Wednesday, April 9, 2014

Today's PD Brought To You By . . . Students

My colleague James had the idea to invite students to our PLC for a panel discussion. It was a very interesting/insightful conversation. The students were pretty honest with us.

First we put together a list of questions. We did this rather quickly, so there is nothing special about them. We just wanted to give students some prompts to get them talking.

Next we selected a group of students. We chose all older students, thinking that they would have had most of the teachers in our little department at one time or another. It turns out they mostly commented on their current classes, so next time we will choose students from every class. We also chose a variety of students in terms of ability level and performance. Finally, we looked for kids who wouldn't shy away from speaking up and giving us some constructive criticism. We ended up with six students, and that was just the right amount.

Finally, we gave each student a personal invitation to come to our meeting and share their thoughts about math class. All of them gladly accepted.

Here are the questions we asked and a summary of the responses. We have about 25 minutes for our PLC meetings, and we finished these six questions with just the right amount of time.

1. Name one thing from one of your math classes that you would NOT change. Why?

  • Having answer banks on homework
  • Activities where we can move like scavenger hunt or quiz/quiz/trade
  • Being forced to organize (a binder or composition notebook)
  • Spiral review helps us remember stuff from earlier in the year
  • Projects/creating things
  • Having assignments on paper (versus out of a textbook)

2. Name one thing that you would change. Why?

  • The answer banks on homework make us too reliant 
  • The paper is too small in the composition notebooks
  • Units should not be longer than two weeks

3. When you miss class, how do you usually get help to make up the work?

  • Edmodo
  • Talk to the teacher
  • Get help from friends/other students in class

4. Do you like us using Edmodo? Is there another way you would like us to post work?

  • Those who use it do like it
  • Only about half of them use it because they don't remember how to log in (!)
  • Edmodo needs to be easier for us to access


5. How do you perceive the advanced classes versus the regular classes?

  • At first when I found out I was not going to be in the advanced class I felt stupid, but now I like that the class is at a good pace for me and I understand what we are doing.
  • I (student in regular) used to cheat a lot last year (love the honesty!). I haven't cheated at all this year because I understand what I'm doing.

6. What would you like to see more of?



  • extra credit
  • games
  • hands-on activities

The hardest part of the whole discussion was NOT responding when students said something negative. When they mentioned a practice they didn't like, my gut instinct was to explain why we do it that way. But that's not what this is about. Listening is key. 

This discussion triggered a few adjustments and more discussions for us. At our next PLC meeting, everyone shared their favorite hands-on type activity or game. Teachers shared specific activities that were mentioned by the students. We also resolved to use Edmodo during class occasionally, just so that everyone knows how to log in and is aware of what resources are available there.

Next time we will get a different set of students and probably write some new questions, but we will definitely do this again.

Tuesday, April 1, 2014

April Fool's Day, Volume II

Teaching relatives is weird, but also pretty fun. I've be able to see my nephew almost every day of his high school career. Two years ago, he pulled a cute little April Fool's joke.

He's a senior this year and his little brother is a freshman. This year they decided to step up the level of their April Foolin'.

It is a good thing I like them . . . because they recruited assistance and spent an hour and a half of their evening on March 31st prepping this April 1st surprise for me:


I couldn't even walk through the door!


And I was a little proud.


I would send them to the office for a detention, but the Principal OK'd the whole thing in advance. 

And the Assistant Principal unlocked my classroom door for them.

How's that for a conspiracy?

Friday, February 14, 2014

On Peer Coaching, Struggling Students, and Green Pens

Backstory #1: I've mentioned before that this is my first year teaching two levels of Algebra 2. The regular (i.e., not advanced) class has challenged me like no other. When things go well, I must document so I can try to make that happen again.

Backstory #2: In our PLC recently, we resolved to look for ways to increase peer tutoring in our classes. This is something that has been important to me for a long time, but lately I've been looking for ways to be more intentional about it.

We are at the end of a unit in Algebra 2 and for the past two days, my lesson activities have looked like this:


Step 1: Finish yesterday's assignment (rational equations, most had 2-3 problems left).
Step 2: Work on a set of 16 review problems. Get a green star from me on each and every problem. (One of my strategies has been to check every problem. It helps me to locate errors and misconceptions, and students seem to be more confident and make more forward progress when they have immediate feedback.)
Step 3:  If you have any incomplete assignments from this unit, work on these pages in your composition notebooks.
Step 4:  Teacher will assign extra practice or tutoring another student.

On Day 1 all students progressed from Step 1 to Step 2. No one finished step 2 entirely. I roamed from table to table answering questions and placing green stars on papers.

Day 2 was perfect. I was a little frantic for the first 10-15 minutes as I ran around with my clip board answering questions, giving green stars, and double checking to make sure everyone was working on the step they were supposed to be working on. But there was a moment, about 20 minutes into the class, when about half of my students had finished step 4, received a green pen, and been assigned to another student who was working on another step. All of the sudden I became an observer to the learning that was happening. I still monitored progress and answered an occasional question, but the students who were assigned to tutoring were doing a GREAT job! They were sitting there, green pens in hand, talking about greatest common factors and common denominators and reciprocals and exponents. This is what I want my class to look like. 


