If the movie `A Christmas Story' were based upon my life story it wouldn't have been a Red Ryder BB Gun with a compass in the stock that was Holy Grail, rather
it would be a two-wheeled contraption of any kind. My mother was convinced that any kind of two-wheeled motorized vehicle was the devil's work. I heard “you'll break your neck” more times than Ralphy heard `you'll shoot your eye out.’

So, I blame my mother for my 45-year obsession with motorcycles. As soon as I graduated from high school and left home I scanned the Lawrence Journal-World want ads for a used bike. The first one I found was a two-stroke Suzuki GS 350. It was not exactly a rolling classic. Its most distinguishing feature was the beautiful trail of blue smoke it left behind.

Over the years since that Suzuki met with an untimely demise on the streets of Lawrence, Kansas, I have owned several different makes and models of motorcycles from dirt bikes to cafĂ© racers to my new Indian cruiser. What I have learned over those years is that motorcycling, like many hobbies, is a subculture filled with subcultures. A casual observer might think a motorcycle is just a motorcycle but a rider knows that the difference between a dirt biker and a chopper rider is vast.

There are dirt bike aficionados, cruiser riders, chopper fans, bobber freaks, sport bikers, adventure cyclists, touring riders, stunters, and just plain commuters. The sport bikers with their high revving speed machines look down their visors at the teacup helmeted leather clad cruiser riders with much disdain. The adventure cyclists clothed in jumpsuits astride SUV like machines with giant metal saddlebags have no use for retro-riding hipsters on stripped down Triumphs.

It's not too much of a stretch to draw comparisons between motorcyclists and Kansans when it comes to politics. We have conservatives, moderates, tea partiers, liberals, libertarians, socialists, and everything in between. Over the past several months my mailbox runneth over with glossy postcards explaining the horrors and dangers of differences between candidates and positions.

If we assembled a random group of motorcyclists we could quickly reach agreement, in spite of our differences, on why we ride and what makes a motorcycle a
motorcycle. However it is not in the best interest of motorcycle apparel makers, magazine publishers, or manufacturers to have agreement. Marketing demands that people identify and behave in ways that create identities around niches. It is the best way to sell more stuff.

If we assembled a group of Kansas voters in a room, the one thing that all could agree on is education is a major issue with Kansas voters. Most all candidates are touting their records of support for schools, students, teachers, and more resources for public education. Based upon the glossy flyers that show up in my mailbox, everyone wants the best for Kansas education.

Unfortunately, much like the motorcycle business, politics demand that we create niches of voters just like subcultures of bikers. The harm of a strategy of identifying
small differences and turning them into big ones is that it polarizes Kansans against one another. An unknowing observer might think that Kansans are all either fascists or communists.

What we know about human behavior and beliefs is that if graphed it looks less like two bubbles separated by a chasm and more like the old bell curve we recognize
from statistics. If we slice the curve in the middle, we polarize 50 percent on the left and 50 percent on the right. If we look at polls in major elections right now we get 50 percent on the left and 50 percent on the right. That view of politics gives too much power to the extremes. The folks at the 49th and 51st percentile have far more in common than those at the 1st and 50th. I propose that after the election we encourage our legislators not to slice from the left or the right but to take a big slice from the middle.

Kansas has long been a progressive, common-sense state. We have done this by taking our slice from the middle. Modern politics are trying to do to our state what is happening to our nation. The attempt to define our country in terms of extreme red or blue ignores the fact that most of us are purple. (Please note this is not an advertisement for the Wildcat nation.)

Whoever wins and whoever loses needs to be prepared to view our state as a whole and not as one side against the other. Let's take our slice out of the middle. A motorcycle has two wheels and engine. Whether it's a Harley-Davidson or a Vespa it is still a motorcycle and it's still fun to ride. Kansans agree that education is the most important issue facing our state. Lets unite around it!

The fact is Kansas education is good but needs to get better. Kansans need to define what our kids need to know and be able to do upon graduation not based upon party lines but based upon what the majority of Kansans in the middle want for their kids. Kansans then need to provide the resources necessary to make this happen. We will never get there if we keep trying to slice the curve from the left and the right. Like it or not, Steelers Wheel was right, ‘Here I am, stuck in the middle with you.”

## Thursday, October 30, 2014

## Friday, October 10, 2014

### Math Myths and Urban Legends

One characteristic of a good friend is that they have the ability to challenge your thinking. Without people like this in your life, it is easy to start thinking that you pretty much know everything. I am fortunate to have a lot of people in my life who challenge my thinking. Recently, a friend asked me about this new math being taught at his son's high school.

The teaching and learning of math is a pet peeve of mine. My biggest complaint about math is the common belief that because the kid who makes $7.50 an hour at the local Gas and Grub got my change wrong, schools have failed at math instruction. If you haven't said it yourself, someone has said it to you.

Let's think about the state of what kids in Kansas know and are able to do compared to the good old days when we could all make change. Folks my age can remember the "advanced kids" were tracked into algebra class in the freshman year. Thirty years later, my kids took algebra in the 7th grade. In my large high school, a handful of kids graduated with four years of math. Now many students go to college with calculus credit already on their transcript. Kids today take and learn more math than they did in the good old days.

The bigger issue is that it is still not enough. Our kids need to have a deeper understanding of math and how to use it. We have to expand our definition of math, and at the same time go deeper with our understanding of math. My friend's concern was that kids were not spending enough time on memorizing math facts, and too much time on learning new and different ways to solve math problems. That concern lays bare education's fundamental math problem.

