The Math Blog

Check back for Mr. Nielsen's thoughts and "a-ha" moments about the middle school math experience!
(Also mirrored on my slow-moving personal blog, edfocus.

October 29, 2011

The Ongoing “Math Wars” – Part One
Kris L. Nielsen

I’m following with great interest the idea that the Connected Mathematics Program is creating rifts and waves among the experts, educators, parents, and administrators of the middle school communities (and Connected Math isn’t the only one). It’s interesting to me because it’s like watching evolution happen before my eyes. Change is hard for many people, and especially for those who have a hard time predicting the future (isn’t that all of us?); but for the success of our children in this global and knowledge-based economy, it is so very crucial.

Keep in mind, the public education system has historically educated our people to the extent of the technological needs. For example, in the agrarian societies of the 18th and 19th centuries, it was only necessary to learn the basic arithmetic that would help a farmer geometrically plan and maintain crops, be able to deduce and predict output from what he planted or grew, and be able to calculate in terms of decimals and money. In other words, the mathematical needs for the average 18th and 19th century citizen were, at most, roughly equivalent to the 6th grade level math we teach today.

As the Industrial Revolution began transforming our country (and the world) there was an obvious need for a more mathematical society. With the growing technological needs of the nation, the education system found a need to educate its citizens up to a high school level. Engineering and manufacturing proficiencies became the new standards by which to match math education. Therefore, the studies of motion and forces—and therefore algebra and eventually calculus—became the pedagogical goal of the public school systems.

The Cold War boosted this need even further, as America strived to maintain competitiveness within an increasingly technological and scientific rival. It was calculus that got us to the Moon, the planets, and beyond (and created methods for launching fiery death around the globe). Thank goodness for calculus!

But it wasn’t for everyone. Not everyone had a hand in the travels among the stars or the planned annihilation of enemies, and those who didn’t still typically only achieved a 9th or 10th grade math education. In order to be part of an economy based on financial growth for the middle class, the skills needed were vastly differentiated, but they didn’t include calculus for much of the population. Those who did use algebra and calculus became proficient in using prescribed algorithms to reach a desired solution to a problem.

Which brings us to the present. We no longer live in a manufacturing or even a technological world—to clarify, although still very important facets of the America’s economy, most citizens will not be working in the manufacturing or technology sectors. Calculus is still widely used in the scientific, engineering, and financial sectors. But most citizens in the 21st century now live in what the researchers call a “knowledge economy,” where a citizen’s worth is based on what that citizen can understand, analyze, predict, and conclude about a problem—and then solve that problem. This set of skills is becoming increasingly reliant on the tools and processes that citizens should learn in their K-12 and postsecondary education.

And right now, that K-12 education is decades behind the needs of the knowledge economy. The good news is we are starting to understand what it will take to catch up. The bad news is we are doing it too slowly. There are several “speed bumps” here, as outlined below:

  • Some experts (those who have come to know the “old school” methods as the path to success) are either slow to get on board or blatantly opposed to the needed changes of our education system.
  • Parents are told by several sources that the changes to the ways that math and language arts are taught are detrimental to their children’s performance on state tests and other assessments. These sources use buzzwords like “fuzzy math” and “no right answers” to persuade parents to speak against the new constructivist approach.
  • Teachers are being asked to redirect their foci and their pedagogies to cater to new ways of thinking and assessing.
  • Students are working harder, longer, and using techniques that do not include stringent and prescribed algorithms and rules that must be memorized.

I use the term “speed bumps” because these are not roadblocks, which cause someone to stop and change direction. A speed bump simply causes us to slow down, evaluate the issues and solutions, and then cautiously move forward (much the same way we want our students to). The last two bullets are actually positive scenarios (except perhaps for the longer and harder work that students must do, but hopefully that will be remedied as we adults get used to teaching them for the new century). Teachers should always be reflecting on their practice and evolving to meet the needs of a changing society. Students should be learning to face novel problems and challenges that they’ve never seen before, and then use their toolboxes of logic and rational thought to solve them.