Things I'm still smiling about:

1. The look on each student's face when they reached step 4 and I handed them a green pen. I have written about green pens before, but I haven't used them a lot in this class. I didn't feel like these students were ready. But on this day I trusted them and they exceeded my expectations. The green pen truly conveys confidence to a student. Students feel honored to receive it.

2. When I borrowed someone's green pen and they said "May I please have the green pen of power back?"

3. Four students who got everything completed and were assigned to extra practice on white boards. They kept asking me for more problems so that they could race. I was using this set of problems from Kate's rational expression speed dating since I already had them printed out. These are not easy, but these "struggling" students were asking for more.

4. Realizing that these students are mastering the exact same content as my advanced algebra 2 classes. We are going more slowly, pausing more for reinforcement and review, but they are doing the same sets of practice problems and the same tests. I was not sure that this would be possible. But maybe it is.

5. My superintendent walked in to visit when the green pen students were all paired up and tutoring away. She is always welcome, of course, but it was nice that she got to see a moment that I was particularly proud of.

And a few reflections:

1. I am wondering if the green pen is so powerful because I use it constantly. I am always walking around, looking at students' work, and giving them green stars when they are good to go. Students might view it as kind of an authority thing. Hence, the way they feel when they receive "the green pen of power". 

2. Using multiple steps for review was a win! I noticed that when students got to step four, they were pumped that I assigned them to tutoring rather than extra practice. And the few who finished up on tutoring were not surprised or upset when I told them they were ready for extra practice. It was right there on the board, so no one was surprised. Truth, I really only cared that everyone made it through step 2. There would have been so many missed opportunities if I had let them stop there!

So, I have plenty of days that don't go as planned, but this was a great day. Here's hoping something in this post will serve to help me re-create it more often. :)

Saturday, January 25, 2014

Sketching f' from f

My calculus class recently finished up sketching a derivative, given the graph of a function.

We began with using spaghetti and estimating the slope at each individual point. Among other things, I used this sheet from Math Teacher Mambo.

I told my students that the next step was to be able to sketch the basic shape of the derivative, sans spaghetti. No more estimating the slope at each individual point.

Students were having some trouble with this (they usually do, hmm). And then I thought about using color-coding, like so . . .


First we identified points where the slope was zero. We marked those in green on the original function and transferred the points to the x-axis of the derivative.


Next we identified regions where the function was increasing (positive slope). We shaded them in yellow and then shaded the corresponding region of the derivative ABOVE the x-axis only.


Then we identified regions where the function was decreasing (negative slope). We shaded those in blue and then shaded the corresponding region of the derivative BELOW the x-axis only.


Now, to sketch the basic shape of the derivative, you draw a graph that hits the green points and stays within the shaded regions.


It worked great! Students were all "Oh, now I get it!" Love those words!

We also needed a way to color-code places where the derivative was undefined, such as sharp points and discontinuities, so we added pink. A pink point translated to a vertical line on the graph of the derivative as a "don't touch this" signal.

Then we did a little more practice by matching some function/derivative cards. These are not my creation, but I am not sure where they came from to give credit.



There used to be lots of arguing and discussing during this activity, this time students breezed through it easy-peasy. I was just sitting there going ". . . but aren't you going to discuss . . . and argue and stuff?"

Next time I'll keep the spaghetti for sure. After that I'll have them try the card matching before the color-coding thing, and then back to the cards.

Tuesday, January 21, 2014

First on the Drop Pile

I wrote about this once before. Go back and read that if you want. Or don't. I'm about to summarize here anyway. :)

Yesterday the math PLC at our school did a "Keep. Drop. Create" activity. Among other things, "questions at the beginning of class" ended up in the drop pile. This is something I have felt strongly about for a while, so I am very happy that our whole department is in agreement.


I am probably preaching to the choir here, but if you give practice assignments on a regular basis and you're using the first ten or fifteen minutes of class to answer questions about yesterday's assignment, you should consider using that time for something else. Here's why:

Low student engagement. During question time, most of our students fit into one of three categories:

1. Students who didn't do much (or any) of the practice. They are now sitting there writing down the problems while you work them out. They're not thinking. They're transcribing.

2. Students who did most of the practice. When they got to a tough problem, they gave up because "I'll just ask that one in class". They learn to wait for help rather than persevering.

3. Students who did all of the practice before coming to class. They are now bored to tears while they watch your performance of math problems they already know how to do. Not learning.

(There may be a fourth category of students who legitimately have a question and are now eagerly anticipating your answer. But there are maybe two students in that category. Also, I would suggest that doing the problem for them while they watch is not the best kind of help.)

