• This study examined the calibration techniques from the adult judgment and decision making literature for the purposes of assessing the adequacy of children's subjective probability judgments. Two hundred eighty-eight children from an inner-city school participated in the study. In accordance with the adult decision making literature, the children were consistently overconfident in their subjective probability judgments Gender and culture were each found to have a significant effect on the degree of overconfidence.

  • The project will research the effectiveness of new information and communication technologies in teaching various scientific and mathematical concepts at secondary level. The project focuses in particular on the analysis of complex data. We will use and adapt innovative instructional material and analyze students' competencies by means of classroom observations and clinical interviews. The interactive constitution of meaning in classroom discourse will be analyzed by means of new interpretative methods of research into classroom interactions. Our goal is to identify and describe more precisely various conceptual barriers that make statistical reasoning difficult for secondary students and to develop and test an instructional sequence that would enable such reasoning at a rudimentary, but statistically valid, level. The project is situated in the context of interdisciplinary research in mathematics education (didactics of mathematics) with relations to the didactics of the sciences.

  • The Open Learning Initiative (OLI) is an open educational resources project at<br>Carnegie Mellon University that began in 2002 with a grant from The William and Flora Hewlett<br>Foundation. OLI creates web-based courses that are designed so that students can learn<br>effectively without an instructor. In addition, the courses are often used by instructors to support<br>and complement face-to-face classroom instruction. Our evaluation efforts have investigated OLI<br>courses' effectiveness in both of these instructional modes - stand-alone and hybrid.<br>This report documents several learning effectiveness studies that were focused on the OLIStatistics<br>course and conducted during Fall 2005, Spring 2006, and Spring 2007. During the Fall<br>2005 and Spring 2006 studies, we collected empirical data about the instructional effectiveness of<br>the OLI-Statistics course in stand-alone mode, as compared to traditional instruction. In both of<br>these studies, in-class exam scores showed no significant difference between students in the<br>stand-alone OLI-Statistics course and students in the traditional instructor-led course. In contrast,<br>during the Spring 2007 study, we explored an accelerated learning hypothesis, namely, that<br>learners using the OLI course in hybrid mode will learn the same amount of material in a<br>significantly shorter period of time with equal learning gains, as compared to students in<br>traditional instruction. In this study, results showed that OLI-Statistics students learned a full<br>semester's worth of material in half as much time and performed as well or better than students<br>learning from traditional instruction over a full semester.

  • Teachers have different things they like to do on the first day of a class. Some get to know their students' names and something about each of them. Some dive right into the subject matter and get things rolling right away. I like to an activity that sets the stage, as it were - that gives the students an overview of what they'll be studying during the year. The following activity is one that serves that purpose for an AP Statistics course. It involves a simulation, a graphical representation, experimental design, data collection, an dhypothesis testing, and it can easily be done in the space of 90 minutes, or 45 minutes if you provide data that were already collected. About a hundred 3-once Dixie cuups areneeded, about three liters of Coke and three liters of Pepsi (less for a small class), and optionally, unsalted crackers for students to 'cleanse the palate." Also you'll need lotso f standard dice: 256 for a class of 32 students working in groups of four, and more for either larger classes or for students working individually. Dice in large quantities can be purchased from school supply houses, and they are such an asset to a statistics class that the purchase of a very large classroom set is well worth the investment. It is also possible to do the activity with fewer dice - one die per student or group - and have each student or group roll a single die repeatedly instead of rolling many dice at once.

  • Scoffoling refers to the instructional support that instructors or more skillful peers offer learners to bridge the gap between their current skill levels and the desired level. An aspect of scaffolding that is olften ignored is the fading of support as the learner masters the skill. It has been suggested that there is a risk of over-relying on the support of integrated media in computer-assisted instruction. A three-dimension (3-D) model of scaffolding that incorporates level of subtask, level of support, and number of repititions of practice has been proposed to vary the technology support systematically in response to the learner's performance. The 3-D contingent scaffolding model was implemented in a comptuer-based instructional program for statistics called "Hypothesis Testing--the Z-test" in order to establish baseline data for integrated media-based instruction or a hypermedia learning environment. The scaffolded instruction was evaluted in terms of knowledge maintenance and transfer by comparing it to full-support instruction and least-support instruction. Findings from 75 college students provide evidence that the scaffolded computer-based instruction promoted knowledge maintenance and improved independent knowledge application, while promoting learning consistently across individuals. Results also show that a dynamic measure of the learner's ability is a better predictor of the learning outcome for subjects using this scaffolded instruction than static measures. The model provides a systemic way to link the concept of scaffolding to integrated media design features using both support building and support fading techniques.

  • Descriptive statistics offer us several averages for a given set of variable numbers. Most elementary courses introduce the mean (i.e., arithmetic mean), the median and the mode.<br>On average, which is supposed to characterize a given distribution of values, is never identical with all the values (except for the trivial case). Each possible suggestion of an average involves some inaccuracy. The answer to the question "what is the best representation of the numbers?" depends on what is meant by "best representation". One could interpret this to mean that the average incurs the least possible "cost" in terms of differences between the average and the actual values. Each definition of the "cost" could be minimized by an appropriate average. Asking students to pay (symbolically) the costs of the errors incurred through use of different averages might introduce the averages via the idea of the least combined error.<br><br>The following procedure, which may be represented as a game in the classroom, has helped my students on both secondary school and college level.

  • Many people are familiar with the calculus reform movement that has been sweeping the country for the last five years, heavily supported by the National Science Foundation. Less well-known is a similar movement within the statistics community that recommends major changes in the content and teaching of introductory statistics courses. NSF has funded numerous projects designed to implement aspects of this reform This proposal outlines a three-stage evaluation to determine the impact of statistics reform efforts on the current teaching of college-level statistics courses.

  • The current mathematics reform movement has recognized that new forms of mathematics teaching will be needed to support the proposed curricular changes. These new forms extend beyond the acquisition of new teaching techniques and trategies to the reconstitution of fundamental notions of teaching, learning, and the nature of mathematics as a discipline, and also to the creation of different classroom opportunities for learning. The means by which teachers effect this kind of transformation are, as yet, little understood. This paper describes a set of component models of the process of teachers' development in mathematics practive. Drawing from theories of cognitive development, the paper focuses on three compoments of the change process: (1) qualitative reorganizations of understanding; (2) orderly progression of changes; and (3) the context and mechanisms by which transitions are effected; and suggests a fourth component--individual motivational and dispositional factors.

  • Six years after the publication of the National Council of Teachers of Mathematics; (NCTM's) Curriculum and Evaluation Standards for School Mathematics, which set the course for a new era of mathematics education reform, professional development for mathematics teachers has moved tothe center of the reform agenda. The argument adequately power the reforms (Cohen, 1990; Little, 1993; Lord, 1994). Rather, they depend on the transformation of teaching in the nation's many classrooms. Many teachers have embarked on the project of changing their teaching toward that envisioned in the Standards. Their work leads us to the follwoing questions: Where are we in our understanding of the nature of this process? How can we help teachers in their efforts to invent a new form of teaching? and How can we continue to learn about what such invention entails?

  • 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).