There is much discussion about the mathematics curriculum in schools. The Core Standards have been adopted by many states and now there are other proposals that will nationalize the curriculum. I fear that imposing these standards, while potentially useful to some teachers, will hamstring good teachers. High priorities in any curriculum must be developing number sense and mathematical reasoning. Spatial visualization activities to engage the whole brain and serve as a basis for making sense of all topics, especially geometry is an essential component. As I have looked at the proposed standards I fail to see incorporation of what we have learned over the past 30 years about how students learn. For example, we must recognize that we are social creatures and that use of collaborative learning is critical in deciding on instructional strategies. No longer can the teacher be the explainer, attempting to transfer knowledge to the minds of others. Individuals must construct knowledge for themselves in a meaningful setting.
Technology has an important place in learning but we must be very careful in its use. When calculators were introduced in schools, students soon became dependent on calculators for performing the four basic operations; rather than relying on number sense, they turn to the calculator when faced with 2 x 10. On the other hand, as Keith Devlin says, complex computations should be done using technology rather than drilling on such tasks as long division. I recently learned of a young child who was performing fantastic tasks with a computer making complex moves but who could not put together a 16 piece wooden puzzle. Some essential pathways had been pruned away because of the lack of tactile experiences. Creative teachers can find fantastic ways to use new technology such as the iPad to facilitate learning.
Teaching is a complex task and good teachers at all levels need the flexibility to plan lessons based on what they know about the children they are teaching. Tasks must be challenging but possible. It makes no sense to "teach" a concept if it is beyond the comprehension of her students just because it is on the standards. Further, if students enter with advanced knowledge, then the teacher must be free to challenge students with more advanced topics. In summary, we must not tie the hands of creative teachers.
