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## Student Engagement with the “Into Math Graph" Tool

We introduce the Into Math Graph tool, which students use to graph how “into" mathematics they are over time. Using this tool can help teachers foster conversations with students and design experiences that focus on engagement from the student’s perspective.

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## Promoting Statistical Literacy through Tuva

A free tool encourages students to engage in the authentic practices of statistics and data analysis.

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## Coding and Calculators

Suggestions for incorporating calculator programming into the mathematics curriculum.

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## Technology Tips: Linear Programming with More Than Two Decision Variables

In a 1999 article in Mathematics Teacher, we demonstrated how graphing systems of linear inequalities could be motivated using real-world linear programming problems (Edwards and Chelst 1999). At that time, the graphs were drawn by hand, and the corner-point principle was applied to find the optimal solution. However, that approach limits the number of decision variables to two, and problems with only two decision variables are often transparent and inauthentic.

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## Triangles from Three Points

Using technology to solve triangle construction problems, students apply their knowledge of points of concurrency, coordinate geometry, and transformational geometry.

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The striking results of this coin-tossing simulation help students understand the law of large numbers.

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## Connecting Research to Teaching: Evaluating and Writing Dynamic Geometry Tasks

The advent of dynamic geometry software has changed the way students draw, construct, and measure by using virtual tools instead of or along with physical tools. Use of technology in general and of dynamic geometry in particular has gained traction in mathematics education, as evidenced in the Common Core State Standards for Mathematics (CCSSI 2010).

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## Equivalent Expressions Using CAS and Paper-and-Pencil Techniques

Designing activities to reconcile multiple representations supports students' focus and fluency.

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## Technology-Enhanced Discovery

Exploration, innovation, proof: For students, teachers, and others who are curious, keeping your mind open and ready to investigate unusual or unexpected properties will always lead to learning something new. Technology can further this process, allowing various behaviors to be analyzed that were previously memorized or poorly understood. This article shares the adventure of one such discovery of exploration, innovation, and proof that was uncovered when a teacher tried to find a smoother way to model conic sections using dynamic technology. When an unexpected pattern regarding the locus of an ellipse's or hyperbola's foci emerged, he pitched the problem to a ninth grader as a challenge, resulting in a marvelous adventure for both teacher and student. Beginning with the evolution of the ideas that led to the discovery of the focal locus and ending with the significant student-written proof and conclusion, we hope to inspire further classroom use of technology to enhance student learning and discovery.

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## Technology Tips: High-Leverage iPad Apps for the Mathematics Classroom

The use of iPads® in the classroom is growing. In the 2013–14 school year, 57 percent of schools planned to invest in iPads (Netop 2013). This investment can benefit mathematics classrooms only if teachers know which apps they can use to help students develop deeper mathematical understanding. Although learning about and developing facility with various apps is valuable for mathematics teachers, the process can be difficult, overwhelming, and time-consuming. To get started, we recommend one app, Dropbox, that can be used to share materials within the classroom setting, and then we suggest three free, easy-to-use mathematics apps: Sketchpad Explorer, Data Analysis, and MathGraph (see the table on p. 711).