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## Characterizing Secondary Teachers’ Structural Reasoning

The Common Core State Standards for Mathematical Practice asks students to look for and make use of structure. Hence, mathematics teacher educators need to prepare teachers to support students’ structural reasoning. In this article, we present tasks and rubrics designed and validated to characterize teachers’ structural reasoning for the purposes of professional development. Initially, tasks were designed and improved using interviews and small pilot studies. Next, we gave written structure tasks to over 600 teachers in two countries and developed and validated rubrics to categorize responses. Our work contributes to the preparation and support of mathematics teachers as they develop their own structural reasoning and their ability to help students develop structural reasoning.

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## The Do Nothing Machine

The Trammel of Archimedes traces an ellipse as the machine’s lever is rotated. Specific measurements of the machine are used to compare the machine’s actions on GeoGebra with the graph of the ellipse and an ellipse formed by the string method.

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## Experience First, Formalize Later

The EFFL model empowers students to build strong conceptual understanding of mathematics through carefully designed, equity-minded activities that disrupt the traditional lecture-based classroom.

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## Using Series to Construct Pythagorean Triples

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## Algebraic Thinking in the Context of Spatial Visualization

This pattern-related problem, appropriate for high school students, involves spatial visualization, promotes geometric and algebraic thinking, and relies on a no-cost computer software program.

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## Math-Inspired Artwork

Students and teachers enjoy exploring the boundaries between mathematics and art.

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## Technology and Median Income Data: Opening Doors

Classroom stories show how using technology to investigate the wage gap provided opportunities to develop students’ identities and agency and enabled a classroom culture of sharing and risk-taking.

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## The Hidden Beauty of Complex Numbers

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## Enacting Co-Craft Questions Using Flexible Teaching Platforms

Teachers can implement a mathematics language routine within in-person/hybrid and remote instructional contexts.

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## Point-Line Ellipses and Hyperbolas

The author alters the definitions of ellipses and hyperbolas by using a line and a point not on the line as the foci, instead of two points. He develops the resulting prototypical diagrams from both synthetic and analytic perspectives, as well as making use of technology.