In modern CAD and CAM manufacturing companies, engineers design parts for machines and consumable goods. Many of these parts are cut on CNC machines. Whether using a CNC lathe, milling machine, or router, the ideas and designs of engineers must be translated into a machine-readable form called G & M Code that can be used to cut parts to precise…

John Dewey discussed the dry school curriculum a century ago. One of the "evils" was a simplified curriculum having an outward appearance of mathematics. Dewey posited that such a simplified curriculum deprived students of opportunities to experience the thought-provoking character of the accumulated wisdom found in human knowledge. Dewey's…

On entering Mr. Wilson's seventh-grade classroom, the authors immediately noticed the students talking about mathematics and their teacher listening to them. To create an interactive learning environment that would stimulate and perpetuate discourse, Wilson discussed two main issues with his students: (1) What the students and teacher would do in…

In this article, the CLICK ("C"omputer Games and "L"iteracy "I"ntegrated with "C"ontent "K"nowledge) design model for high school education is proposed and developed as an instructional response to concerns about content coverage versus deeper content knowledge, learners' inability to grasp the meanings embedded in complex text, and disregard for…

The purpose of this article is to define and clarify the process of instructional problem-solving using assessment data within action research (AR) and Response to Intervention (RtI). Similarities between AR and RtI are defined and compared. Lastly, specific resources and examples of the instructional problem-solving process of AR within…

Achieving success takes hard work and perseverance, but another crucial ingredient is the ability to learn from failure. Instructors must encourage students to make mistakes within the classroom so they will attempt great things outside it. This is where the freedom of trial and error should be championed, to be able to hone students' skills so…

John Dewey was inspired by what he termed "the miracle of shared experience and shared communication." His faith in the power of individuals working in democratic association also included warnings of a darker side, the "monstrosities" that individuals can become when they live and work in isolation from others. In this…

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,…