Teaching gerrymandering in our high school geometry classrooms provides students with a unique opportunity to use mathematics to describe, analyze and make sense of the world around them. Our purpose is to provide our students the opportunity to apply learned definitions and formulas of area and perimeter to a sociopolitical context. We present a…

This conversation is a slightly modified version of an interview with Dr. Peter Liljedahl, Professor of Mathematics Education. The interview was conducted by "JMETC" Guest Editors on March 8, 2021 and was based on Dr. Liljedahl's December 7, 2020 colloquium presentation "Building Thinking Classrooms: A Case of Results First…

In this paper I describe classroom experiences with pre-service secondary mathematics teachers (PSMTs) investigating and extending patterns embedded in the Pythagorean configuration. This geometric figure is a fruitful source of mathematical tasks to help students, including PSMTs, further develop habits of mind such as visualization,…

This paper provides empirical findings from a study that examined how three grade 7-12 flipped mathematics educators utilized class time when implementing a flipped learning model. Additionally, the researchers investigated the educators' purposes for various in-class tasks as well as their general use of class time. The data revealed flipped…

At grade 7, Common Core's content standards call for the use of long division to find the decimal representation of a rational number. With an eye to reconciling this requirement with Common Core's call for "a balanced combination of procedure and understanding," a more transparent form of long division is developed. This leads to the…

This paper offers an account of what early mathematics education could look like in an age of young digital natives. Each "Tubby," as the tablets are called, presents Nicole (our generic little child) with stimulating mathematics microworlds, from which, beginning at age 3, she can learn basic math concepts, as well as methods of…

In this paper I describe how I have used the classic buried treasure problem with prospective and practicing mathematics teachers to enhance their problem solving abilities and disposition to integrate interactive geometry software (IGS) into the learning environment. I illustrate how IGS may be used as a strategic tool to gain insight into the…

This paper discusses a classroom experience in which a group of prospective secondary mathematics teachers were asked to create, cooperatively (in class) and individually, problems related to Viviani's problem using a problem-posing framework. When appropriate, students used Sketchpad to explore the problem to better understand its attributes…

Advances in computer graphics have provided mathematicians with the ability to create stunning visualizations, both to gain insight and to help demonstrate the beauty of mathematics to others. As educators these tools can be particularly important as we search for ways to work with students raised with constant visual stimulation, from video games…

In this article, the authors explore framing, a non-multiplicative technique commonly employed by students as they construct similar shapes. When students frame, they add (or subtract) a "border" of fixed width about a geometric object. Although the approach does not yield similar shapes in general, the mathematical underpinnings of…

This paper is a descriptive and preliminary report on recent efforts to address two questions: 1) Can school mathematics be used to enhance our students' ability to understand their changing world? and 2) What role might computer technology play in this regard? After recounting some of the mathematical tools that led to a better understanding of…

Video games have tremendous potential in mathematics education, yet there is a push to simply add mathematics to a video game without regard to whether the game structure suits the mathematics, and without regard to the level of mathematical thought being learned in the game. Are students practicing facts, or are they problem-solving? This paper…

Developing curriculum and instruction for mathematics education and designing technologically enhanced learning environments are often pursued separately, but may need to be addressed together to effectively link the strengths of technology to performance in mathematics and conceptual understanding. This paper addresses current challenges with…

In the late Fall of 2012, the Museum of Mathematics ("MoMath") will open in New York City and will be the only museum dedicated solely to mathematics in the United States. The content and design of most of the exhibits are not yet available to the public but some information about how the Museum will use technology has been released. The…

Interactive Whiteboards (IWBs) are becoming commonplace throughout primary, secondary, and postsecondary classrooms. However, the focus of the associated lesson creation & management software tools delivered with IWBs has been the primary grades, while secondary and postsecondary mathematics lessons have requirements beyond what is delivered…