0 Write Your Own Word Problem. Also: Why Am I Doing This?

My Algebra 2 students are working on some word problems that set up as systems. They are finding out how many of each type of ticket was sold for the homecoming dance or how many quarters and dimes make $3.45 -- that type of thing.

I thought that students would better understand the process if they wrote their own problem, so I wrote up the sheet below. In the interest of spending less time at the front of the room blah-blah-ing away, I wrote it so that students can read the instructions and work through the process on their own. They start with a problem we've already solved, and replace its parts one at a time. They will illustrate and solve the problem when they are done.

Write Your Own WP

Here's my reflection:

Students seemed to really enjoy this activity. They all dug in and did it. I just walked around and answered a few questions here and there. I also asked each student to check in with me at a couple of different points to make sure they were on track. When they finished, they were just tickled that their problem worked out as planned. In the end, they were more confident about these problems.

I like this activity, I really do. But . . .

I am really wondering if it makes sense to keep doing these types of problems this way, or at all.  The whole process is quite hand hold-y. Students are really just learning to follow a procedure here. I am sure there is a better way to teach systems. Keep the old-school word problems, or ditch them? Replace them with what?

Conclusion: Today I accomplished exactly what I tried to accomplish. However, I am not sure if what I am accomplishing is what I really want to/should accomplish.

Detail: Write Your Own Word Problem. Also: Why Am I Doing This?

0 Happy Endings (Mostly)

Last day of school. The end is always bittersweet. I hate good-byes and generally dislike the ending of things, but I am looking forward to time at home with my 2-year-old and resting up for a fresh start next year. I have a list of things to do over the summer, both work and fun. I love how this year is ending. Mostly.

This activity went better than I hoped:  Try to write an equivalent for the numbers 1-100 using four 4's and any mathematical procedure. Autograph your solution. It was nice to see students work on this when they were otherwise ready to be done with thinking. I really loved seeing factorials and other creative solutions as they showed up.

I always get especially attached to my seniors in physics and calculus. A group of students in my physics class did a skit as part of their senior class variety show. There was Humpty Dumpty falling off of a wall, and calculations for force and final velocity. Oh, and a senior boy dressed as me, singing to the class and offering to have everyone over for meatloaf. I am not sure that the crowd understood our inside jokes, but it warmed my heart. Here they are, don't they look like a fun group?

There was a class t-shirt. "Life doesn't come with an answer book". I love to say that. It used to be true, before Google. Now I have to insert the word "always".

My algebra students worked pretty diligently on their final projects. Speaking of final projects, today I am more in love with blogging than ever. I posted about this project just a few days ago, and received some wonderful comments. Thanks to others being kind enough to read and thoughtful enough to comment, I now know how to make the project better for next time. Thank you, blogosphere! I hope that I can return the favor.

And, one not-so-happy ending . . . One of my favorite colleagues has officially announced that she is leaving. I will move to her room next year, trading my cinderblock walls for a lovely corner window. The view is street side parking and a railroad track, but I am looking forward to seeing sunshine and the first snowflakes falling next winter . . .

. . . Still, I would be much happier if she was staying! We have been through a lot together these last seven years:  Tornado recovery, a trailer classroom, celebrity sightings, and learning (the hard way) that the top shelf in the closet won’t hold a full set of textbooks. Together we conquered our state's math assessment. We shared the victory of watching our most struggling students succeed. Working with her made me a better teacher. I am going to miss you, friend in the middle. We all will.

Detail: Happy Endings (Mostly)

0 Everyone Failed (and What's Up With Probability?)

In a job interview, I was once asked how I would respond if my entire class did poorly on a test.

I answered that I would look for another way to teach the topic and re-assess the students, but I also said that this was an unlikely scenario in my classroom. I plan to know if my students are struggling (and do something about it) before a big test rolls around. Test scores rarely surprise me . . . until recently.

I had an all-class fail. The words "all-class" and "fail" are a bit of an exaggeration, but the majority of my students scored below an 80% with lots of failing grades. Ugh.

