We present an algorithm for solving the time-dependent Schrödinger equation that is based on the finite-difference expression of the kinetic energy operator. Students who have some knowledge of linear algebra can understand the theory used to derive the algorithm. This is because the finite-difference kinetic energy matrix and the Hückel matrix…

In this paper it is demonstrated how the free, and easily downloadable, software package called SMath Studio can be used to set up a model of alpha-particle scattering. The basic physics of the motion of an alpha-particle in the nuclear coulomb field is used to produce a simple stepwise computer algorithm which, in conjunction with a novel set of…

To fulfill the Standards for Mathematical Practice (National Governors Association Center for Best Practices & Council of Chief State School Officers [NGA Center & CCSSO], 2010), it is important for teachers to empower students to critique, revise, and expand their ideas as they solve problems. However, students often face challenges such…

When it comes to teaching vocabulary in foreign language classes words are often taught in isolation, without regard to the context in which they appear. The paper draws attention to the importance of teaching words in context so that the meaning of a word often results from the meaning of a larger construction it is part of. After presenting the…

Environmental education for all students is becoming more urgent as societies strive to deal with challenges such as climate change and loss of biodiversity. Teachers have an important role to play in defining the environmental knowledge, beliefs, and actions of the next generation. Understanding the anthropogenic inputs responsible for alteration…

Activities for Students appears five times each year in Mathematics Teacher, promoting student-centered activities that teachers can adapt for use in their own classroom. In the course of the activities presented here, students will "look for and make use of structure" by observing algebraic patterns in the power rule and "use…

In this paper, an example is offered of a problem-solving task for senior secondary school students which was given in the context of a story. As the story unfolds, the task requires progressively more complex forms of linear programming to be applied. Coding in MATLAB is used throughout the task in such a way that it supports the increasing…

Against the backdrop of half a century of research in mathematics problem solving, Polya's last stage is especially conspicuous--by the scarcity of research on it! Much of the research focused on the first three stages (J.M. Francisco and C.A. Maher, "Conditions for promoting reasoning in problem solving: Insights from a longitudinal…

We have applied the "practical paradigm" in teaching problem solving to secondary school students. The key feature of the practical paradigm is the use of a practical worksheet to guide the students' processes in problem solving. In this paper, we report the diffusion of the practical paradigm to university level courses for prospective…

Computer programming in undergraduate engineering education all too often begins and ends with the freshman programming course. Improvements in computer technology and curriculum revision have improved this situation, but often at the expense of the students' learning due to the use of commercial "black box" software. This paper describes the…

Last summer, the Democracy Imperative and the Deliberative Democracy Consortium, two national networks linking academics and deliberative democracy practitioners, hosted a national conference, No Better Time: Promising Opportunities in Deliberative Democracy for Educators and Practitioners ("No Better Time," 2010). Over 250 civic leaders,…

A common problem addressed in Managerial and Cost Accounting classes is that of selecting an optimal production mix given scarce resources. That is, if a firm produces a number of different products, and is faced with scarce resources (e.g., limitations on labor, materials, or machine time), what combination of products yields the greatest profit…

This book presents a schoolwide model of instructional support designed to make the most of available time, resources, and personnel--one that is also fully compatible with other problem-solving models, such as response to intervention. The authors provide a comprehensive and cohesive framework for linking assessment and intervention. They show…

A little imagination, a little drama, a little mystery. Using the guided inquiry model in this updated, second edition, students become detectives at Information Headquarters. They solve a mystery-and enhance their problem-solving and literacy skills. Middle school is a crucial time in the development of problem-solving, critical-thinking, and…

In this note, we demonstrate with illustrations two different ways that MS Excel can be used to solve Linear Systems of Equation, Linear Programming Problems, and Matrix Inversion Problems. The advantage of using MS Excel is its availability and transparency (the user is responsible for most of the details of how a problem is solved). Further, we…