Working with language-independent logic structures can help students develop both inductive and deductive reasoning skills. The Japanese publisher Nikoli (with resources available both in print and online) produces a treasure trove of language-independent logic puzzles. The Nikoli print resources are mostly in Japanese, creating the extra…

Mathematical argumentation is an essential part of the discipline of mathematics and a key indicator of mathematical proficiency. In the process of constructing arguments and critiquing the reasoning of others, students build their understanding of underlying mathematical ideas and engage in critical sense-making activity (Yackel and Hanna 2003).…

Graphing functions is an important topic in algebra and precalculus high school courses. The functions that are usually discussed include polynomials, rational, exponential, and trigonometric functions along with their inverses. These functions can be used to teach different aspects of function theory: domain, range, monotonicity, inverse…

The Tower of Hanoi is an old, popular, and engaging puzzle. It is an exceptional puzzle too considering how effective it can be in engendering multiple valuable outcomes when used as a tool for learning. One of the fundamental goals of mathematics teacher preparation is to enable the prospective teacher to develop mathematical habits of mind and…

It is no easy feat to engage young people with abstract material as well as push them to greater depths of understanding. Add in the extra pressures of curriculum expectations and standards and the problem is exacerbated. Projects designed around standards and having multiple entry points clearly offer students the best opportunity to engage with…

There is a growing interest in using a flipped classroom format in day-to-day teaching. Direct computer-based individual instruction outside the classroom and interactive group learning activities inside the classroom are the two essential components of the flipped classroom model. By watching instructional videos, students can work through some…

In the set of fractal activities described in this article, students will accomplish much more than just creating a fun set of cards that simply resemble an art project. Goals of this activity, designed for an algebra 1 class, are to encourage students to generate data, look for and analyze patterns, and create their own models--all from a set of…

Assessment and instruction are interwoven in mathematically rich formative assessment tasks, so employing these tasks in the classrooms is an exciting and time-efficient opportunity. To provide a window into how these tasks work in the classroom, this article analyzes summaries of student work on such a task and considers several students'…

This article describes the authors' three-component instructional sequence--a before-class activity, a during-class activity, and an after-class activity--which supports students in becoming self-regulated proof learners by actively developing class-based criteria for proof. All four authors implemented this sequence in their classrooms, and the…

Since the 1950s, the understanding of how the base 10 system works has been encouraged through alternative base systems (Price 1995; Woodward 2004). If high school students are given opportunities to learn other base systems and analyze what they denote, we believe that they will better understand the structure of base 10 and its operations…

The dice game Farkle provides an excellent basis for four activities that reinforce probability and expected value concepts for students in an introductory statistics class. These concepts appear in the increasingly popular AP statistics course (Peck 2011) and are used in analyzing ethical issues from insurance and gambling (COMAP 2009; Woodward…

Students often have difficulty with graphing inequalities (see Filloy, Rojano, and Rubio 2002; Drijvers 2002), and J. Matt Switzer's students were no exception. Although students can produce graphs for simple inequalities, they often struggle when the format of the inequality is unfamiliar. Even when producing a correct graph of an…

The Common Core State Standards (CCSSI 2010) and NCTM's (2014) "Principles to Actions" agree that "for meaningful learning of mathematics, tools and technology must be indispensable features of the classroom . . . that support students in exploring mathematics as well as in making sense of concepts and procedures and engaging in…

Integrated approaches to education in science, technology, engineering, and mathematics (STEM), especially those set in the context of real-world situations, can motivate and deepen students' learning of the STEM subjects (National Academy of Engineering and National Research Council 2014). This article describes two integrated investigations used…

The Common Core State Standards for Mathematics (CCSSI 2010) asks students in as early as fourth grade to solve word problems using equations with variables. Equations studied at this level generate a single solution, such as the equation x + 10 = 25. For students in fifth grade, the Common Core standard for algebraic thinking expects them to…