I am content with how I navigated the aftermath. Now I am just thinking about how to avoid the entire scenario in the future. Here is what I have learned:

1.  It is never okay to skip some type of formative assessment. I was in a rush for part of the unit, and I relied way too much on facial expressions and nodding heads and trusted that the students were understanding.

2.  Adjust for extra time with wacky schedules. We had a weird week with in-service and parent-teacher conferences right in the middle of this unit. I saw my students one full day and two half days for that entire week. I kept plowing through.

3.  The importance of #1 doubles if it is your first time teaching a topic. I rarely teach any topics that I haven't taught before. This unit was 100% from scratch. Planning was a struggle. I had no reference point for knowing which parts would be difficult for students, what common errors would occur, and such.

Finally, what's up with probability?


Is the whole permutation/combination/probability thing just really hard to teach? It seems innocent enough on the surface, but I am now convinced of its underlying evil.

Next time will be better, I'm sure.

Detail: Everyone Failed (and What's Up With Probability?)

0 Teaching Them to Persevere

My name is Amy, and I have been an overly helpful teacher. I will admit that the first-year version of myself took a lot of satisfaction in being able to explain something so well that no one had any questions.

Even now, I still have to fight the urge to rush in and save the day whenever my students are showing signs of distress. And it works both ways. My students expect me to rescue them. When I throw something overly challenging at them, they freak out. Panic. Even shut down.

I just want them to try something. Anything. Just play with it. Think about it. Make an effort.

In order for a culture shift to happen in my classroom, we have to take baby steps.

Here is what I've been trying lately, and students have been responding really well:

First of all, I've been trying to present the most challenging of problems in class rather than sending them for homework. For now, students need to know they have a safety net.

I begin by saying something like, "Guys, I could stand up here and do this for you, but you already know how to copy stuff. You're going to learn a lot more if you struggle with it yourself first."

I set a time limit, so they know I will not leave them flailing indefinitely.

I expect them to try something, anything.

I walk around the room to monitor progress. I try not to say too much. I must resist my natural urge to throw out life preservers.

Once most everyone has something on paper, I go ahead and silently write something on the board. A hint. A first step. Something. Most of the students will already be there, a few will go "oh, yeah", and erase/adjust what they have on their paper.

I give more time, then another step or hint. Repeat as needed.

By the time we are done, I am amazed by how many students have been able to stay a few steps ahead of me. Of those that got stuck along the way, many just had minor errors that they were able to fix by looking at my hints and then continue on their own.

The more I do this, the more students are seeing the value in diving in without me. There was actually a moment when I started to work out a challenging problem in front of the class and someone says, "Hey, can we try this one ourselves first"?  Of course you can. What was I thinking? (Inside, I'm doing a victory dance!)

Maybe I am training myself as much as the students.

Baby steps.

Detail: Teaching Them to Persevere

0 Green Pen is the New High Five

Backstory #1:  I am trying a new bell work procedure this year. In short, I walk around the room with a handful of green fork pens. When someone finishes the bell work correctly, they get a green star and a green pen. Now they are qualified to coach and star papers for other students, and so on, until everyone is done.

Backstory #2:  I had an interesting conversation with a colleague recently. She mentioned that our German exchange student is used to finishing his work early. In Germany, he was always expected to help students who were still working. He observed that we don't do that much in our school. I rarely have students with nothing to do, but it made me think about how to more intentionally utilize students who "get it" to assist those who are struggling.

Fast forward to yesterday . . . My students were working on word problems.

I told students to do just one problem, and raise their hand to check it with me. In my mind, I was thinking that I wanted to make sure everyone was on the right track before moving on. But I had nothing else for them to do when they finished. Some were struggling away, and others were finished, twiddling thumbs, and otherwise disengaging.

In my head I was reminding myself . . . Always, ALWAYS, have something for next.

Then, light bulb! It occurs to me that my little green pen bell work procedure would be perfect for more than just bell work.

