Category Archives: Reflection

This Week in My Math Life

I joined ICTM and NCTM this week.  I’m 4.5 years into my math teaching career and I’ve never actually been a member of any professional organization relating to my content area until three days ago.  I feel good about that.  Maybe all it will be is something to add to my LinkedIn profile, but I hope not.  There is some “member’s only” content associated with both org’s, and I’m aspiring to use a bit of it.

My joining ICTM was sparked by Thursday’s outing to the regional conference at Southern Illinois University Carbondale.  I should have made a major post on that event, but time elapsed, I didn’t write, and now I don’t think I’d do it appropriate justice.  In short, I went to three breakout sessions and listened to a keynote speaker.  I honestly can’t remember who the keynote speaker was, but she didn’t really move the needle anyway, so I won’t spend the time looking it up.  What I did take away was getting to meet and hear from (in Sessions 1 and 3) a middle school math teacher from Charleston, IL.  I’ll link to his stuff and share his name in a later post, but he got me energized.  Ask my wife, that’s hard to do.  He doesn’t use homework scores as part of his summative grades, and he’s into curriculum planning.  So that had me listening.

Lastly, my high school hosted the Illinois Council for Teacher’s of Mathematics Regional Math Contest yesterday.  Happy to say we won *every* event and will be headed to the state contest on May 3.  Competition was weak this year due to our main competitor moving to a different regional location, but a win is a win, and I was proud of our kids.

More AP Calc Time?

I’m not sure what I’m doing differently–I’m going to think on this–but I’m finding myself with more time to tackle homework problems in depth and more time to spend teaching this year in my two AP Calculus classes.  It’s a wonderful development for which I must find the cause.  I need it to continue.  4th year teaching this subject, and I just might finally have made an improvement.  Slow, but steady, I suppose.

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.

I Never Learned THAT In EDUC 311

I also thought about titling this post “You Jam It, You Fix It” or “You Don’t Have to Call Service Repair For That” or “Your 60 Copies of This 12 Page, Duplexed, Hole-Punched Corner-Stapled Packet Just Had to Be Done at 7:56am?” or “First One In Makes The Coffee.”

Let me tell you how my day began. I woke up 45 minutes late because I forgot I had reset my alarm to my wife’s wake-up time when I left the house yesterday. Somehow I only made it out of my house 20 minutes late, and I set off on my bike for school. [Side note: I ride my uncle’s old brown roadster with a faded nylon saddlebag my dad put on it while he owned the bike. I don’t feel particularly avuncular or fatherly on my 8 block trek to school — just slightly embarrassed.]

No time to slowly settle in at the desk this morning as I prefer, I immediately start putting together folders of the handouts I’ll need for my 5 (!) preps I’m teaching this year. Uh-oh. I need copies for first period. Open the document, make a small change to page 1 of 3, CTRL-P, 30 copies, single-sided, 3-hole punch, diagonal staple upper-left corner, ENTER. Now, you should know my entire floor of hm… maybe 25 teachers share two networked copiers in a copy room located in the middle of our horseshoe-inspired 2nd floor.

This is where my story starts to heat up.

Usually by the time I make it to the copy room, my print job has begun and is well on its way to being finished. I might hesitate to send this medium-sized job to the copy machine before school when the copy room is crammed, but I’ve got time. When I dropped off my lunch at the refrigerator minutes earlier (also located in the copy room), I was the only one there. As I unlock the door to enter, before I ever switch the lights on, I can sense a disturbance in the force. My copy machine isn’t running. Uh-oh again.

Now, I know teachers who would be humanly blue-screened at this point. I’ve listened to so many similar stories where my colleagues walked back to their classrooms, printed the job one more time, walked back to the copy room, again saw nothing, and then gave up (only later to have 2 sets of the same worksheet waiting for them 2 days later). It’s like seeing the round peg won’t fit in the square hole, so trying two round pegs might do the trick.

I’m not that guy. I’m a fixer. Read the display screen. Copier needs staples. Ok, bend down, open the front left door, press lever K, pull out fancy plastic staple holder. Hm… It has staples. Shake it. Press on some of the corners. Blow in it like you did Tecmo Super Bowl. Reinsert staple cartridge, replace lever K, shut door, check display screen. Printing! A victory!

Wait… where’s the first document? Why aren’t my packets printing? Read the display screen. Paper jam in Area B. ORLY? My vainglorious attempt at repair had been struck down in seconds.

In my experience, about 85% of my colleagues at this point would go find the keyboarding teacher. Why? I really haven’t deciphered that one yet. They seem to look at her like the copy machine genie. I think it’s because she has the phone number for tech support in her speed dial.

I’m not that guy. Bend down, open the front right door, release lever B, attempt to visually locate paper jam. Fail. Open paper drawer 1, remove some paper, peer behind drawer to the entry of Area B. Gotcha! Jam located! Reach arm behind the — arm doesn’t fit. Hm… Spin the wheel to pull paper from Area A to Area B. Paper is in a sideways orientation not directly under a rubber paper grabber on the spin-wheel thing. Fine. Push paper drawer 1 in about 2/5 of the way. Arm fits! Clasp corner of shredded paper between thumb and forefinger. Pull slowly, making sure not the rip the paper further, causing complete meltdown and destruction of copier/day/life. Success! Replace all open doors, drawers, levers, and other mechanisms. Look, listen. Warmth! Paper! Documents! Win!

When was I supposed to learn this stuff? Fundamental copy room lessons for all new teachers.

  • It might not actually be broken. Give fixing it a try.
  • Do not leave the copy machine with a jam. This is paramount. Do something about it. Fix it, find someone, call someone, do something. No man left behind!
  • Don’t print a 10 minute job when there are 6 other people in line.
  • Don’t print a 10 minute job at 8:02am.
  • Print the large jobs after school or during your planning period.
  • If you pick up someone else’s copies by mistake, return them to the copy room.
  • If you notice the coffee in the coffee machine is cold and dry, make some coffee. Even if you don’t drink it. You’ll be loved. (Editor’s note: I don’t do this)
  • Don’t leave your molded, smelly, nastiness in the fridge. All perishable food has a one-day limit. Bring it, eat it, repeat. You have a fridge at home for a reason.

There needs to be a course with this stuff. It needs to be taught by office managers with guest lectures by tenured K-12 teachers. You should get field experience in fixing a copier, what all the buttons on a copier do, and making coffee. You should have to write Hemingway-esque papers on these subjects. It needs to happen.

Now, I’m not without error. This very same day, I was printing 100 grid sheets for my Algebra 1 students by sending the document from my classroom computer, when I accidentally selected the staple option. That was a disaster-in-waiting. I rushed to the copy room, the machine was as hot as my grandma’s fried okra, but a few button presses later, and I had the job canceled. Whew! But, see, I knew how to do this. I knew. From experience.

New teachers should walk in with this knowledge. They just should.