Presented is a example that shows why a certain technical lemma is necessary for a valid proof of Galois Theory. The usual proof of Galois' Theory is included as well as one using the lemma. (KR)

Presented is an alternate way to derive R from Taylor's Theorem without involving the (n + 1)st derivative of f. Included is the procedure for estimating the bounds of R. (KR)

Developed is a condition, expressed in terms of an index, that ensures that a quasinormal subgroup is normal. The arguments suggest a variety of exercises for a course in group theory or Galois theory. Included are the definitions, lemmas, and proofs. (KR)

Presented are activities that help students understand the idea of a vector field. Included are definitions, flow lines, tangential and normal components along curves, flux and work, field conservation, and differential equations. (KR)

Three worksheets are provided to help secondary students explore relationships among the areas of a variety of similar figures constructed on the sides of right triangles. The activity is extended to include the relationship among the lengths of the sides of the right triangle. Included are several student worksheets. (DC)

Assignment projects for high-achieving ninth graders were developed, and a comparative evaluation study indicated that they were effective. It bacame clear that teachers needed more practical support, so a diagnostic study was undertaken, leading to the establishment of a link between a categorization of student difficulties and a hierarchy of…

Describes a consumer science fair to help students develop problem-solving skills and become savvy consumers. (MKR)

Uses probability models in problem-solving activities based on an episode of the television show "Gunsmoke." (MKR)

Utilizing three exemplary problem-solving tasks within an arithmetic framework, this article discusses the four focal components deemed necessary for the improvement of mathematics teaching, namely task appropriateness, avenues of classroom discourse, the intellectual climate within the classroom, and proper and effective methods of analysis. (JJK)

Described is a strategy that allows students to experiment with probability without applying formulas to solve problems. Students are able to intuitively develop concepts of probability before formal definitions and properties. Sample problems are included along with BASIC programs for some of the problems. (KR)

Activities that illustrate a problem-solving approach to teaching grouping symbols, such as parentheses and brackets, are described. Suggested exercises, answers to those exercises, and variations of this activity are included. (KR)

Presented are 44 examples in which students are invited to guess what pattern of numbers is emerging and to decide whether the pattern will persist. Topics of examples include Pascal's triangle, integers, vertices, Fibonacci numbers, power series, partition functions, and Euler's theorem. The answers to all problems are included. (KR)

This paper describes a method of understanding student problem-solving behavior during computer-assisted instruction using trigonometry as the example domain. Instead of attempting to model the student's process for solving problems, techniques which infer the equivalence between two adjacent steps in the student's process are used to determine…

Describes computer simulation programs that take elementary and secondary students exploring. One has students act as Magellan commanding his ship to reinforce history, geography, decision-making, and resource management skills. Another has students use problem-solving skills to venture across oceans and find trading routes to the Orient. (SM)

Presented is a conversation with students that gives an insight into the ways students think about decimals. Students were introduced, with the use of a calculator, to decimal notation and systematic experimentation. What students had learned throughout this conversation is discussed. (KR)