Mathematics Education: Taking a Clue
From the Recent Technological Revolution

Documentation outline: Putting it all together

1. Informal problem statement

   From the NCTM Standards:

   A vision for school mathematics is built around five overall curricular goals for students to achieve: learning to value mathematics, becoming confident in one's own ability, becoming a mathematical problem solver, learning to communicate mathematically, and learning to reason mathematically.

2. Requirements document

   Requirements document is the result of the Definition Stage. It serves to establish common grounds between the parties concerned. Requirements document avoids ambiguity inherent in common language.

   We wish the student be a learner and the acquired knowledge be pluggable.

   (The student should know how to use his knowledge and, if necessary, make up for what he does not know. It also goes without saying that a learner has appreciation for knowledge and knowledge acquisition. As a matter of course, a learner has complete confidence in his ability to learn.)

3. Functional Specifications

   Functional Specifications result from the Analysis Stage. Functional Specifications articulate analysts' belief as to what it takes to satisfy the requirements.

   1. Foster teacher's scholarship: require knowledge, innovation, and sharing.

   2. Create an environment bolstering motivation so that students' every day experience does not conflict with the annunciated goals.

   3. Make materials available in a variety of formats so that each student will get as much as possible and in the format individually best suitable.

   4. Emphasize object-orientation of math knowledge so that the acquired knowledge be pluggable, and include both conceptual and practical, abstract and concrete, classes and objects.

4. Design document

   The Design document is a blueprint for an implementation of Functional Specifications.

   1. Let teachers publish. Publish on the Web. Share experiences. Collecting links is not enough. Classify links. Links may be a part but should not be the sole content of new documents. Reward teacher-scholars.

   2. Stop promoting utility of mathematics and start promoting its cultural value and consistency of its organization. Be honest. Cut this Knot!

   3. Make knowledge of a subject a prerequisite for teaching this subject. Elementary school teachers must understand the conceptual side of mathematics on par with their middle school colleagues.

   4. Support research into and development of object oriented tools that help conceptualize from examples and sort out the acquired concepts.