The author analyzes his 11-year-old daughter's investigation of patterns in multiplication. In an investigation initiated herself, Becca generates hypotheses, discovers patterns, asks questions, and discards procedures that do not produce desired results. Providing a classroom environment that values questioning is a key recommendation. (MLN)

Identifies the types of reasoning involved in middle grade mathematics with regard to multiplicative structures and the difficulties students have with the concepts, why these difficulties might occur, and the interconnections within this content area. Offers four recommendations for the preparation and professional development of teachers.…

Developed for elementary teachers, this activity unit is designed to teach students the importance of estimation in developing quantitative thinking. Nine ways in which estimation is useful to students are listed, and five general guidelines are offered to the teacher for planning estimation activities. Specific guidelines are provided for…

This module is the fifth in a series of 12 learning modules designed to teach occupational mathematics. Blocks of informative material and rules are followed by examples and practice problems. The solutions to the practice problems are found at the end of the module. Specific topics covered include calculator multiplication of decimals,…

This set of papers, selected from presentations at the Fourth and Fifth Annual Conferences of the Research Council for Diagnostic and Prescriptive Mathematics, are of primary interest to mathematics educators. In the first paper, Romberg describes a model for diagnosing mathematical learning difficulties which extends the diagnostic process beyond…

The concept of multiplication is described and illustrated using several different representational systems. A conceptual approach to teaching mathematics is compared with the procedural approach commonly found in the school curriculum. Four different methods of representing the multiplication process with numbers larger than ten are presented:…

This guide represents the final experimental version of a pilot project which was conducted in the United States between 1973 and 1976. The ideas and the manner of presentation are based on the works of Georges and Frederique Papy. They are recognized for having introduced colored arrow drawings ("papygrams") and models of our numeration…

Two alternative representations for the concept of common multiples are presented. These representations can be modeled on or off the computer. (PK)

Describes the development of a method of identifying motivational and educational attributes through student reports of what they like and what they perceive they are learning. Applications of the method to microcomputer software and traditional classroom activities are compared. (23 references) (MBR)

A Copy, Cover, and Compare procedure was found to produce large improvements in the accuracy of the multiplication facts of two middle school students with attention deficit disorder or attention deficit-hyperactivity disorder. The addition of a token economy program produced only small improvements in performance. (Author/PB)

Three experiments compared the effects of interspersal drill and practice using 30% new items/70% review items with 100% new items, with a total of 17 students (ages 9 to 17) having behavior disorders, emotional handicaps, learning disabilities, or mild mental retardation. The ratios were compared for instruction in spelling, multiplication facts,…

Assessed the achievement in addition, subtraction, multiplication, and division of 93 fourth graders before and after they received either computer or traditional classroom drill-and-practice instruction. Students who received computer instruction showed greater increases in achievement scores in subtraction and multiplication than did students…

The focus in this report is the concept of what it means to "do mathematics" in the context of a group working committee of teachers and researchers committed to reforming mathematics teaching. During a regular meeting of this group of teachers and researchers, the participants explored the mathematical reasoning embedded in one…

Two experiments in instructional supervision were conducted to support teachers in changing their teaching behavior as they implemented a new math curriculum. The focus of the investigation was a method of teaching multiplication and principles of effective teaching. In the first experiment, instructional supervision, both with and without…

There is substantial empirical evidence showing the impact of the type of numbers in the solution of problems with a multiplicative structure. The theory of the intuitive models of arithmetic operations is today the most plausible theoretical account for these findings. In an attempt to contribute to a better understanding of the effects of number…