Geometric Translations: An Interactive Approach Based on Students' Concept Images

We present activities are based on the nature of middle-school students' concept images of geometric translations. We propose the use of interactive GeoGebra files, prototypical examples, and nonexamples. These are chosen to help students develop their thinking through the natural stages of thinking about translation as a motion. We discuss the importance of geometric transformations in the learning of geometry, and the central role of examples and nonexamples in the learning of mathematical concepts. We describe three stages in middle-school students' thinking about geometric translations as motion translations; and some misconceptions found in research studies. Twelve activities constitute the main body of the article. We discuss more advanced stages in the understanding of geometric translations that will need to be addressed beyond the middle-school. View Articl

Helping a Young Child Connect Fact Family Addition and Subtraction using Tools

In order to help children become effective at addition and subtraction, it is important to provide them with an opportunity to investigate and discover the interconnectedness of the two operations. Fact families are one method teachers use to try and help children develop and understand how the operations relate to one another. This paper documents a strategy that was used with a seven year old boy to help him connect addition to subtraction. The strategy incorporated flash card tools to help him create logical problems to discover the mathematical relationship of fact families. With just a few trials, the child was able to create and explain problems that demonstrated the interconnectedness of fact families through addition and subtraction. The model was successful in helping the child advance his understanding. Additionally, it can be extended to more complex addition and subtraction problems as well as multiplication and division fact families

Helping a Young Child Connect Fact Family Addition and Subtraction using Tools

In order to help children become effective at addition and subtraction, it is important to provide them with an opportunity to investigate and discover the interconnectedness of the two operations. Fact families are one method teachers use to try and help children develop and understand how the operations relate to one another. This paper documents a strategy that was used with a seven year old boy to help him connect addition to subtraction. The strategy incorporated flash card tools to help him create logical problems to discover the mathematical relationship of fact families. With just a few trials, the child was able to create and explain problems that demonstrated the interconnectedness of fact families through addition and subtraction. The model was successful in helping the child advance his understanding. Additionally, it can be extended to more complex addition and subtraction problems as well as multiplication and division fact families