## Sunday, November 18, 2012

### What being a dance teacher taught me

Before I was a math teacher, while I was still in undergrad, I was a dance teacher.  It seems silly writing this now, because at the time I was going to school to become a math teacher, but I didn't take the job to learn a thing about teaching.  I took the job because I wanted to keep dancing.  That's all.  It was very selfish.

Looking back now, I realize that I actually did learn a thing or two about teaching that can carried to the math classroom.

A lovely demonstration doesn't do the students squat if they don't get to practice.  I would have gotten fired from my job if I showed up every day and put on a mini-production for my students, but never taught them how to do any of the moves I just demonstrated.  I know that probably seems like a "duh" to most middle school and high school teachers, but that's honestly how I spent my first couple years as a teacher (it was at the college level, but still).  I would come to class, having prepared every word I was going to say, and deliver what I felt was a pretty darn good lecture.  And, then...I would cross my fingers and hope my students did the homework.  Sorry to all my students those years.  Truly.

A good teacher gets everyone involved.  All the time.  A ballet student is not going to learn a thing if she says, "I think I'll just sit in the back and take notes on this one."  Ok, I didn't have any dance students want to take notes, but I did have students who were very reluctant to try new jumps or new turns, or new shoes for crying out loud.  I learned that in those cases, it's important to break down every single move until you can figure out where the block in the body is.  It was also important to point out what the student was doing right.

Mirrors.  Mirrors are essential to a good dance lesson.  Why?  Because dancers have to learn what their bodies look like when they move in different ways.  Eventually, a good dancer who has practiced in front of mirrors long enough can just feel what the body looks like.  She knows when she royally screwed up a pirouette and she knows when she nailed a grande jete.  This is what we try to foster in our math students, too.  We want students who can feel when something isn't going right.  When their answer isn't reasonable, when their proof is just getting messier and messier, when the calculator's window needs to be adjusted.  These things don't happen, though, unless students get mirrors with which to evaluate their work on regular basis.  Metacognition and all that jazz.

I tried to find some kind of picture of me as a dancer as proof that this is a real thing.  But, I guess my mom must have most of that stuff.  The only thing I could find on my laptop was this video.  If I remember correctly, this was my last semester of college.  I was practicing at the studio I taught at for a dance I was going to perform at my school's Chapel later that week.

## Saturday, November 17, 2012

### A Day in the Life: 11.14.12

6:30  Phone alarm goes off and cats know it's time for breakfast.  Text hubby Good Morning and that I can't wait for him to get back from a business trip tonight.

6:31  By now cats are furious.  Feed them.  Shower.  Wake up.  Dry hair.  Get ready for the day.  Check ingredients for a cake I know I need to bake later.

7:40  Drive to school.

7:48  Arrive at school and wonder why the faculty lot is full already (7:50 is our official start time, but still...). Oh, yeah, Faculty Meeting today.  That's why I opt for the afternoon meeting.  Walk up to the third floor with one of the science teachers.  I love my floor of all math and science teachers.  I arrive at my door, and a student is waiting for me, ready to ask questions about a Pre-Calc quiz.  I tell him we're going to take one more day to review.  I start arranging my desks in five groups.  Recruit aforementioned student to help.  Turn  on SMARTBoard, TV, and computer.  Check emails.  Log onto school attendance/grading system.  Quickly enter the 100 or so scores from yesterday's Algebra II test that I graded util 10:30 last night.  Co-worker comes in and greets me with Starbucks.  This is going to be a good day.

8:15  First bell rings.  Students enter, surprised by the arrangement of desks.  "Are we not having a quiz today?  Is it going to be a group quiz?!"  I give them instructions to take a seat anywhere for now but not unpack.

8:20  Second bell rings.  I explain that we're taking one more day to review the material on the upcoming quiz, and why what we're studying now is valuable and I want them to know it well.  I also explain that the students will lead the review today.  I rearrange them a bit, making sure there's at least one math superstar in each of the five groups.  I assign each group a team leader (the superstar).  Each group has a problem on every desk (Group 1 has a different problem from Group 2, etc).  I explain how today's review will go:  each group will work on the exercise on their desks.  If they have any questions, they can ask their team leader.  After seven minutes, the team leader will choose a new leader.  That leader will stay behind to explain the problem to the next group. Every one else rotates on to the next set of desks.  We'll repeat this five more times.  Because this is a small class (24 students) everyone will get a chance to lead at least once.

