Math has taken another hit. This time, it’s from Andrew Hacker, emeritus professor of political science at Queens College, City of New York, whose piece “Is Algebra Necessary?” appeared in the July 28, 2012, New York Times Opinion section. His premise is that since so many kids and adults find math hard, it just shouldn’t be required. Or at least, they shouldn’t be subjected to the algebra, geometry, more algebra, calculus sequence that had been the US math sequence for so long.
Here’s Hacker’s initial thesis: “Making mathematics mandatory prevents us from discovering and developing young talent. In the interest of maintaining rigor, we’re actually depleting our pool of brainpower.” His support rests on statistics of high school dropout rates (75% of ninth graders complete high school) and the role he sees algebra playing in that rate. I have no doubt algebra is a serious stumbling block for many students. Does this mean we should toss it out and teach calculating the Consumer Price Index instead, as Hacker suggests? No, although some shift in how we educate our children in math is definitely in order.
First, let’s clarify our terms. Arithmetic is what you were taught before algebra, at least in most schools and certainly what you experienced in grade school if you’re now in your 40s. Addition, subtraction, multiplication, and division (including that long kind Hacker says is essential). Fractions, decimals, and percents appear, with a nod to generally single-step word problems for application. Arithmetic is number-crunching. It can be taught with algorithms and tricks or deep conceptual understanding, although it’s too often taught the former way rather than the latter.
Arithmetic is not mathematics. Math is problem solving and reasoning, relying less on rules and more on understanding the way numbers and geometry works. Math uses those skills in arithmetic to problem-solve and reason, but not all arithmetic needs to be in place before math is taught. In fact, the best arithmetic teaching puts math at its heart.
It’s been said that arithmetic is to math as spelling is to writing. You’d not mistake a great speller for a fine writer, and while a fine writer should produce a product with conventional spelling, one must not wait to spell all the words one could ever want to use in order to start writing. We teach our kids to write before they can spell well, allowing both to develop together. The same relationship can and should exist between arithmetic and math.
Math matters. Like it or not, some degree of math comfort and skill is mandatory for full participation in today’s world. A sound mathematical education opens doors into the STEM jobs that increase in number by the day. A good understanding of numbers makes economics, politics, and social science more accessible. It allows people to understand credit, mortgages, taxes, and savings. If we drop our current math requirements in high school, shifting them to simply consumer math, as it was called in my high school years, we vastly under-prepare our children for the options ahead.
Hacker agrees that math matters.
Quantitative literacy clearly is useful in weighing all manner of public policies, from the Affordable Care Act, to the costs and benefits of environmental regulation, to the impact of climate change. Being able to detect and identify ideology at work behind the numbers is of obvious use. Ours is fast becoming a statistical age, which raises the bar for informed citizenship. What is needed is not textbook formulas but greater understanding of where various numbers come from, and what they actually convey. (Hacker)
But then he backpedals, wondering why we subject our “potential poets and philosophers” to the traditional math sequence rather than nurturing their talents. My answer is because we really don’t know at 14 what path many kids will choose. We need to prepare them for more options that whatever their fancy of the week may be. I agree with Hacker’s assessment that today’s math path is likely outdated. I’d prefer to see more integrated math, weaving algebra and geometry together and focusing on applications across the disciplines.
What Hacker fails to address is the why behind the algebra fear and failure at the high school a college level. Early elementary math matters, whether at home or at school. Math (or actually arithmetic) taught as rote memorization with no deeper applications is like teaching spelling without writing, scales without true music, or love via self-help manual rather than personal experience. It deadens math. Kids aren’t born fearing and hating math. Aversions to math are learned, often from those teaching them math. Hacker spreads this sense of math as too hard in his final paragraph: “This of math as a huge boulder we make everyone pull, without assessing what all this pain achieves.”
What if, from the start, we taught our children to look at math with wonder. What if we nixed the “drill and kill” and senseless algorithms in favor of teaching actual math. I picked Singapore Math for a reason (reviewed here). It teaches math along with the arithmetic. The whys of the processes are right there, and the word problems (especially those from the Challenging Word Problem series) demand complex problem solving. There’s no waiting until algebra to think in math fluently. It starts in the first books. Singapore isn’t alone in this process. The arithmetic my sons learned at age 4 and 5 in Montessori was rooted in deep understanding of how the numbers work. Heavily manipulative-based and backed my a masterful teacher, they learned WHY regrouping works for subtraction and what is truly going on in long multiplication problems. (Note: Manipulatives are not the key here. The key is excellent instruction about the concepts paired with judicious use of manipulatives, followed by transitioning to abstract work without those hands-on items.)
Curriculum matters. What matters more is teachers (parents of homeschoolers, that’s you or whomever to entrust your children to for their math education). The best curriculum in the world won’t teach mathematical thinking if the educator is uncomfortable with the subject matter. Hacker’s treatise focuses on high school mathematics education, but he’s focusing on the wrong end. Those math teachers went into teaching to teach math, a subject they likely deeply appreciate and understand. But what about our elementary kids, at home or at school? While I know there are exceptions, I sense the comfort level with math (not arithmetic by algorithm) isn’t high for many elementary teachers, and I know it’s not present for many parents. (That’s why Saxon sells so well. It’s easy to use, highly scripted, and able to be turned over entirely to the kids early. And it’s arithmetic. Not math.)
So what to do? If you’re a homeschooling parent, find a curriculum that supports deep mathematical thinking. If you kids are young, rejoice. You can easily learn along with them. Singapore Math and Mammoth Math are fine elementary programs. Art of Problem Solving offers excellent texts for the set ready for pre-algebra and beyond, and Singapore has an integrated math progression for the post-elementary level. Too intimidating? Consider adding in supplemental math into your existing arithmetic program (see list below). Anything that demonstrates the wonder of math over the tedium works toward supporting young learners of math.
Hacker makes a few good points. Teaching more practical mathematics in high school makes sense. Not everyone will choose a path that requires calculus, and that’s fine. But rerouting the mathematical train before algebra is begun seems foolhardy and shortsighted. At 14, the age many American children face algebra (and I’d argue that’s way too late for math to truly begin), we don’t allow kids to drive, vote, sign a contract, or work most jobs. I’d add to that list we shouldn’t allow them to limit their career options by opting out of algebra either. Instead we should be making math meaningful during the elementary years rather than simply teaching rote arithmetic skills while bemoaning how hard math is. As parents and teachers, we can emphasize the utility of math and encourage deeper mathematical thinking skills, both by curriculum choice and in supplementary reading and discussion. We should not abandon algebra nor the rest of higher math. Rather we should provide proper support from the start to make that math not only possible to do but delightful to explore.
More reading on mathematics education:
- U.S Teachers Not Well Prepared to Teach Mathematics, Study Says
- I’m Bad at Math, and I’m Fine with That!
- Adding it Up: Helping Children Understand Mathematics (available to read online)
- Arithmetic for Parents (Ron Aharoni)
Supplementary resources for all ages:
- Calculus By and For Young People (Don Cohen)
- Challenge Math (or any title by Edward Zaccaro)
- G is for Googol (David M. Schwartz)
- The Man Who Counted (Malba Tahan)
- A Gebra Named Al (Wendy Isdell)
- The Number Devil (Hans Magnus Enzensberger)
- The Adventures of Penrose the Mathematical Cat (or any other book by Theoni Pappas)
- Sir Cumference of the First Round table (or any title by Cindy Neuschwander)
- Anno’s Mysterious Counting Jar (or any title by Mitsumasa Anno)