Productive mathematical conversations are a significant component of developing students' mathematical understanding and ability to effectively communicate their thinking, and the types of questions teachers ask can either hinder or advance that development. Seeking to understand students' thinking while monitoring their initial work on a task…

This chapter describes the importance of self-determination for transitions and supports for adults with disabilities. Self-determination is defined and its application to the disability context examined, followed by an overview of a multicomponent model to engage adults with disabilities to self-regulate problem solving to set and attain life and…

What do nonroutine algebra problems look like for a second-year algebra course, and where can such problems be found? Starting from the belief that even challenging, nonroutine problems should be solvable with the resources that students possess, Benjamin Dickman proceeded to formulate a small collection of tasks to push students into integrating…

We propose that there exists mathematical knowledge for teaching (MKT) specific to visual representations (VRs), abbreviated MKT-VR. We define a VR as a graphic creation, such as a diagram or drawing, which illustrates quantities and shows quantitative relationships or which illustrates geometric properties of figures and shows geometric…

Global education is a cross curricular discipline, originating in the 1970s and 1980s, developed for schools by international educators in the United Kingdom, Europe and North America. One definition describes it as "education which promotes the knowledge, attitudes and skills relevant to living responsibly in a multicultural, interdependent…

How do scientists make inferences for something they cannot directly observe? The Black Box approach seems ideal to help students understand how scientists work. Black Boxes are sealed units; their interior is not accessible. The effort to determine their possible content (internal structure) demands successive modifications in hypothesis,…

Advancement of self-regulation during complex problem solving and the development of strategical reasoning are among the central educational goals linked to 21st century skills. In this paper we introduce the notion of "Stepped Tasks", which are specially designed in Top-Down structure to achieve these goals in mathematics instruction.…

Nations of the world share concerns on many critical issues in such a way that communication and collaboration are important skills for the 21st century (Trilling and Fadel 2009). Hence, connecting global issues to the mathematics classroom is important. Through such learning experiences, students can appreciate that mathematics has a special…

Community-university partnerships create opportunities for researchers and practitioners to collaborate on the implementation and measurement of innovative consultation frameworks, and to explore the role of consultant competencies in working with school leadership teams. The purpose of this article is to introduce an empirically based approach,…

COVID-19 is the first global pandemic in the age of the internet and the world has collectively documented the virus's spread, offering a unique opportunity to study both the virus and the streams related to COVID-19, on topics from testing access to income to race. They develop their own research question to investigate the relationship between…

Too often, high school algebra students encounter topics in a discrete, disconnected fashion. In the authors' first years of teaching, they found students to be adept at solving problems they were currently studying; for instance, they could solve quadratics during a quadratics unit. Too often, however, students struggled with that same content…

Understanding the solution of a problem may require the reader to have background knowledge on the subject. For instance, finding an integer which, when divided by a nonzero integer leaves a remainder; but when divided by another nonzero integer may leave a different remainder. To find a smallest positive integer or a set of integers following the…

As a self described lesson collector, author Charles Lovett enjoys gathering "interesting" lessons and teasing them apart to find out what makes them "tick", particularly the pedagogy. He often wonders what decisions the teacher made that generated such an interesting and successful learning environment. Here he describes a…

Around 430 BCE it is reported that a typhoid epidemic carried off about a quarter of the population of Athens in ancient Greece. When the gods were asked what could be done to halt this raging epidemic, they apparently replied that the altar in the Temple of Apollo in Delios would have to be doubled in size. After several attempts to double the…

The mathematics education literature shows that encouraging students to develop multiple solutions for given problems has a positive effect on students' understanding and creativity. In this paper, we present an example of multiple-solution problems in statistics involving a set of non-traditional dice. In particular, we consider the exact…