In this article, Ceyanes, Lockwood, and Gill use "The Geometer's Sketchpad" in a sequence of algebra lessons to introduce quadratic functions as the product of two linear functions. The lessons provide an enriched look at the creation of parabolas and allow students to experience the foundational idea that all functions are…

Stephanie Whitney teaches in the department of teacher education at DePaul University in Chicago, Illinois. Her interest is in how students reason and make sense of mathematics, and how teachers can promote this behavior. Students should engage in reasoning and sense making daily in their mathematics classes. It is often through students'…

Formulas, problem types, keywords, and tricky techniques can certainly be valuable tools for successful counters. However, they can easily become substitutes for critical thinking about counting problems and for deep consideration of the set of outcomes. Formulas and techniques should serve as tools for students as they think critically about…

Given the teacher-as-technician view and the instrumentalist values that pervade professional schools, practices, and policy decisions (Kinsella & Pitman, 2012a; Zeichner, 2012) with regard to teacher qualification, evidence-based practices, and scripted curricula, there is growing concern that something of fundamental importance and moral…

Sets in the game "Set" are lines in a certain four-dimensional space. Here we introduce planes into the game, leading to interesting mathematical questions, some of which we solve, and to a wonderful variation on the game "Set," in which every tableau of nine cards must contain at least one configuration for a player to pick up.

A comparative analysis of 51 case problems used in five problem-based pedagogical models was conducted to examine whether there are differences in their characteristics and the implications of such differences on the selection and generation of ill-structured case problems. The five pedagogical models were: situated learning, goal-based scenario,…

The context of this paper is a strategy at a large Australian university that involves embedding a new graduate quality 'cultural competence' and lifting the profile of Aboriginal and Torres Strait Islander cultures, experiences and histories. It has been argued that the inclusion of Indigenous knowledges is essential for the decolonisation of our…

According to the National Center for Education Statistics (2016), the number of public school students in the United States who were English learners (ELs) was estimated at 4.5 million. However, in 2005, the national standardized testing scores (Fry 2007) show that about 51 percent of eighth-grade EL students were behind other students in reading…

This paper presents an innovative project-based learning activity meant to support language beginner students to develop, via their core curriculum, five enterprise capabilities ("authentic problem-solving;" "innovation and creativity;" "risk-taking;" "taking action;" and "true collaboration"),…

Background: In this paper, I share a case study of a teacher's work on mathematics tasks in the context of a 'mathematics for teaching' course aiming to develop mathematical content understandings and mathematical practices among primary teachers in one South African province. The course was developed in a national context of concerns about the…

This essay is grounded in the scholarship of teaching and learning and will focus specifically on the ways in which the Harry Potter books highlight the diversity of learning and teaching styles; privilege active experiential learning and problem solving over passive rote learning; and emphasize the benefits of collaboration over competition.…

Teachers continue to face the challenge of identifying efficaciously gifted students' learning capacity in its multiple forms. While most educators acknowledge its multidimensional characteristics, the protocols used to identify it are frequently evaluated as unnecessarily restrictive. This study investigates an assessment tool that could…

This study introduces a teaching concept based on the Standard Model of particle physics. It comprises two consecutive chapters--elementary particles and fundamental interactions. The rationale of this concept is that the fundamental principles of particle physics can run as the golden thread through the whole physics curriculum. The design…

The Maker Movement has taken the educational field by storm due to its perceived potential as a driver of creativity, excitement, and innovation (Honey & Kanter, [Honey, M., 2013]; Martinez & Stager, [Martin, L., 2013]). Making is promoted as advancing entrepreneurship, developing science, technology, engineering, and mathematics (STEM)…

This is the fourth paper in our Light-Emitting Diodes series. The series aims to create a systematic library of LED-based materials and to provide readers with the description of experiments and the pedagogical treatment that would help their students construct, test, and apply physics concepts and mathematical relations. The first paper provided…