How we Think

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

I. INTRODUCTION TO EVALUATION. 1. Evaluation's Basic Purpose, Uses, and Conceptual Distinctions. 2. Origins of Modern Program Evaluation. 3. Recent Developments and Trends in Evaluation. II. ALTERNATIVE APPROACHES TO PROGRAM EVALUATION. 4. Alternative Views of Evaluation. 5. Objectives-Oriented Evaluation Approaches. 6. Management-Oriented Evaluation Approaches. 7. Consumer-Oriented Evaluation Approaches. 8. Expertise-Oriented Evaluation Approaches. 9. Adversary-Oriented Evaluation Approaches. 10. Participant-Oriented Evaluation Approaches. 11. Alternative Evaluation Approaches: A Summary and Comparative Analysis. III. PRACTICAL GUIDELINES FOR PLANNING EVALUATION. 12. Clarifying the Evaluation Request and Responsibilities. 13. Setting Boundaries and Analyzing the Evaluation Context. 14. Identifying and Selecting the Evaluative Questions and Criteria. 15. Planning How to Conduct the Evaluation. IV. PRACTICAL GUIDELINES FOR CONDUCTING AND USING EVALUATIONS. 16. Dealing with Political, Ethical, and Interpersonal Aspects of Evaluation. 17. Collecting, Analyzing, and Interpreting Quantitative Information. 18. Collecting, Analyzing, and Interpreting Qualitative Information. 19. Reporting and Using Evaluation Information. 20. Evaluating Evaluations. V. EMERGING AND FUTURE SETTINGS FOR PROGRAM EVALUATION. 21. Conducting Multiple-Site Evaluation Studies. 22. Conducting Evaluations of Organizations Renewal and Training in Corporate and Nonprofit Settings. 23. The Future of Evaluation. Appendix: Some General Areas of Competence Important in Education Evaluation.

http://platform.almanhal.com/Files/?ID=T2-41793-MLA0011322.pdf

تقويم البرنامج : طرق بديلة و إرشادات عملية = Program evaluation Alternative Approaches and Practical Guidelines

Social Learning and Clinical Psychology.

This article describes the ICAP framework that defines cognitive engagement activities on the basis of students’ overt behaviors and proposes that engagement behaviors can be categorized and differentiated into one of four modes: Interactive, Constructive, Active, and Passive. The ICAP hypothesis predicts that as students become more engaged with the learning materials, from passive to active to constructive to interactive, their learning will increase. We suggest possible knowledge-change processes that support the ICAP hypothesis and address the limitations and caveats of the hypothesis. In addition, empirical validation for the hypothesis is provided by examining laboratory and classroom studies that focus on three specific engagement activities: note taking, concept mapping and self-explaining. We also consider how ICAP can be used as a tool for explaining discrepant findings, dictate the proper choice of a control condition, and evaluate students’ outputs. Finally, we briefly compare ICAP to existing...

The ICAP Framework: Linking Cognitive Engagement to Active Learning Outcomes.

In the first phase of this study an interdisciplinary curriculum unit was developed centered on the concept of sustainable development in tropical rainforests. The centerpiece of the interdisciplinary unit was the investigation of a simulated environmental problem which required students to develop and then decide on a solution, having weighed a spectrum of possibilities previously explored in class activities and discussions. In the second phase of the study, nine science teachers implemented the curriculum unit in their classrooms after attending a two-day training workshop. Teachers first administered environmental decision-making pretests to their students who had been randomly assigned in intact classes to experimental (interdisciplinary rainforest curriculum unit) and control (conventional curriculum) groups. On completion of the three-week unit, environmental decision-making posttests were completed by both experimental and control students. Inferential results implied that students exposed to the interdisciplinary curriculum unit offered more supporting statements for their environmental decisions as compared to control students. It was evident that females used more alternative reasoning categories than their male counterparts when reaching an environmental decision. These results support the use of interdisciplinary curricula for enriching the environmental decision-making of secondary students.

/pdf/the-effects-of-an-interdisciplinary-curriculum-unit-on-the-5fgf55ymeq.pdf

The Effects of an Interdisciplinary Curriculum Unit on the Environmental Decision-Making of Secondary School Students.

