Interviews with (n=55) children and their teachers in years one, two, and three showed a closer association between knowledge of place value and levels of counting than between levels of counting and the ability to explain the counting sequence. (13 references) (MKR)

Describes the process through which four high-achieving second graders constructed their knowledge and misconceptions of rounding concepts gained from using computer-based practice sessions which provided full solutions to examples but without verbal explanations. (31 references) (MKR)

Describes the use of the "Microsoft Flight Simulator" with Dutch students 12- to 16-years-old to apply mathematical knowledge to real-life situations. The use of an overhead projector for class flights is described; and student activities, including converting metric units and drawing maps of the landscape, are explained. (LRW)

Investigates the probability of winning the largest prize at Bingo through a series of five simpler problems. Investigations are conducted with the aid of either BASIC computer programs, spreadsheets, or a computer algebra system such as Mathematica. Provides sample data tables to illustrate findings. (MDH)

Reviews the logic underlying mathematical induction and presents 10 tasks designed to help students develop a conceptual framework for mathematical induction. (Contains 20 references.) (MDH)

Prior studies indicate that, given time to develop their own algorithms, primary students will process multidigit addition or subtraction problems from left to right. Gives evidence to support that idea, describes methods of getting students to invent their own algorithms, and discusses advantages of child-invented procedures. (21 references) (MDH)

Presents 5 activities for the K-1, 2-3, 4-5, 6-8 grade levels and for in the home in which students explore the concept of combinations. Each activity includes a lesson plan to investigate a combinatorics problem appropriate for that grade level. Provides reproducible worksheets. (MDH)

Presents two seasonally related investigations involving arithmetic series to develop critical thinking: (1) the number of candles needed for the eight nights of Hanukkah, and (2) the number of presents given during "The Twelve Days of Christmas." Students also calculated the amount of money needed to buy all the presents. (MDH)

Describes Vygotsky's zones of proximal development, the importance of social interaction in learning through problem solving, and the benefits of modeling. Presents three implications for teaching and learning mathematics based on a teaching experiment focusing on these constructs. (MDH)

Examined the possibility of gender-by-content achievement differences in computer-based instruction (CBI) in mathematics and language arts. From a study of eighth-grade students (n=50), one of the findings was a significant three-way interaction between gender and ability from the pretest to the posttest in mathematics CBI but not in language arts…

Discussion of how visual analogies aid students' understanding of math and science focuses on new types of representations that use computers. Topics addressed include understanding and cognitive performance; the role of representations in understanding, including examples; evidence of instructional effectiveness of new representations; and…

Activities embedded within events in two math classes were examined to determine patterns that suggested the teacher's knowledge in one content area, mathematics. An external representation of the teacher's classroom "script" was constructed to illuminate the essential elements of the script and what connections existed within the script…

Benefits of using trade books in secondary mathematics and science are constructed knowledge, vicarious experiences of the science and mathematics process, positive attitudes toward science and mathematics, and higher levels of literacy. Includes samples of books and quotes. (56 references) (Author/MKR)

Provides secondary mathematics and science teachers with a variety of methods for incorporating trade books into instruction. Includes group problem solving, art projects, poem and song composition, drama, and character journal writing. Provides a list of 40 mathematical and science trade books. (26 references) (Author/MKR)

Presents eight activities that make mathematical connections across the curriculum and which help teachers learn how to design their own activities. (Author/MKR)