• School Mathematics
• /
• v.13 no.1
• /
• pp.207-227
• /
• 2011

This study developed a statistical thinking level with constructs framework from based on Jones, Thornton, Langrall, & Mooney (2000) to analyze the 6th graders' thinking level shown on their survey activities. It was modified by 5 constructs framework such as collecting, describing, organizing, representing, and analyzing and interpreting data with four thinking levels, which represent a continuum from idiosyncratic to analytic reasoning. As a result, among four levels such as idiosyncratic level (level 1), transitional level (level 2), quantitative level (level 3), and analytical level (level 4), levels of two through four are shown on statistical thinking levels in this study.

• Journal of Gifted/Talented Education
• /
• v.22 no.3
• /
• pp.503-525
• /
• 2012

This study compared levels of mathematically talented students' statistical thinking with those of non-talented students in statistical modeling and sampling distribution understanding. t tests were conducted to test for statistically significant differences between mathematically gifted students and non-gifted students. In case of statistical modeling, for both of elementary and middle school graders, the t tests show that there is a statistically significant difference between mathematically gifted students and non-gifted students. Table of frequencies of each level, however, shows that levels of mathematically gifted students' thinking were not distributed at the high levels but were overlapped with those of non-gifted students. A similar tendency is also present in sampling distribution understanding. These results are thought-provoking results in statistics instruction for mathematically talented students.

• Journal of Educational Research in Mathematics
• /
• v.21 no.2
• /
• pp.201-220
• /
• 2011

This study investigates levels of thinking of elementary and middle school students doing their tasks of explaining and dealing with variability. According to results, on the task of explaining variability in the measurement settings five levels of thinking were identified: a lack of understanding of explanation of the causes, an insufficient understanding of the causes, an offer of physical causes, consideration of unexplained causes as the source of variability, and consideration of unexplained causes as quasi-chance variability. Also, in the chance settings five levels of thinking were identified: a lack of understanding of explanation of the causes, an insufficient understanding of the causes, an offer of physical causes, recognition of chance variability, and consideration of causes of distribution. On the task of dealing with variability in both the measurement and chance settings five levels of thinking were identified: a lack of understanding of dealing with variability, no physical control and improper statistical control, no physical control and proper statistical control, physical control and improper statistical control, and physical control and proper statistical control.

• Journal of Gifted/Talented Education
• /
• v.23 no.3
• /
• pp.387-406
• /
• 2013

This study compared levels of mathematically talented students' statistical thinking with those of non-talented students in the noticing of statistical variability. t tests were conducted to test for statistically significant differences between mathematically gifted students and non-gifted students. Results for the t-test shows that there is no difference between the TE students' and NE students' noticing of variability in the measurement settings. Meanwhile, the t-test results also show that there is a difference between the TM students' and NM students' noticing of variability in the both measurement and chance settings. Table of frequencies of each level, however, shows that levels of mathematically gifted students' thinking were not distributed at the high levels but were overlapped with those of non-gifted students. These results are thought-provoking results in statistics instruction for mathematically talented students.

• School Mathematics
• /
• v.12 no.4
• /
• pp.547-561
• /
• 2010

Even though statistics is considered as one of the areas of mathematical science in the school curriculum, it has been well documented that statistics has distinct features compared to mathematics. However, there is little empirical educational research showing distinct features of statistics, especially research into the understanding of statistical concepts which are different from other areas in school mathematics. In addition, there is little discussion of a relationship between the ability of mathematical thinking and the ability of understanding statistical concepts. This study extracted some important concepts which consist of the fundamental statistical reasoning and investigated how mathematically high achieving students understood these concepts. As a result, there were both kinds of concepts that mathematically high achieving students developed well or not. There is a weak correlation between mathematical ability and the level of understanding statistical concepts.

• Journal of Educational Research in Mathematics
• /
• v.20 no.3
• /
• pp.339-356
• /
• 2010

It is important for children to develop statistical reasoning as they think through data. In particular, it is imperative to provide children instructional situations in which they are encouraged to consider variability in data because the ability to reason about variability is fundamental to the development of statistical reasoning. Many researchers argue that even highperforming mathematics students show low levels of statistical reasoning; interventions attending to pedagogical concerns about child ren's statistical reasoning are, thus, necessary. The purpose of this study was to investigate 15 gifted elementary students' various ways of understanding important statistical concepts, with particular attention given to 3 students' reasoning about data that emerged as they engaged in the process of generating and graphing data. Analysis revealed that in recognizing variability in a context involving data, mathematically gifted students did not show any difference from previous results with general students. The authors suggest that our current statistics education may not help elementary students understand variability in their development of statistical reasoning.

