Mr. Howen

I was cleaning out my inbox and saw that I was still getting Tumblr e-mails after not posting for like, a decade. Decided to stop in and see what has changed. Considering I didn’t post anything except things that might make me look more hirable, I can’t tell much of a difference. 

Updated my info anyway; it’s weird to see how much different my life was 11 years ago. No kids, no job (yet), just pure optimism and a general lack of experience not being a student. 

If you’re wondering what happened in those 11 years, let me catch you up to speed:

Got that job at CLS. 

Left that job at CLS to move back to NorCal with the birth of my eldest, got a job at my old high school.

Fired from that job (mid-year!) because the school’s money management was poor. 

Got a new job at the local high school, had kids #2 and #3, ‘not renewed’ after working there three and a half years. Class management is hard.

Got a job at the local community college, not teaching for the first time since ... well, my last post. But it’s steady and I’ve been here over four years.

I have been hired by Christ Lutheran School in West Covina to teach pre-algebra, algebra 1, geometry, and Bible.

From this point on, this website will be devoted to reporting on homework assignments, class activities and announcements, and anything else that is relevant to my classes. 

I look forward to seeing how this will work for me throughout the year.

200% of Nothing, the book I mentioned earlier, turned out to be just ok. It started out promising, but towards the middle the author got really political, and I don't do political. He sounded like an uncle at a family get-together who rambles on and on about how the government and the media are ruining society until everyone else excuses themselves to help with the dishes. Granted, he's not necessarily wrong about the abuses that go on in those arenas, but it's not always what you say but how you say it. That said, I would probably recommend certain sections of the book for reading.

The next book I read (skimmed, rather) was Taxicab Geometry by Eugene Krause. This is much less a book to read than a guide to the multitude of exercises in it. The premise of Taxicab Geometry is simple: In standard Euclidean geometry, a distance between two points is always a straight line. However, in real life, taxis will not usually drive in a straight line to get from point A to point B. The book deals extensively with the coordinate plane and how not only distance is altered, but also radii of circles (as well as the circles themselves) and ellipses. I don't think I would use this book in my general instruction, but it might be a good activity for a high-performing student looking to have fun with puzzles. 

Get real / Be rational (the same as one of my original posts here)

I keep it real

A fine line (one of my favorites)

I think I've finally figured out the 'Monty Hall Problem'. It was mentioned in the book I introduced in my last post, "200% of Nothing". When I first heard it, I was skeptical. Then, I was absolutely against it. This post was actually intended to make it look ridiculous and point out the obvious. However, when I searched for a picture to put up with my lambasting of the problem, I found one that I was able to wrap my mind around. 

And now I'm a believer.

If you're unfamiliar with the problem, here's a quick explanation. Behind three doors (of a game show, maybe) are a goat, another goat, and a car. You pick door 1, 2 or 3, which you believe hides the car. One door is opened, revealing a goat. Now, there are two doors: one with a goat, one with a car. Most people (like myself, until just now) believe the odds to be 50-50. However, mathematically, you are more likely to win if you switch doors.

Why? It doesn't make sense. One door hides a goat, the other a car. Switching should be irrelevant. I once drew this grid:

Situation 1. You picked the car: Switch = loss. Stay = win.

Situation 2. You picked the goat: Switch = win. Stay = loss.

Two wins, two losses. 2 wins out of 4 possible moves is 2/4 = 1/2 = 50%.

However- here's the rub.

My logic would work if Situations 1 and 2 were equally likely. But, as you can clearly see from the image, since there are two goats and one car, you are more likely to have initially picked a goat. Therefore, Situation 2 is twice as likely to occur than Situation 1 (2/3 = 2 x 1/3). Therefore, it would be best to switch, as Situation 2 yields a winning scenario when the doors are switched.

If the experiment were tweaked so that there were 4 doors (2 cars, 2 goats), and 2 doors were opened (1 car, 1 goat), then the logic would dictate that switching is irrelevant, because the initial odds of picking a goat would be 50-50, not 2-1. Each situation would be on equal footing, unlike the 3-door scenario. 

