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## Thinking Like a Mathematician

The moves that mathematicians use to generate new questions can also be used by teachers and students to tie content together and spur exploration.

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## Why Is the Midpoint an Average?

The relationship between a midpoint and an average showcases the interplay between procedural knowledge and conceptual knowledge in learning mathematics for teaching.

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## Finding Skewed Lattice Rectangles

Many mathematics instructors attempt to insert guided exploration into their courses. However, exploration tasks frequently come across to students as contrived, pertinent only to the most recently covered section of the textbook. In addition, students usually assume that the teacher already knows the answers to these explorations.

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## A Coordinate Proof of the Pythagorean Theorem

Readers comment on published articles and share their mathematical interests.

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## Mathematical Lens: Shining the Light on Mathematics

Students analyze a photograph to solve mathematical questions related to the images captured in the photograph. This month, photographs of the Al Bahr Towers in Abu Dhabi generate questions on area, the Pythagorean theorem and special right triangles, and trigonometric regression.

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## Calendar and Solutions – March 2013

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## Archetypal Mathematics

Students analyze a photograph to solve mathematical questions related to the images captured in the photograph. This month, photographs of ancient arches lead to a discussion of inscribed polygons.

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## Back to Treasure Island

Some twenty years ago, when I was a university student, one of my lecturers presented a problem that he called Treasure Island. At first glance, the problem appeared to be unsolvable. After students made some futile attempts, the lecturer presented the surprising solution, without providing any explanation or even a hint. I spent the rest of the lecture thinking about the problem and trying to discover a solution.

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## February 2016

A set of problems of many types.

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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.