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Amanda K. Riske, Catherine E. Cullicott, Amanda Mohammad Mirzaei, Amanda Jansen, and James Middleton

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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Dung Tran and Barbara J. Dougherty

The choice and context of authentic problems—such as designing a staircase or a soda can—illustrate the modeling process in several stages.

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Aaron Trocki

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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Daniel Brahier, Steve Leinwand, and DeAnn Huinker

The National Council of Teachers of Mathematics (NCTM) launched the “standards-based” education movement in North America in 1989 with the release of Curriculum and Evaluation Standards for School Mathematics, an unprecedented action to promote systemic improvement in mathematics education. Now, twenty-five years later, the widespread adoption of the Common Core State Standards for Mathematics (CCSSM) by forty-five states provides an opportunity to reenergize and focus our commitment to significant improvement in mathematics education (CCSSI 2010).

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Marlena Herman and Jay Schiffman

The process of prime factor splicing to generate home primes raises opportunity for conjecture and exploration.

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D. Bruce Jackson

Given two slices of bread—a problem and the answer—students fill in the fixings: their own mathematics reasoning.

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Jim Fey, Sol Garfunkel, Diane Briars, Andy Isaacs, Henry Pollak, Eric Robinson, Richard Scheaffer, Alan Schoenfeld, Cathy Seeley, Dan Teague, and Zalman Usiskin

Countries that have made progress on international assessments of mathematics achievement have national consensus on goals and sustained commitment to change over time. The Common Core State Standards provide a framework for such effort in the U. S., if we focus on five key elements of curriculum, teaching, and assessment.

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Shiv Karunakaran, Ben Freeburn, Nursen Konuk, and Fran Arbaugh

Preservice mathematics teachers are entrusted with developing their future students' interest in and ability to do mathematics effectively. Various policy documents place an importance on being able to reason about and prove mathematical claims. However, it is not enough for these preservice teachers, and their future students, to have a narrow focus on only one type of proof (demonstration proof), as opposed to other forms of proof, such as generic example proofs or pictorial proofs. This article examines the effectiveness of a course on reasoning and proving on preservice teachers' awareness of and abilities to recognize and construct generic example proofs. The findings support assertions that such a course can and does change preservice teachers' capability with generic example proofs.

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Darla R. Berks and Amber N. Vlasnik

Two teachers discuss the planning and observed results of an introductory problem to help students nail a conceptual approach to solving systems of equations.

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Rachel Levy

The mathematical concept of slope can be made real through a set of simple, inexpensive, and safe experiments that can be conducted in the classroom or at home. The experiments help connect the idea of slope with physical phenomena related to surface tension. In the experiments, changes in surface tension across the surface of the water, which correspond to greater slopes on the graph, lead to increased motion of the fluid. The mathematical content, targeted to middle school and high school students, can be used in a classroom or workshop setting and can be tailored to a single session of thirty to ninety minutes.