미국의 “전국 수학 교사 협의회”(National Council of Teachers of Mathematics, NCTM)는 1989년부터 〈학교 수학의 교육과정과 평가 규준〉(1989), 〈수학 가르침(교수)의 전문성 규준〉(1991), 〈학교 수학의 평가(시험) 규준〉(NCTM, 1995), 〈학교 수학의 원리와 규준〉(2000)을 출판하여 미국의 수학 교육 의 전망(목표, 나아갈 길)과 규준(실행 지침)을 제시하였다. 수학 교사들로 구성된 미국의 NCTM은 학생, 학부모, 학교 행정가 등 많은 사람들과 힘을 합하여 모든 학생들에게 수준 높은 수학 교육을 받을 수 있는 여건(환경, 기회)을 조성하는 데 구심점의 역할을 하였다. 한편 많은 관련 단체들은 여러 배경과 능력을 가진 학생들이 전문성을 지닌 교사(특수 교사를 일컫는 밀이 아니다. 수학 교과를 이해하고 수학의 전문성과 특수성을 가르칠 수 있는 일반 교사를 일컫는 말이다.)로부터 미래를 대비해 평등하고, 진취적이며, 지원이 잘 이루어지고, 공학 도구(IT)가 잘 갖춰진 환경에서 중요한 수학적 아이디어를 이해하면서 학습할 수 있는 수학 교실(미국에서는 우리나라처럼 수학 교사가 수학 시간에 학생의 방(교실: Homeroom)에 찾아가지 않고 학생들이 선생의 방(수학 교실: Classroom)을 찾아온다. 전형적인 수학 교실의 사진은 2쪽에 나와 있다.)을 만들기 위해 함께 힘썼다. NCTM에서 출간한 여러 규준들은 우리나라의 제6차와 제7차 교육과정에도 큰 영향을 미쳤다. 이 글에서는 NCTM(2000)에서 제시한 학습 원리를 간단히 살펴본 다음 이를 중심으로 현재 미국 수학 교육의 교수ㆍ학습 이론의 동향을 살펴본다.

미국 NCTM의 Principles and Standards for School Mathematics에 나타난 수학과 교수,학습의 이론

This is probably the most popular design of experiments (DOE) book. It is unquestionably the leading DOE book in industry. So I am excepting it from the usual disdain I show for the  fth edition (5E) of any book, even though it follows the fourth edition (4E) by only four years. See Grice (2000) for a report on the 4E. Very likely this book bears little resemblance to the  rst edition way back in the 1970s. The author has taken particular care with this latest edition to reorganize the book to be consistent with modern DOE practice rather than classical DOE presentation. The primary change has been to move the chapters on regression modeling and response surface methods forward in the book. In the 4E these were the last two chapters in the book. In the 5E they follow the chapters on factorial and fractional factorial designs. Three chapters on “other designs” now close out the book. This certainly gives the book a better  ow for industry short courses. Perhaps these will simply be referenced as arcane methods in the sixth edition! Other production values in the book also continue to improve. There are many high-quality graphical displays. There is much use of printouts from Minitab and Design-Expert. A student version of Design-Export comes with the book. There is also an instructor’s CD-ROM with supplemental material to make the book suitable for more advanced courses. There is the now-essential Web site that has more information to help students and instructors. Perhaps if I were teaching DOE for master’s-level statisticians, the recent book by Dean and Voss (1999), reviewed by Amidan (2000), would be my choice. However, for most other audiences this is the complete DOE book. Industrial statisticians should get a copy of the new version and ensure its exposure to the relevant people in their organization.