8:40  The students have rotated a couple times now and have mastered the format of the review.  I learned this technique from a colleague and make a mental note to thank her.  I hear great discussions going on.  Students teaching students!  A teacher's dream.  It's unnatural for me to just stand by my desk and not help, but, today, they really don't need me.

9:10  We finish the last round and I ask the students to rearrange my desks to their normal positions.  I ask for feedback on the review.  Students say it was very helpful and that they're much more optimistic about the quiz now.  We'll see how it goes tomorrow.  I remind students to check the homework folder for any graded homework they need to pick up.

9:15  Bell rings and I wish my students a wonderful morning.  I open my Notebook slides for today's Algebra II lesson.  As students walk in, I hand back tests, congratulating most of them, as this class did much better on this assessment than on the last one (both were on quadratics).

9:20  Bell rings again and I welcome the students.  There were instructions on the board to grab a worksheet on the way in.  Most have done so.  I let them know that if they are not happy with their test grade, they are required to come see me three times before Thanksgiving (with their test on them), and then I will give them access to a make-up version of the test.  The intercom announces the voice of a principal, asking teachers to turn their televisions to Channel 78 for today's school news.  My TV is already on this channel, so I just turn up the volume.  As students watch, I take attendance.

9:25  Today's lesson is a bit of review material that I want to make sure the kids are solid on before we enter the next chapter on polynomial functions.  I start with the extra credit writing assignment I gave them on yesterday's test.  The assignment was to explain what the calculator is graphing when you type in y=x^2+7x+10 and to give at least one point they knew was on the graph for certain and to explain their logic.  No one gave a good answer to this.  No, not one of out my eight dozen Algebra II students.  So, we'll try again today.  I ask someone--anyone!--to give me a point s/he KNOWS is on this graph, without looking at the calculator. *Cue crickets chirping*  Eventually we get to (0,10).  I ask for another point.  Then another.  Could we do another?  On the back of the worksheet, I ask them to find three more points they know will be on this graph.  We talk some more.  Then I ask them to answer the original question again.  What does the graph of y=x^2+7x+10 mean??  I call on some students to read their answers.  I hear good phrases like "infinitely many ordered pairs" and I'm satiated for the time being.  But we are not done with this story.

9:40  Have students turn to the front of the worksheet again.  Explain the reasoning for today's lesson (review so we get to the really good stuff).  My go-to strategy with Algebra II is to do a problem with them and then have them try some on their own while I walk around taking questions.  I'm not a homework-giver in Algebra II (though I am in Pre-Calc), so it's important that they get the practice time they need in class.  We work on adding and subtracting polynomials.

9:55  Switch to multiplying monomials with like bases.  Ask students to turn to the back and summarize their findings in complete sentence(s).  Call on students to share their answers.  Explain how "adding the exponents together" doesn't qualify as a complete sentence.

10:00  Try some slightly more difficult exercises to practice the shortcut they remembered/discovered.

10:10  Give students a couple review problems on graphing linear inequalities.  (Yeah, it's random, but I'm a firm believer in review.)

10:15  Bell rings.  Tell students where to turn in worksheets, remind them about the opportunity to take a make-up test, and wish them a great morning.  Next class (Algebra II) starts to enter.  I hand their tests back as well.

10:20  Bell rings again.  I welcome the class back.  This hour goes very similar to the one before.

11:12  Dismiss students who are enrolled in a tech course off campus and need to catch the bus.

11:15  Recruit the students who are finished with the worksheet to rearrange my room for next hour's Pre-Calc class.

11:20  Bell rings.  Wish students a good day.

11:25  Bell rings again.  This class runs similar to my first hour.  Students are thrilled they have one more day to study.  I explain how the review will go and they have at it.  I intentionally gave the hardest problem to the group closest to my desk, so I could help those groups throughout the hour if need be.  But, they don't need me (hoorah!).

12:18  I ask for formula sheets back as well as feedback.  This class liked the review as well.

12:20  Bell rings.  No time for students to rearrange my 36 desks, so I'll have to do that after remediation time.  A few students stay to ask questions.  This is their lunchtime, but it's my time to remediate any students that need it (I assign those who have D's and F's).  One student also comes from 2nd hour Algebra II to gain access to that make-up test.

12:50  I dismiss students who are there for remediation (I assigned 4 Algebra II students, but most were gone today).  They go eat lunch.  One stays behind to tell me the reason she's been missing so much class is because she's 9 weeks pregnant.  I try to focus on the joy (a new human being!) and not the hardship I know she'll have to endure for the next several years.