• Communications of Mathematical Education
• /
• v.11
• /
• pp.127-144
• /
• 2001

본 연구는 확률의 다양한 의미를 반영한 초등학교 확률 학습 프로그램을 개발하고, 개발된 프로그램의 적용 가능성을 알아보는데 목적을 두고 있다. 먼저 확률의 다양한 의미를 반영한 초등학교 확률 학습프로그램을 개발하기 위하여, 프로그램의 기본 방향을 설정하고, 확률의 다양한 의미를 반영하기 위한 교수 방법을 마련하였다. 개발된 프로그램은 초등학교 6학년 한 단원 분량인 7차시로 이루어져 있다. 다음으로 프로그램 시행 전에 실시한 검사에서 확률적 사고 수준이 상 ${\cdot}$ 중 ${\cdot}$ 하인 것으로 나타난 세 명의 학생을 연구 대상으로 개발된 프로그램을 시행하였다. 프로그램 적용 전 ${\cdot}$ 후에 실시한 지필 평가와 비디오 카메라로 녹음한 수업 내용과 학생들의 학습지를 검토하여 프로그램 적용 전, 1${\sim}$7 각 차시 후, 프로그램 적용 후의 시기로 나누어 분석한 결과, 세 학생 모두 확률적 사고 수준이 가장 높은 수준인 4수준으로 발전하였다. 본 연구의 결과, 확률을 이론적 의미 뿐 아니라 경험적 ${\cdot}$ 통계적 의미로 접근하면 초등학교 학생들도 확률 개념을 학습할 수 있었다. 따라서 확률을 다양한 관점으로 접근한다면, 초등학교에서도 독립성, 조건부 확률 같은 개념을 유의미하게 학습할 수 있을 것이다.

• Communications of Mathematical Education
• /
• v.11
• /
• pp.107-126
• /
• 2001

우리는 흔히 21C를 정보화 시대라고 하며 우리에게 주어지는 정보들 또한 일기예보와 같은 일상적인 분야에서 여론 조사와 같은 전문적인 분야에 이르기까지 아주 다양하다. 이런 정보들은 통계영역과 아주 밀접하며 이런 정보들을 통계적으로 바르게 해석하고 추론하여 일반화하는 등 일련의 과정들을 요구한다. 이런 상황아래 본 연구에서는 6차 초등학교 수학 교과서에서 여러 통계학 영역 중 그래프 형태로 가장 먼저 도입되는 막대그래프에 중점을 두어 현행 교과서에서 학습 내용과 학습 과정의 문제점에는 어떤 것이 있으며 아울러 그래프 이해력에 필요한 요소나 인지적 사고 능력, 그래프 이해력의 수준을 알아보고, 이를 바탕으로 여러 문헌을 통해 본 연구자가 나름대로 구안한 통계적 기법을 사용한 교수 ${\cdot}$ 학습 과정을 실험반에 적용한 후 그래프 이해력 사전 ${\cdot}$ 사후 검사를 비교함으로써 통계적 기법을 사용한 교수 ${\cdot}$ 학습 과정이 그래프 이해력에 어떠한 영향을 미치는지 알아보고자 한다.

• The Mathematical Education
• /
• v.58 no.1
• /
• pp.139-160
• /
• 2019

This study attempts to examine statistical tasks in the middle-school mathematics textbooks of Korea and Connected Mathematics 3 [CMP] of the US in terms of an opportunity-to-learn for statistical reasoning. We utilized an analytical framework consisting of types of context, statistical reasoning level, cognitive demand of the tasks, and types of student response. The findings from the task analysis suggested that Korean textbooks focused on finding answers by applying previously learned algorithms or formulas and thus provided students with very limited opportunities to experience statistical reasoning. Also, the results proposed that the mathematical tasks in statistics unit of CMP3 offer more essential and complex tasks that promote students' conceptual understanding of various statistical ideas and statistical reasoning in a meaningful way.

• Journal of Korean Society of Transportation
• /
• v.17 no.3
• /
• pp.21-30
• /
• 1999

One of the major tasks of a Police station is the management of road traffic accidents. Each police station is responsible for keeping Traffic Accident Records (TAR) which can be used as the basis of statistical analyses. Results of such statistical analyses have been applied to establishing effective traffic Plans and safety Policies at the macro level. In this Paper, we apply QFD in a way that each police station can set and implement specific policies according to the local characteristics. Cluster analysis is employed to find black spots in each local area. Poisson repression is used to identify the area specific factors related to various types of road accidents. Results of such statistical analyses are applied to QFD. Our approach is expected to contribute to reduce various types of area specific road traffic accidents.