We have many questions about how math is being taught and why it "changed". Information is increasing at a very rapid speed. We must prepare students for jobs that have not yet been created! What a daunting task -- to provide students with the information they need even as information is increasing exponentially and to also teach students how to use the information in ways that do not even exist.
When I was in school, personal computers were not available or even talked about. Cell phones? Nonexistent. School prepared us for either college or a blue collar job in a local factory. People entered the work force either after high school or college and stayed in the job for 30 years and then retired. People had a career -- one career. The information we were taught was to prepare us to get into college or to give us enough basic information to learn a factory skill. Factory jobs allowed you to begin work - often at the bottom -- and work your way up if you had basic skills and a good work ethic. College allowed you to begin work in a field that you "learned" in your last two years of college. Those days no longer exist.
While the above is a simplified scenario, it nevertheless conveys the "big picture." Today, people entering the work force will most likely have multiple jobs and multiple careers. Working in the same job type and especially with the same company is a rarity. Jobs are much more specialized, and more and more companies are providing the specific training needed for their company. So what do students need to have? An in depth understanding in different content areas that will allow them to use the information -- use the information in ways that we do not know yet.
All of that leads up to why we teach math differently. Many students have gone through math classes and learned formulas, short cuts and catchy phrases in order to perform well on a math test. However, knowing the formula and applying the formula are totally different. Here are two basic examples: Elementary students often learned how to "borrow" by "going next door", "marking the number out and putting a one up top", or any number of other tricks. When it came to understanding place value and why the tricks worked, students did not understand. So the student is then not able to use that information in any other context except stacking two numbers on top of each other and subtracting. A second example is the Pythagorean Theorem, a2 + b2 = c2 . If a student only knows the formula but has no idea how to use it, the theorem becomes just a formula.
To compete for jobs that do not yet exist and to be able to use information that is rapidly expanding, we must teach students mathematics concepts. Students must understand the how and why in order to be able to use the information to solve problems. And, not to just solve problems that say "solve using the Pythagorean Theorem, but problems that require knowing that the Pythagorean Theorem is what is needed to solve the problem. (Example: A newly-planted tree needs to be staked with three wires. Each wire is attached to the trunk 3 ft. above the ground, and then anchored to the ground 4 ft. from the base of the tree. How much wire is needed for 6 trees?)
Preparing students for the future means teaching math differently. It means teaching students the why and the how of how math works. And, that looks different.
