Preservice Teachers' Use of Multiple Representations In Solving Arithmetic Mean Problems

The development of preservice teachers' views of various mathematical concepts involves building a repertoire of flexible representations of the concepts they teach. In this study, science and mathematics preservice teachers (n = 19) were asked to solve graphical and numerical problems involving the arithmetic mean and to provide two different solutions for each problem. Background information about the preservice teachers was obtained, including subject area specialty, type of statistics courses previously taken, type of science laboratory courses previously taken, and prior experience with real data outside the classroom. In solving the problems, some participants presented two different methods: algorithmic computation and balancing deviations about the mean. A significant difference was found between science and mathematics preservice teachers in the use of balancing deviations to solve the problems but not in the use of the computational algorithm.     

Preparation and decarboxylative rearrangement of (Z)-enyne esters

A method to assemble (Z)-enyne esters via palladium-catalyzed cross coupling reactions of enol tosylates is reported. A base-mediated one-pot decarboxylative rearrangement of the enynes to enones is described. The scope of this process is examined.     

Introducing oblique norms into multiple criteria programming

We propose to use block norms to generate nondominated solutions of multiple criteria programs and introduce the new concept of the oblique norm that is specially tailored to handle general problems. We prove the equivalence of finding the properly nondominated solutions of a multiple criteria program and solving its scalarization by means of oblique norms.     

Unilateral recurrent laryngeal nerve paralysis:The importance of “preoperative” voice therapy

This preliminary retrospective study of 19 female patients and 22male patients with unilateral recurrent nerve lesions demonstrated the promise of objective measurements in predicting the need for surgery, the efficacy of voice therapy in ameliorating vocal symptoms, and the effects of therapy in conjunction with surgery. Sixty-eight percent (68%) of the female patients and 64% of the male patients did not elect to have surgery. Outcome satisfaction of nonsurgical and surgical patients appeared to be similar. The data from this study support the importance of preoperative therapy for patients with unilateral vocal fold paralysis.     

George B. Dantzig and systems optimization

We pay homage to George B. Dantzig by describing a less well-known part of his legacy–his early and dedicated championship of the importance of systems optimization in solving complex real-world problems.