the new math..continued....Follow

You can reread the thread (or the other two just like it) if you want to see the uses for estimation for later years, so I don't need to start reciting those again.

As far as skillsets go, estimation works with quite a few of them in math, but the most clear cut one is probably with quick evaluations. Good estimation skills allow people to quickly guage whether or not answers are reasonable. Training the skill trains their ability to see these things. And if we want to talk practicality, if you can estimate an answer, you can use other math tricks to reach the exact answer quicker.

Stupid easy example: Say if I want to figure out what 20x19 is. Using estimation, I know that the answer will be close to 20x20 or 400, an easy value to come up with on the spot. Simply subtract 20 from that and you've got 380, the answer.

It's stuff like that which gives young students a better grasp of the reasoning behind the math. Do you remember how students are taught to do long multiplication like that? It involves writing the numbers above each other and doing a little matrix-like thing with carrying numbers around. It works, but it can be a little abstract for young students.


Then later you get to the more complex applications, like the ones in calculus and such. What would you suggest, that the education system save teaching this simple yet useful technique until late high school and college? That would be denying how practical it is in both education and real life until then.

Education isn't just about rote memorization. While you might like to argue that estimation is just a slipshod way of solving a problem, that's not the case. Early on, it's method of thought which gives you a quick take on a problem, allows you to see whether your answers are reasonable, or lets you work with numbers in a less formulaic manner. Later on, estimation provides the backbone to the theory of calculus.

That's the kind of theory that I'm talking about. Not just memorizing the forumula's, but actually knowing your way around the numbers. Being able to quickly toss them around in your head to not only reach an exact answer quicker, but also help yourself by just being able to look at a problem and gauge in what realm your answer should theoretically lie.

That's how you get mastery of the subject. Not just knowing the formulas.

Estimation isn't being used to replace actual math knowledge, it's teaching a new skill set to young students who may not have developed it yet.

Beyond just the time-saving aspect, I'd think it would open up students' minds to new angles at which to attack a problem (math or otherwise). This will come in handy later in classes like geometry and college calculus, in which there is not always a set-in-stone procedure through which to solve every problem. The student must devise their own path to the solution, and techniques like estimation may help them to recognize patterns such as "this integral looks like it could be solved by trigonometric substitution." Perhaps it even helps develop the other side of the brain.

It's a similar concept to something from reading classes in 3rd grade or whenever. We were taught the difference between "skimming" and "scanning," and how to use them to our advantage. It certainly wasn't about standardized testing, and no teacher was suggesting that we skim great works of literature rather than read them. It was giving us a new skill set.