• The Mathematical Education
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• v.41 no.3
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• pp.291-318
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• 2002

We investigated on the primary school children's abilities of formal reasoning. Seventy students in grade 5 participated in the study. They responsed their best reactions on the problems constituted of three parts requiring the informal or formal reasoning and generalization. Their reactions are classified by some criteria depending the level of reasoning. About 10 students showed that they constructed a kind of scheme for solving the problems, similar to formal reasoning and beyond naive informal reasoning. And about 30 students did so partially. We concluded that the teaching and learning of reasoning by the progressive increasing the degree of rigor from grade 5 is possible.

• Journal of The Korean Association For Science Education
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• v.29 no.2
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• pp.253-266
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• 2009

This study was focused on analyzing students' informal reasoning patterns and their considerations in decision-making on socioscientific issues. This study involved 20 undergraduate students (10 biology majors and 10 non-biology majors) and showed how the two groups responded on socioscientific issues. Semi-structured interviews were conducted twice respectively based on six scenarios of gene therapy and human cloning. The result showed 93% of the total number of participants' decisions were made by rationalistic reasoning, whereas emotional reasoning was 49%, and intuitive reasoning was 27%. Students usually used two or three informal reasoning patterns together. Most of the students took more consideration on social factors. Some perceived ethical and moral implications of the issues, but they did not consider them seriously. They made their decisions depending on their own values, etc. 65% of the participants got their information on socioscientific issues from the mass media. Biology majors hardly used intuitive reasoning compared to non-biology majors. The Biology major group took into deep considerations on socioscientific issues while the non-biology major group seemed to interpret the given scenarios simply. This implied that the content knowledge was a significant factor of their decision-making. Therefore, it is necessary to develop proper science courses for non-major students to improve their decision-making on socioscientific issues. So, when we develop educational materials or programs, we should consider students' reasoning patterns, their considerations in decision-making, and their content knowledge. And because the mass media has the potential to play a key role for an effective education, we need to make a plan to make a practical application.

• Journal of Elementary Mathematics Education in Korea
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• v.19 no.4
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• pp.457-484
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• 2015

This study aims to investigate an approach to teach proportional reasoning in elementary mathematics class by analyzing the proportional strategies the students use to solve the proportional reasoning tasks and their percentages of correct answers. For this research 174 sixth graders are examined. The instrument test consists of various questions types in reference to the previous study; the proportional reasoning tasks are divided into algebraic-geometric, quantitative-qualitative and missing value-comparisons tasks. Comparing the percentages of correct answers according to the task types, the algebraic tasks are higher than the geometric tasks, quantitative tasks are higher than the qualitative tasks, and missing value tasks are higher than the comparisons tasks. As to the strategies that students employed, the percentage of using the informal strategy such as factor strategy and unit rate strategy is relatively higher than that of using the formal strategy, even after learning the cross product strategy. As an insightful approach for teaching proportional reasoning, based on the study results, it is suggested to teach the informal strategy explicitly instead of the informal strategy, reinforce the qualitative reasoning while combining the qualitative with the quantitative reasoning, and balance the various task types in the mathematics classroom.

• School Mathematics
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• v.14 no.4
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• pp.445-468
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• 2012

This study is tried in order to link informal arithmetic reasoning to formal algebraic reasoning. In this study, we investigated elementary school student's non-formal algebraic reasoning used in algebraic problem solving. The result of we investigated algebraic reasoning of 839 students from grade 1 to 6 in two schools, Korea, we could recognize that they used various arithmetic reasoning and pre-formal algebraic reasoning which is the other than that is proposed in the text book in word problem solving related to the linear systems of equation. Reasoning strategies were diverse depending on structure of meaning and operational of problems. And we analyzed the cause of failure of reasoning in algebraic problem solving. Especially, 'quantitative reasoning', 'proportional reasoning' are turned into 'non-formal method of substitution' and 'non-formal method of addition and subtraction'. We discussed possibilities that we are able to connect these pre-formal algebraic reasoning to formal algebraic reasoning.

• Journal of Korean Elementary Science Education
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• v.42 no.3
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• pp.421-433
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• 2023

This study examined the reasoning of gifted elementary science students in a socioscientific issues (SSI) classroom discussion on COVID-19-related trash disposal challenges. This study aimed to understand the characteristics of evidence use and decision-making difficulties in each type of SSI-related reasoning. To this end, the transcripts of 17 gifted students of elementary science discussing SSIs in a classroom were analyzed within the framework of informal reasoning. The analysis framework was categorized into three types according to the primary influence involved in reasoning: rational, emotional, and intuitive. The analysis showed that students exhibited four categories of evidence use in SSI reasoning. First, in the rational reasoning category, students deemed and recorded scientific knowledge, numbers, and statistics as objective evidence. However, students who experienced difficulty in investigating such scientific data were less likely to have factored them in subsequent decisions. Second, in the emotional reasoning category, students' solutions varied considerably depending on the perspective they empathized with and reasoned from. Differences in their views led to conflicting perspectives on SSIs and consequent disagreement. Third, in the intuitive reasoning category, students disagreed with the opinions of their peers but did not explain their positions precisely. Intuitive reasoning also created challenges as students avoided problem-solving in the discussion and did not critically examine their opinions. Fourth, a mixed category of reasoning emerged: intuition combined with rationality or emotion. When combined with emotion, intuitive reasoning was characterized by deep empathy arising from personal experience, and when combined with rationality, the result was only an impulsive reaction. These findings indicate that research on student understanding and faculty knowledge of SSIs discussed in classrooms should consider the difficulties in informal reasoning and decision-making.

