Imagination: thinking outside the box, thinking creatively, dreaming up new projects and new methods of teaching, learning, and communicating)

Investigation: hands-on exploration of mathematics - what can you discover? Where do your discoveries lead? What connections are there?

Interaction: collaboration with colleagues and with students - communicating, questioning, listening, gaining knowledge and new ideas

Illumination: discovering principles, connections and applications across the curriculum and in "real life"; communicating what you have learned.

Students can also benefit greatly from opportunities to interact. When students work together, whether they are working on their homework, or on a collaborative project, they benefit from the interaction. Even just studying together for a test allows opportunities to question each other, share knowledge, and practice what they have learned. Working on creative projects in small groups gives students excellent chances to learn - particularly if the project allows exploration and experimentation. Allowing students to figure things out for themselves is a very valuable learning opportunity. Therefore projects which begin with hands-on investigative opportunities (with computers or with compasses, protractors, rulers, string, mirrors, etc.) allow the greatest opportunities for discussion, questioning, even arguing - a passionate argument about what is true can be the highlight of a math class!

This photo is from the NCTM web pages on implement the new Principles and Standards. To learn more about the NCTM, click on the link below:


While you are reading these I-MATH pages, think of ways in which your students can benefit from the activities that described here. Perhaps you will want to weave some of these activities into a fairly traditional mathematics classroom, or possibly find that you want to change many of the methods you have used in the past.

The key thought here is interaction, an ongoing and ever-changing exchange of ideas, questions, and answers.

Go on to Illumination

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