The power of feedback.

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

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Methods in Educational Research: From Theory to Practice

McKenney, S. (2012, 4-5 September). What is educational design research? Invited lecture for the Crossfield Graduate School at the University of St. Gallen, St. Gallen, Switzerland.

What is educational design research

The National Council of Teachers of Mathematics

A perceived lack of engagement of many students in middle years mathematics classes provides a challenge for educators. In this article we report a project that investigated students' perceptions of the extent to which their own efforts influence their achievement at mathematics and their life opportunities. We conducted 2 hour interviews with over 50 students, as well as collecting other data. The results suggest that a student's orientation to learning mathematics is not predicted by their achievement. Even students who were confident, successful and persistent exhibited short-term goals. It seems that classroom culture may be an important determinant of under-participation in schooling.

Perhaps the Decision of Some Students not to Engage in Learning Mathematics in School is Deliberate

Commissioned by the Department of Education, Employment and Training, the Catholic Education Office (Melbourne) and the Association of Independent Schools Victoria

Early Numeracy Research Project Final Report, February, 2002

Understanding, assessing and developing children's mathematical thinking: the power of a one-to-one interview for preservice teachers in providing insights into appropriate pedagogical practices

Much is known about what constitutes successful teaching in mathematics (Anthony & Walshaw, 2009; Australian Association of Mathematics Teachers, 2006; Franke, Kazemi, & Battey, 2007) and the key ingredients of effective professional development programs (D. J. Clarke, 1994; D. J. Clarke & Hollingsworth, 2002; Organisation for Economic Cooperation and Development, 2005; Sowder, 2007). In particular, successful programs are ongoing, and provide opportunities for practice, feedback and follow-up support. They ‘involve teachers in learning activities that are similar to ones they will use with their students, and encourage the development of teachers’ learning communities’ (OECD, 2005, Chapter 4, p. 1). Additionally, for mathematics teacher education, it is critical to develop teachers’ pedagogical content knowledge (AAMT, 2006; Malara & Zan, 2008; Sowder, 2007) and to view teachers as decision makers (Malara & Zan, 2008; Muir & Beswick, 2007; Ruthven & Goodchild, 2008). Knowledge of practice is a type of knowledge generated when teachers investigate learning and teaching in their own classrooms and school sites, which may be a form of school-based teacher development (Ruthven & Goodchild, 2008; Sowder, 2007). Sometimes these school-based studies of practice involve action research and the knowledge created is the result of a dialogic cycle comprising research, scholarly knowledge, teaching, and craft knowledge (Ruthven & Goodchild, 2008). Often teachers value the knowledge that arises from such activities because the outcomes are personally significant and context-specific (Putnam & Borko, 2000). Amid the array of school-based professional development initiatives reported (Gu & Wang, 2006; Johnson, 2009; Meiers, 2007; Muir & Beswick, 2007; Ruthven & Goodchild, 2008; Seidel, Sturmer, Blomberg, Kobarg, & Schwindt, 2010; Shepherd, 2006; Smith, 2002), there has been increased interest in

/pdf/fostering-professional-learning-communities-beyond-school-3196p3k4pk.pdf

Fostering Professional Learning Communities Beyond School Boundaries

Responding to an instrument we developed to give insights into students’ orientation to, and motivation for, learning mathematics, Year 8 students showed more confidence in their ability to learn mathematics and in their persistence than observations of their classes would indicate is warranted. They identified a negative influence of peers for some classmates but less for themselves, and had modest career aspirations. We believe teachers can assist students by becoming aware of their orientations to learning, their perceptions of the value of schooling, and their further vocational aspirations, and by finding ways to overcome factors inhibiting their engagement in school.

Andrea McDonough

Papers

Perhaps the Decision of Some Students not to Engage in Learning Mathematics in School is Deliberate

Early Numeracy Research Project Final Report, February, 2002

Understanding, assessing and developing children's mathematical thinking: the power of a one-to-one interview for preservice teachers in providing insights into appropriate pedagogical practices

Fostering Professional Learning Communities Beyond School Boundaries

Eliciting positive student motivation for learning mathematics