It is important to estimate the number of examinees who reached a test item, because item difficulty is defined by the number who answered correctly divided by the number who reached the item. A new method is presented and compared to the previously used definition of three categories of response to an item: (1) answered; (2) omitted--a…

This is one of a series of geometry modules developed for use by secondary students in a laboratory setting. The thrust of this module is to introduce the student to transformations by having the student physically transform sets of points. Heavy use of manipulatives is made to aid the student in the transforming activity. Individual sections…

The author suggests ideas intended to lead to independent study on topics including trigonometry, Pythagoras, algebra, transformational geometry, primes, and countability. The ideas are based on Islamic patterns devised using a square lattice of dots and repeated reflections. (PK)

Presents an interdisciplinary project for precalculus classes that allows students to increase their understanding of the mathematics of transformations of periodic functions and helps them see mathematics in art. Uses an applet that produces high-quality graphs and real works of art by using combinations of transformations of the sine and cosine…

A procedure is described for estimating the reliability and conditional standard errors of measurement of scale scores incorporating the discrete transformation of raw scores to scale scores. The method is illustrated using a strong true score model, and practical applications are described. (SLD)

Twelve middle school students, working in pairs, used a computer microworld to explore introductory geometric transformational concepts. Despite a tendency for symbolic overgeneralization, the students were able to use visual feedback from the microworld and discussions with partners to correct their own mistakes. (Author/JJK)

An algebra class activity of creating computer graphics by connecting a series of ordered number pairs with subsequent investigations involving the transformations of the functional relationship between the elements of those ordered pairs is presented. (JJK)

Presents a lesson in which students communicate verbally and in writing to create and describe geometric transformations, develop vocabulary, demonstrate ability to give unambiguous instructions to translate a triangle, form and test conjectures, and create extensions of problems. Includes reproducible student worksheets and questions for…

Three teaching experiments are reported which study aspects of a diagnostic teaching methodology. An experiment in the field of directional quantities showed a positive relationship between the intensity of discussion and amount of learning; one on fractions and another on geometric reflections showed good two-month retention under the…

The sixteen chapters of this book provide the core material for the Elements of Mathematics Program, a secondary sequence developed for highly motivated students with strong verbal abilities. The sequence is based on a functional-relational approach to mathematics teaching, and emphasizes teaching by analysis of real-life situations. This text is…

One class of interactive, computer-based learning environments (microworlds) for the exploration of school mathematics (and science) entails the incorporation of appropriate concepts within the engaging context of self-directed discovery learning. The objective of this research was to investigate and describe in detail the constructive learning…

This is one of a series of geometry modules developed for use by secondary students in a laboratory setting. The purpose of this module is to teach solution of proportions, concepts and theorems of triangle similarity, solution of the Pythagorean Theorem, solution of the isosceles right triangle, and concepts involving "rep-tile" figures…

When repeated measures are obtained on the same subjects, interobservation dependencies frequently are generated. The major ways in which these dependencies can arise are illustrated and it is shown how these dependencies may invalidate the use of analysis of variance (ANOVA) and its extension, trend analysis, as methods of evaluating the data of…

Presents an introduction to the study of projective geometry, including a definition and some analagous examples using the overhead projector. Illustrates the principle of duality, Desargues' theorem, Poppus' theorem, and Pascal's theorem. (TW)

Investigates whether elementary school students can construct operations of thought for integers and integer addition crucial for understanding elementary algebra. Two sixth graders were taught using a computer. Results included both students being able to construct mental operations for negating arbitrary integers and determining sign and…