Introduction to the Practice of Statistics

Null hypothesis significance testing (NHST) has several shortcomings that are likely contributing factors behind the widely debated replication crisis of (cognitive) neuroscience, psychology and biomedical science in general. We review these shortcomings and suggest that, after about 60 years of negative experience, NHST should no longer be the default, dominant statistical practice of all biomedical and psychological research. If theoretical predictions are weak we should not rely on all or nothing hypothesis tests. Different inferential methods may be most suitable for different types of research questions. Whenever researchers use NHST they should justify its use, and publish pre-study power calculations and effect sizes, including negative findings. Hypothesis-testing studies should be pre-registered and optimally raw data published. The current statistics lite educational approach for students that has sustained the widespread, spurious use of NHST should be phased out. Instead, we should encourage either more in-depth statistical training of more researchers and/or more widespread involvement of professional statisticians in all research.

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When Null Hypothesis Significance Testing Is Unsuitable for Research: A Reassessment

Informal inferential reasoning is a relatively recent concept in the research literature. Several research studies have defined this type of cognitive process in slightly different ways. In this paper, a working definition of informal inferential reasoning based on an analysis of the key aspects of statistical inference, and on research from educational psychology, science education, and mathematics education is presented. Based on the literature reviewed and the working definition, suggestions are made for the types of tasks that can be used to study the nature and development of informal inferential reasoning. Suggestions for future research are offered along with implications for teaching.

A framework to support research on informal inferential reasoning

We want to express digital communication with a human touch. So we pay attention to the properties of a door because it links one place to another. We think the linking of different places and sharing of places is one of the substantial qualities of network technology. Another reason that we focus on a door is because it bears great meanings. For example, a door is the first spot for a meeting with someone or for kissing someone goodbye. It could be your children, spouse, or your friends. These days, we talk and say hello to friends by Messenger or mobiles. Accustomed to digital devices which neglect time or space, we expect that the devices can carry our emotions to others. However, these have limits in expression. We want to show through the our work "The Door" that network technology should have a little more humanity and love in the near future.

The Door

Students’ misconceptions of statistical inference: A review of the empirical evidence from research on statistics education

Although a number of instruments for assessing attitudes toward statistics have been developed, several questions with regard to the structure and item functioning remain unresolved. In this study, the structure of the Survey of Attitudes Toward Statistics (SATS-36), a widely used questionnaire to measure six aspects of students’ attitudes toward statistics, is investigated. This study addresses the previously unexplored issue of individual item functioning. Based on confirmatory factor analysis using individual items, the results suggest that the SATS-36 can be improved by removing some poorly functioning items and that depending on the goals of a specific study either six subscales could be used or three of them (Affect, Cognitive Competence, and Difficulty) can be combined into one subscale without losing much information. \nFirst published May 2011 at Statistics Education Research Journal: Archives

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Measuring statistics attitudes: structure of the survey of attitudes toward statistics (sats-36)

Both researchers and teachers of statistics have made considerable efforts during the last decades to re-conceptualize statistics courses in accordance with the general reform movement in mathemati...

How Confident Are Students in Their Misconceptions about Hypothesis Tests

Despite the relevance of correlational studies for most research domains, many students, teachers, and researchers alike hold misconceptions concerning the Pearson product-moment correlation coefficient. One of these, the transitivity misconception, has not yet been documented in a systematic way. This paper summarizes the first empirical study, using 279 university students, and examines the relationship between student-based and task-based factors and the appearance of this misconception. In particular, two task-based factors seemed to have a significant effect on its appearance. In addition, the respondents’ level of confidence in their answer to the transitivity item was significantly lower than for most other times.

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The transitivity misconception of pearson's correlation coefficient 5

This study uses the Attitudes Toward Statistics (ATS) scale (Wise 1985) to investigate the attitudes toward statistics and the relationship of those attitudes with short- and long-term statistics e...

Stijn Vanhoof

Papers

Students’ misconceptions of statistical inference: A review of the empirical evidence from research on statistics education

Measuring statistics attitudes: structure of the survey of attitudes toward statistics (sats-36)

How Confident Are Students in Their Misconceptions about Hypothesis Tests

The transitivity misconception of pearson's correlation coefficient 5

Attitudes toward statistics and their relationship with short- and long-term exam results