I picked up my supply of green fork pens and walked around the room answering questions as usual. When someone finished I gave them a green star and a green pen and the instructions -- "Now, look for someone (near you) who could use your help". They already knew what to do, since we've been doing this routine for bell work. Some of them amazed me with their ability to help someone else. I was helping one student when I saw another hand go up, so I directed someone with a green pen to head over there. I overheard the green pen student helping the other one find the mistake. I couldn't believe I was just going to have them sit there doing nothing for a few minutes while I ran around like a crazy person trying to answer all these questions and check all these papers.

I have tried to create a classroom culture of students coaching other students. I have my desks arranged in partners, and I talk about how everyone in the room is a teacher. Students are encouraged to ask their partner a question before me. Still, I have some students who are reluctant to request help from the person sitting next to them and other students who prefer not to be bothered.

I realized yesterday that I need to give students specific opportunities to coach someone else, and specific instructions on how to do so. What if completing a problem and checking in with your neighbor became the norm? I also discovered that my more advanced students are so much happier and more willing to help someone else AFTER they have had an opportunity to complete the problem on their own.

As an extra bonus, I also learned that the green pen has sort of become a status symbol of accomplishment in my classroom. Handing a student a green pen is a pat on the back, a passing of the baton, a rite of passage in the form of a writing utensil.

I hope to keep an eye out for students who never get a green pen in their hands and try to make it happen. I saw a struggling student light up yesterday when I handed him a green pen. "I've never gotten a green pen", he said. Sometimes it is the smallest things . . .

Detail: Green Pen is the New High Five

0 Factoring Woes

My students are doing okay with factoring overall, but it has been a struggle.

This is the graphic organizer I ended up using this year:

Students find it helpful, which is a good thing. I like/hate it.

I want them to be able to factor without it.

Here are some things I am thinking of changing for next year:

1.  Fewer methods:  Reduce the number of factoring strategies, so students have less to sort through. I am thinking I could teach trinomials with ax^2 first, and then apply that method to trinomials where a=1. Students should be able to adapt to the simpler situation, and they'll have one less method to remember.

2.  Figure out how to connect the type of polynomial with the name of the method and how that method is completed:  I am currently expecting students to see a trinomial, then identify that it has a leading coefficient, then recognize that they should use the "airplane" method, and then remember how to do the airplane method. So complicated! It is kind of amazing that any of them can do this at all.

One of my students pointed out that the arrows I am drawing for the "airplane" method resemble a trident. What if I renamed the "airplane" method the "trident" method? That seems like a better connection between the original expression and what you do with it. (Trinomial = Trident method?).

3.  School-wide consistency:  There are only three math teachers in our school. Why haven't we done this already? No idea. We definitely need to get together and agree on an approach to factoring so that students aren't seeing a completely new process from year to year.

4.  Find a hook:  I haven't figured out how to motivate factoring beyond, "You are going to need to use this all kinds of ways later this year and next year".

All things to keep in mind for next time . . .

Unless . . . Is there a magic factoring wand that I don't know about?

Detail: Factoring Woes

0 Top 10 for 2011

After a year of blogging, I have one regret:  The length of my url. It is embarrassing. Seriously, what was I thinking? I thought it had to match the name of my blog. (I would make that shorter too, if I had a do-over). Oh well . . .

To celebrate the end of a year, I thought I would do a collection of most-read posts from 2011 (And one from 2010):

Scavenger Hunt:  Students partner up and pick a starting point. Then they search for the answer which leads to another problem. Great way to review.

Stations Review and Practice:  Students get a card with a couple of problems to work out. After a set time limit, they pass the card and receive another. New card has solutions to the previous one, and a new set of problems. Repeat. Also a great way to review.

Cake Day in Calculus:  Use cake to practice volumes of rotation.

The Loop for Logs:  A handy trick for switching log form to exponential.

8 weeks, 8 pencils . . . :  The end to your pencil-less, pen-less, and eraser-less student woes.

Crazy for Conic Cards (and a follow-up):  Cindy Johnson's conic cards changed my life. :)

A Fun Way to Start Class:  The truth, I want to do this soooo bad. But I'm not sure I can pull it off.

