Maintains that certain concepts in mathematics are difficult to learn because of problematic continuity from prior knowledge to new concepts. Focuses on the problems of conceptual change connected with the learning of calculus and the shift from rational to real numbers. Summarizes the results of a study involving secondary students. (MJP)

Describes the use of a simple inexpensive model of a five-legged table in a physics course for industrial-design students to spark useful discussion about several aspects of statics. (WRM)

Offers ideas for 15 active learning experiences that use the concept of "10" for 3- to 5-year olds. Included are mathematics activities, language activities, and music and movement activities. Each activity description includes the objective, a list of materials needed, and steps for completing the activity. (KB)

In science teaching, Aristotelian physics is often presented in a fragmentary and oversimplified way which distorts the true meaning of Aristotelian concepts. Discusses some mistakes that originate from a partial reading of Aristotle's work. Contains 32 references. (Author/WRM)

Three studies involving 4-year olds and 5-year olds from Hong Kong (samples of 36, 10, and 12) and the United States show that Chinese children surpass their English and American counterparts in rote counting and place value numeration as well as embedded ten-cardinal understanding. Implications are discussed. (SLD)

The Optimizer in Quattro Pro and the Solver in Excel software programs make solving linear and nonlinear optimization problems feasible for business mathematics students. Proposes ways in which the Optimizer or Solver can be coaxed into solving systems of linear equations. (ASK)

Describes an activity designed to connect geometry with real life for seventh grade students. This activity centers on an elementary investigation of the rigidity characteristics of triangles. Students also discuss the similarities and differences of polygons. (ASK)

Studied the role mathematical world views, as domain-centered epistemological beliefs, played in the academic lives of upper secondary school students in Germany participating in the Third International Mathematics and Science Study (TIMSS). World views were substantial predictors of achievement in advanced mathematics, even when controlling for…

Examines approaches to mathematics instruction for elementary and secondary education. Topics include curriculum proposals by the National Council of Teachers of Mathematics; content standards; a growing emphasis on increasing achievement; textbooks; and other books, including picture books, which include mathematics concepts. (LRW)

Discusses using children's literature to introduce mathematical concepts to middle school students. Provides an annotated list of novels and recommends development of concepts, processes, and attitudes to motivate students' intellectual explorations. (JPB)

A study examined understanding of number line concepts by 4th grade culturally and linguistically diverse (CLD) students (n=30), students with learning disabilities (n=23), and 21 controls. CLD students with disabilities demonstrated difficulty due to several factors beyond lack of language competence, including failure to apply number lines to…

Tested effects of a structured intervention in teaching children to represent addition and subtraction. Found significant differences between two study groups in terms of affecting the addition and subtraction operations and ability to determine which operation was appropriate. Results suggest children's exploration of real world situations should…

Describes the refinement of a conception in the domain of linear functions. Examples show how students refine their use of the x-intercept in equations of the form "y=mx+b" by narrowing problem contexts, making connections between conceptions, using a mathematical procedure, and refining verbal descriptions. Resources that teachers can draw on to…

Describes computer software called Shemesh designed for learning equivalence-classes of fractions. Describes interviews with fifth-grade students who used the software in their learning activities. Evidence indicates initial actual development of desired mathematical concepts. (Author/MM)

Describes proven assessment strategies, which, used separately or in combination, can help young ESL students express their understanding of math concepts while building their English-language skills: Manipulative objects, diagrams, and physical movement. Also describes other assessment techniques including self-assessment, interviewing, and…