They're ready to learn. If there is a portion of the class period that students are most ready to do something, it is at the beginning. Don't lose them here.

Opportunity cost.  Instructional time is precious. Let's use those ten minutes for something else. Something that engages all students. We are working on a list.

In the mean time, we have decided to have little slips of scrap paper cut up and ready to go. At any moment we can do a quick formative assessment by posting a problem, collecting the slips, sorting them into piles, and identifying where students are having trouble.


What will you do with your extra ten minutes?

Or, an even better question, what other "math class traditions" need to go on the drop pile?

Sunday, January 5, 2014

So Long, 2013

2013 brought a few firsts to my classroom (and life):

1.  I started SBG in my Calculus class. And I am wondering what took me so long. Students loved it. They liked that they could focus on learning without the stress. I loved that my valdectorian-competing students had complete control over their grades. Want a higher grade? All you need to do is simply demonstrate a higher level of knowledge. Boom. That's it. Next stop, my Algebra 2 classes. In order for SBG to be successful here, I must figure out how to be more efficient with all the paper work and re-assessing.

2.  Two Algebra 2s. This year my school decided to offer two levels of Algebra 2. I teach both. The basic level Algebra 2 was especially challenging. I think every student in that room hated math and everything associated with it. At least it felt that way some days. I put a lot of energy into managing behavior and felt like I didn't do justice to the math. It was just tough. Really tough. I have an opening in my schedule for second semester, so I will be able to split that class into two sections. I am very much looking forward to working with smaller groups. It will be better. I am feeling determined and hopeful.

3. I decided my (non-advanced) Algebra 2 class would be the best place to start Interactive Notebooks. I am pretty sure that what I am doing does not count as a true INB. There are no beautiful foldables or elaborate color-coded notes. (Even though I wish there were). But there is a lot of stuff glued into a notebook. I like that the constraints of the page size forced me to edit content and constantly ask what was really important for students to know/do. All but 1 or 2 students had perfectly completed/organized notebooks at the end of the semester. When it was time to review, everyone could easily locate what they were looking for. There is something about numbering pages and filling out tables of contents and gluing notes or practice into a composition notebook that equals organizational magic. I had my challenges with this group, but locating someone's missing assignment was not one of them.

4. On a personal note, and because I cannot resist writing about it, I ran my first EVER half marathon in 2013. This was a pretty big deal for me. I was the kid who dreaded, every year of my entire life, the day in PE class when we had to run a mile. As an adult I have loved what running has done for me . . . I am healthier, I have found friendships with running buddies, and I've figured out that I am capable of so much more than I ever imagined. I love sharing this story with my students, as many of them experience math the way that I experienced running. I like to think that I understand what they are feeling in some way.

I wish I could hug the guy who took this picture around mile 8 or so because . . . people behind me!


Lastly, because I hate to break tradition, my most-read (or least not-read?) posts from the last year:

How I Taught End Behavior:  This is my goal . . . more lessons like this where students are sorting and looking for patterns and figuring things out. More students doing, less teacher telling.

Trig Hand: Trick alert! My mistake was using this in my Algebra 2 classes. I won't do that again, even after focusing on the conceptual understanding. But I will use this with my Calculus students, and I have used it myself since I discovered it.

Plethora of Practice: I made two sets of cards for evaluating trig ratios, and found a lot of different ways to use them for a variety of practice sessions.

Desmos Test Question: I fell in love with Desmos this year, and I am still discovering all the many ways I can use this tool in my classroom. Here I used it for assessment.

Diving Into Programming: This year I dipped my toes into simple programming on a TI-83/84 calculator. After a few days, I am convinced that programming has a place in every math classroom. My dream is to have a project to go with each unit of the classes I teach. And the entry is so much lower than you think. You can do this, too.

This Lesson Cost $1: My intro to the zero product property.

Unit Circle: This post exemplifies what I love about blogging. I came asking for help, and I received some really helpful comments. I am thankful.

Happy 2014!!

Friday, December 13, 2013

Domain & Range from a Graph

My students have never had such accuracy in identifying domain and range from a graph.

Thanks to this little unsuspecting guy.


I blindfolded him and gave him eyes on the sides of his head.


And then he took a stroll across the x-axis to find to find domain.

Now the x-values that are included in the domain can be determined by stating the x-values where our little friend can "see" the graph.

Can he see it here? No.


What about here? No.


What is the smallest x-value where he can see the graph?  -9


Can he see it here? Yes


What is the largest x-value where he can see the graph? 9


So the domain is [-9, 9]

To find range, he strolls up the y-axis.


For a function that doesn't have endpoints, we talked about what the function looks like beyond the plane that is shown. Students really didn't have trouble with this.


All this silliness is the result of desperation.

For the first time ever, I am teaching two levels of Algebra 2. I am finding that some of my "standard" explanations aren't working with the "not advanced" group.

So then I'm all "Okay, that didn't work. Here, let me grab this toy bug from my closet." And stuff like this happens.