12:52  I start to rearrange the desks.  Turns out it's a lot easier to mess them up than get them back together.  Another student from my 2nd hour class comes in.  He says he wants to talk about the back part of the test...but doesn't have the test with him.  I bring out another copy and we discuss how to use the discriminant to determine the number and types of solutions a quadratic equation will have.

1:05  I wonder if I have enough time to grab lunch today.  Most days I just wait until my plan (2:30), but I think I can grab something to eat today.  I head to the math lounge to heat up my lunch.

1:10 Take my lunch to my colleague's room across the hall from my room.  This is my first interaction with an adult all day.

1:23  Head back to my room.  Thirteen full minutes for lunch--that's actually a good day.  Once I get to my door, students are waiting for me.

1:25  First bell rings.  I check to see if there are any emails I need to respond to asap.  I try to stay on top of emails as they come in throughout the day.  Sometimes that's easier said than done.

1:30  Second bell rings.  I welcome students while I continue to pass back their tests.  Class runs pretty similar to my last Algebra II classes, with the exception that this class wants to see one of the test problems worked.  It seems like they're just buying time, so I work the problem somewhat quickly and move on to the lesson.

2:25  Bell rings and I wish students a wonderful day.

2:27  Collapse in my chair.  Have I sat down at all today?  Have I gone to the restroom yet?  I should do that.

2:28  Use the restroom.  This is my planning period, but I oftentimes have one or two students in my classroom during this time for one reason or the other.  Today, a student from 5th hour is staying to gain access to the make-up test.  I ask her to correct her first test on a clean sheet of paper, showing all work.  When she finishes, we talk about her mistakes.  I feel confident enough to give her a make-up tomorrow.  While she works, I work, too, planning for Friday's Pre-Calculus lesson (Law of Sines) and tomorrow's Algebra II lesson (multiplying polynomials).  We're going to try lattice multiplication tomorrow and see how it goes.

3:25  Bell rings.  School's out, but I feel nowhere close to being ready to leave work.  I put my planning aside for a few minutes, meet another math teacher in her room, and we get ready to attend the afternoon faculty meeting (whoever thought of offering two meetings on the same day was a GENIUS).

3:30  Faculty meeting.

4:10  I head back to my room.  A student I don't recognize meets me at the door.  "Are you the math Mrs. Peterson?!"  "I am!"  "I need help in Pre-Calc!  Can you tutor me?"  I make a quick judgment call.  She's not my student, but I'm not going to refuse helping her.  I tell her she's welcome to come to my remediation sessions anytime.

4:12  Back to planning.

4:30  A friend calls and asks if I want to have dinner with her (she knows my husband won't be home til late).  I say sushi sounds amazing.  I have to stay a bit longer, but I promise to give her a call when I get ready to leave.

4:32  More planning.

5:30  I make all the copies I need for tomorrow's Pre-Calc quiz.

5:32  I turn off my TV and computer and lock up for the day.  I'm quite impressed with my early departure time, especially with the faculty meeting.

5:45  Arrive at friend's house.  We decide to pick up Target sushi because I have to bake some cakes (and hence pick up some supplies) for an International Dinner my husband's work is hosting tomorrow.  I decide on Philadelphia Rolls.  Yum.

6:00  Check out at Target and drive to my apartment.

6:10  Arrive at my apartment.  The cats want more food.  I feed them before I change out of work clothes.

6:15  My friend and I scroll through Netflix, deciding on a movie to watch.  We settle with First Wives Club.

6:18  Movie and sushi.  If hubby has to be away, this is the way to spend it.

7:40  Movie finishes and I take my friend back to her house.

8:00  Back to my place.  I need to start those cakes for tomorrow.  I decide I'll bake the cakes tonight and finish the glaze tomorrow before we leave.  The cake I'm baking is called Silvia Torta, named after the queen of Sweden.  I want to bake three of them, so I triple the recipe, converting from metric to English as I go along (good thing I'm decent at math).

8:30  Realize this is not going to be enough batter for three cakes.  I pour the batter into two pans.

8:35  Start another batch for the third pan (1.5 times the recipe, I remind myself).

8:50  Finish the third batch.  Pour.  Put all three pans in the oven.  Set timer for 10 minutes.

8:52  Check personal email.

9:00  Timer goes off for cakes.  I rotate them and set the time for another 10 minutes.