What's so very interesting and applicable about this is that I had this scenario presented to me at least four times before, in varying media (class lecture, animated video, written form). It's safe to say that each time the problem was presented, it was not presented incorrectly. Why, then, did it take me so many times to finally get it? Is it the quantity of demonstrations that did it? Possible, but I reread that portion of the book several times, and actually became more indignant at the 'foolishness' of the author. I believe it was the method of presentation that did the trick. I am a very visual person, so pictures and videos are usually the best way for me to learn something. The video I watched years ago probably didn't work because of how it was verbally explained (which may have been perfectly sensical to its creator). With the still image, I was able to stare at it for a few minutes and come to my own realization. You can't give someone learning. It must be internalized or 'wrapped around by the mind'. Once I could explain it in my own terms, I was able to learn. 

I just started reading this book, which I found in my alma mater's library. At its heart, it seeks to help 'innumerate' people (a term coined by a fellow named Douglas Hofstadter, meaning "unwilling or unable to understand basic mathematical ideas as they apply to life") to not get suckered by organizations who use math and numbers to twist information (intentionally or not) for their own purposes. It's an engaging read so far, and gives a healthy dose of common sense. This is from the preface:

What if you are already a mathematician and don't know it? Near the end of this book you will learn that we all use logic (of a largely unconscious kind) to take us through everything from business meetings to family dinners. If only we could be good conscious mathematicians!

At the conscious level, too many of us are still innumerate. We cannot deal with fractions, large numbers, percentages, and other relatively simple mathematical concepts. Meanwhile, we are beset more than ever by the abuses that stem from this innumeracy. And those who abuse mathematics also abuse us. We become prey to commercial chicanery, financial foolery, medical quackery, and numerical terrorism from pressure groups, all because we are unable (or unwilling) to think clearly for a few moments. In almost every case, the mathematics involved is something we learned, or should have learned, in elementary school or high school.

Just finished Stand and Deliver. Inspiring. It's success stories like these that will keep me teaching year after year. I'm not expecting to bring a 'barrio school' to a turnaround like he did, but every year, there is usually at least one student who will leave the classroom in a much better state than when he/she began. 

4 units over 6 weeks put the final nail in the coffin that is my career as a student. I don't think it has quite sunk in yet; ever since I was a little kid growing up in the early 90's, that was my occupation. I measured the year from September to June, with summer being the gap of weightlessness. I suppose that part will not die out, considering my profession of choice. 

Nearly 20 years later, I'm no longer a student. I finally get the chance to 1) perfect my craft and 2) get paid for it. As a student, you take a class once (hopefully) and then you're done. As a professional, each year (month, week, day, period) is a new chance to improve myself. As an analytical person, I'm always looking for ways to improve. It will also be nice to get paid for my work. Right now, I live off of my wife's salary, which is enough, but it will be nice to help pay off loans and save up for a family and a house. 

Math does not have to bear the weight of dullness. I believe one of the reasons that today's students perform poorly in math is because they do not and cannot find it interesting, therefore their natural curiosity cannot propel them to succeed. If a student can't stop reading Dickens, he or she will not have trouble in English. How many students do math problems for fun? How many solve an equation just so they can know something new? 

I have asked, I have been asked, and I will be asked again, "What is the point? When am I ever going to use this in real life?"

Bad answers:

"Oh, there will be a time when you will use it, just you wait..." That's just not true.

"Well, it's in the standards, so we have to teach it and you have to learn it." Should we really teach students to blindly accept what they're fed? That's the direct opposite of critical thinking.

Good answers:

"Some people, like the ones who design cars, airplanes, and robots, use math all the time." If you've ever watched a show like Mythbusters and you thought, 'Man, that would be a cool job,' then keep your math skills up and always stay curious.

It's getting to the end of my career as a student teacher, and coinciding with the summer break is job hunting season. It's exciting and terrifying at the same time. It's a competitive market and there are plenty of universities in the area that are sending out graduates with resumés who may want the same job that I do. Fortunately, I will hold a sought-after math credential, I have additional areas of expertise that others may not have (possible film credential, football coaching experience, ASB experience), and I am good at what I do. And I'm only going to get better.

This site was inspired by a recent course I took at UCI that dealt with technology in the classroom. For right now, it serves as a reference for possible employers to get to know a little more about who I am, what I am like, and what I can do. In the (near) future, when I have my very own students, I plan to convert the site from a marketing tool to a classroom tool, where students can access class information, extra homework help/tips, math videos or podcasts, and anything else that might be helpful outside of the classroom.

I hope you find this website intriguing and informative.