Dear Caitilin, Why is today’s elementary level math so confusing? Has mathematics education always been this controversial?
Common Core! State Standards! Testing! These are the hot issues in mathematics education in our times, and they are issues we hear about daily, on the news, on Facebook, from our friends. All these ideas arise out of the good intention to see that America’s children are educated for success in today’s world. Of course, the reality is far from that utopian vision. One problem is that it is not the case that implementing the standards associated with the Common Core inevitably raises educational standards. A friend in Indiana, for instance, realized that in her district, which is not a stellar one, the Common Core standards were appreciably lower than the previous, but recently revamped, ones. Indiana has now opted to drop the standards mandated by the Common Core, and once again developed its own State Standards for mathematics education.
There is a sense, a sense based in fact, I hasten to add, that a sizable population of parents in the United States are all up in arms, reacting and railing against the changes to education resulting from school districts’ aligning their curriculum with the Common Core standards. Often they receive the response, “If you don’t like what’s happening in the public schools, pull your kids out. Send them to private school, or homeschool!” But many of those who rail against common core already are homeschooling; they rail precisely because of those not-their-own children who haven’t got other options; they rail on behalf of kids whose parents may not be able to help them negotiate a new method for doing the math problems they come home with at night. It’s not that the only complainers are those who have kids in the system; in fact, many from outside the system see things about it that concern them, and seek to have their concerns addressed for the sake of those who cannot seek redress for themselves.
A friend of mine recently wrote an impassioned Facebook post in support of the methods for teaching mathematics which correspond with Common Core standards. She rejoiced in the fact that her daughter was unfazed by either new material or by word problems because she could just “get out her tools” (number lines, tally marks, etc.) and plow ahead. This is wonderful–it IS extremely satisfying to see one’s children learning, to see them achieving academic success–and nothing I say here is to downplay the importance of that success in children’s lives.
However, there are a couple of problems with her statement:
1) Why on earth would/should her daughter freak out when presented with new material? Who told her that word problems were hard, and worthy of a freak-out?
2) Why should she need “tools” to work through problems in material and concepts she, presumably, has been introduced to and understands, simply because it is presented in word problem form? These tools, increasingly, are taking the place of conceptual or practical understanding of mathematical ideas.
Let’s remember, first off, that all these tools that the kids are being given are just that, tools. They are just tools, approaches, methods. Using any particular “tool” oughtn’t to be held up as an end in itself, and any given “tool” ought be used to build mathematical fluency, so that the students can move away from needing them. Otherwise the use of the “tools” can too easily become nothing more than a glorified version of counting on one’s fingers–fine in kindergarten, not so fine in 7th grade. The idea is that the students are to know a variety of ways to approach a problem, and implement the one that best suits the problem itself, as well as their own learning style. Again, this is fine; any good math teacher has always demonstrated various methods for arriving at correct answers. The problem lies in placing use of a particular method ahead of the result.
The math program I use at home with my children, for instance, makes a point of teaching multiple approaches to problems. Teaching multiple approaches is not an issue. But when Approach A is privileged over Approach B simply because A is new and B is old, that IS a problem. The purpose is to be able to do arithmetic, exercise logic, perform higher mathematical operations, whatever–in other words, to be educated in the concepts. The purpose of math class is NOT to demonstrate whether you’ve fully grasped every possible strategy for approaching the problem. Once you’ve got one that works for you, great, use it! But requiring every student to solve problems in the same way just because that’s THE tool of the day is silly.
In the end, though, I believe our concerns about mathematics education are misplaced. It’s not simply the standards set by the Common Core that are the problem; rather, it is a group of inferior math curricula which are often, perhaps even usually, taught by teachers ill-prepared to do so that should worry parents. When students are never exposed to an efficient method for performing mathematical operations, hearing instead sentiments like “Don’t worry about getting the right answer, just see what you can do,” then parents should worry. When we no longer teach math, but only play in it as in a sandpile, shifting its beautiful principles to suit our own laziness–it is then that we should be fearful.
Caitilin Fiona–Caitilin is the mother of six children, ranging from high school down to early elementary, all of whom she has homeschooled from the beginning. Her particular interests in the homeschool universe include teaching Latin, Shakespeare, and Great Books. Outside of homeschooling, her interests include languages, literature, theology, cookery and nutrition, movies, and fooling around, er, researching on the Internet.