The New York State Education Department (NYSED) has a partnership with NWEA for the development of the 2024 Grades 3-8 English Language Arts Tests. Teachers from across the State work with NYSED in a variety of activities to ensure the validity and reliability of the New York State Testing Program (NYSTP). The 2024 Grades 6 and 7 English Language…

Valid proofs need not be in the traditional two-column format. This classroom activity allows students to explore, discuss, and use specialized facts to create a general statement of truth.

In this paper, we propose a potential interactional explanation of tertiary-to-secondary (dis)continuity: that of authority relations. Using secondary mathematics teachers' proof validations across two contexts, we suggest that secondary teachers' conceptions of authority shape their capacity to reconcile their positions as former mathematics…

Since the 1970s, the Mathematical Association of America's (MAA) journals "Mathematics Magazine" and "College Mathematics Journal" have published "Proofs without Words" (PWWs) (Nelsen 1993). "PWWs are pictures or diagrams that help the reader see why a particular mathematical statement may be true and how one…

Many ways exist to engage students without detracting from the mathematics. Certainly some are high-tech options, such as video games, online trivia sites, and PowerPoint® presentations that follow the same model as Jeopardy; but sometimes low-tech options can be just as powerful. One exciting way to connect with students is by incorporating…

One method of proof is to provide a logical argument that demonstrates the existence of a mathematical object (e.g., a number) that can be used to prove or disprove a conjecture or statement. Some such proofs result in the actual identification of such an object, whereas others just demonstrate that such an object exists. These types of proofs are…

Constructing viable arguments and reasoning abstractly is an essential part of the Common Core State Standards for Mathematics (CCSSI 2010). This article discusses the scenarios in which a mathematical task is impossible to accomplish, as well as how to approach impossible scenarios in the classroom. The concept of proof is introduced as the…

People are regularly confronted with environmental and science-related issues presented to them in newspapers, on television, or even in their own doctor's office. Often the information they use to inform their decisions on matters of science may be ambiguous and contradictory. This article presents an activity that investigates how students deal…

To engage students, many teachers wish to connect the mathematics they are teaching to other branches of mathematics or to real-world applications. The lesson presented in this article, which uses the algebraic skill of finding the equation of a line between two points and the geometric axiom that any two points define a line, does both. A…

Writing is an important content area that pervades all subject areas and is required for post-school success, yet many students with autism spectrum disorders (ASD) often struggle in written expression. In this article we discuss the characteristics of students with ASD that make writing difficult, and the strengths, such as the use of technology,…

This guide attempts to address an aspect of secondary CTE (Career and Technical Education) that has received little attention; the assessment literacy of educators. School leaders need to go beyond ensuring routine compliance with external and internal regulatory forces to identify ways in which CTE program teachers might better understand…

This article reports findings from a multi-year study of teachers' conceptual change coincident with the development of instructional expertise among teachers involved in educational reform efforts in schools in Santiago, Chile. Conceptual change in teachers is important because recent research indicates that students of teachers who function at…

The one theorem just about every student remembers from school is the theorem about the side lengths of a right angled triangle which Euclid attributed to Pythagoras when writing Proposition 47 of "The Elements". Usually first met in middle school, the student will be continually exposed throughout their mathematical education to the…

Today's students must be more than good test takers. They must be able to collaborate, innovate, and think critically to solve real-world problems. As content demands increase, how can teachers make time to teach these advanced skills? "Sparking Student Synapses, Grades 9-12" describes how master teacher Nigel Scozzi used Rich Allen's Green Light…

While serving in the U.S. Congress, Abraham Lincoln, a self-taught learner, mastered Euclid's Elements (Basler 1953). Most students today do not study mathematics for recreation. Unlike Lincoln, they need a little help in learning how to write a geometry proof. Today's technology--specifically, The Geometer's Sketchpad[R] (GSP)--can help make…