I-MATH
Imagination
I-MATH
Imagination
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.
We sometimes have critical moments in our learning and teaching -
moments when we experience a surge of creativity, learn a new method
that really "clicks" with us, or try something new with our students
which really works. In my years of teaching, I can vividly recall
four very profound moments (though they were more than just a few
moments in time!) The ideas that came from these experiences now form
the basis of my philosophy of teaching, and I would like to share
them with you.
1) Cooperative learning, collaborative learning: there are many definitions for these two phrases, but the key issue is that students (and teachers!) can benefit from working with others, discussing, questioning, and even arguing.
2) Interactive mathematics software: there are many types of software, but in my opinion those that give opportunities for students to experiment, discover, and create, provide the best opportunities for learning.
3) Writing in Mathematics: communicating one's ideas by writing, drawing, and explaining, has profound value in the educational process. We often learn best when we try to explain to others, and giving students this opportunity can enrich their experiences of mathematics.
4) The internet and email not only allow fast and successful opportunities to learn information, but open our classrooms to the entire world. Students and teachers can now become part of a larger, global community, discovering new information and ideas, and allowing us to publish our own projects and creations.
All of these four, if they are new to you, will require you to use your imagination, creativity, and willingness to experiment with new methods, media, and ideas.
All of these four have increased the opportunities for students and teachers to exercise and expand their imaginations and their abilities to create. School does not need to be a static place where information passes one way, "down" to the students. The most effective teacher might not be the one who limits their job to interpreting the textbook for the student.
Imagination is enabled by investigation, interaction, and illumination, and the four are inextricably linked.
In these web pages, I hope you will read, explore, and let your imagination lead you to new methods of teaching and learning mathematics.