Logarithm Love:  Oh, if every unit went this well . . .

Color Coding: For Sketching Piecewise:  This trick helped my students sketch piecewise functions with ease. And they get to color.

Super Speedy Quiztastic Fun:  A fun way to practice short mental calculations.

Detail: Top 10 for 2011

0 Fraction Exponents. Easy.

Have you ever found yourself teaching a certain thing a certain way for years, and then one day you think about changing your explanation just a teeny tiny bit? And the new way makes infinite more sense to students, and the thing that used to be impossibly hard is now easy? And then you wonder what took you so long to find that more easy/obvious way of explaining something?

That happened to me today with fractions as exponents.

I won't bother to mention how I used to teach it. It was bad. Very bad.

Today, I started by showing them this, and they all shouted several people went "x squared!".

Then I asked them HOW they knew it was x squared. Somebody pointed out that three x-squareds multiply to equal x^6. Someone else said that you divide 6 by 3.

I made a big deal about writing x^(6/3) before writing the answer as x squared. And we did several more of these including some square roots, so they could see that you divide by two.

Then I showed them this, and gave some time to think about it and write down what they thought the answer should be.

Almost every single student wrote down x^(2/3)! And there were angels singing.

Then we worked on going backwards, which was no biggie at all.  Given x^(1/2), students could easily rewrite as square root of x and so on.

And then I didn't know what to do, because it used to take me a full class period to teach that. And some students would still be sitting there going, "Huh?". But today they just got it in, like, five minutes.

I realize that there is nothing earth-shattering about this method. The thing is, I've taught it this way before. Only I didn't lead with this part. I ended with this part. All I did today was change the order.

Oh, I love these moments of finding the tiniest little change that makes a huge difference.

Detail: Fraction Exponents. Easy.

0 The Question Reveals . . .

I saw this quote somewhere a while ago, I don't remember where:

"It is better to solve one problem five ways than to solve five problems one way."

Recently, for bell work, I asked my students to give a response to that quote. I was kind of proud of myself, because it might be the first time my bell work has been something other than a problem to solve. The lesson for the day was solving quadratic inequalities both algebraically and graphically (they have done both, but I wanted students to see them side-by-side), so it seemed to fit.

The responses were limited to just a few thoughts:

You can use one method to check another method.
Sometimes one of the methods may not work.
You might forget one method so you could use another.

I am not sure what I was looking for. Maybe I was hoping that someone would think about how solving a problem multiple ways helps you better understand the concepts and how they all fit together?

What I think is interesting, is how much these answers reveal about where my students are at in their understanding of math. To my students, math is still a bunch of procedures to remember and repeat.

And here's the thing:  I think I am still mostly teaching that way.

Detail: The Question Reveals . . .

0 Today's Million Dollar Question

I have been struggling a bit this year with getting a student or two to show steps/process/work/setups (or whatever you call it when you say that it isn't okay to give a lonely answer with no justification). The silver lining is that this struggle forces me to think about WHY students should show work.  Here are a few reasons I have:

Showing steps . . .
Puts the focus on the process, rather than the solution.
Communicates your solution to others.
Makes it possible for you (or someone helping you) to locate your mistakes.
Slows you down, so fewer careless mistakes happen.
Gives evidence your answer is right.
Demonstrates your understanding.
Helps reduce cheating. (Some might still copy, but at least they must copy the work too.)
Finally, in my class an answer bank is given. Showing steps keeps practice from becoming nothing more than a matching game.

I am also asking myself some questions like . . . WHY do some students struggle with showing work?

Maybe because . . .
It takes too much time.
They can do it mentally.
They don't know how to show work.
They are bored.
They don't believe in its value.
They are cheating.

Writing this, I realized that when a student is repeatedly refusing to show their process, I tend to go straight to negative assumptions. I assume they are being stubborn and uncooperative, or that they must be cheating.

I am going to try to put the whole issue in a more positive light and see where the students are coming from. Maybe these students think that showing steps is just for the teacher's sake, and has no benefit to them personally.

