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William P. Love

The concept of infinity has fascinated the human race for thousands of years. Who among us has never been awed by the mysterious and often paradoxical nature of the infinite? The ancient Greeks were fascinated by infinity, and they struggled with its nature. They left for us many unanswered questions including Zeno's famous paradoxes. The concept of infinity is with us today, and many ideas in modern mathematics are dependent on the infinitely large or the infinitely small. But most people's ideas about infinity are very vague and unclear, existing in that fuzzy realm of the twilight zone

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Thomas A. Romberg

On March 12, 1967 the following headune appeared in the New York Times: “United States Gets Low Marks in Math.” A 250-word article followed summarizing the failure of American schools to win the international mathematics race. Emotional reaction to this account was instantaneous. Parents, teachers, educators, and even Congressmen, taking the article at face value began demanding ex planations. as if the lid had been lifted from a teeming educational scandal. Even today the vestiges of this account linger to haunt the image of mathematics education.

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Na'ilah Suad Nasir and Maxine McKinney de Royston

This article explores how issues of power and identity play out in mathematical practices and offers a perspective on how we might better understand the sociopolitical nature of teaching and learning mathematics. We present data from studies of mathematics teaching and learning in out-of-school settings, offering a sociocultural, then a sociopolitical analysis (attending to race, identity, and power), noting the value of the latter. In doing so, we develop a set of theoretical tools that move us from the sociocultural to the sociopolitical in studies of mathematics teaching and learning.

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Rochelle Gutiérrez

Over the past decade, the mathematics education research community has incorporated more sociocultural perspectives into its ways of understanding and examining teaching and learning. However, researchers who have a long history of addressing anti-racism and social justice issues in mathematics have moved beyond this sociocultural view to espouse sociopolitical concepts and theories, highlighting identity and power at play. This article highlights some promising conceptual tools from critical theory (including critical race theory/Latcrit theory) and post-structuralism and makes an argument for why taking the sociopolitical turn is important for both researchers and practitioners. Potential benefits and challenges of this turn are also discussed.

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Lawrence M. Clark, Jill Neumayer DePiper, Toya Jones Frank, Masako Nishio, Patricia F. Campbell, Toni M. Smith, Matthew J. Griffin, Amber H. Rust, Darcy L. Conant and Youyoung Choi

This study investigates relationships between teacher characteristics and teachers' beliefs about mathematics teaching and learning and the extent to which teachers claim awareness of their students' mathematical dispositions. A professional background survey, a beliefs and awareness survey, and a teacher mathematical knowledge assessment were administered to 259 novice upper-elementary and 184 novice middle-grades teachers. Regression analyses revealed statistically significant relationships between teachers' beliefs and awareness and teachers' mathematical knowledge, special education certification, race, gender, and the percentage of their students with free and reduced meal status. This report offers interpretations of findings and implications for mathematics teacher education.

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Emma C. Carroll

Great inventions from the history of mathematics are finding a real place in mathematics for the elementary school. One such idea—Napier's conception of logarithms as a comparison between two moving points, one generating an arithmetical and the other a geometric progression—developed into a challenging activity for my fourth- and fifth-graders. When they witnessed the simplicity and beauty of reducing difficult multiplication and division into easy addition and subtraction through a simple “log” table, eager experimenters took over, tried the “logs,” checked results with the more cumbersome multiplication and division, and raced home with “log” table copies to share the magic with parents.

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Lola May

In this period of education it would seem the pressure is on to cram more and more into heads in a mad race to produce more and more right answers in shorter and shorter periods of time. It was decided in Winnetka, Illinois, to produce a laboratory setting of Jeaming, a place where children could have searching experiences that would challenge them to use their thinking power, a place where children could make mistakes, leam from them, and thereby build more adequate comprehensive thinking power.

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B. Ross Taylor

We are preparing today's elementary school students to live in the information society of the twenty-first century. In that society, whether one is a “have” or a “have not” will be determined largely by one' s education; the ability to do mathematics and solve problems will be essential. Today we have dramatic racial inequities in employment and income. We also have great disparities by race in students' achievement and participation in mathematics. To reduce the inequities in society tomorrow, we must address the disparitie in mathematics today. In my opinion, this challenge is the major issue in mathematics education today.

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Robert Q. Berry III

This article is about 8 African American middle school boys who have experienced success in mathematics. Working within a phenomenological methodological framework, the researcher investigated the limitations these students encounter and the compensating factors they experience. Critical race theory was the theoretical framework for this study; counter-storytelling was utilized to capture the boys' experiences, which is in stark contrast to the dominant literature concerning African American males and mathematics. Five themes emerged from the data: (a) early educational experiences, (b) recognition of abilities and how it was achieved, (c) support systems, (d) positive mathematical and academic identity, and (e) alternative identities.

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Eugene R. Smith, Harry D. Gaylord, Geo. Gailey Chambers, William E. Breckenridge and William S. Schlauch

Edited by W. H. Metzler

Educators are generally agreed that the genesis of knowledge in the individual should follow the line of evolution by which the race conquered and learned to interpret its environment. When challenged by a new situation man bent his energies to the solution of the problem that perplexed him. His environment presented a series of problems to him and out of the series of efforts to feed, clothe, and shelter himself, and harness the forces of Nature the sciences gradually differentiated out of a mass of common knowledge. Mathematical relations were investigated first because they were involved in solving some definite problem in which the investigators were interested.