The importance of developing reasoning and justification has been highlighted in "Principles and Standards for School Mathematics" (NCTM 2000). The Common Core State Standards for Mathematics (CCSSI 2010) further reiterates the importance of reasoning and proof in several standards for mathematical practice. Students of all grades are…

Students around the world have difficulties in learning about fractions. In many countries, the average student never gains a conceptual knowledge of fractions. This research guide provides suggestions for teachers and administrators looking to improve fraction instruction in their classrooms or schools. The recommendations are based on a…

Genetic algorithms (GAs) are a problem solving strategy that uses stochastic search. Since their introduction (Holland, 1975), GAs have proven to be particularly useful for solving problems that are "intractable" using classical methods. The language of genetic algorithms (GAs) is heavily laced with biological metaphors from evolutionary…

Problem solving is presented as a resource for creating curriculum through reflections on intuition such as: exploring available intuitions, making explicit the intuitions used, and using intuition to generalize. (MP)

Four activities with window panes are described and illustrated as they extend children's knowledge of fractional numbers. (MNS)

Presented are eight student worksheets of block problems. Included are diagrams of the squares and hollow squares involved and a separate answer sheet for the problems. (CW)

A teacher describes a banking unit used in a sixth-grade mathematics class. Students learned the value of money by receiving a pretend paycheck for their chosen occupation and paying weekly, monthly, and annual bills. (MP)

The author advocates the use of questions whose relevance to the topic being studied as not immediately apparent, as a method of broadening students' facility and interest in their mathematics classes. (SD)

Mathematics in nature and in the technological world is discussed. Outdoor activities with mathematical content are listed. (JP)

An example of how geometry serves as a model in the real world is outlined, with suggestions on how it might be used at the high school level. (MNS)

The symposium is seen to create an opportunity for students to understand the way mathematics is actually used in their own fields and to understand both their own potential as mathematics users and inherent difficulties in modeling. The symposium acts as a capstone for a two-semester, introductory calculus course. (MP)

A police officer presented a question about a formula on speeding. This application was a good real-world example of radicals to present in an algebra class. How it was used is presented. (MNS)

Part I describes the presentation of six different proofs of the Pythagorean Theorem by groups of three students in a party atmosphere. Part II delineates the analysis behind a student conjecture concerning the area of certain closed polar-coordinate figures. Part III proposes a categorical worksheet for determining when to apply the proper rule…

This handbook was developed to help the vocational teacher aid students in solving mathematical problems in vocational education classes. Most of the examples in the handbook were derived from metal-working and industrial mechanics classes; however, the procedures explained through them will work in any vocational class. The handbook is divided…