Mathematics as Communication
The NCTM (National Council of Teacher of Mathematics) recommends several standards for all levels of mathematics. These standards have been nationally recognized as a model for the standards movement. One of the standards for students in grade nine through twelve is that mathematics can be used as communication.
This standard states that mathematics curriculum should include further development of written as well as verbal communication. These communication skills should then be linked to mathematics and used to further the development of students. If a student is able to use a formula to state that the volume of a box is "l x w x h," the student would not fully understand the underlying concepts as much as if they discussed several methods for figuring out the volume of the box.
Using mathematics as communication has several components that could easily be implemented in a high school mathematics class. The first item is to reflect on mathematical ideas. I feel that by writing at the end of a class or at the beginning of the next day's class on the prior can lead to the students thinking about what they did that day. Math journals can also be used to complete weekly reflections on the week's classes. Another item is to generate definitions by investigation. Again, using the volume definition paper to investigate different methods of finding volume leads to the students constructing their own meanings.
The next section involves expressing mathematical ideas in written and verbal formats. By using any kind of report or journal, students express their thoughts in writing. One project I would love to do in a class is to have the students present a different topic. The student would have to study the section, consult with the teacher, and then prepare a 10-minute presentation using any type of visual aids needed. This would force the students to verbalize their own thoughts and ideas on a topic. This exercise would also allow students to develop their presentation and speech skills. The next area to study involves appreciating the power of mathematical notations. One way to try this is to present the students with an expression in mathematical notation and have to students explain its meaning. This should go beyond just "speaking the notation," but actually explaining it. For example, everyone knows this: √ 3. This can be verbalized as "the square root of three," but what does it really mean to take a square root? This could be an excellent journal entry or serve as a weekly project.
Finally, students should be able to read and question mathematical writings. One of the best sources for these writings are mathematical journals. The teacher should bring in copies of these journals from the school library, or go to a library classroom if one exists. Each student should be required to choose an article, read it, ask the teacher as well as other students questions about what they have read, and then write a summary paper about the article. This paper should include a brief summary of the article, their reflection on the article, and any questions they encountered during and after reading the article.
Overall, this was just one of fourteen different standards set for high school mathematics students. I felt that this issue crosses the many different classes very well. In education today, there is a push for more cross-curriculum interaction. I strongly believe that students constantly need to work on their communication skills, and math class should not be an exception.