9:02  Math Twitterblogosphere time!  I check Twitter and read some of my favorite math blogs.

9:10  Timer goes off again.  Cakes are almost done I rotate them once more and set the timer for a final 5 minutes before going back to the internet.

9:15  Cakes are done.  Apartment smells tasty.  Glad my husband will come home to this smell tonight, because it's not often I have food made any more.

9:30  Start to write my Day in the Life post.  It's getting too long.  Oh well.

9:47  Get a text from husband that he just landed in Tulsa.  Yes!

10:05  He enters the apartment with a "Hi, Love!  You've been baking?"  My heart is happy to hear his voice again.  We talk and catch each other up on the day before heading to bed.

10:30  Ablutions.

10:37  Sleep.

## Monday, November 12, 2012

### When I had to defend my profession twice in one hour

This Saturday I was at wedding, and I started talking to one of my friend's brothers, whom I've known for several years.  This brother is a senior engineering major and is currently tutoring two students in Algebra II.  He said something to the effect of, "I don't think the teacher took the traditional route to become a teacher, and you can tell, she just doesn't really know what she's doing!"

"How can you tell?" I asked, trying to mask my anger at his accusation.

"Well, one of the kids will come home with stuff she's written on the board, and it's just totally wrong!"

"And how do you know that the student didn't copy it incorrectly?"

Mmmmhmm.  That's what I thought.

My grief:  I hate how many times people assume we went into teaching because we couldn't do anything else.  This is a kid who hasn't even graduated college yet, and he feels he has more math knowledge than someone who breathes it day in and day out.  Listen up.  We went to school, too.  And most of us were freaking awesome at it.  That's why we became teachers--to stay in school and share what we love with other students.

Fast forward a few minutes, and my husband and I are leaving the reception early to catch up with a couple from our church, both of whom are youth pastors.  When they asked me how my job is going the man proceeded to tell me:

"You just have to make it interesting for the kids, you know?  Relate it to their lives.  Like video games and stuff."[1]

My grief:  Why do people assume that we don't try to make mathematics interesting?  Do they really think I sit at my desk pondering, "My, now how boring could I possibly make this?"  I'm also sick of hearing, 'Relate it to their lives!'  Good God, I'm trying, but these kids can't add or multiply rational numbers, and by the end of the year they're supposed to recognize conic sections, sequences and series, and logarithmic functions.  If it's so easy, you try it.  Please.  Oh, and while you're at it, go ahead and throw in some video games.  Because that's not a disaster waiting to happen.

Here's the thing:  I'm not trying to be down on my profession.  (Although it was a rough day at school, so I should probably wait to post this.)  But, it's just very clear to me that teaching is something people think they know so much about (because they've all been in the presence of multiple teachers), but unless you are a teacher or you live with one, you really have no idea what it's like.

That's why I'm very enthusiastic about A Day in the Life of  Math Educator.  I plan to write mine sometime this week.  Consider what you just suffered through the prologue.

[1]  Do I tell you how to do your job?

## Sunday, November 11, 2012

I felt like my students were not yet ready to test on quadratics again (all methods of solving), so on Friday we took a day to recap what they've learned so far by writing RAFTs.

When I first heard about RAFTs, I was pretty excited, but I wasn't sure how juniors and seniors would respond.  To be honest, we do some pretty cheese-ball stuff in my classes, and I think this qualifies as such.  But, cheese-ball can be hilarious.  Here's evidence of the hilarity:

Role: Discriminant
Audience: America
Topic: The usefulness of the discriminant

Dear people of America,
 They drew this on their paper, but I'm too lazy to scan it
Are you tired of solving quadratic equations and wondering what the answer should be?  You waste minute upon upon trying to figure out when to stop solving.  Not with the discriminant.  With the discriminant you can instantly know what to look for while solving.  The problem under the square rot becomes hardly a problem at all if you vote to keep discriminant around.  Do yourself a favor, and check 'Yes" for "Vision D"!
Sincerely,
Board of Discriminants

*****

Role:  i
Audience: Negativity
Format: Letter
Topic: How i and the negative numbers work together

Dear Negativity,
Your square root is always bringing us together.  At first we had a problem because you were always being fake, but then I came around and made being a real a possibility.  I know that sometimes your square root makes you feel imaginary but I'm always there to rescue you when he does that.  Many, many years ago you were a problem to everyone and no one knew how to fix you.  When I came along things changed and your negativity no longer was a problem.  I love you and your square root.
Sincerely,
i

*****

Role:  i, The Illusionist
Audience: Potential magic show-goers
Topic: The coolness of i

Hi, my name is "i."  Some call me "Imaginary," and some call me "Illusion."  If you come out to this amazing show you won't regret it!  There are many fascinating things about me that I would like to show you!  Depending on when you catch me at the show, depends on my reality.  Let's just say there is a certain pattern to me.  Sometimes I am just imaginary when I feel like being myself, but I can also be in the form of -1, -i, and 1.  Do you think you can figure me out?  Come to the show and you will see!  Or will you...?

