Category Archives: Mathtwitterblogosphere

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.


#myFavFriday – The ICTM State Math Contest and HS Memories

As the year drags on, I’m sure I’ll exhaust you with my thoughts on the ICTM Math Contest, but for now, let’s just get introduced.

Me in 2003, holding the State Championship trophy

The Illinois Council of Teachers of Mathematics runs one of the largest high school student math contests in the entire country (I’ve heard it’s the largest, but I don’t have proof).

Here’s the contest in a nutshell.  Before the State Contest, teams must first compete in and win a Regional Contest.  All four grade levels compete in the following competitions:

  • Written Tests (20 questions, 50 minutes, Freshmen take Algebra 1, Sophomores – Geometry, Juniors – Algebra 2, Seniors – Precalc)
  • 8 Person Teams (20 questions, 20 minutes, no calculators, both a Frosh-Soph and a JR-SR team)
  • 2 Person Teams (Head to head, 10 questions, displayed 1 at a time, first to raise answer receives most points)
  • Calculator (5 students, 20 questions, 20 minutes, any calculator is allowed)
  • Oral Competition (1 student and 1 assistant study upper level topic in math in weeks preceding event, makes 7 minute presentation on 3-5 questions after given 10 minutes to prepare answers)
  • Relay (State contest only, 4 students in seated one behind the other, first student’s answer is passed back and used as part of 2nd student’s problem, and so on, first group done wins most points)

That was the incredibly short version of the competitions.  Trust me, I could write much, much more on the details, strategies, scoring,  rules, etc, but I’ll spare you this time.

I competed as a student from 2000-2003, and I’ve been a coach since 2009.

This is the part where I brag a little.  When I was a student, my team never lost. Tiny Herrin, IL, just 45 minutes from Kentucky went up again the likes of University of Chicago Lab School and Walter Payton Academy among others to dominate math problems year after year.  You see, my friends (team) and I were a rare bunch.  Among the six of us who made of the “scoring team,” we’re now 2 math teachers, a computer programmer at MSFT, an engineer at GM, an accountant at an automobile parts manufacturer, and a medical doctor.

We won the Algebra 1 competition as Freshmen, Geometry as sophomores, Algebra 2 as Juniors, and Precalc as seniors.  To cap off that senior year, we won the big team trophy for the only time in school history.  Our team picture still hangs on the wall of the commons area at the school I once attended and now am employed.  It’s a pretty cool feeling.

If you’re still with me here on this bragging session, I’ve saved the best for last.

The Contest has its own song.  Let that sink it.  There’s a song.

And guess what.  As my first year coaching, I brought along my video camera and recorded it.  And uploaded it to Youtube.  And you get to see it.

My First #Made4Math Monday Post (Even Though It’s Sunday) – WHITEBOARDS

Looking back, I believe this is the first non-digital thing I’ve ever *made* for my classroom.

As you read this, please note that the whole idea of  “whiteboarding” was new to me until I really started ready math blogs heavily this summer.  Almost all credit for this post goes Bowman Dickson, and some other math teachers I stalk on Twitter.  You (probably don’t) know who you are.

So the idea is to create some cheap, generously sized whiteboards for students to use in the classroom for practice problems, games, and other learning activities.  The idea is for these not to be individual student whiteboards, but instead a large enough blank space for 2 to 3 students to work at once.

Here’s my take.  I accidentally passed up my left turn to go to Target today and had to pull a turnaround in the parking lot at Home Depot.  “Wait, I want to go in here,” I told me wife.  “They might have some showerboard.”  As confused as she was, if Ash has her B&N nook in hand, she’s agreeable to about anything.

Home Depot had just what I needed.  They call it Panel Board.  Sheets measure 8’x4′, and they were just under $12.  I asked the first worker I saw if he could cut the board into 6 rectangle for me.  I could see his brain starting to jam up.  I reiterated, “6 rectangle, they should be 24″x32″.”  He starts doing some nervous figuring, but I calmed his nerves when I told him I was a calculus teacher.  At that point, he was happy to help.  He even remarked on how he’s heard a lot of teachers are having to buy all their desk/room supplies and how it’s a raw deal. Yes, yes, it is.  I bought two boards, and had them cut in about 5 minutes time.  Total cost, $25 after tax.

Now, once the boards are cut, the edges are a bit rough, and they are susceptible to getting nicks and gashes in the whiteboard surface.

