Total Quality Management (TQM) is a poor fit with higher education and can only be made to fit by major reshaping either of TQM to a more appropriate methodology (and hence not TQM), or of higher education to an image of organisation that fits TQM. The paper revisits longstanding concerns about multiple aspects of TQM from a critical systems…

Students' mathematical problem-solving experiences are fraught with failed attempts, wrong turns, and partial successes that move in fits and jerks, oscillating between periods of inactivity, stalled progress, rapid advancement, and epiphanies. Students' problem-solving journals, however, do not always reflect this rather organic process. Without…

Problem solving theory and practice suggest that thinking is more important to solving problems than knowledge and that it is possible to teach thinking in situations where little or no knowledge of the problem is needed. Such an assumption has led problem solving advocates to champion "content-less heuristics" as the primary element of problem…

Coding interactional data for statistical analysis presents theoretical, methodological and practical challenges. Coding schemes rely on categories that are decided by their relevance to the analytical problem under investigation. We suggest that (1) endogenous and publicly displayed concerns of participants provide for the observable organisation…

The golden ratio appears in a classical mechanics coupled-oscillator problem that many undergraduates may not solve. Once the symmetry is broken in a more standard problem, the golden ratio appears. Several student exercises arise from the problem considered in this paper.

Seeking more effective mathematics instruction, this author decided to incorporate Cognitively Guided Instruction (CGI) into first-grade classroom lessons. Students in CGI mathematics classrooms are prompted to use their prior knowledge to solve new problems, establish cognitive structures to which new learning can be connected, and be driven by…

This paper, the second of a two part article, expands on an idea that appeared in literature in the 1950s to show that by restricting the domain to those complex numbers that map onto real numbers, representations of functions other than the ones in the real plane are obtained. In other words, the well-known curves in the real plane only depict…

In this article, the author reflects on her session at the 2006 conference, including the learning styles and strategies she observed. In her session, they explored some of the more unusual aspects of convex polyhedra (with regular faces), including the notions of "valence" and "species". Although the session was about shape and space, there was…

Handling problems in schools is inevitable. Administrators often must make decisions on critical issues and incidents, such as determining disciplinary actions and consequences for student misbehavior, and confrontations with irate parents. In all such cases, they must be able to provide necessary assistance in solving problems while avoiding the…

A method called the Remainder Method is proposed for the calculation of sample quantiles of a given order, for example, quartiles, hexatiles, octatiles, deciles and percentiles assuming that all the observations are distinct. Proof is given for a special case of deciles. The criterion "equisegmentation" is proposed, namely that the number of…

This article presents a rich geometry problem and discusses its solution. A variety of mathematically correct justifications for this answer are provided. (Contains 2 figures.)

The purpose of this article is to present a collection of problems that allow students to investigate magic squares and Latin squares, formulate their own conjectures about these mathematical objects, look for arguments supporting or disproving their conjectures, and finally establish and prove mathematical assertions. Each problem is completed…

This article describes how to incorporate problem-solving investigations in a fourth-grade classroom within a structured and rigid mathematics program.

Every day, schools and communities across the U.S. identify millions of young children as "at risk"--especially those with a minority background, who live in poor neighborhoods or are learning English as a second language. FPG's Project U-STARS-PLUS (Using Science, Talents, and Abilities to Recognize Students-Promoting Learning for…

Preservice preparation courses for elementary teachers of science can provide opportunities to build pedagogical content knowledge. One common concern of preservice teachers is how to cope with a preplanned lesson that does not proceed as planned. Providing opportunities for preservice teachers to experience the unexpected actually immerses them…