Teaching and Learning Mathematics With Interactive Spreadsheets

Learning to teach mathematics at the middle and secondary levels should include many opportunities for teachers to learn how to use technology to better understand mathematics themselves and promote students' learning of mathematical concepts with technology-enabled pedagogy. This article highlights work done in a variety of preservice and in-service mathematics teacher education courses to help teachers use commonly available spreadsheets as an interactive exploratory learning tool. Several examples of teachers' subsequent use of spreadsheets in their own teaching are also discussed.     

Teacher Rationales for Scoring Students' Problem Solving Work

This article presents the scores teachers assigned to samples of actual students' problem-solving work and the rationales teachers provided for these scores. These rationales may reflect teachers' values relative to aspects of mathematical problem solving. It may be that when teachers can express rationales for scoring students' work, they are able to justify their evaluation of what students can “know and do” in mathematics.     

PDMS bonding by means of a portable, low-cost corona system

A hand-held corona treater is presented as an effective, inexpensive, and portable alternative for irreversible bonding of polydimethylsiloxane (PDMS) to glass.     

A clinical study of failure in microchannel cooled diodes used in large laser systems

In this paper we investigate the source of failure in commercial, microchannel cooled CW diode bars placed in 12 bar horizontal arrays. The arrays were used to pump Nd:YAG rods in our 10 kW developmental laser. The laser was operated at low duty factor over a period of over 2 years. Experimental evidence indicated that the sudden, catastrophic failure was because of degraded cooling. We used optical microscopes, an X-ray microfocus imager, and a thermal neutron scattering camera to look inside the microcoolers. Our investigations revealed only one possible failure mechanism: cooling flow reduction because of delamination of the Au coating the walls of the microcoolers and the entrapment of Au flakes within the microchannel structures. We observed blisters in the microcoolers under working bars, and flake-like structures in the microcoolers under burnt-out bars (all taken from the laser). We observed no evidence of either massive blockages because of electrochemical deposits, or of corrosion/erosion in the microchannel walls. Integral operation times of the high flow-rate cooling system and of the diodes themselves were too short by one and two orders of magnitude, respectively, to explain the observed failures. Microchannel immersion times in the deionized water were, however, long enough to allow for corrosion of metals that may have been exposed through defects in the Au coatings. Three-dimensional heat flow simulations showed that blockage of multiple microchannels towards the edge of a bar can easily lead to catastrophic temperature increases.