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

∗The book reviewed is Benchmarks for Scientific Literacy, American Association for the Advancement of Science, Project 2061, Oxford University Press, New York and Oxford (1993), pp. 448, $21‐95 (pbk), ISBN 0‐19‐508986‐3.

Benchmarks for Science Literacy: a review symposium∗

Curriculum analysis, modification, and enactment are core components of teacher practice. Beginning teachers rely heavily on curriculum materials that are often of poor quality to guide their practice. As a result, we argue that preservice teachers need to learn how to use curriculum materials for effective teaching. To address this concern, the authors conducted a study in which three teacher educators taught elementary science methods courses incorporating a major focus on curriculum analysis and modification based on Project 2061 Instructional Analysis Criteria. Analysis of pre–post assessments, classroom artifacts, classroom dialogue, and postcourse interviews indicated that preservice teachers accurately applied and appropriated a modest set of criteria whose intended meanings most closely matched their own understandings, were most closely aligned with their own goals and criteria, or were made accessible through systematic use and attention within the methods sections. However, many did not find the materials analysis criteria useful or comprehensible and based their curricular decisions on their own criteria. Furthermore, some preservice teachers resisted engaging in these practices that may have seemed too analytical, inauthentic, and destabilizing. These findings pointed us toward a revised theoretical framework and new approaches to better support preservice teachers' effective participation with curriculum materials. © 2008 Wiley Periodicals, Inc. Sci Ed92:345–377, 2008

https://onlinelibrary.wiley.com/doi/pdf/10.1002/sce.20243

Helping Elementary Preservice Teachers Learn to Use Curriculum Materials for Effective Science Teaching

Background/ContextThis opening article, like the other articles in this special issue, is situated in scholarship that attempts to understand the racialized nature of mathematics education in the U...

https://journals.sagepub.com/doi/pdf/10.1177/016146811311500206

What Mathematics Education Might Learn from the Work of Well-Respected African American Mathematics Teachers in Urban Schools.

Mandatory numeracy tests have become commonplace in many countries, heralding a new era in school assessment. New forms of accountability and an increased emphasis on national and international standards (and benchmarks) have the potential to reshape mathematics curricula. It is noteworthy that the mathematics items used in these tests are rich in graphics. Many of the items, for example, require students to have an understanding of information graphics (for example, maps, charts and graphs) in order to solve the tasks. This investigation classifies mathematics items in Australia's inaugural national numeracy tests and considers the effect such standardised testing will have on practice. It is argued that the design of mathematics items is more likely to be a reliable indication of student performance if graphical, linguistic and contextual components are considered both in isolation and in integrated ways as essential elements of task design.

National numeracy tests: A graphic tells a thousand words

summary measures In order to compare middles andspreads, students need bothprocedural knowledge andconceptual understanding of themeasures used to describe them. representations In order to compare sets of data,students need to know how torepresent data in different formsand how to read and interpretvarious given representations. Data: Diagram to Aid Assessment Task Design Project 2061/AAAS Work in Progress Please do not quote, cite, or copy 7/17/03Contexts for the "representations" and"summary measures" idea sets, the"key ideas" and the "learning goal": * data presented in any form, e.g. raw, tabular, graphical * calculators allowed By the end of 8th grade,students should know thatcomparison of data from twogroups should involvecomparing both their middlesand the spread around them.9D/M4Select and use anappropriate measureof central tendencyto describe a set ofdata, includingmean, median, andmode. DS3Determine themean, median,mode, and rangefor a set, or sets, ofdata, presented invarious forms. DS2

/pdf/research-issues-in-the-improvement-of-mathematics-teaching-1dp37ydkdm.pdf

Research Issues in the Improvement of Mathematics Teaching and Learning through Professional Development

Alignment has taken on increased importance given the current high-stakes nature of assessment. To make well-informed decisions about student learning on the basis of test results, assessment items need to be well aligned with standards. Project 2061 of the American Association for the Advancement of Science (AAAS) has developed a procedure for analyzing the content and quality of assessment items. The authors of this study used this alignment procedure to closely examine 2 mathematics assessment items. Student work on these 2 items was analyzed to determine whether the conclusions reached through the use of the alignment procedure could be validated. It was found that the Project 2061 alignment procedure was effective in providing a tool for in-depth analysis of the mathematical content of the item and a set of standards and in identifying 1 particular content standard that was most closely aligned with the standard. Through analyzing student work samples and student interviews, it was also found that st...

Alignment of Content and Effectiveness of Mathematics Assessment Items.

thinking when you were looking at the diagram?” “It looks like the keel of a boat.” There comes a moment in every teacher’s experience when you ask a student a question and his or her answer is not what you expected—startling, perhaps. Such was our experience as researchers when we asked fourth graders to work on the task in figure 1 and talk to us about it. Surprisingly, Joey was not seeing two figures at all. Instead, his attention was focused on the space between the figures. This is an example of the lessons we learned from students about this task, one of the released items from the 1996 FourthGrade National Assessment of Educational Progress (NAEP). The task is scored with a fivepoint rubric, based on the number of likenesses and differences between the shapes that students identify in their responses (see fig. 2). The purpose of our work was to analyze the alignment between the task and certain benchmarks and standards, and whether the task elicits student thinking that matches the quality of the learning goals. While performing our analysis, we learned that good alignment with a standard does not necessarily mean that the task is of high quality. As this article describes, careful analysis of student interviews and papers showed us certain flaws in the task, even though the task was highly aligned with a Standard from NCTM’s Principles and Standards for School Mathematics (2000).

Lessons Learned from Students about Assessment and Instruction.

/pdf/an-analysis-of-gender-differences-on-performance-assessment-k224uhxml8.pdf

Linda Dager Wilson

Papers

Research Issues in the Improvement of Mathematics Teaching and Learning through Professional Development

Alignment of Content and Effectiveness of Mathematics Assessment Items.

Lessons Learned from Students about Assessment and Instruction.

An Analysis of Gender Differences on Performance Assessment in Mathematics--A Follow-Up Study.

On Tests, Small Changes Make a Big Difference.