An education major enrolled in a mathematics education course ponders confusing definitions of "multiplication" functions in dictionaries and in a handout on Euclid. This student teacher wants to teach elementary students what multiplication really is, not just impart an algorithmic skill. (MLH)

Describes EquiX, a search language for XML that combines querying with searching to query the data and the meta-data content of Web pages. Topics include search engines; a data model for XML documents; search query syntax; search query semantics; an algorithm for evaluating a query on a document; and indexing EquiX queries. (LRW)

Twenty-four students who scored 650 or more on the Scholastic Aptitude Test Mathematics test (SAT-M) were asked to think aloud while solving 13 mathematics items in either multiple-choice or free-response format. Strategies students used to solve the items were classified as either algorithmic or insightful. Data analyses indicated that items in…

It is unrealistic to suppose that standard item response theory (IRT) models will be appropriate for all new and currently considered computer-based tests. In addition to developing new models, researchers will need to give some attention to the possibility of constructing and analyzing new tests without the aid of strong models. Computerized…

The main objective of this study is to construct models based on strategies students use to solve chemistry problems and to show that these models form sequences of progressive transitions similar to what Lakatos (1970) in the history of science refers to as progressive 'problemshifts' that increase the explanatory' heuristic power of the models.…

The Sixth International Congress on Mathematical Education (ICME-6) was special in that it provided a context commemorating the life and work of George Polya (1887-1985) whose native land was Hungary and to whom all those interested in the teaching of mathematical problem solving owe a great debt. What follows in this publication is a collection…

An approach to teaching children aged 12 through 14 a substantial course about computers is described. Topics covered include simple algorithms, information and communication, man-machine communication, the concept of a system, the definition of a system, and the use of files. (SD)

The process of developing a computer program that can turn French text into speech is described. The program is designed to change a conventionally-spelled text into a phonemic transcription with an accuracy level of over 99.9%, divide the text into breath-groups that are syntactically correct and not over 14 syllables long, treat the unstable…

A joint maximum likelihood estimation algorithm, based on the partial compensatory multidimensional logistic model (PCML) proposed by L. Zeng (1989), is presented. The algorithm simultaneously estimates item difficulty parameters, the strength of each dimension, and individuals' abilities on each of the dimensions involved in arriving at a correct…

The Mantel-Haenszel (MH) procedure attempts to identify and quantify differential item performance (item bias). This paper summarizes the MH statistics, and identifies the parameters they estimate. An equivalent procedure based on the Rasch model is described. The theoretical properties of the two approaches are compared and shown to require the…

The illustrative method of teaching employed in most undergraduate accounting courses is becoming increasingly burdensome to professors and students due to the rapid proliferation of accounting and auditing professional standards and the increased complexity of the tax law. This teaching method may be near the breaking point in upper division…

This paper describes the Structure-Mapping Engine (SME), a cognitive simulation program for studying human analogical processing. SME is based on Gentner's Structure-Mapping theory of analogy, and provides a "tool kit" for constructing matching algorithms consistent with this theory. This flexibility enhances cognitive simulation studies by…

An algorithm is first defined by an example of making pancakes and then through discussion of how computers operate. The understanding that human beings bring to a task is contrasted with this algorithmic processing. In the second section, the question of understanding is related to learning algorithmic performance, with counting used as the…

Arguments for and against the use of computers in mathematics classes have centered on whether students benefit from or are merely hindered by practicing computational skills. This paper claims that the true essence of mathematics lies not in computation, basically a mechanical operation, but in problem-solving. Since no amount of computational…

This is the second unit of a 15-unit School Mathematics Study Group (SMSG) mathematics text for high school students. Topics presented in the first chapter (Informal Algorithms and Flow Charts) include: changing a flat tire; algorithms, flow charts, and computers; assignment and variables; input and output; using a variable as a counter; decisions…