Recent college graduates are entering a competitive workforce that demands strong communication, teamwork, and problem-solving skills. However, many recent surveys and reports describe college graduates as deficient in these skills. For two courses at separate institutions, we each framed a course as a job, playing the role of a supervisor or…

This paper explores the proposition that teaching of critical thinking (CT) should include: (1) identifying and addressing the many environmental variables acting as barriers to our human thinking, i.e., an open system approach, and (2) utilizing the interrelatedness of the CT building blocks, i.e., creative thinking techniques, levels of…

In "MT218" the author looked at the possibility of basing a classroom activity on a simple, though not totally transparent, number-theoretic result. In this article he considers another relatively straightforward idea from number theory that could be used either as a lesson starter or as the basis of a more substantial task, requiring students to…

It seems rather surprising that any given polynomial p(x) with nonnegative integer coefficients can be determined by just the two values p(1) and p(a), where a is any integer greater than p(1). This result has become known as the "perplexing polynomial puzzle." Here, we address the natural question of what might be required to determine a…

Mathematics teachers confront dozens of daily decisions about how to instruct students. It is well established that high-quality instruction provides benefits for students with diverse learning and family backgrounds. However, it is often difficult for teachers to identify the critical aspects of a successful mathematics lesson as they strive to…

Establishing caring communities in child care centers is one of the most important, yet challenging undertakings for early childhood professionals. Lessons in accomplishing this goal can be learned from the inhabitants of the island communities of coastal Maine who work together to overcome the challenges of living in remote locations. In this…

This project served as a capstone event for the United States Military Academy sophomore Calculus II course. This multi-disciplinary problem-solving exercise motivated the link between math and biology and many other fields of study. The seven-lesson block of instruction was developed to show students how mathematics play a role in every…

This paper is concerned with the relationship between authenticity and adult learning and prompted by some studies in which adult "authentic learning" is a central concept. The implication revealed by them is that real-worldness of learning contexts, learning content and learning tasks is perceived as conferring authenticity on learning. Here,…

This article describes a design problem that not only takes students through the technological design process, but it also provides them with real-world problem-solving experience as it relates to the manufacturing and engineering fields. It begins with a scenario placing the student as a custom wheel designer for an automotive manufacturing…

This paper outlines the solution that the Team of Austria found to problem number 7, "skateboarder", presented in the finals of the 22nd International Young Physicists' Tournament (IYPT) in Tianjin, China. We investigated how a skateboarder can accelerate from rest on a horizontal surface without touching an external support. The focus was laid on…

A perennial problem in computer-aided assessment is that "a right answer", pedagogically speaking, is not the same thing as "a mathematically correct expression", as verified by a computer algebra system, or indeed other techniques such as random evaluation. Paper I in this series considered the difference in cases where there was "the right…

In this sequence 1/1, 7/5, 41/29, 239/169 and so on, Thomas notes that the sequence converges to square root of 2. By observation, the sequence of numbers in the numerator of the above sequence, have a pattern of generation which is the same as that in the denominator. That is, the next term is found by multiplying the previous term by six and…

Most often radio dials of analogue radios are not uniformly graded; the frequencies are cramped on the left side or on the right side. This makes tuning more difficult. Why are dials made this way? We shall see here that simple calculus can help understand this problem and solve it. (Contains 7 figures.)

Mathematics teachers are often asked, "What is the most difficult topic for you to teach?" Their answer is teaching students to count. The concepts can be challenging and slippery to apply in problems. Many times, no rigid procedures or formulas can be used to solve the problems directly, and students simply do not know where or how to approach…

How can statistics clearly be mathematical and yet distinct from mathematics? The answer lies in the reality that statistics is both an art and a science, and both aspects are important for teaching and learning statistics. Statistics is a mathematical science in that it applies mathematical theories and techniques. Mathematics provides the…