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## Take a Seat at the Equation Café

Design projects to encourage your students’ self-efficacy and motivate mathematics learning by helping them apply their prior knowledge from real-world experiences.

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## Parameters, Sliders, Marble Slides, Oh My!

Three different technological activities to explore parameters of quadratic functions each has its own pros and cons.

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## The Opportunities of No-Solution Problems

When students encounter unusual situations or exceptions to rules, they can become frustrated and can question their understanding of particular topics. In this article, I share some practical tips.

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## Visualizing Complex Roots of a Quadratic Equation

A quadratic equation was the basis for activities involving both concrete and technological representations.

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## Engaging Students through Modeling

How would students feel when learning through the use of mathematical modeling? On investigation, this article reveals that students felt better prepared for assessments, learned valuable life skills, and saw the relevance of mathematics to their lives outside of the classroom.

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## Rough-Draft Thinking and Revising in Mathematics

Ear to the Ground features voices from various corners of the mathematics education world.

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## Atypical Arrays to Stimulate Multiplicative Thinking

Two types of tasks have the potential to help second graders attend to structure and use initialmultiplicative ideas in their strategies to find the total.

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## Improving Preservice Secondary Mathematics Teachers' Capability With Generic Example Proofs

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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## Strengthening Discussions

Teachers can foster strategy sharing by attending to the cognitive demands that students experience while talking, listening, and making mistakes.

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## Is It a Pattern?

A child's decision-making photo activity about pattern identification presents implications for teaching and learning patterns in the early years.