Or, maybe they genuinely don't know how to express how they got the answer.

It also has me thinking about the types of questions I am asking. If someone can calculate the answer mentally, maybe the question wasn't challenging enough?

How do you motivate students to show their thoughts?

Detail: Today's Million Dollar Question

0 I Need Adventure (also my trial run of Solve, Crumple, Toss)

Yesterday I tried another goodie from f(t) . . . Solve, Crumple, Toss. Just in case you've never read that post, make sure you read the part about how you should use "6-8 problems with somewhat lengthy solutions". I either skipped or disregarded that part of the description, and it was the downfall of the day.

My students are working on writing linear equations in standard form, given different types of information. I just printed up twelve problems, six per page. Students cut them apart, worked them out (one at a time) and brought them to me to check. If all was dandy, then they got to take a shot for points.  If not, I sent them on their way to keep trying and encouraged partners to check each other's wrong answers and help find the errors. I had no time to coach and help find errors myself, because I had a line of students waiting for me to check their answers. I expected them to finish all twelve problems and make twelve shots. Fine as long as I have a student shooting, like, every eleven seconds. Note to self: Fewer, more complex problems next time!!!

The student response ranged from a few who acted totally tortured because they had to get up out of their seat twelve times, all the way to enthusiastic participation by many. This was fun and productive, and there will definitely be a next time.

In related news, I realized how much more I enjoy my job when I am trying something new. I have been teaching the same classes in the same school for 6 years now, so it is super easy to just pull out what I did last year and do it again. I don't want to take that approach to teaching, so I am always looking for ways to improve on what I have already done. Still, I think my best lessons are the ones that I create from scratch with a fresh perspective.

So today I am just thinking about the payoff for extra time spent trying something new. Sometimes these things work, and sometimes they don't. Still, I am happiest when I am being adventurous.

Detail: I Need Adventure (also my trial run of Solve, Crumple, Toss)

0 I Stopped Answering Questions

Not really . . . but I did stop using 10-15 minutes at the beginning of class to discuss and answer questions on the previous day's assignment.

Initially, it was an experiment. I felt like students weren't really invested in this time, and that most of them were falling into one of four categories:

1.  The procrastinators:  These students were using this time to finish the assignment.
2.  The ones who lacked perseverance:  These students would encounter a challenging problem and then stop working on it (or not even attempt it in the first place) because they could just "ask about it in class".
3.  The ones who were really engaged:  Most days, it felt like maybe 2 kids.
4.  The ones who were bored:  These students had the assignment finished and were ready to move on to  a new lesson.

So I stopped spending time on questions. (My students have answers, so they can check for correctness as they practice). And this is what happened:

1.  Most of the procrastinators found a time to finish the assignment before class.
2.  Many more students persevered through challenging problems because they didn't have the crutch of asking about it later.
3.  Many with legitimate questions would drop by before school to ask. Most of our students arrive 30 minutes before first bell, so this works well at our school.
4.  Most everyone started finishing the assignment outside of class.

These outcomes alone were enough for me to turn my experiment into a permanent routine, but there was another benefit that I wasn't expecting . . . I suddenly had an extra 10 - 15 minutes in every class period. What can you do with an extra 10 - 15 minutes?! Here's how I use the extra time:

I use a few bell work problems every day (I am testing out a new bell work strategy, more on that later) to review and check for understanding. If there are any major misconceptions, I can usually identify and address them during this time.

While teaching a new lesson, I have a lot more time for practice and checking for understanding. I still do a lot of talking, but I also do a lot of pausing while students try this or that and check with me (or a partner). I have time to work in several mini-formative checks, and address common misconceptions. The result is fewer issues on the practice/assignment, which in turn further reduces the need for the question/discussion time at the beginning of class the next day.

Sometimes I still wonder if I should bring back the question time, structured differently to eliminate the problems I was having. I haven't done this because I don't miss it. And neither do my students. I realized today that in 2 or 3 years, I haven't had a single student complain about why I don't answer questions at the beginning of class.