So I need something to smooth the edges.  What fixes everything? Duct tape.  I’ve seen all the fancy print Duck Tape brand duct tape recently (my wife’s cousin even asked for it for her birthday), so I was really hoping to find some tiger stripe print at Target (school mascot).  Failed in that search (but don’t worry, they had pink zebra, because, you know, all the pink zebras out there are so popular.  Geesh.).  I did however, find some neon orange, and I already had black at home.  That will do, I thought.

So I came home and started wrapping up the boards.  Here’s what they look like so far.

I ran out of black tape after I wrapped 7 of them, so five more to go.  But overall, I’m very happy with the effect.  I think they’re going to work great, and I’m excited to get them in my classroom and see what they kids think.

The project, of course, still needs some thought.  First, I don’t have markers or erasers.  Druin says cutting up some felt from Hobby Lobby is the way to go.  I might try that, but I’m not sure how soon I’ll make it to the store.  As far as markers, I’ve been seeing 4 packs of Expo markers on sale for $2 all over the place lately, so I guess I could invest in some of those.  Might shop around a little.

I’m also going to need to read this post from Bowman again.  I find out there’s a whole “whiteboarding” culture out there on the mathblogosphere, and I’m just a newbie to the game.  I need some ideas on student activities, games, and other math-y stuff to do with the boards.

But all in all, that was my big afternoon project.  Hope you like it.  I’ll answer any questions you have in the comments.  Need to go buy some more black duct tape now.

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.

New Blogger Initiative: Week One

Here goes.

Prompt 4:  Respond

This prompt really didn’t speak to me when I initially read the email from Sam and Julie.  That was Wednesday, the first day kids reported to school for the year.  All I could really do that day was introduce myself, hand out books, read through the agenda and syllabus, and maybe ask a few kids how their they spent their summers.  The usual.

Today was different.  Today I taught.  And the picture of the graphing calculators rises to the top.

We have a seven period day at my high school; I get one planning period and six classes to teach (I’ll save this rant for another day, but I want to mention I have five preps this year.  I only ever teach one class more than once.).  Bookending my day are AP Calculus AB in the morning and AP Calculus BC in the afternoon.  This year, to begin each of these classes, I’m going off-book for the Precalculus review.  After teaching Calc for 2 years, I feel like I have a pretty good handle on what topics my students should know well before we hit Limits.

In my opinion (subject to change), the most important concept is recognizing functions in their algebraic form and visualizing the graph mentally.  I’ve noticed that the students who work problems with the most speed and precision are the ones who best understand the analytic and graphical connection of a function.

So in Calc AB, I start talking about Parent Functions.  y=x, y=x^2, yada, yada, yada.  What does the graph of y=x look like class?  Crickets.  And I know I’ve got a wall to climb.

Similar story in Calc BC.  I give a worksheet with the graph of a piecewise function, f.  I ask them to graph y=|f(x)|, y=f(-x), y=(x-1), yada, yada, yada.  Better results than AB, but nothing to write home about.

New goal:  If I teach these kids anything this year, it better be for them to recognize 10 or 12 parent functions and their corresponding graphs.  And they’re going to know how to translate them all over the place.  And this stuff is going to be automatic.  If they can do this, I hold, the Calculus will have more meaning, make more sense, be easier.  And what high school student doesn’t want his homework to be easier?

On this Friday night, I’m concerned.  Functions and graphs and translations are things they should know.  Right?  My Precalc review should last days, not weeks.  *blurg*

So where does the graphing calculator come into play?  THEY ALL HAVE THEM.  Our math department hands out TI-8x’s like Fire Sauce packets in the drive-thru at Taco Bell to students who don’t have one of their own.  Even more, these students have had them for 2-3 years.

How do I respond to the picture?  I want to stand on my desk and loudly ask my Calculus students what they’ve been doing with those $120 paperweights they carry around.  They do more than add and subtract and play Tetris, I want to sarcastically exclaim.  But I don’t.  And I won’t.  I don’t know the circumstances of their knowledge gaps, so I won’t hold them guilty.  What I will do is make sure I incorporate the “Y=” button on the graphing calculator into every Calculus lesson I teach until I can see some light at the end of the tunnel.

Hold me to that last promise there, blog readers.  My students will benefit.  And so will I.