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Lingguo Bu

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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Lingguo Bu

The rise of dynamic modeling and 3-D design technologies provides appealing opportunities for mathematics teachers to reconsider a host of pedagogical issues in mathematics education, ranging from motivation to application and from visualization to physical manipulation. This article reports on a classroom teaching experiment about cube spinning, integrating traditional tools, GeoGebra (www.geogebra.org), and 3-D design and printing technologies. It highlights the rich interplay between worthwhile mathematical tasks and the strategic use of diverse technologies in sustaining sense making and problem solving with a group of prospective teachers.

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Lingguo Bu and Angel Marjanovich

The Milk Fat problem provides a rich context for looking into students' understanding of percentages as well as the complexity of these problems.