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• Author or Editor: Jane Jane Lo
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## Teaching teachers through justifying activities

Prospective teachers need not waffle about developing the knowledge required to serve up appetizing justification and problem-solving methods to their elementary school students.

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## Selecting GeoGebra Applets for Learning Goals

In this article, we discuss issues to consider when using learning goals to strategically select applets from a large public database and some pitfalls to avoid, namely being aware of error-prone applets.

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## Math by the Month: Comparing Sizes

This month's problems are all about measurements related to sizes in the world, such as gigantic candy bars, signs, and animals. The letters on the famous Hollywood sign are 50 feet tall. The wooden Trojan horse was so big that a small army of soldiers could hide inside.

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## Taiwanese Arithmetic and Algebra

Developing problem solving and reasoning, deepening number and symbol sense, and promoting arithmetic and algebraic connections are tenets of Taiwan's Basic Competency Test.

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## Developing Ratio and Proportion Schemes: A Story of a Fifth Grader

There is a growing theoretical consensus that the concepts of ratio and proportion do not develop in isolation. Rather, they are part of the individual's multiplicative conceptual field, which includes other concepts such as multiplication, division, and rational numbers. The current study attempted to clarify the beginning of this developmental process. One fifth-grade student, Bruce, was encouraged to schematize his trial-and-error-based method, which was effective in solving so-called missing-value tasks. This study describes several advancements Bruce made during the teaching experiment and analyzes the challenges Bruce faced in attempting to schematize his method. Finally, the mathematical knowledge Bruce needed to further develop his ratio and proportion concepts is identified. The findings provide additional support for the view that the development of ratio and proportion concepts is embedded within the development of the multiplicative conceptual field.

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## A Bargain Price for Teaching about Percentage

Develop mathematical knowledge by analyzing common student errors and discussing arithmetic, algebraic, and pictorial reasoning.

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## Discuss Similarity Using Visual Intuition

Incorporate simple and complex figures, distortion and proportion, and visual reasoning into your discussion of similarity.

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## Math by the Month: Sweet play

As part of her holiday preparations, Cathy decorates sugar cubes. Cathy's aunt, Ms. Betty, runs a bakery and likes to think of ways to make her store more attractive, especially for holidays. She enjoys cutting, arranging, and designing seasonal displays with her famous brownies almost as much as she enjoys baking them. And everyone loves the different sizes of Ms. Kate's chocolate sticks.

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## Reasoning about Composite Shapes with Transformations

Flexible tasks increase students’ understanding of the properties of triangles, quadrilaterals, and transformations as well as provide opportunities for making and testing conjectures and arguments.

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## Developing Ratio Concepts: An Asian Perspective

The following vignette illustrates how a taiwanese textbook series envisions introducing the concept of ratio.