This article discusses how technology, in conjunction with carefully designed tasks and orchestrated discussions, has the potential to both reveal students' mathematical practices and to provide opportunities to shape those practices. Four specific mathematical practices that tend to be associated with problem-solving situations are examined: (1)…

The Program for International Assessment of Adult Competencies, better known as PIAAC, developed a numeracy assessment framework that was used internationally to assess adults' numeracy skills. The assessment gauged adults' (aged 16-65 years) numeracy skills across a full range, from adults with very low levels of numeracy to college level math…

The National Center for Leadership in Intensive Intervention (NCLII), a consortium funded by the Office of Special Education Programs (OSEP), prepares special education leaders to become experts in research on intensive intervention for students with disabilities who have persistent and severe academic (e.g., reading and math) and behavioral…

In an environment of rapid and unpredictable change determined and directed by technologies that are constantly changing, the assumption that being technologically literate is the key to being a sustained, contributing life-long learner is well founded. However, technological literacy is seldom referred to or considered in academic arguments as a…

After nearly two decades of federal and state accountability requirements relying on conventional standardized assessments, Virginia and several other states are moving to create more balanced approaches to statewide assessment systems that include the use of performance assessments. But Palm (2008) states, "Performance assessment can mean…

Having a great teacher in every classroom is the collective goal and teacher leadership roles help to reach that goal in several ways. First, teacher leadership roles provide a needed platform for teachers to share what they are best at. This could include opening their doors to colleagues, serving as coaches or peer evaluators, sharing…

Do your students think a triangle can be constructed from any three given line segments? Do they believe that a transformation affects only the pre-image--not the whole plane? Do they understand that examples--no matter how many they find--cannot prove a conjecture but one counterexample is sufficient to disprove it? "What tasks can you…

Suggests teachers consider a microworld design for facilitating LOGO environments in their classrooms; defines microworld; discusses three stages of microworld design; and describes four levels of progressive involvement in the programing aspects of LOGO in which teachers must participate--learning colleague, programer, designer and consultant,…

The meaning of critical thinking is discussed. Teachers should be able to separate what they mean by critical thinking, creative thinking, and practical thinking. By separating these meanings, teachers can better identify the components of critical thinking and improve their teaching. (RM)

This paper discusses the curriculum and students' and teachers' conceptions of proof. It goes on to discuss university students' difficulties with proving related to understanding and using definitions and theorems, understanding the structure of a proof, knowing how to read and check proofs, knowing and using relevant concepts, bringing…

The purpose of this study is to contribute to an understanding of how errors could be employed in mathematics instruction so that the students use them constructively in support of their learning of mathematics. A teaching experiment was designed to create an ideal context in which the pedagogical approach to errors as springboards could be…

Designed to help teachers find an effective approach in teaching expository writing, this guide divides expository writing into five main types: definition/classification, comparison/contrast, thesis/proof, problem/solution, and inference (drawing conclusions). Five different starter techniques are presented with each of the five main types of…

This article defines collaborative consultation and teaching and discusses key skills for successful collaboration. Sample forms include a rating scale to evaluate team communication, a checklist to review roles and professional expectations, a lesson plan form, a form for identifying setting demands and classroom expectations, and an…

Presents three teaching strategies requiring active student participation in which students (1) create and solve their own word problems; (2) generate trigonometric expressions to be solved by their classmates; and (3) act as points to model a basic locus of points. (MDH)

Intended to introduce educators in secondary schools and colleges to discussion promoting economic literacy for all students, this paper offers a critique of the typical economics curriculum, a rationale for economics education, and a working definition of economic literacy. The first section reviews and critiques current curriculum planning in…