I-MATH

Illumination

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.

Illumination, therefore, is what we do when we teach. To the best of our abilities, we want to help students understand mathematics, learn the content, but most important, we want to enable them to construct and create mathematics for themselves. We want to assist our colleagues by sharing what we learn and keeping up on open dialogue with them as they learn new media and methods.

We can illuminate mathematics for our students, and for other teachers, by participating in an active community of teachers and learners in our own schools, in the State of Hawaii, and in the world, via exchange of interactive mathematics computer files, through participation in conferences, through E-School, through email and interaction over the internet.

Mathematics can be memorized, it can be taught as if to a passive audience: we could view our students as empty receptacles waiting to be filled. However, our goal in I-MATH is to enable our students to become active learners, and to inspire them to want to learn mathematics as active and creative participants.

Through Investigation, Interaction, and Imagination, we can illuminate mathematics for our students, and enable them to become active participants in their own learning.

We can illuminate their way by allowing them opportunities to investigate mathematics in an interactive way, with hands-on, guided explorations of our own design. We can encourage them, and give them opportunities to interact with each other. We can call upon their imaginations to discover the principles of mathematics and create projects that illuminate their own discoveries

We can introduce them to interactive mathematics software that enables them to investigate.

We can allow them to interact with each other in class and via email. We can enable them to interact with other students and teachers via the internet, at sites such as The Math Forum.

We can encourage them to use their imaginations to create projects that demonstrate the mathematics they are learning, and that teach others.

And finally, we can assist them by teaching them how to communicate their ideas to others. We can assist them and allow them to illuminate mathematics for others, by communicating with other students in writing, projects, email, and by creating web pages of their own.

"Instructional programs from pre kindergarten through grade 12 should enable all students to organize and consolidate their mathematical thinking though communication; communicate their mathematical thinking coherently and clearly to peers, teachers, and others; analyze and evaluate the mathematical thinking and strategies of others; use the language of mathematics to express mathematical ideas precisely.

As students are asked to communicate about the mathematics they are studying: to justify their reasoning to a classmate or to formulate a question about something that is puzzling--they gain insights into their thinking. In order to communicate their thinking to others, students naturally reflect on their learning and organize and consolidate their thinking about mathematics.

Students should be encouraged to increase their ability to express themselves clearly and coherently. As they become older, their styles of argument and dialogue should more closely adhere to established conventions, and students should become more aware of, and responsive to, their audience. The ability to write about mathematics should be particularly nurtured across the grades.

By working on problems with classmates, students also have opportunities to see the perspectives and methods of others. They can learn to understand and evaluate the thinking of others and to build on those ideas.

They may benefit from the insights of students who solve the problem using a visual representation. Students need to learn to weigh the strengths and limitations of different approaches, thus becoming critical thinkers about mathematics."