868 NOTICES OF THE AMS VOLUME 47, NUMBER 8 In April 2000 the National Council of Teachers of Mathematics (NCTM) released Principles and Standards for School Mathematics—the culmination of a multifaceted, three-year effort to update NCTM’s earlier standards documents and to set forth goals and recommendations for mathematics education in the prekindergarten-through-grade-twelve years. As the chair of the Writing Group, I had the privilege to interact with all aspects of the development and review of this document and with the committed groups of people, including the members of the Writing Group, who contributed immeasurably to this process. This article provides some background about NCTM and the standards, the process of development, efforts to gather input and feedback, and ways in which feedback from the mathematics community influenced the document. The article concludes with a section that provides some suggestions for mathematicians who are interested in using Principles and Standards.

https://www.aps.edu/academics/common-core-state-standards/documents/comm-ferrini.pdf

Principles and Standards for School Mathematics: A Guide for Mathematicians

Este libro describe un importante conjunto de habilidades clave que aumentan el aprendizaje mas profundo, la preparacion para la universidad y la carrera, el aprendizaje centrado en el estudiante y el pensamiento de orden superior. Estas etiquetas incluyen habilidades cognitivas y no cognitivas, como pensamiento critico, resolucion de problemas, colaboracion, comunicacion efectiva, motivacion, persistencia y aprender a aprender. Las habilidades del siglo XXI tambien incluyen creatividad, innovacion y etica que son importantes para el exito posterior y pueden desarrollarse en entornos de aprendizaje formales o informales. Este informe tambien describe como estas habilidades se relacionan entre si y con las habilidades y contenidos academicos mas tradicionales en las disciplinas clave de lectura, matematicas y ciencias. Educacion para la vida y el trabajo: Desarrollar conocimientos y habilidades transferibles en el siglo XXI resume los hallazgos de la investigacion que investiga la importancia de tales habilidades para el exito en la educacion, el trabajo y otras areas de responsabilidad adulta y que demuestra la importancia de desarrollar estas habilidades. en la educacion K-16. En este informe, se identifican caracteristicas relacionadas con el aprendizaje de estas habilidades, que incluyen desarrollo profesional docente, curriculo, evaluacion, programas extraescolares y extraescolares y centros de aprendizaje informal como exhibiciones y museos.

Education for Life and Work: Developing Transferable Knowledge and Skills in the 21st Century

This study illuminates claims that teachers' mathematical knowledge plays an important role in their teaching of this subject matter. In particular, we focus on teachers' mathematical knowledge for teaching (MKT), which includes both the mathematical knowledge that is common to individuals working in diverse professions and the mathematical knowledge that is specialized to teaching. We use a series of five case studies and associated quantitative data to detail how MKT is associated with the mathematical quality of instruction. Although there is a significant, strong, and positive association between levels of MKT and the mathematical quality of instruction, we also find that there are a number of important factors that mediate this relationship, either supporting or hindering teachers' use of knowledge in practice.

https://www.tandfonline.com/doi/pdf/10.1080/07370000802177235

Mathematical Knowledge for Teaching and the Mathematical Quality of Instruction: An Exploratory Study

This article describes tools for measuring the content of instruction, the content of instructional materials, and the alignment between these. Illustrative findings about the use of these tools are reported, and possible additional uses, both for research and practice, are discussed. The validity of data produced through use of these tools is found to be quite good. An agenda for future work is sketched—both for improvement of the quality and versatility of the tools and for use of the tools in research and practice.

Measuring the Content of Instruction: Uses in Research and Practice

This article presents the results of a meta-analysis of 58 studies of mathematics interventions for elementary students with special needs. Interventions in three different domains were selected: preparatory mathematics, basic skills, and problem-solving strategies. The majority of the included studies described interventions in the domain of basic skills. In general, these interventions were also the most effective. Furthermore, a few specific characteristics were found to influence the outcomes of the studies. In addition to the duration of the intervention, the particular method of intervention proved important: Direct instruction and self-instruction were found to be more effective than mediated instruction. Interventions involving the use of computer-assisted instruction and peer tutoring showed smaller effects than interventions not including these supports.

Mathematics Interventions for Children with Special Educational Needs A Meta-Analysis

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.

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