Observation of negative differential conductance in a reverse-biased Ni/Ge Schottky diode

We report the experimental observation of negative differential conductance in a Ni/Ge Schottky diode. With the aid of theoretical models and numerical simulation we show that, at reverse bias, electons tunnel into the high electric field of the depletion region. This scatters the electrons into the upper valley of the Ge conduction band, which has a lower mobility. The observed negative differential conductance is hence attributed to the transferred-electron effect. This shows that Schottky contacts can be used to create hot electrons for transferred-electron devices

Like Terms: What’s in a Name?

This article discusses a lesson in which students’ knowledge of operations with number and the base-10 place value system was connected with operations with algebraic polynomial expressions

When Products are Sums

When we open up the classroom to student thinking we run into discoveries and conjectures that adults would likely not see, blocked by the constraints and conventions we have accepted in our own thinking. It is this lack in established constraints and conventions that can enable young thinkers to explore the world of mathematics more unencumbered. The risk of content unfamiliarity in such learning environments is not for the students; it is for their teachers (Ball, Thames, & Phelps, 2008; Chazan, 1999; Liping Ma, 1999). We want to relay one such instance in which a third grade student saw a new connection that stimulated us to investigate the mathematics of the situation in greater depth. In this article we want to show how this novel idea can be explored by students at multiple grade levels in different ways. The tasks at hand are especially well suited to address several of the mathematical practices standards from the Common Core State Standards, such as reason abstractly and quantitatively, look for and make use of structure, and look for and make use of regularity in repeated reasoning

Alternate Conceptions of Preservice Elementary Teachers: The Itakura Method

In this study, we determined the effectiveness of the inquiry-based Itakura method for mediating alternate conceptions of preservice elementary teachers (N = 38) in an integrated mathematics, science, and technology methods course. We investigated alternate conceptions in the expansion of solids due to heating. There was a significant increase in participants’ immediate learning gains after participating in the Itakura method. Retention data was gathered after 1, 2, and 3 months. After 3 months, retention levels dropped slightly, but not significantly. Responses revealed that the majority of the participants did not revert back to alternate conceptions after 3 months