete materials.

• School Mathematics
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• v.11 no.2
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• pp.243-260
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• 2009

In this paper, we have designed a teaching unit for the learning mathematising of secondary pre-service teachers by exploring generalized fibonacci sequences. First, we have found useful formulas for general terms of generalized fibonacci sequences which are expressed as combinatoric notations. Second, by using these formulas and CAS graphing calculator, we can help secondary pre-service teachers to conjecture and discuss the limit of the sequence given by the rations of two adjacent terms of an m-step fibonacci sequence. These processes can remind secondary pre-service teachers of a series of some mathematical principles.