Broadening the definition of mathematics
Activity: Take a moment brainstorm some ideas as to what mathematics is or what it encompasses. Before you continue with this lesson, write your ideas in the discussion box below and submit them. Don't peek at the rest of the lesson or what others have written yet.
Most intervention programs and methods rely upon pulling out a student for direct instruction on some particular mathematical skill, and focus heavily on the mastery of a particular procedure. Borgioli explained this narrowing of focus by stating that “special education policy, research, and practice, are grounded in a traditionalist perspective that embraces behaviorism and a narrow vision of what counts as mathematics and mathematics proficiency.” (2008, p. 142).
Activity (Continued) Now, read this quote from the National Research Council: Mathematics reveals hidden patterns that help us under- stand the world around us. Now much more than arithmetic and geometry, mathematics today is a diverse discipline that deals with data, measurements, and observations from sci- ence; with inference, deduction, and proof; and with math- ematical models of natural phenomena, of human behavior, and of social systems. The cycle from data to deduction to application recurs everywhere mathematics is used, from everyday household tasks such as planning a long automobile trip to major man- agement problems such as scheduling airline traffic or man- aging investment portfolios. The process of "doing" math- ematics is far more than just calculation or deduction; it involves observation of patterns, testing of conjectures, and estimation of results. As a practical matter, mathematics is a science of pattern and order. Its domain is not molecules or cells, but num- bers, chance, form, algorithms, and change. As a science of abstract objects, mathematics relies on logic rather than on observation as its standard of truth, yet employs obser- vation, simulation, and even experimentation as means of discovering truth.
(http://archive.org/stream/everybodycountsa003730mbp/everybodycountsa003730mbp_djvu.txt)
How does this differ from the definition that you initially came up with? How does this compare with other defintions that people have posted? Post about this in the comments below, and compare your answers to other students.
In the next section, we'll take a look at collaborative groupwork and have you complete an initial self-assessment in order to reflect on your current practices.