Implications of Informal Education Experiences for Mathematics Teachers' Ability to Make Connections Beyond Formal Classroom

The Common Core Standard for Mathematical Practice 4: Model with Mathematics specifies that mathematically proficient students are able to make connections between school mathematics and its applications to solving real‐world problems. Hence, mathematics teachers are expected to incorporate connections between mathematical concepts they teach and their applications to solving problems arising in real‐world situation. Clearly, it is assumed that the teachers themselves are able to make such connections. On the other hand, research shows that mathematics teachers find it difficult to make those connections. In this paper, we present the results of the study that investigated the ways in which exploring mathematics in informal sites, and in particular science museum, assist teachers with making connections between school mathematics and its applications in real world.     

由有理数Cauchy列定义的实数的无限十进小数展开

讨论了有理数Cauchy列定义的实数系的一种等价形式———无限十进小数展开,定义了其上的算术运算与顺序并证明了它们和已有的定义一致.     

Gender Differences Regarding Mathematics Achievement: The Case of Turkish Middle School Students

The purpose of this study was to explore gender differences in mathematics achievement as demonstrated by performance on the mathematics subsection of a nationwide high school entrance examination in Turkey. In this study, the cities in Turkey were separated into five groups according to their level of economic development. The analysis was based on 2647 students that were randomly selected from these five different groups of cities. Although results indicated a statistically significant difference in mathematics achievement in favor of cities with the highest economic status, the effect size was quite small, which indicates the difference was not practically significant. Results also showed the effect sizes for gender differences in mathematics achievement were very small in all groups of cities. It was concluded that socio‐economic development of the regions was not a critical factor for gender differences in mathematics achievement.     

Mathematics Teaching and Learning as a Mediating Process: The Case of Tape Diagrams

This article examines how visual representations may mediate the teaching and learning of mathematics over time in Japanese elementary classrooms. Using the Zone of Proximal Development Mathematical Learning Model (Murata & Fuson, 2006 Murata, A. and Fuson, K. C. 2006. Teaching as assisting individual constructive paths within an interdependent class learning zone: Japanese first graders learning to add using ten. Journal for Research in Mathematics Education., 37(5): 421–456. [Web of Science ®] , [Google Scholar]; Fuson & Murata, 2007 Fuson, K. C. and Murata, A. 2007. Integrating the NRC principles and the NCTM process standards: Cognitively guided teaching to individualize instruction within whole-class activities and move all students within their learning path. National Council of Supervisors of Mathematics Journal, 10(1): 72–91.  [Google Scholar]), the process of mediation is explicated. The tape diagram, a central visual representation used in Japanese mathematics curriculum, is explored for its roles and the student learning that is intended to be mediated over time, illuminating aspects of the process. The study argues that the consistent and coherent use of one representation can bridge student understanding over time, focusing on mathematical relationships and problem-solving processes. The study also suggests different instructional approaches between U.S. and Japanese curricula that are reflected in the uses of representations.     

The Cyclical Relationship Between Research and Standards: The Case of Principles and Standards for School Mathematics

The link between standards and research may not be clearcut. However, in this article the authors argue that there is a notable relationship between standards and research, one that is cyclical in nature. Using the standards for school mathematics developed by the National Council of Teachers of Mathematics (NCTM) as a case in point, the authors examine how NCTM's standards have influenced the agenda for mathematics education research and stimulated research on the impact of those standards. In turn, this and other research played a significant role in the development of NCTM's new Principles and Standards for School Mathematics. The authors conclude with a discussion of ways in which the Principles and Standards may continue this cyclical relationship in coming years, potentially promoting investigation of new research areas and systematic research on the impact of standards.     

The Early History of the Cornell Mathematics Department: A Case Study in the Emergence of the American Mathematical Research Community

In this paper I describe the early history of the Cornell University mathematics department in the historical context of the late 19th century. In particular, I show that it is a case study of the emergence of the American mathematical community.Copyright 1998 Academic Press.En este ensayo, describo la premera historia de departamento de matematica de Cornell Universitad en el contexto de Siglo XIX. En particular, demonstro que este departamento es un ejemplo do lar emergencia de communidad matematica de Estados Unidos.Copyright 1998 Academic Press.In dieser Arbeit beschreibe ich die Frühgeschichte des Mathematics Department der Cornell University während des ausgehenden neunzehnten Jahrhunderts. Ich zeige insbesondere, daβ diese Geschichte als Fallstudie für die Entstehung der amerikanischen Mathematikergemeinschaft angesehen werden kann.Copyright 1998 Academic Press.MSC 1991 subject classification: 01A55, 01A73.     

Challenging Preservice Teachers' Mathematical Understanding: The Case of Division by Zero

Preservice elementary school teachers' fragmented understanding of mathematics is widely documented in the research literature. Their understanding of division by 0 is no exception. This article reports on two teacher education tasks and experiences designed to challenge and extend preservice teachers' understanding of division by 0. These tasks asked preservice teachers to investigate division by 0 in the context of responding to students' erroneous mathematical ideas and were respectively structured so that the question was investigated through discussion with peers and through independent investigation. Results revealed that preservice teachers gained new mathematical (what the answer is and why it is so) and pedagogical (how they might explain it to students) insights through both experiences. However, the quality of these insights were related to the participants' disposition to justify their thinking and (or) to investigate mathematics they did not understand. The study's results highlight the value of using teacher learning tasks that situate mathematical inquiry in teaching practice but also highlight the challenge for teacher educators to design experiences that help preservice teachers see the importance of, and develop the tools and inclination for, mathematical inquiry that is needed for teaching mathematics with understanding.     

Making Sense Of the Sixties: Campus in Crisis by Buell G. Gallagher and Conscription,Protest, and Social Conflict: The Life and Death of a Draft Resistance Movement by Michael Useem

Abstract

From Brown to Bakke: The Supreme Court and School Integration 1954–1978 by J. Harvie Wilkinson III. New York: Oxford University Press, 368 pages, $17.95.