Student trajectories in high school mathematics: Issues of choice,support, and identity‐making

Abstract

This study explores the range of experiences students have when making two kinds of decisions in relation to high school mathematics courses: what course to take, and how to and how much to apply themselves. Looking at the choices of students about to enter Grade 10, the first decision is their choice of courses. In mathematics, students leaving Grade 9 selected one course (usually), from five possibilities, for their Grade 10 year: an advanced‐placement Honours stream, an academic course with a traditional symbol‐manipulation approach, an academic course with a technology‐based applications approach, a non‐academic mathematics‐for‐citizenship course, and (as an imposed choice) repeating the Grade 9 mathematics course. The second point of decision‐making occurred within their mathematics and science courses—students constantly made choices about how, and how much, to apply themselves to the challenges of succeeding in the courses they had chosen. These students’ course choices, to a considerable extent, conformed to expectations based on the influence of socioeconomic status and prior achievement. Overwhelmingly, students were concerned more in the credentialing value of courses than their educational value or structural nature. Within their courses, most students focused their attention on doing the work rather than the content or the learning process. Students reported being encouraged to do their work by teachers, but could not provide any indication of tactical support with becoming effective learners. The final outcomes of the students’ marks suggest that, in the context of the study, Grade 10 mathematics courses are much more effective as gate‐keeping mechanisms than as opportunities for students to improve and succeed.     

Distributed MEMS analog phase shifter with enhanced tuning

The design, fabrication, and measurement of a tunable microwave phase shifter is described. The phase shifter combines two techniques: a distributed capacitance transmission line phase shifter, and a large tuning range radio frequency (RF) microelectromechanical system (MEMS) capacitor. The resulting device is a large bandwidth, continuously tunable, low-loss phase shifter, with state-of-the-art performance. Measurements indicate analog tuning of 170/spl deg/ phase shift per dB loss is possible at 40 GHz, with a 538/spl deg/ phase shift per centimeter. The structure is realized with high-Q MEMS varactors, capable of tuning C/sub max//C/sub min/= 3.4. To our knowledge, this presents the lowest loss analog millimeter wave phase shifter performance to date.