Report

  • In this report we present the results of an international research study on the training of researchers in mathematics education. The study was carried out by some members of The International Study Group on Theory of Mathematics Education.<br><br>The research consisted of developing a questionnaire which was mailed to numerous institutions all over the world, and the anlaysis of the answers which were received.<br><br>The main objective of the study was to collect international data about the training of researchers in mathematics education and to establish an information network about graduate programs in the field.<br><br>A total of about 150 questionnaires were sent out and 78 answers received. Fifteen of these answers came from universities that wish to participate in the network but which do not at present have a program.

  • In this report we present the results of an international research study on the training of researchers in mathematics education. The study was carried out by some members of The International Study Group on Theory of Mathematics Education.<br><br>The research consisted of developing a questionnaire which was mailed to numerous institutions all over the world, and the anlaysis of the answers which were received.<br><br>The main objective of the study was to collect international data about the training of researchers in mathematics education and to establish an information network about graduate programs in the field.<br><br>A total of about 150 questionnaires were sent out and 78 answers received. Fifteen of these answers came from universities that wish to participate in the network but which do not at present have a program.

  • The standard error of measurement (SEM) is the standard deviation of errors of measrement that are associated with test scores from a particular groups of examinees. When used to calculate confidence bands atound obtained test scores, it can be helpful in expressing the unreliability of indicidual test scores in an understandable way. Score bands can also be used to interpret intrainducidual and interindicidual score differences. Interprester should be wary of over-interpretaion when using approximations for correctly calculated score bands. It is recommened that SEMs at various score levels be used in calculating score bands rather than a single SEM value.

  • The topic of test reliability is about the relative consistency of test scores and other educational and psychological measurements. In this module, the idea of consistency is illustrated with reference to two sets of test scores. A mathematical model is developed to explain both relative consistency and relative inconsistency of measurements. A means of indexing reliability is derived using the model. Practical methods of estimating reliability indices are considered, together with factors that influence the reliability index of a set of measurements and the interpretation that can be made of that index.

  • Statistical literacy is essential in our personal lives as consumers, citizens and professionals. Statistics plays a role in our health and happiness. Sound statistical reasoning skills take a long time to develop. They cannot be honed to the level needed in the modern world through one high school course. The surest way to reach the necessary skill level is to begin the educational process in the elementary grades and keep strengthening and expanding these skills throughout the middle and high school years. A statistically literate high school graduate will know how to interpret the data in the morning newspaper and will ask the right questions about statistical claims. He or she will be comfortable handling quantitative decisions that come up on the job, and will be able to make informed decision about quality of life issues.<br><br>The remainder of this document lays out a framework for educational programs designed to help students achieve this noble end.

  • 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.

  • This paper presents a strategy for the wise use of information technologies to<br>support significant improvements in school mathematics and science. As a result,<br>this article makes no attempt to cover the entire educational technology landscape<br>with an even hand. What is attempted is to map out a balanced strategy that cash-strapped schools could pursue as part of a larger effort to make substantial<br>improvements in teaching in these fields.

  • 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.

  • An important topic presented in introductory statistics courses is the estimation of population parameters using samples. Students learn that when estimating population variances using sample data, we always get an underestimate of the population variance if we divide by n rather than n-1. One implication of this correction is that the degree of bias gets smaller as the sample gets larger and larger. This paper explains the nature of bias and correction in the estimated variance and discusses the properties of a good estimator (unbiasedness, consistency, efficiency, and sufficiency). A BASIC computer program that is based on Monte Carlo methods is introduced, which can be used to teach students the concept of bias in estimating variance. The program is included in this paper. This type of treatment is needed because surprisingly few students or researchers understand this bias and why a correction for bias is needed. One table and three graphs summarize the analyses. A 10-item list of references is included, and two appendices present the computer program and five examples of its use. (Author/SLD)

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