October 25th: Post 2 of 3

"In mathematics, you don't understand things. You just get used to them." -- Johann von Neumann

Truer words were never spoken. At least at the preliminary stages, math learning requires a number of leaps of faith before true understanding can develop. This week we are exploring mental math as an extension of our previous estimating, adding and subtraction lessons. The hope is that we will become more comfortable with the processes that will enable higher-level learning later in the year. 

These activities are abstract at best, but grounded in very important theories. These used to be taught by memory and rule (much like multiplication facts), but my preference is to build a thorough understanding of "why" through varied types of instruction. So far we have tried student-teaching, group problem solving, visualization and a variety of more conventional techniques. I think the results have been generally positive, and should get better as I introduce a few more ideas. Here are a couple of these upcoming features:

• Students (in role as explorers) will have to calculate/estimate volumes, distances, money and sizes in order to carry out their trip. This will mesh nicely with mapping outcomes.
• Students will run/own a mock business/organization. They will be able to choose between owning a soccer team and owning a small business. There will be small daily variables that will affect their success and the choices they will have to make. By seeing the concrete results of their calculations and subsequent decisions, I hope the students will buy into the processes and techniques they are learning.

A last note on math: I am carrying out multiplication activities as a class several times a week to build comfort levels and gauge ability and interest. I would encourage you to check back through the last week or so of blog posts (and on the sidebar) to find some activities that will help keep multiplication practice fun at home. Tomorrow, I will send home some sheets to help with multiplication "Fact Practice" at home.

I will leave you with another quote: 

"Mathematics consists in proving the most obvious thing in the least obvious way." -- George Polya