This paper examines the conflict in interest between teaching experiments and professional learning when they are combined in a research project. The study reported in this paper is the fourth year of a five year longitudinal study on the introduction of early algebraic concepts. The ten teacher participants are from five state primary schools in…

The authors have attempted to implement "less is more" in a variety of educational contexts. The schools they have been part of include a pilot school in Boston, New Mission High School(New Mission), a charter school in Fitchburg, North Central Charter Essential School (NCCES), and a charter school in Devens, Francis W. Parker Charter…

The study examined the effect of parental involvement on students' mathematics achievement. The investigator selected four Algebra I classes taught by one teacher and randomly placed two classes in the control group and two classes in the experimental group. The parents of the students in the treatment group received monitoring sheets twice a…

The What Works Clearinghouse (WWC) reviewed interventions to promote middle school students' math knowledge and skills. Because there is some variation in how school districts organize middle school, we considered curricula aimed at students in grades 6 through 9, covering one or more of the following content areas: numbers and operations,…

Mathematics can be used to analyze musical rhythms, to study the sound waves that produce musical notes, to explain why instruments are tuned, and to compose music. This book explores the relationship between mathematics and music through proportions, patterns, Fibonacci numbers or the Golden Ratio, geometric transformations, trigonometric…

This paper introduces a multi-dimensional, multi-level framework for analyzing students' social interaction and individual action during collaborative problem solving. Crossing the dimensions of problem knowledge distribution and degree of cooperation yields six possible social interactions: piecemeal guessing, joint construction, lecture,…

This paper describes an intervention in two Algebra II classes in which the graphing calculator was incorporated into the curriculum as often as possible. The targeted population consisted of high school students in a growing middle to upper class community located in a suburb of a large city. The problem of a lack of understanding of the…

This book contains a classroom-tested approach to the teaching of problem solving to all students in Grades 4-6, regardless of ability. Information on problem solving in general is provided, then mathematical problems on logic, whole numbers, number theory, fractions, decimals, geometry, ratio, proportion, percent, probability, sets, and…

This study ascertained the relative effectiveness of writing assignments in mathematics compared to traditional assignments on the performance of students (N=83) in an elementary, college algebra course. Students were placed into experimental and control groups based on the nature of assignments given. Control subjects were given 15 assignments…

A set of computer-oriented, supplemental activities is offered which can be used with a course in advanced algebra and trigonometry. The activities involve use of the BASIC programming language; it is assumed that the teacher is familiar with programming in BASIC. Students will learn some BASIC; however, the intent is not to develop proficient…

Students were given the problem: Given a deck of cards in a certain order, after how many shuffles will it return to its original order? They worked with small decks of cards to develop a general formula, but were unhappy with the results. (SD)

A series of problems involving number theory, the law of cosines, and geometric interpretations of solutions to equations is discussed. (SD)

Games and puzzles in which a checkerboard can be used to develop mathematical concepts are described. (SD)

Four problems in which elementary mathematics can be used in constructing models are described. (SD)

A series of puzzle-type activities combining arithmetic reasoning and geometric figures is described and illustrated. (SD)