Detail: I Stopped Answering Questions

0 My Thoughts On Homework

Lately I have been thinking about how I assign, collect, and give points (or not) for homework. (For the record, when I say ‘homework’ I really mean ‘practice’. I want my students to practice every day. Sometimes they practice at home.)

I know a lot of bloggers have had success with not giving points for homework, but I am not ready to go there yet. I tried not giving points once during my first year of teaching and it was a disaster. Then again, lots of things during my first year of teaching were a disaster. But if giving students a score on a paper helps them to reflect on the quality of their efforts as they practice math, then I’m okay with using points.

So this is what I do . . . In bold is the thing I am trying to accomplish, and after that is how I attempt to make it happen.

1.     The perfect system emphasizes quality practice. Students need to reflect and make corrections as they are working:  I spend a lot of time teaching students how to practice. I want them to work out a problem, and then check the answer and find any mistakes and revise their work as needed. I hate to say just “show your work”. I do emphasize the importance of justifying your solution so that you can communicate to others how you found it, and prove it is correct. I make up a page of problems where some are perfect, others are missing work/justification, others have a wrong answer, and some have a right answer but the work/justification is incorrect or incomplete. Then students work with a partner to critique and discuss the quality of the practice. This takes time, but it is worth it.

2.     A good system gives students feedback while they are working, whether at home or at school. Ideally, they can find out if their answer is right or wrong without being told the actual correct answer: I put the answers to the problems in random order in the margin of the assignment. When students finish a problem, they find the answer in the margin and cross it out.  The only drawback here is that they can use the process of elimination to know the answer to the problems at the bottom of the page. Still, it works pretty well. I am thinking of tweaking this a little this year using the sum of a couple answers (sort of like Kate’s Add ‘em up). Instead of writing all the answers in the margin, I think I will try something like “the sum of #1 and #2 is _____”.  Then they will know if they need to fix their work without giving away any answers.

3.     If points are given, the points should reflect the quality of the practice vs. the number of answers that are correct on the first try:  A problem counts for points if it has correct work (or justification of some kind) leading to the correct answer, regardless of how many tries it takes you to get there. I don’t really even think of it as a “homework” grade. I want the point value to help students think about how well they are practicing. Hmm, maybe I will start calling it the “quality of practice” grade. Or something like that . . . I will have to think of something more catchy.

4.    If points are given, the system minimizes teacher time spent grading and recording:  My students spend so much time learning what good practice looks like that they know whether a problem they have finished qualifies. It has correct work leading to the correct answer and it counts, or it doesn’t. So students take the number of problems that qualify as good practice divided by the total number of problems times 5 (because I want a practice assignment with 20 short problems to have the same value as a practice assignment with 4 or 5 lengthy ones). I will even put that formula at the top of the paper to make it simple. Round the number to the nearest tenth and hand it in. Teacher records that number.

I am pretty happy with this system, but I still have a few problems. Sometimes students put a score on their paper that isn’t accurate (pretty easy to catch). Sometimes students rely too heavily on clues from the answers in the margin (maybe my little tweak will help that). Sometimes students copy their friend’s homework in the hallway before school (but at least they have to copy the work, too).

What's your homework system?

Detail: My Thoughts On Homework

0 A New Elephant

This is the time of the year when I finally feel like I can breathe a little . . . State assessments are over. The results were great, what was I worried about? (Well, there was one oh-so-frustrating exception that I want to blog about, but shouldn't.) And, I have my plans pretty much laid out for the rest of the year.

With all these things squared away, I really start to reflect on how the year has been. I try to focus on some areas to improve for next year, or just some new things that I would like to try. Then I make a long list, and delete some stuff until it feels halfway reasonable. I will get as much of these done as possible before school is out in seven weeks, do some over the summer, and then work on the rest during the next year.

Here is my list, and also possibly the titles of my next ten posts:

Physics:
1. More meaningful lab experiences.

Calculus:
2. Video lectures and experimenting with inverted classroom.

