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 underrepresentation of women at the top of math-intensive fields is controversial, with competing claims of biological and sociocultural causation. The authors develop a framework to delineate possible causal pathways and evaluate evidence for each. Biological evidence is contradictory and inconclusive. Although cross-cultural and cross-cohort differences suggest a powerful effect of sociocultural context, evidence for specific factors is inconsistent and contradictory. Factors unique to underrepresentation in math-intensive fields include the following: (a) Math-proficient women disproportionately prefer careers in non–math-intensive fields and are more likely to leave math-intensive careers as they advance; (b) more men than women score in the extreme math-proficient range on gatekeeper tests, such as the SAT Mathematics and the Graduate Record Examinations Quantitative Reasoning sections; (c) women with high math competence are disproportionately more likely to have high verbal competence, allowing greater choice of professions; and (d) in some math-intensive fields, women with children are penalized in promotion rates. The evidence indicates that women’s preferences, potentially representing both free and constrained choices, constitute the most powerful explanatory factor; a secondary factor is performance on gatekeeper tests, most likely resulting from sociocultural rather than biological causes.

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Women's underrepresentation in science: sociocultural and biological considerations.

Women obtain more than half of U.S. undergraduate degrees in biology, chemistry, and mathematics, yet they earn less than 20% of computer science, engineering, and physics undergraduate degrees (National Science Foundation, 2014a). Gender differences in interest in computer science, engineering, and physics appear even before college. Why are women represented in some science, technology, engineering, and mathematics (STEM) fields more than others? We conduct a critical review of the most commonly cited factors explaining gender disparities in STEM participation and investigate whether these factors explain differential gender participation across STEM fields. Math performance and discrimination influence who enters STEM, but there is little evidence to date that these factors explain why women's underrepresentation is relatively worse in some STEM fields. We introduce a model with three overarching factors to explain the larger gender gaps in participation in computer science, engineering, and physics than in biology, chemistry, and mathematics: (a) masculine cultures that signal a lower sense of belonging to women than men, (b) a lack of sufficient early experience with computer science, engineering, and physics, and (c) gender gaps in self-efficacy. Efforts to increase women's participation in computer science, engineering, and physics may benefit from changing masculine cultures and providing students with early experiences that signal equally to both girls and boys that they belong and can succeed in these fields. (PsycINFO Database Record

https://psycnet.apa.org/journals/bul/143/1/1.pdf

Why are some STEM fields more gender balanced than others

We tested whether mental rotation training improved math performance in 6- to 8-year-olds. Children were pretested on a range of number and math skills. Then one group received a single session of mental rotation training using an object completion task that had previously improved spatial ability in children this age (Ehrlich, Levine, & Goldin-Meadow, 2006). The remaining children completed crossword puzzles instead. Children's posttest scores revealed that those in the spatial training group improved significantly on calculation problems. In contrast, children in the control group did not improve on any math tasks. Further analyses revealed that the spatial training group's improvement was largely due to better performance on missing term problems (e.g., 4 + ____ = 11).

Spatial Training Improves Children's Mathematics Ability

found that his parietal cortex, an area of the brain used for spatial and mathematical thinking, was unusually large and oddly configured, and likely supported him in imagining the universe in innovative ways. Einstein was unique, but he certainly was not the only scientist to depend on his ability to think spatially. Watson and Crick’s discovery of the structure of DNA, for example, was centrally about fitting a three-dimensional spatial model to existing flat images of the molecule. The fact is, many people who work in the sciences rely on their ability to think spatially, even if they do not make grand discoveries. Geoscientists visualize the processes that affect the formation of the earth. Engineers anticipate how various forces may affect the design of a structure. And neurosurgeons draw on MRIs to visualize particular brain areas that may determine the outcome of a surgical procedure. So, is spatial thinking really a key to science, technology, engineering, and mathematics—the so-called STEM disciplines? Yes. Scores of high-quality studies conducted over the past 50 years indicate that spatial thinking is central to STEM success. One of the most important studies is called Project Talent; it followed By Nora S. Newcombe

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Picture This: Increasing Math and Science Learning by Improving Spatial Thinking.

This study investigated the use of block-building interventions to develop spatial-reasoning skills in kindergartners. Two intervention conditions and a control condition were included to determine, first, whether the block building activities themselves benefited children's spatial skills, and secondly, whether a story context further improved learning. Spatial measures included: spatial visualization, mental rotation, and block building. Results showed: for block building, interventions within a story context improved performance compared to the other two conditions. For spatial visualization, both types of block-building interventions improved performance compared to the control condition. Findings suggest: (1) storytelling provides an effective context for teaching spatial content, (2) teaching block building develops wider spatial skills, and (3) 3-dimensional mental rotation tasks show a male advantage in kindergartners.

The Development of Spatial Skills Through Interventions Involving Block Building Activities

Intensely involved in the kindergarten block center, Adam, Colton and Connor were conversing enthusiastically as they changed the structure they were building. I overheard phrases such as “Try this,” “Wait, too low,” and “That won’t be strong enough.” When I sat down close to the boys, Connor invited me to observe what they were attempting. He said, “Look at the car ramp we’re building.” The other boys (who were playing nearby) chimed in to explain that they were having trouble getting the ramp tall enough without collapsing so their car could run down it and reach a place about three feet away. They told me that when they put the car on top of the ramp, the structure kept toppling down as shown in the following excerpt.

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Building Curriculum during Block Play

/pdf/united-way-bright-beginnings-on-professional-development-and-f5675aytn1.pdf

Nicole Andrews

Papers

The Development of Spatial Skills Through Interventions Involving Block Building Activities

Building Curriculum during Block Play

United Way Bright Beginnings on Professional Development and Retention Among Administrators and Teachers

Prekindergarten Academies— A Snapshot of Teachers Engaged in Professional Development

Petrification