In the good old days, we memorized the multiplication tables. We worked on speed addition and subtraction. A good memory made you a good math student. As an educator, I have heard countless parents talk about the fact that their kids were straight A math students until Algebra, and suddenly they were getting D's and F’s. Once a student gets to algebra, statistics, physics, chemistry, geometry, finance, economics, etc., memorization of the multiplication tables isn't the advantage that it once was. A deep understanding of math skills is far more valuable.

I often challenge people by asking what 1/3 divided by 7/16 is. Most everyone knows how to find the answer is to invert and multiply. Duh. Then I ask them to explain what 1/3 divided by 7/16 means. Most stare at me blankly. We memorize algorithms and formulas, but we don't understand what the numbers mean. When letters start to take the place of numbers, memorized applications have less power.

So how do we teach deeper math understanding? That is a question for experts in math instruction, but we don't do it by teaching math the way we always did it. My friend sent a problem that involved asking the student to solve the following: 86-12=? An explanation of one way to find the answer was to round to the nearest five, subtract, then add what your rounded back in. (I shortened it, but you get the gist.) The idea is that fives are easier to visualize (tens even more so).

What struck me about this "new math" is that my grandfather (not the same one who counted pinheads on the bus) taught me this method when I was a kid. He could do lengthy arithmetic problems in his head by using strategies like rounding and finger math. He also had a strange way of working long division that I have seen in some YouTube videos being described as an "ingenious new method."

My grandfather fought in WWI, and received his terminal degree (8th grade diploma) over a century ago. He didn't know calculus or statistics but he understood the concepts of math. The barn he built 100 years ago is still standing, so we can assume he understood geometry and angles. The family farm is still the family farm, so we can assume he understood finance.

So I started out by arguing that kids today know more math than ever, and then I tell you that my grandfather understood math better than many of our students do now? My point is that we have moved away from understanding math and more toward just following a formula and getting an answer. If we want to move beyond where we are, we will have to help kids know and be able to do both.

That is the conclusion my friend and I reached anyway. Maybe you will reach a different one, but please be open-minded enough to think that the way we have always done it may not be the best way. Oh, and as far as making change? My grandfather wasn't very good at that, because he always just rounded up to the nearest dollar on our wages when we worked for him. That's the kind of guy he was.

The teaching and learning of math is a pet peeve of mine. My biggest complaint about math is the common belief that because the kid who makes $7.50 an hour at the local Gas and Grub got my change wrong, schools have failed at math instruction. If you haven't said it yourself, someone has said it to you.

Let's think about the state of what kids in Kansas know and are able to do compared to the good old days when we could all make change. Folks my age can remember the "advanced kids" were tracked into algebra class in the freshman year. Thirty years later, my kids took algebra in the 7th grade. In my large high school, a handful of kids graduated with four years of math. Now many students go to college with calculus credit already on their transcript. Kids today take and learn more math than they did in the good old days.

The bigger issue is that it is still not enough. Our kids need to have a deeper understanding of math and how to use it. We have to expand our definition of math, and at the same time go deeper with our understanding of math. My friend's concern was that kids were not spending enough time on memorizing math facts, and too much time on learning new and different ways to solve math problems. That concern lays bare education's fundamental math problem.

In the good old days, we memorized the multiplication tables. We worked on speed addition and subtraction. A good memory made you a good math student. As an educator, I have heard countless parents talk about the fact that their kids were straight A math students until Algebra, and suddenly they were getting D's and F’s. Once a student gets to algebra, statistics, physics, chemistry, geometry, finance, economics, etc., memorization of the multiplication tables isn't the advantage that it once was. A deep understanding of math skills is far more valuable.

I often challenge people by asking what 1/3 divided by 7/16 is. Most everyone knows how to find the answer is to invert and multiply. Duh. Then I ask them to explain what 1/3 divided by 7/16 means. Most stare at me blankly. We memorize algorithms and formulas, but we don't understand what the numbers mean. When letters start to take the place of numbers, memorized applications have less power.

So how do we teach deeper math understanding? That is a question for experts in math instruction, but we don't do it by teaching math the way we always did it. My friend sent a problem that involved asking the student to solve the following: 86-12=? An explanation of one way to find the answer was to round to the nearest five, subtract, then add what your rounded back in. (I shortened it, but you get the gist.) The idea is that fives are easier to visualize (tens even more so).

What struck me about this "new math" is that my grandfather (not the same one who counted pinheads on the bus) taught me this method when I was a kid. He could do lengthy arithmetic problems in his head by using strategies like rounding and finger math. He also had a strange way of working long division that I have seen in some YouTube videos being described as an "ingenious new method."

My grandfather fought in WWI, and received his terminal degree (8th grade diploma) over a century ago. He didn't know calculus or statistics but he understood the concepts of math. The barn he built 100 years ago is still standing, so we can assume he understood geometry and angles. The family farm is still the family farm, so we can assume he understood finance.

So I started out by arguing that kids today know more math than ever, and then I tell you that my grandfather understood math better than many of our students do now? My point is that we have moved away from understanding math and more toward just following a formula and getting an answer. If we want to move beyond where we are, we will have to help kids know and be able to do both.

That is the conclusion my friend and I reached anyway. Maybe you will reach a different one, but please be open-minded enough to think that the way we have always done it may not be the best way. Oh, and as far as making change? My grandfather wasn't very good at that, because he always just rounded up to the nearest dollar on our wages when we worked for him. That's the kind of guy he was.

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