Research

  • This paper is organized so that over arching themes from the research are presented, followed by brief summaries of findings about particular topics centeral to the use of spreadsheets/graphing tools and data analysis/probability tools. The research summaries themselves and information about specific software follow. These summaries were written with a focus on the effects of mathematics software on middle grades students' learning of mathematics as well as impacts on other types of outcomes. The primary focus of this paper is on research about students' use of spreadsheets, data analysis/statistics, and probability software. The secondary focus is on research about graphing software.

  • Describes a study of high school students that investigated the use of microcomputers to teach principles relating to the design and interpretation of graphs. Results related to student achievement, higher order thinking skills, and behavioral protocols are discussed. A sample assignment sheet and test questions are appended.

  • This paper describes how one group of students came to reason about data while developing statistical understandings related to exploratory data analysis. Episodes taken from a 7th grade classroom in which a 12-week teaching experiment was conducted are presented. One of the goals of the teaching experiment was to investigate ways to support middle school students' development of statistical reasoning proactively. The use of computer tools was viewed as an integral aspect of statistical reasoning rather than an add-on. Two computer tools were designed with the intention of supporting students' emerging mathematical notions while simultaneously providing them with tools for data analysis. The intent of the instructional sequences developed in the course of the teaching experiment is outlined first. The rest of the paper consists of descriptions of episodes from the classroom that highlight students' development of sophisticated ways to reason about data.

  • This paper focuses on how notions of inference can be fostered in middle school through the use of carefully designed tasks, open-ended software simulation tools, and social activity that focuses on making data-based arguments. We analyzed interactions between two sixth-grade students who used software tools to formulate and evaluate inferences during a 12-day instructional program that utilized Probability Explorer software as a primary investigation tool. A variety of the software tools enabled students to understand the interplay between empirical and theoretical probability, recognize the importance of using larger samples to make inferences, and justify their claims with data-based evidence.

  • The development of the Probability Explorer is based on pedagogical<br>implications of constructivist learning theory. The tools available in the environment<br>have provided children with opportunities to extend their understandings of random<br>phenomenon and support their development of graphical and numerical data analysis<br>skills. The open-ended design allows users to explore a variety of simple and compound<br>experiments and to extend the limitations of physical devices with dynamic digital<br>experiences.

  • Different studies on how well people take sample size into account have found a wide range of solution rates. In a recent review Sedlmeier and Gigerenzer (1997) suggested that a substantial part of the variation in results can be explained by the fact that experimenters have used two different types of sample-size tasks, one involving frequency distributions and the other sampling distributions. This suggestion rested on an analysis of studies that , with one exception, did not systematically manipulate type of distribution versions. In Study 1, a substantial difference between solution rates for the two types of tasks was found. Study 2 replicated this finding and ruled out an alternative explanation for it, namely, that the solution rate for sampling distribution tasks was lower because the information they contained was harder to extract than that in frequency distribution tasks. Finally, in Study 3 an attempt was make to reduce the gap between the solution rates for the two types of tasks by giving participants as many hints, the gap in performance remained. A new computational model of statistical reasoning specifies cognitive processes that might explain why people are better at solving frequency than sampling distribution tasks.

  • According to Jacob Bernoulli, even the 'stupidest man' knows that the larger one's sample of observations, the more confidence one can have in being close to the truth about the phenomenon observed. Two-and-a-half centuries later, psychologists empirically tested people's intuitions about sample size. One group of such studies found participants attentive to sample size; another found participants ignoring it. We suggest an explanation for a substantial part of these inconsistent findings. We propose the hypothesis that human intuition conforms to the 'empirical law of large numbers' distinguish between two kinds of tasks--one that can be solved by this intuition (frequency distributions) and one for which it is not sufficient (sampling distributions). A review of the literature reveals that this distinction can explain a substantial part of the apparently inconsistent results.

  • This paper examines the effects of quantitative literacy on the likelihood of employment among young adults in the United States. The data set used in the 1985 Young Adult Literacy Assessment Survey. This survey of persons 21 to 25 years old makes available scores achieved by individuals sampled on a test measuring proficiency in the application of arithmetic skills to practical problems encountered every day. We use these scores as one of a set of variables in a probit model explaining the probability of a person being fully employed. It is found that quantitative literacy skills are a major factor raising the likelihood of full-time employment. Furthermore, low quantitative literacy appears to be critical in explaining the lower probability of employment of young Black Americans relative to Whites.

  • The eight tables in this chapter present details concerning first-year courses in calculus and statistics taught in four-year colleges and universities. Mainstream and non-mainstream calculus are studied separately, as are elementary statistics courses taught in mathematics departments and in statistics departments. ("Mainstream calculus" refers to those calculus courses that lead to the usual upper division mathematical sciences courses; all others are called "non-mainstream calculus.") In each case, the tables present data answering the two broad questions "Who<br>teaches these courses?" and "How are these courses taught?" Sections of Chapter 6 study the same questions in the two-year college environment.

  • Every CBMS survey continues longitudinal studies of fall term undergraduate enrollments in the mathematics programs of two-year colleges and in the<br>mathematics and statistics departments of four-year colleges and universities. Every CBMS survey includes departments that offer associate, bachelors, masters,<br>and doctoral degrees. Every CBMS survey also studies the demographics of the faculty in those programs and departments and examines the undergraduate curriculum to determine what is taught, who teaches it, and how it is taught. In addition, each CBMS<br>survey selects a family of special topics for study.<br><br>Chapter 1 of this report, and particularly the data highlights section of Chapter 1, gives an executive summary of CBMS2000 findings on the various longitudinal issues studied since 1965, presented at a broad level of aggregation. Individual tables are<br>discussed in more detail after the data highlights section. Chapter 2 presents CBMS2000 findings on the special topics chosen for the fall 2000 study. Subsequent chapters disaggregate Chapter 1 material. For example, Chapter 3 examines enrollment and curricular variations among four-year mathematics and statistics departments that offer bachelors, masters, or doctoral degrees as their highest degrees,<br>and Chapter 5 contains data on individual first-year courses. Chapter 4 presents four-year faculty demographic data broken down by department type. Chapters 6 and 7 present detailed studies of curricular and personnel issues in two-year college<br>mathematics programs.

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