# Just Some Cell Phone Photos From Denver

So I had the amazing opportunity to spend the weekend in Denver, visiting a best friend and seeing the Denver Broncos football game.  Yeah.  Week 1 of Peyton Manning’s new team.  Rather than listen to my boring recap, I’ll just share some cell phone photos I took along the way.

The view out of the terminal at Lambert Airport in St. Louis

The first dinner I had in Denver – Chicken & Waffles. Not as good as it sounds. Did I mention the restaurant was called Euclid?

My walking view of Mile High Stadium

The view from my seat, 2.5 hours before kickoff.

Starting lineup. The Broncos ran out of … the bronco. You cannot believe how loud this place was when Peyton was introduced.

Part of the pregame show.  There was seriously a lot of balloons.

This was very cool. They had members from about 7 different branches of military/police.

I took this right before Knowshon Moreno rushed into the end zone for the first touchdown of the season.  After this, my phone died. No more pictures of the game. 😦

I was lucky enough to get a window seat on the way home. This was my view.

Making the turn back into Lambert. I was almost looking straight down at the ground. Was my phone supposed to be off during this flight?

So I know this wasn’t exactly a math related post, but you’ll have to deal.  The hotel we stayed at had a restaurant called Pi Kitchen + Bar.  Its menu was a circle, and happy hour was from 3:14p to 6:28p.  We had dinner at a dive bar called Euclid.  Their drinks were arranged in complexity, Algebra’s were the lightest, Calculus’ were the strongest.  I had a Trigonometry.

Math is everywhere.

# The Educational Narrative

I was tweeting and grading last night.  That happens a lot, and I still haven’t decided if  it’s a good or bad idea.  Sometimes, put words behind my quick thoughts is a good way to remember them for the next day when I’m debriefing a test.  But at the same time, I’m also worried that I might “overshare,” and make public something that should stay private.  I guess this is a discussion for another time.  Anyway, an unintended result of last night’s session was my unpremeditated use of the phrase “educational narrative.”

I’ve thought about the question before, but I think this was the first time I’ve successfully worded it in a way that others might also be able to submit their thoughts.

My answer?  Yes, I believe that the overall picture of a student’s (or group of students) grades throughout the semester tell a story.  I believe that story has characters, rising action, climax(es), falling action, and resolutions.  Think of it like this.  Time and assignment/test names are on the x-axis, and percentages are on the y-axis.  Here’s a simplified view of what I’m talking about.

So the graph looks like a scatter plot.  I really think a teacher/parent/administrator/student could learn a lot from this.  Examine the scores.  Examine how they relate to the x-axis.  Here’s what I thought.

So in our little example, Johnny starts as an average student, scores in the 70’s and 80’s.  But he takes a leap to a score in the high 90’s  at the beginning of November.  The first question I’m asking is, “Why?”.  Could it be because he prefers the chill in the air that comes in the late Fall?  Doubt it.  Could it be a topic that Johnny has some existing knowledge of, and thus, can perform better on assessments?  Possibly.  Or could it be that Johnny isn’t the most skilled test taker, but he’s awesome on class projects?  Bingo.  And we have a climax.

You get the idea.  The point I was trying to make in my tweet was that I wouldn’t go back in my gradebook and inflate test scores because of corrections.  I think that alters the story.  Makes it tell a lie.  I’ll keep the original test score, and create a new assignment for corrections.  The more accurately I can read and understand the educational narrative, the better I can impact it, predict it, and influence it.

I really do believe I’m onto something here.  As a teacher, I should care just as much about the last test score as I should the next.

What do you think?

# HS Math & The “Dump” Theory

Several years ago, a good friend of mine, who happens to be a junior college math professor (unrelated), described to me his “dump” theory.  He said his brain had reached maximum capacity, and in order learn a new nugget of information, he had to “dump” or forget something else in order to make room for it.  Of course, he was completely kidding.  Nevertheless, I’ve seen evidence of his dump theory every year I’ve been teaching.

Many (most?) of my students seem to believe that math classes are entirely self-contained.  That is to say, Algebra 2 is the equivalent of Home Economics.  There is no prerequisite — anyone is eligible to sit the course.  And there is no class which comes immediately after it — Home Ec 2?

They can’t seem to grasp the idea that they might need to be able to factor  a polynomial to complete a Calculus problem or divide fractions to complete a Trigonometry problem.  They must, must, believe that whatever is necessary to achieve maximum learning this year will be taught this year.

I graded the first Calculus tests of the year earlier tonight.  I had to stop counting how many times my students factored $x^2+25$.  I never even tried to count how many BC students tried to cancel addends and minuends in a rational expression.  My favorite is when they cancel the $x$ from $\cos{x}$ with another $x$ from the denominator.  What?!?

I know I’m probably preaching to the choir, and I apologize.  I’m just tired of spending days reteaching fractions, properties of exponents/radicals, factoring, solving equations, the quadratic formula, the unit circle, function transformations, and a dozen other things in every single course I teach, no matter the level.

Who is to blame for the problem?  Well, the students, duh!  Right?  I don’t know… I lean toward no.  I think we, the teachers, are much to blame.  How often do I ask my students to practice in May something they learned in October?  If it doesn’t directly apply to the problem of the day, I can honestly say, I don’t.  Not very often, at least.  And I’ll guess I’m not alone in that boat.  It’s not that practice makes perfect.  It’s that practice negates the dump theory.  If my students practice the old stuff often enough, they won’t have time to forget it all.

So what do I do?  I remind my classes at the beginning of the year, at the end of each semester, quarter, unit, chapter, section, and day that this class is not Home Economics.  You actually have to carry with you the skills you learn from day to day or you will fail.  Fail.  But words don’t always work.

This year, I’ve begun something else.  I stopped making my tests self-contained.  Every quiz and test I’ve given this year (not many, just yet) has incorporated old material.  Without a solid basis of material for this year so far, I’m testing on what the students should know from their previous courses.  The first quiz in Calculus was on function transformations.  The first quiz in Trigonometry was on operations with fractions.

In my classes that are primarily Juniors and Seniors, I’m starting every day with 3 warm-up problems from an ACT practice test.  And sometimes I’ll leave them on the board for the Freshmen to try.  This is a great way to get a variety of topics incorporated on a daily basis.

If I want my students to understand that they can’t “dump” what they learned in math last year, then the standards I set for myself and for them need to be raised.