Part two of this entry will focus on what the “new, new math” looks like and why it’s so important to teach it, study it, and reflect on it. We do know one thing: the old way of learning math (and language arts) is ineffective in this new global knowledge economy. Students are woefully unprepared for college and even less so for the workplace. It is no longer sufficient to make students memorize the steps to solve one type of problem; they must be given the opportunity to construct ways to solve many types of problems.

November 20, 2011
The Ongoing "Math Wars" -- Part Two
Kris L. Nielsen

I will try my best not to inject too many personal anecdotes here, but I do want to relate the “new math” to the “old math” as we knew it. The transitions of mathematics education in the past decade have been an answer to the call of the collegiate and working worlds. There are simply too many complaints coming from those sectors suggesting that our high school graduates are not prepared to meet the challenges that are required of them. Allow me to briefly discuss this problem.

In the past, the emphasis in math education was the content. There were defined skills and concepts that had to be learned—and tested—to assure that students could work their way through a prescribed problem in order to reach a desired solution. An example of this is the need for a physics student to find a formula that matched the scenario of launching a rocket into orbit around Earth. In the age of slide rules and massive computers (which, incidentally, had less computing power than today’s pocket smartphones), scientists relied on their own ability to such problems accurately and precisely. Likewise, astronauts aboard that craft needed the ability to solve formula problems in case something went wrong with the automatic navigation systems.

When old folks like me talk about the great things we achieved with a paper and pencil, this is what we’re griping about. However, of all the students graduating into the 21st-century knowledge economy, there are very few who are going to need to know this stuff. Additionally, our technology is much more capable of handling such mundane tasks. Shouldn’t we let technology do the hard work so that we can use our valuable time to do the important work?

Mathematics skills are handy tools. We must know what they are, how they work, and how to use them. But—and this is a big but—this is not the end. Assuming that a tool is necessary to someone’s life to begin with, it can quickly become obsolete if the need arises for a more suitable tool. Sometimes new tools must be invented or old tools modified in order to meet a new challenge; often a variety of different tools are needed to achieve one goal.

My first car was a 1974 Chevrolet Camaro. It had a small-block 400 V8 under the hood and a powerful transmission to help it go fast. I loved that car, but it was in constant need of maintenance (it was as old as I was at the time—20 years). My standard 45-piece toolkit included socket wrenches, screwdrivers, a torque wrench, and a few necessary drivers. It was plenty for me to get in there and fix whatever was in need of maintenance. I could solve any problem in my car with that toolkit.

Now, imagine me bringing that toolkit to try and fix my neighbor’s 2011 Chevrolet Camaro. The biggest difference between the two models is the computer—my car didn’t have one; my neighbor’s car has a pretty advanced one. A standard toolkit like mine is virtually useless against the needs of advanced technology. If my neighbor needed someone to perform maintenance or fix a problem on his car, he would be foolish to hire me. My tools and my knowledge are obsolete and completely inadequate to perform the tasks needed under those circumstances.

The parallel here should be clear: the tools of the 21st century citizen are vastly different from the tools of the 20th century citizen. From personal experience and research, I can easily suggest that the high school education happening now is exactly the same as that which happened 20 years ago. This is not an exaggeration. The biggest sources of all of the changes are technology and globalization. The tools we were taught to use in the 20th century were not designed to deal with the problems of evolving technology and global economics. Most importantly, they do not give us the ability to solve the most important and pressing problems of the 21st century.

Those companies who need high-performing problem solvers would be foolish to hire graduates from average American high schools, equipped with 20th century tools. Top-tier universities are finding a shortage of qualified incoming freshman. And the global knowledge economy is also quickly finding that American toolkits are obsolete and inadequate.

So, what do we do about it? This will be my focus in part three.