The guide is divided into three sections Section one looks at the rationale of Western Oregon State College’s teacher work sample methodology (TWSM) and defines what the TWSM is and what it is comprised of Section two gives an overview of the measures used in the TWSM, as well as TWSM rubrics and a sample of scored teacher work samples Section three discusses the uses and users of TWSM, its data management and school in-service requirements and issues

A guide to teacher work sample methodology

This research, a collaboration of an international aid organisation, an institute of higher education, and an external evaluation consultant, assesses the early literacy, numeracy, and school attendance outcomes resulting from an early childhood development programme undertaken in several villages in the province of Makira, Solomon Islands. The programme was designed to enable kindergarten provision, including teacher education and development, as an early childhood development strategy. This research focused on assessing programme impact in terms of early literacy, numeracy, and school attendance for children who had participated in kindergarten in Makira Province, compared against a matched group of children in another province of Solomon Islands who did not experience the early childhood programme. The findings of the study indicate both a statistically and educationally significant impact of village-based kindergarten on children's literacy and numeracy as well as their school attendance. Thes...

The impact of village-based kindergarten on early literacy, numeracy, and school attendance in Solomon Islands

Achievement gaps by student and school socio-economic status: A comparison of Australia and Canada

Maths by Email (MbE) is a free fortnightly email newsletter produced during 2010 through a partnership between CSIRO Education and the Australian Mathematical Sciences Institute (AMSI), with funding from the Australian Government Department of Education, Employment and Workplace Relations (DEEWR). The principal aim of MbE has been “to communicate that mathematics is making a valuable contribution to the community, is relevant, beautiful, interesting and enjoyable and provides many employment opportunities.” 

This evaluation study was commissioned to provide independent feedback to the editors and publisher of the Maths by Email (MbE) initiative to potentially improve the service and to inform decision making regarding future plans for the service. In detail, the study was concerned with (i) who is using MbE and how it is being used, (ii) the extent to which MbE is meeting its stated aims, (iii) the effectiveness of the various components of MbE newsletters, (iv) the delivery mechanism, and, (v) possible improvements to the newsletter.
 
The evaluation methodology comprised two voluntary online subscriber surveys and regular written feedback from the evaluation team on successive issues of the newsletter. Details of survey questions were negotiated between the evaluation team and the CSIRO personnel. Written feedback identified some early concerns with the level of sophistication of early issues and offered educational, mathematical and layout advice on the various newsletter components. 

An initial survey in May 2010 attracted 586 respondents, self-identified as teachers, parents and students, with interests at upper primary, lower secondary and senior secondary levels of schooling. Analysis of survey data suggested a high level of satisfaction by respondents with the newsletter‟s characteristics and significant progress towards achieving the stated aims. The various components of the newsletters were well-received, especially the Hands-on Activity, the Feature Article and the Brain Teasers. Questions asked specifically of teachers provided evidence that the materials were being successfully used in classrooms at all levels, especially in the target age group. As the survey was completed after many subscribers had seen only a few issues, the data were regarded as providing formative feedback to the publishers. 

The second survey in October/November 2010 repeated many of the same questions, although more detailed information was obtained regarding the perceived effects of the newsletter on subscriber views, identified as the principal aim of Maths by Email. The survey attracted 902 responses from subscribers, with a good spread across categories such as levels of school interest and from teachers, parents and students. Teachers comprised around half the respondents. 

Responses were similar to those in the first survey, and the same high levels of satisfaction with the newsletter and its various components were reported. As in the initial survey, around 95% of respondents reported that they would recommend a subscription for Maths by Email to others. The analysis of perceived effects of the newsletter on attitudes towards mathematics suggested that large proportions of readers reported positive changes in attitudes towards the relevance and beauty of mathematics, interest in mathematics and careers related to mathematics. Most of the rest of the respondents already had positive attitudes towards these, suggesting that there is a ceiling effect involved. Detailed analyses of written responses to open survey question have explored the ways in which teachers use the newsletter and materials successfully with students and colleagues as well as subscriber advice for further refinements and improvements. 

A series of specific recommendations encourage the publishers to retain the newsletter in its current format, which appears to be very successful and well received by the overwhelming majority of subscribers. Advice is also offered regarding publicising the newsletter more widely to ensure that the good work is taken advantage of by a wider community of students, teachers and others.

/pdf/evaluation-of-maths-by-email-final-report-4haa767erp.pdf

Andrew McConney

Papers

The Effects of an Interdisciplinary Curriculum Unit on the Environmental Decision-Making of Secondary School Students.

A guide to teacher work sample methodology

The impact of village-based kindergarten on early literacy, numeracy, and school attendance in Solomon Islands

Achievement gaps by student and school socio-economic status: A comparison of Australia and Canada

Evaluation of "Maths by Email." Final Report.