Basics of qualitative research: Grounded theory procedures and techniques

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

Subtractive Schooling: US-Mexican Youth and the Politics of Caring: A. Valenzuela

/pdf/review-of-principles-to-actions-ensuring-mathematical-2na9nugf41.pdf

Review of Principles to Actions: Ensuring Mathematical Success for All

Reign of Error: The Hoax of the Privatization Movement and the Danger to America's Public Schools Diane Ravirch New York: Knopf, 2013. 416 pages. $14-34 USD/Paperbac Diane Ravitch spent decades advocating metrics and alternatives for elementary and secondary public school reform, including some years in government implementing the current assessment-as-accountability regime, but, by 2006, she doubted her own prescription for public school ills. This itch in her mind turned into two books, The Life and Death of the Great American School System, a careful mea culpa regarding testing and a data-driven attack on data-fixation, and, most recently, Reign of Error. As a New York University research professor of education, she also founded an organization, the Network for Public Education (NPE). All of these efforts are aimed fundamentally at the primary and secondary educational systems in the U.S., but the arguments are relevant to community colleges, particularly in the Obama administration. Community colleges today face such questions of "reform"--Ravitch often puts this word in doubtful quotes--and the community college may fall for the same hoax. Ravitch outlines the view of "reformers" in chapters 3-8 of Life and Death and chapters 2-4 and 14-20 of Reign of Error as seeing schools preparing children to become participants in the society's economy. This vision, argues Ravitch, emphasizes two elements: standardized tests and social engineering. Standardized tests are the first social modality by which academic competition is exercised. At this level, a child is getting practice and developing skills that suit one for a competitive economy: self-control, the efficient use of instrumental reason, calculations of utility, innovation, initiative-taking, and so on; but more specifically, job-relevant skills come along eventually, and by assessing disaggregated skills instead of the aggregated judgment that grades make, the system can more precisely sort its future workers. Educational services deliverers get their own grade, from their output--from the scores that their students make, assessed over time. The other element comparative testing emphasizes is a social engineering aspect: that people of differential abilities and aptitudes will be sorted by testing into those career and academic pathways in which they will be comparatively advantaged--on the Adam Smith and David Ricardo model, more or less. Market utility is the appropriate standard of judgment for an individual, according to the reformers' view, because it is the standard of judgment for a collectivity. The strength of corporations (the "bottom line") and countries (military, GDP) is similarly assessed quantitatively. In advanced societies, the citizen labor force is stratified according to performance, which is measured by one "earning what one deserves"--by differential monetary life outcomes. A well-formed education system thus prepares each person for the slot in the economy in which she is most apt to attain her greatest comparative advantage--that which will, among the measurable outcomes, result in her maximum lifetime income-earning potential. Privatization melds public and private interest, in this view, because it allows maximum room for competitive pressures to sort out to any desired level of detail the most efficient producers of society-specific, needed workforce skills. Assessing student learning disaggregated by skill performance facilitates tracking students into the most contributory pathways and prepares them for competitive job-hunting and job-keeping. Similarly, assessing instruction drives teachers and teaching institutions into the most efficient delivery of the most demanded knowledge and skills. Anything that gets in the way of this quantized, data-driven approach is a market inefficiency--as well as, on the reformers' view, a social anachronism and a political albatross. …

Reign of Error: The Hoax of the Privatization Movement and the Danger to America's Public Schools

Mathematics Education at Highly Effective Schools That Serve the Poor: Strategies for Change

The implementation of the Common Core State Standards for Mathematics (National Governors Association Center for Best Practices & Council of Chief State School Officers, 2010) has the potential to move forward key features of standards-based reforms in mathematics that have been promoted in the United States for more than 2 decades (e.g., National Council of Teachers of Mathematics, 1989, 2000; National Science Foundation, 1996). We believe that this is an especially opportune time to purposely focus on improving the mathematics education of students who have historically been denied access to a high-quality and rigorous mathematics education in the United States, specifically low-income students and students of color (e.g., Kitchen, DePree, Celedon-Pattichis, & Brinkerhoff, 2007; Leonard & Martin, 2013). We discuss a challenge to realizing standards-based reforms in mathematics in the United States: computer-based interventions in mathematics classrooms.

https://www.jstor.org/stable/10.5951/jresematheduc.47.1.0003

Research Commentary: Educational Technology--An Equity Challenge to the Common Core.

I am afraid that our system is not as progressive as I and some of the teachers are, or are willing to be. I feel discomaged from the administration level and sense that change will be hard A reality check says that my district, New Mexico, and many areas ate having the same problem [ .... ] I am a progressive thinker, ready fm change and anything that will improve student involvement in their education, but often see my ideas seen as radical

Getting Real about Mathematics Education Reform in High-Poverty Communities.

Research is needed to understand the impact of high-stakes testing on teachers’ practices and consequently on their students, particularly at schools that serve large numbers of low-income students and students of color. In this research study, we examined how a state’s annual high-stakes test and administrative mandates influenced the assessment practices of mathematics teachers at a highly diverse urban high school. Among the most compelling findings was that students at Chavez High (a pseudonym) were labeled based upon their test performance, that this label tended to persist at the school, and that instructional decisions were made based upon these labels. This practice of attaching a label to students based upon their performance on the high-stakes test constructed some students as less capable than others in mathematics. Such practices contribute to the historic legacy in the U.S. of denying poor students and students of color access to a challenging education in mathematics.

The Legacy Continues: "The Test" and Denying Access to a Challenging Mathematics Education for Historically Marginalized Students

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...

Richard Kitchen

Papers

Mathematics Education at Highly Effective Schools That Serve the Poor: Strategies for Change

Research Commentary: Educational Technology--An Equity Challenge to the Common Core.

Getting Real about Mathematics Education Reform in High-Poverty Communities.

The Legacy Continues: "The Test" and Denying Access to a Challenging Mathematics Education for Historically Marginalized Students

Alignment of Content and Effectiveness of Mathematics Assessment Items.