• Communications of Mathematical Education
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• v.24 no.2
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• pp.345-363
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• 2010

The purpose of this study is to investigate and analyze informal knowledge of students who do not learn the conception of proportion and to identify how the informal knowledge can be used for teaching the conception of proportion in order to present an effective method of teaching the conception. For doing this, proportion was classified into direct and inverse proportion, and 'What are the informal knowledge of students?' were researched. The subjects of this study were 117 sixth-graders who did not have prior learning on direct and inverse proportion. A total eleven problems including seven for direct proportion and four for inverse proportion, all of them related to daily life. The result are as follows; Even though students didn't learn about proportion, they solve the problems of proportion using informal knowledge such as multiplicative reasoning, proportion reasoning, single-unit strategy etc. This result implies mathematics education emphasizes student's informal knowledge for improving their mathematical ability.

• Journal of Educational Research in Mathematics
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• v.25 no.1
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• pp.21-58
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• 2015

The aim of this study is to look into the didactical background for teaching proportional reasoning in elementary school mathematics and offer suggestions to improve teaching proportional reasoning in the future. In order to attain these purposes, this study extracted and examined key ideas with respect to the didactical background on teaching proportional reasoning through a theoretical consideration regarding various studies on proportional reasoning. Based on such examination, this study compared and analyzed textbooks used in the United States, the United Kingdom, and South Korea. In the light of such theoretical consideration and analytical results, this study provided suggestions for improving teaching proportional reasoning in elementary schools in Korea as follows: giving much weight on proportional reasoning, emphasizing multiplicative comparison and discerning between additive comparison and multiplicative comparison, underlining the ratio concept as an equivalent relation, balancing between comparisons tasks and missing value tasks inclusive of quantitative and qualitative, algebraic and geometrical aspects, emphasizing informal strategies of students before teaching cross-product method, and utilizing informal and pre-formal models actively.

• Communications of Mathematical Education
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• v.23 no.1
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• pp.145-174
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• 2009

Based on the thinking that people can understand more clearly when the problem is related with their prior knowledge, the Purpose of this study was to analysis students' informal knowledge, which is constructed through their mathematical experience in the context of real-world situations. According to this purpose, the following research questions were. 1) What is the characteristics of students' informal knowledge about fraction before formal fraction instruction in school? 2) What is the difference of informal knowledge of fraction according to reasoning ability and grade. To investigate these questions, 18 children of first, second and third grade(6 children per each grade) in C elementary school were selected. Among the various concept of fraction, part-whole fraction, quotient fraction, ratio fraction and measure fraction were selected for the interview. I recorded the interview on digital camera, drew up a protocol about interview contents, and analyzed and discussed them after numbering and comment. The conclusions are as follows: First, students already constructed informal knowledge before they learned formal knowledge about fraction. Among students' informal knowledge they knew correct concepts based on formal knowledge, but they also have ideas that would lead to misconceptions. Second, the informal knowledge constructed by children were different according to grade. This is because the informal knowledge is influenced by various experience on learning and everyday life. And the students having higher reasoning ability represented higher levels of knowledge. Third, because children are using informal knowledge from everyday life to learn formal knowledge, we should use these informal knowledge to instruct more efficiently.

• School Mathematics
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• v.4 no.1
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• pp.1-13
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• 2002

The purpose of this study is to investigate the reasons and backgrounds of drawing auxiliary lines in the proof of geometry. In most of proofs in geometry, drawing auxiliary lines provide important clues, thus they play a key role in deductive proof. However, many student tend to have difficulties of drawing auxiliary lines because there seems to be no general rule to produce auxiliary lines. To alleviate such difficulties, informal activities need to be encouraged prior to draw auxiliary lines in rigorous deductive proof. Informal activities are considered to be contrasting to deductive proof, but at the same time they are connected to deductive proof because each in formal activity can be mathematically represented. For example, the informal activities such as fliping and superimposing can be mathematically translated into bisecting line and congruence. To elaborate this idea, some examples from the middle school mathematics were chosen to corroborate the relation between informal activities and deductive proof. This attempt could be a stepping stone to the discussion of how to teach auxiliary lines and deductive reasoning.

• Research in Mathematical Education
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• v.17 no.4
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• pp.243-266
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• 2013

Accompanied with ongoing calls for reform in statistics curriculum, mathematics and statistics teachers purposefully have been reconsidering the curriculum and the content taught in statistics classes. Changes made are centered around statistical inference since teachers recognize that students struggle with understanding the ideas and concepts used in statistical reasoning. Despite the efforts to change the curriculum, studies are sparse on the topic of characterizing student learning and understanding of statistical inference. Moreover, there are no tools to evaluate students' statistical reasoning in a coherent way. In response to the need for a research instrument, in a series of research study, the researcher developed a reliable and valid measure to assess students' inferential reasoning in statistics (IRS). This paper describes processes of test blueprint development that has been conducted from review of the literature and expert reviews.