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## Capturing Mathematical Curiosity with Notice and Wonder

Capturing students' own observations before solving a problem propelled a culture of sense making by meeting needs typical of middle school learners.

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## Connecting Quadratics, Line Segments, Continued Fractions, and Matrices

One of the many benefits of teaching mathematics is having the opportunity to encounter unexpected mathematical connections while planning lessons or exploring ideas with students and colleagues. Consider the two problems in figure 1.

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## Letters to the editor

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## May 2019 Calendar and Solutions

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## Transforming Middle School Geometry Instruction

Students move from slides, flips, and turns into reasoning about the characteristics of rigid transformations.

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## April 2019 Calendar and Solutions

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## Building Sets, Video Games, and Scatterplots

Explore the creation of a unique problem-based learning (PBL) experience.

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## The Sound of Thunder

You may have heard that if you are outside and see a flash of lightning, you can estimate the distance between you and the lightning strike fairly well by counting the number of seconds that pass between the lightning flash and the clap of thunder. The rule of thumb is that for every 5 seconds that pass before you hear the thunder, the lightning strike is 1 mile away.

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## Isle of Cats

What happens with cat populations when they are not controlled? Consider the case of Aoshima Island in Japan. Aoshima Island is called a cat island: Its cat population is 130 and growing; its human population is 13. The cats live in colonies and are fed and cared for by people who live on the islands.

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## Linguistic Conventions of Mathematical Proof Writing at the Undergraduate Level: Mathematicians' and Students' Perspectives

This study examined the genre of undergraduate mathematical proof writing by asking mathematicians and undergraduate students to read 7 partial proofs and identify and discuss uses of mathematical language that were out of the ordinary with respect to what they considered conventional mathematical proof writing. Three main themes emerged: First, mathematicians believed that mathematical language should obey the conventions of academic language, whereas students were either unaware of these conventions or unaware that these conventions applied to proof writing. Second, students did not fully understand the nuances involved in how mathematicians introduce objects in proofs. Third, mathematicians focused on the context of the proof to decide how formal a proof should be, whereas students did not seem to be aware of the importance of this factor.