Highlighting non-parabolic bands in semiconductors

The parabolic approximation to the dispersion relation is a simplification that has often been adopted for the electronic band structure of most semiconductors near the edges of the fundamental bandgap. A non-parabolic approximation can be justified which will better describe the properties of semiconductors of narrow bandgaps for which a reduction to a quadratic form is not accurate enough, nor always warranted. It also stands for a better approximation in III–V compounds and for more complex thermoelectric materials. Some of the consequences of adopting non-parabolic bands will be highlighted, as well as approximate expressions for statistical properties. It is emphasized that many properties of semiconductors are not difficult to calculate with non-parabolic bands, which may have a wider range of applications in actual materials. These calculations can then be introduced in solid state physics and statistical physics courses through projects and homework problem sets. Specific examples are discussed designed to clarify basic physics concepts in semiconductors.

Light Inextensible Strings (Thread) Under Tension in the Schwarzschild Geometry

Light inextensible string under tension is a stalwart feature of elementary physics. Here I show how considering such a string in the vicinity of a black hole, with the help of computer algebra systems, can generate insight into the Schwarzschild geometry in the context of an undergraduate homework problem. Light taut strings minimize their proper length, given by integrating the spatial component of the Schwarzschild metric along the string. The path itself is given by straightforward numerical solution to the Euler–Lagrange equations. If the string is entirely outside the event horizon, its closest approach to the singularity is tangential. At this point the string is visibly curved, surely a memorable and informative insight. The geometry of the Schwarzschild metric induces some interesting nonlocal phenomena: if the distance of closest approach is less than about [Formula: see text], the string self-intersects, even though it is everywhere under tension. Light taut strings furnish a third interpretation of the concept “straight line”, the other two being null geodesics and free-fall world lines. All the software used is available under the GPL.1

Assessing Online Student Performance via participation, and Examinations as Alternative Measures

Online homework is a relatively new instruction and evaluation technique. While it appears to be an effective tool, empirical studies of its efficacy suggests they have not been done. This paper analyzes correlations among systematic class participation scores, online homework scores and test results from two sections of Effective People Management and two sections of Advanced Human Resource Management taught at a Middle Eastern University – University of Kurdistan Hewler in fall semester 2017.Collection of data were made in four classes of two modules with the outcomes and implications suggesting students were expected to attempt to work on each homework problem three times and were allowed as many attempts as they wished within time limits set by the instructor. Homework problems were made available for extra credit immediately after a new chapter was introduced

Student preference between single-box and multi-box homework problem answers using WeBWorK, an online homework system

WeBWorK is an open-source online homework platform used in mathematics as well as engineering, where students can be assigned calculated answer engineering science problems. Problems with staged answers (multi-box) problems are possible on this system, and could offer feedback for the answers at each intermediate step of the solution. This would allow students to determine the step where they had an error (or deficit in understanding), similar to providing a hint on what their specific error was in adaptive feedback systems.Second-year students in a mechanical engineering program were exposed to both single- and multi-box questions in WeBWorK and were asked to give feedback about their preferences. The vast majority of students reported that they believed that the multi-box questions provided them good feedback on which step or calculation had error(s). They also pointed out the multi-box problems sped up finding errors in their solutions. However, a large minority indicated concern that multi-box problems constrained the solution to a particular path.Based on these results, providing some multi-box problems may assist students in finding their errors through more detailed feedback on their solution. This may be more effective earlier in a particular topic or in the first problems at any given complexity.

Promoting Long-lasting Learning Through Instructional Design

Passively listening to a lecture (deWinstanley & Bjork, 2002), skimming a textbook chapter, or googling for an answer to a homework problem is not conducive to deep and lasting high-order learning. At the same time, presenting complex concepts in problem-based classes might overload students’ working memory capacity. Effective student learning necessitates students to process information in their working memories, as well as storing information, facts and skills, in their long-term memories. Students must then be able to retrieve this information into their working memory in the future, in order to apply the information to new situations. That is, students must be able to recognize the characteristics of a future situation or problem and correctly retrieve the appropriate information stored in their long-term memory (Kirschner, Sweller, & Clark, 2006) to tackle the issue. Using the framework of Cognitive Load Theory, this article proposes an instructional model that promotes five strategies for learning and teaching; i.e. spacing, retrieval practice, elaboration, interleaving, and concrete examples, to effectively help students store and retrieve information from their long-term memory.