Algebra. For many, the word causes heart palpitations at the thought of letters mixed with numbers. To others, algebra is the gateway to higher mathematical pursuits.
Statistics show algebra to be the most common stumbling block for high school and college students. It should come as no surprise, then, that administrators tasked with raising graduation rates while reducing expenses would question why algebra is necessary for everyone.
From the Los Angeles Times:
The chancellor of the California Community Colleges system says intermediate algebra should no longer be required to earn an associate degree – unless students are in the fields of science, technology, engineering or math. [STEM] Chancellor Eloy Ortiz Oakley, who heads the nation’s largest community college system of 114 campuses, told The Times that intermediate algebra is seen as a major barrier … preventing too many from completing degrees. About three-fourths of those who transfer to four-year universities are non-STEM majors, he said, who should be able to demonstrate quantitative reasoning skills by taking statistics or other math courses more applicable to their fields.
High failure rates in college algebra are common nationwide. Post-secondary instructors will tell you it is not uncommon for students to take the course a second, third, even fourth time or more. From their perspective, it is easy to see that Oakley is correct that there should be a way for non-STEM majors to learn the reasoning skills at the root of algebra without the abstract concepts many find so challenging.
Schools within the Technical College System of Georgia (Full disclosure: The author is a full-time math instructor at a TCSG school, and opinions presented are his own) are beginning to steer non-STEM majors into statistics and quantitative reasoning, which are less abstract and more applicable to non-STEM work experiences than algebra.
Statistics and quantitative skills are far more useful for the average person. With a greater emphasis on statistics and mathematical reasoning, the average person becomes better informed and more capable in the workplace at large. That can’t be a bad thing, and non-STEM majors will be better off following that route.
The flip side of the coin, though, is downright alarming. Our supposed best and brightest – STEM majors – are also struggling in math. Bigly.
A large number of college freshmen exhibit a truly stunning level of deficiency in mathematics. The same is true for those making the leap from middle to high school.
It was hoped that Common Core would help remedy this situation, but that has not come to fruition. Conceptually, Common Core math is a great idea – get students to think about math the same way that a math genius thinks about it, and they’ll succeed.
Though a great idea in theory, the rollout has been awful. If you are the parent of a school-age child, you’ve been witness to that fact.
Those who succeed in math do so because they have a keen number sense, and they use it to develop shortcuts in their problem-solving methods. For example, we’ve traditionally added 13 and 17 vertically – first adding the ones column and carrying, then adding the tens column to get a total of 30.
But students with strong number sense inherently think of 13 as 10 + 3 and 17 as 10 + 7. They then add the 3 and 7 to get 10, followed by adding that 10 with the other two to get 30. On paper, it looks something like this:
13 + 17
10 + 3 + 10 + 7
10 + 10 + 3 + 7
10 + 10 + (3 + 7)
10 + 10 + 10 = 30
It seems unnecessarily long and complex, but students with sound number sense perform all these operations in a split second. This is but one example of many.
The problem is that we’re asking people who’ve never had to think this way before to teach children how to do it. At the end of the day, everyone – student, teacher, and parents – comes away frustrated. The issue actually predates Common Core, but has become magnified since its inception.
This is not to say that elementary teachers are bad or lazy or stupid, but rather that we’re not training them well and we’re asking them to teach subjects they admittedly don’t fully understand. As a thirteen-year veteran of teaching high school math, this writer has been witness to multiple otherwise great elementary teachers saying “I’m just not good at math”.
Starting in middle school, math teachers are required to specialize in mathematics. That’s not always the case at the elementary level – which is why one of the most important questions to ask at the elementary open house is “What were your favorite subjects?”
Put another way, I love my general practitioner. He’s got the most knowledge and best bedside manner of any doctor I’ve ever known. But if he told me I needed a liver transplant, I’d want a specialist to do it.
In short, we often ask general education practitioners to give our kids number sense transplants, even though number sense is the key to math success and those practitioners don’t fully understand it.
There are many things we can do to fix our math problem. The three below would make for a good start.
First, train our educators better. Teaching math well requires that one have a much deeper understanding of content than the level at which they’re teaching.
Second, redesign our curriculum with a focus on number sense and other overarching concepts at the earliest levels.
Third, change our expectations. Our workforce is quickly shifting toward skilled trade workers. Our training of that workforce should be shifting as well.
Increased post-secondary opportunities mean that we no longer need to require that everyone learn everything. We need to explain to them the importance of getting to work on time and increasing their value to their employer. They should be able to file their taxes, apply for a mortgage, and know where and how to vote.
They should also understand that every choice they make – including what they choose to learn – comes with both opportunities and consequences. But not everyone needs to know how to solve a logarithmic equation.
And as a colleague noted last week – let’s talk about literature. Do I really have any reason to drag out those old Beowulf notes?