*****

I let my students work in "groups" of ones, twos, or threes.  They brainstormed on whiteboards, and then wrote their final product on a clean sheet of paper.  The activity took about thirty minutes.  A few of my students had written RAFTs before, but most of them had not.  So there was a lot of "I don't get what you want us to do."  And there were a few kids who just sat there for the first few minutes, which I'm pretty ok with.

I definitely had to encourage some students more than I did others.  But, reading the final drafts was both fun and enlightening for me.  It's clear that there are some topics that the students really understand, and some that we really need to discuss further.  This is what I love about writing in math class:  it's incredibly revealing, is it not?

[1] Sounds more like an infomercial to me, but to each his own.

## Saturday, November 3, 2012

### Warm Up for i

Sometimes we have to relish in the little things, right?

This is a warm up I gave to my Algebra II students, just a couple days after they had first been introduced to i:

While I do like the warm up, what I'm really quite proud of is how I implemented/graded it.  When students felt like they had finished the warm up, I had them let me know.  I checked their work quickly.  If I liked what I saw, they were given the day's assignment (and a 100% for the warm up).  If not, they were given some verbal questions from myself, such as...

"You say i is imaginary, but you also say it's equal to -1?  Are you saying it's impossible (not real) to lose a dollar (-1)?"

"i is equal to the square root of 1?  But the square root of 1 is...?  Oh, so we need two symbols for the multiplicative identity now?"

"i is equal to i?  Try again.  This time tell me something."

Yes, I was harsh and sarcastic.  But this is an important concept.

Eventually, everyone had true sentences on his/her paper (which means everyone who came to class got a 100).

Each day I've been doing an "EOI Preview" as a warm up and I've been taking the highest 3-4 grades for the week.  This warm up gave everyone a chance to get an excellent grade in for the week, and I didn't let students move on until they could articulate the truth.

I know, I know...I really need to switch to Standards-Based Grading.  Sigh...

## Thursday, November 1, 2012

### They're going to be prepared for calc...so help me God

I've written before about how I feel like a concept we think our students get that they really don't get is the composition of certain functions, specifically trig functions and log functions.  I made a vow to myself to emphasize compositions with my Pre-Calc students a lot this year, so that when they do get to calculus, the Chain Rule and u-substitutions will be two of their best friends, as opposed to worst enemies.

I was reminded of this vow when I asked a student to read an exercise from the book out loud.  The exercise started like this:

$sin(\pi /2-x)$

And this is how she read it:

"Sin" [as in a transgression, not a trigonometric function] "times pi over two minus x."

I wanted to say, "When have you EVER heard anyone say it like that, girl?"  But, I remained calm.  I ignored the mispronunciation (we have bigger fish to fry here), and focused on the "times" part.

It seems like every time I have this conversation ("It's not 'f times x,' it's 'f of x,' guys."), I feel like the kids are just nodding to get me to shut up.  I can't blame them.  I did the same thing in grad school [way] more than once.  As long as I make the prof think I understand what he's saying, all will be well.

But, inputs.  They're kinda a big deal.  What worries me is that it seems like students often view inputs as some kind of multiplication as opposed to actual arguments, which makes sense as the notation is very similar (parenthesis for both).

I continued to notice this was a problem as we were verifying trig identities.  I don't know if the kids just got so into the proofs that they forgot a few fundamental things...like what sine and cosine are...or what was going through their heads exactly.  But, let me tell you, I saw crap like following slide all. the. time.  So, I made them figure it out:

I would not tell them what was wrong, but I did mention it was subtle.  When they finally started figuring it out, we talked about why we need all those theta's!  Our dear trig functions are meaningless without them!

It's a small step, but if it gets them to remember that these trig functions must have an angle at which they're to be evaluated, even if that angle is arbitrary, well, then, that's a good thing.