Algebra 2:
3. Look for ways to go more in-depth with fewer topics (like this year with logs)
4. More effective use of ACT practice questions.
5. Look at order of topics (parent functions/transformations first?).
6. Look at how I teach/review factoring.
7. Make sure all topics are aligned to College Readiness/ACT Standards.
8. Look at homework collection/grading procedures.

All:
9. Learn more about Common Core Standards, recently adopted in Kansas.
10. Work on atmosphere of partner cooperation/peer tutoring.

Despite my efforts to edit, the list is still a bit overwhelming.

This calls for the elephant-eating approach:

One. Bite. At. A. Time.

Detail: A New Elephant

0 Best Advice from a College Professor

I got some advice from a college professor my freshman year that I really took to heart. When we were getting ready to head out for a break (like Thanksgiving, or Spring Break), he would tell us to make our vacations a true vacation. He would tell us to write all the papers and finish all the projects before we went home, and then leave all the school work behind and truly enjoy the time with our families and friends. You don't have to feel guilty because you should be doing something else, and you don't find yourself stressed out at the end of the break over what you didn't get done.

I realize this is not earth-shattering advice, but the 18-year-old version of myself thought it was genius. I have tried to carry that advice into my professional career. I will not take work home for vacations. Occasionally, I try to do the same for weekends. I make lists, I cross things off, and I use my time on the job as efficiently as possible. I have turned into a true anti-procrastinator.

Last friday, I left my classroom for Spring Break with all the grading complete, plans laid out for the following week, and a clean desk. I walked floated out of the building and I did not think of school for the entire week. So refreshing!

I love my job, and I want to be good at it. It actually takes effort to NOT sit around mentally evaluating my grading system or how I can do a better job teaching properties for logarithms or what I should do for an end of the year project in Calculus. But I am convinced these mental breaks make me a better teacher. So I give myself permission.

Thank you, Mr. College Professor.  I am not sure I remember all the identifying characteristics of the various architectural styles, but you taught me how to relax.

Detail: Best Advice from a College Professor

0 Planting Seeds

I've been thinking about something cool (yet, a tiny bit disturbing) that happened a while ago in my Calculus class:

My students were solving a problem and encountered a quadratic equation that could not be factored. They freaked a little. (As their algebra 2 teacher, so did I). I gave them a chance to think about it, and someone suggested the quadratic formula. Then someone remembered the song that I had taught them. And, be still my heart, someone else noticed that since a = 1 and b = even number -- it would be super easy to complete the square. And they started discussing how to do that. I was proud.

With that problem completed and about ten minutes left in class, I wrote "ax^2 + bx + c = 0" on the board. I asked them if they thought they could complete the square with that. Working as a class (there are only ten of them), they figured out that they needed to divide by a . . . and et cetera et cetera.

I could not believe their reaction when the quadratic formula showed up. They were blown away! They were actually LAUGHING and saying how awesome that was. At this point, I should have reveled in the beauty of their mathematical discovery. Instead, I started thinking about what a rotten Algebra 2 teacher I must be. This should not have been brand new information.

So, I asked them if they remembered that I had shown them this same thing two years ago in Algebra 2. Someone said "Yeah, but this time it makes sense!". I am not sure if that comment made me feel worse or better. Then I realized that they did remember how to use the quadratic formula and how to complete the square, and when to apply those methods. The only piece that was missing was the connection between the two.

I thought about it for awhile and I decided that connections just take time. The more we learn, the more the pieces start to fit together in different ways. I remember that when I took Calc 1, I really didn't understand what I was doing. I think I was halfway through Calc 2 before the light bulb went on. Then it kind of all made sense to me at once.

I guess I don't need to be so hard on myself if the students don't get 100% of everything the first time they see it. I am planting the seeds that will lead to discoveries and connections down the road. Sometimes this will happen in the future without my knowing. This time, I was lucky enough to be there to watch it happen.

Detail: Planting Seeds

0 I Want To Be . . .

. . . like the best teacher I ever had.

