Literature Index

Are SAT scores useful predictors of success in college? I led a group of mathematics majors at Oberlin College in an exploration of this question as the core of a one-credit course, entitled Data Analysis, last year. This course, MATH 337, is an adjunct to the standard, junior-level, two semester sequence in probability and mathematical statistics that we offer each year at Oberlin. Unlike most statistics courses for mathematics majors, the Data Analysis course allows - indeed, it forces - students to "get their hands dirty" exploring real data and trying to answer real questions. Each year I select a set of data, such as the SAT data, to serve as the central focus of the course. I believe that it is imperative that student learn something of how statistical theory is applied in practice and I try to show this side of statistics in the courses I teach at all levels. However, it is particularly difficult to cover much material on applied statistics while at the same time covering the many important topics in the mathematical statistics course - probability, random variables, functions of random variables, expectation, the central limit theorem, estimators, confidence intervals, hypothesis testing, and others - that are fundamental to the discipline and are an essential foundation for advanced (graduate) training in statistics. The Data Analysis course provides a workable solution to this problem.

This chapter reports on student performance with data and chance by examining individual 1996 NAEP items or clusters of related items and where available samples of student responses to constructed-response questions. The focus of this chapter is on four categories that are often interrelated: central tendency, reasoning with data, graphical data displays, and probability and chance. In addition to reporting and interpreting performance based on NAEP results, for some short and extended constructed-response items we also examined a set of sample student responses. This sample was not a representative sample of all responses; rather it was a convenience sample of non-blank responses. Some of the items described in this chapter were extended constructed-response tasks, a type of NAEP item that is discussed extensively in chapter 11 by Silver, Alacaci, and Stylianou.

School are flocking to software publishers to equip their newly acquied compuers with the latest in software. Electronic graphing tools are an important component of any computer tool kit. Graphers..Data Explorere...Math Lab Toolkit...Green Globs and Graphing Equations...Symbols and Graphs...First Workshop...The Graph Club.. The 199701998 SUMBURST educational software catalogue alone lists these 7 electronic graphing tools. In many schools today, it is not unusual to see students projects with computer-generated graphs lining school hallways. Parents are delighted that their children are sorking with data and using computers to peoduce neat , professional -looking products that incorporate graphs along with the textk, graphics, and tables they have come to look for.<br><br>Yet the fact that students are graphing with computers doesn't, in and of itself, mean that they are developing rich understandings of data and of the subtleties of data representation. Rather, too often they use the tool to produce "quick but meaningless graphs" without having a real grasp of the nature of the data with which they are working (Ainley and Pratt, 1995, p. 438). Graphs, generated by hand or electronically, must not be relegated to the passive role of presentation tools. Rather, they need to become central components of a wider analytical activity, used to interpret the data, identify trends and make predictions (Parker, 1992; Aily and Pratt, 1995).

Real data and statistical techniques can motivate many traditional mathematical topics at the secondary level. Collectively, the important statistical ideas and ways of reasoning can be developed in the context of studying mathematics. The study of formulas, linearity, centers, inequalities, matrices, and logarithms can be embedded in data and statistics and used to lay the foundation for the mathematics and to demonstrate the relevance of statistics to the world. Data Driven Mathematics provides teachers and students with application based activities that makes this happen and that can be used in conjunction with a standard mathematics course or to design a data based statistics course.