The idea of common core math is to develop understanding, rather than superficial rote methods in the interest of global competition in STEM and related. The problem with this ideology, is that for the majority of folks out there, getting the right answer quickly rather than really understanding whats going on under the hood makes no sense.
Consider these 4 students and how parents would respond.
1. Little Bobby doesn’t show his work, but gets the right answer. He gets a low grade as when queried, he embraces rote methods with very little understanding of what he is doing.
2 Little Suzy shows her work, makes a mechanical error in writing mid way through the exercises using a unique method,but gets the answer wrong. She gets a higher grade than Bobby as she shows understanding of the process.
3. Little Annie who shows her work and gets the right answer. She gets a higher grade than both Bobby and Suzy, but her approach is purely mechanical. She only uses the methods a given teacher uses over and over, and freaks out when her plug and chug doesn’t work.
4. Little Joey shows his work and gets the right answer. He gets extra points, as he is using a number of methods to get the right answer. He may not always choose the optimum approach, but is demonstrating a deeper level of understanding across a multitude of approaches.
The global competition ideology is the following.
On the job site, little Bobby and Annie will build bridges that if they deviate very far from what he’s seen before will run into trouble. They are likely to be relegated to mundane work. Suzy while potentially error prone if paired up with someone to verify her work is likely to push the envelope. Joey is likely to do well no matter what or where he goes. Global competition suggests we need a lot more Suzy and Joeys than we need Bobbys and Annies… The status quo says Bobby’s and Annies should rule, that is until they are run over by the competition.
The status quo is that 99%+ of society uses rote, and short of a few math nerd teachers, very few outside of some STEM sectors have a rock solid math foundation… This sets the stage for examples like this to propagate which just adds insult to injury.
The above is a terrible example of a decent method. Such is commonly used for doing mental math with large numbers, fractions, and even mixed unit problems like time/date calculations. Mental math while useful to solve equations in mid sentence is a cool and at times a useful thing… but the intuition developed from doing so is where the economic value adder really comes into being. Ie, computers, math models, simulations are all good things, but you must have a pretty good idea of what the answer is before you begin or you will shoot yourself in the foot.
Such is pretty common among the majority of STEM folks I’ve worked with over the years… (and many older tradespeople as well… I’ve known retired carpenters, bricklayers, and machinists who can run math circles around some recent engineering grads who are lost without their computer models.) More often than not, such is the result of having to throw out rote math concepts and rebuilding a foundation from scratch… or in the case of oldsters, because using a slide rule pretty much mandated a solid foundation if they wanted the cool projects rather than the mundane.
I’m not a teacher, but the idea of a firm foundation rather than quick and dirty methods which have to be unlearned later makes sense… Alas doing so goes against the grain of society, many parents who will have fits with low grades for Bobbys who still get the “right” answer, and some suggest that math understanding is too advanced for young kids and that rote should be good enough. I don’t know what the answer is… but hiding ones head in the sand has generally proven not to work out all that well.