I am not one for New Year's resolutions.  But if I am going to shoot for something, then I want to be like my elementary school PE teacher.  Strange choice for best teacher ever, I guess.  Especially since I was a super academic school-loving kid.  I loved school supplies.  I loved books.  And I loved getting A's.  I was successful at most things school related, except PE.

I was the smallest kid in my class, and I was not born with a single ounce of athletic ability.  None.  If PE involved running, I was one of the last to finish.  If it involved basketball, I could not even throw the ball high enough to reach the basket.

But Mr. Mosher understood what I was capable of, and he inspired me.  He rewarded my sustained effort.  After I finished the mile, he would say "I'm so proud of you, Amy, because you never stopped running."  He taught me to measure success by improvement, always letting me know if my time or distance or whatever was better than the time before.

He recognized when one of my accomplishments was a really big deal.  I think I was in the second or third grade when I actually threw the basketball high enough and it miraculously dropped through the hoop.  He saw it happen and came running from across the gym to congratulate me.  I had a sense that he really cared about me.

I learned some really important life lessons in his class:

1.  I learned that it was okay to not be the best at everything.
2.  I learned that it was valuable to work hard on something, even if I knew I would never be as successful as someone else.
3.  I learned how to improve by competing against myself.

I know that there are students in my class who experience math the way that I experienced PE as a child.      I also know that I am a long way from being the kind of teacher Mr. Mosher was.  In a perfect world, I would love for my students to learn those same lessons.

Detail: I Want To Be . . .

0 Never Say Its Easy

I used to try to alleviate my students’ stress level by telling them that what they were about to learn would be easy.  I had good intentions . . . I just wanted them to relax a little and trust me.  It was a bad idea.

This played out for real in my most recent unit on radicals.  My Algebra II kids always struggle with this.  Square roots aren’t so bad, but when you throw in cubed roots and beyond plus rationalizing the denominator and solving radical equations . . . well, they struggle.  So, this time around I told them how hard it was going to be.  Brace yourselves, I told them.  You are going to have to work harder than you have ever worked to figure this stuff out. 

They killed it.  Highest scores EVER.

So then I realized that telling them it is easy sets up a lose/lose situation for students.  One of two things is going to happen:

1.     They’re successful, but it is no big deal.  Who is proud of being successful with something that is supposed to be easy?

2.     They’re not successful, and it is depressing.  Not only were you unsuccessful, you were unsuccessful with something that your teacher says should have been a piece of cake.

Telling them it is hard sets up more of a win/break even situation:

1.     They’re successful, and they can be proud of it.  They just accomplished the impossible!

2.     They’re not successful.  But after all, it was hard.

I am going to try to stop saying anything is easy.

Detail: Never Say Its Easy

0 Green Stars

First of all, I ditched my red pen a long time ago.  I read somewhere that red pen causes extra anxiety in students, but mostly I gave it up because I love the color green.  Green is my signature color.  So I do all of my grading in green felt tip pen.

When I am teaching my students something that I know they are going to have a hard time with, I tell them to do problem #whatever and then raise their hand to get a green star from me.  This gives me a chance to check in with each student individually and see if they are on track.  It also gives me a chance to help them correct any errors that they are making.  It is simple, but it works amazingly well.

What is surprising to me about this little trick is that students really seem to care about getting a green star!  Class will be over, and I will have a few stragglers lined up to get their green stars before they leave the room.  On the occasion when I check someone's paper but forget the green star, they will certainly remind me.  Sure, I have a few who don't understand and they don't want me to know that they don't know what they are doing.  They will try to get by without checking in with me, but I know who they are and I make a point to check in with them. 


My physics class is smaller and when I do this with them I usually have 3-5 problems that I want to check.  So, they get a green star for the first one, a smiley face for the second one, etc.  Then for the last problem I let them pick what they want.  The requests have included a heart, a penguin, a flying squirrel, and beyond.  Sometimes they tear off my little pictures and tuck them in their notebooks.  So it is just a fun way for me to give each student some individual attention.

Detail: Green Stars