NCTM Process Standards Problem-Solving in Essay

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This engaged the whole class, regardless of their previous comfort level with mathematics. Graphing was also helpful for students to visualize what things really 'meant' in terms of the numbers they were studying.

Communication

Solving word problems as a class in a hands-on fashion forced all students to communicate with one another about mathematics. This increased student comfort levels and generated a collective interest in the mathematical solving process.

Students were given stories that illustrated mathematical concepts to read and asked to tell their own 'stories' to show they could understand mathematical concepts in a qualitative fashion. They were often asked to interpret graphs using verbal descriptions.

One of the most popular activities was the use of online research. Students were asked to research concepts on the web, such as examples of fractions, proportional rectangles, or the use of certain calculation techniques, and report back on their independent research the next day. This also fulfilled the need to encourage students to communicate about mathematics on a personal level.

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Connections

Students were encouraged to see how math functioned in their daily lives, such as portioning out time; dividing physical objects fractionally; understanding fractions as operators in real life objects (like a pie); measuring how long it took them to complete an activity; and understanding how math was used in architecture in a series of problems revolving around the construction and design of the Mackinac suspension bridge.

Representation

Some of the most challenging exercises for students included understanding variables and proportions and what those ideas meant, conceptually. Using visual representations to understand abstractions proved essential, such as finding a 'mistake' on an Oriental carpet that was not consistent with a numerical patterning sequence. For some students, being allowed to describe concepts such as variables in words or representing them in pictures was an important learning step before they could understand more conventional numerical representations on….....

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