Saturday, September 29, 2012

Notebook Check Strategy

I refuse to spend time grading notebook organization.  I know teachers who do this and I remember taking many classes in school in which there were binder checks.  Personally, I think trading notebooks to check them in class is a waste of instructional time.  Collecting them to check myself is just plain daunting.  And for what?  It's not like grading a student's organization indicates their mastery of the content the subject requires them to learn.  I'm terribly disorganized when it comes to paperwork, but I know my math! 

The only benefit of checking notebooks in the traditional way is that it encourages students to have the life skill of being organized.  I've started a notebook check this year that goes a step further to ensure a student is familiar with the location of papers in his binder.  After all, I want students to be able to reference their notes as needed to help them attack problems.  When we have a few minutes at the end of class to spare, I pull out a stack of "cat cash," the money in our grade level economy.  I name a paper and award $5 to the first child who can find it and $1 to any other student who can find it before I call out the next paper.  The catch- it must be in the binder rings in the right section to count.  I run through three or four papers and that's it.  In about 3 minutes, we've checked every binder in the room.  I've done this twice so far this year and the students have responded well.  I've reminded them of this system when I pass back papers and it appears that this year more students are actually using the binder rings instead of a folder or the pocket inside the binder's cover (or the trash can). 

What do you do to encourage your students to be organized? 

Friday, September 28, 2012

Classifying Systems of Linear Equations.

 I set my students to work today on a sorting activity for systems of linear equations.  Systems is a review topic from Algebra I, but a topic that still gives many of them trouble.  I gave the students this paper to cut apart:

After a few minutes of cutting, I gave them this chart onto which they pasted the vocabulary and examples after solving the systems on the reverse of the paper.  
 They ended up with a chart like this one. 

What worked well: The students were able to self-check because they knew there would be two of each type of system.  Since there were 6 graphs, the students had a couple of opportunities to practice the solutions to each kind of system. 

What needs improvement: I should have labeled the systems and graphs with A-F prior to copying the sheets; I had the kids do the labels instead.  The kids complained that the graph paper was too small, though most of them managed just fine. 

UPDATE 1/6/13: The files shown below are available for download as a pdf.  I've marked the graphs and systems A-F as indicated above.  Thanks for visiting!   

Wednesday, September 26, 2012

Implementing Rich Mathematical Tasks

My school system is partially through the transition to Common Core Mathematics.  Our lower elementary grades have fully transitioned, HS Geometry has transitioned, and 8th grade has transitioned to the point where we're teaching both the old and new together this year!  As part of the transition, 8th grade students who previously passed Algebra I in 7th grade are enrolled in a course we've titled "Intermediate Algebra."  The course resembles traditional Algebra II in a lot of ways and is designed to fill the gap that would be made by students moving directly from our state's Algebra I/Data Analysis curriculum into CC Algebra II.

One of the expectations for the course this year is that I provide my students with rich mathematical tasks with an open-ended quality.  I was a bit hesitant to get started with these as the students I teach haven't had many experiences with open-ended problem solving.  I feared they would be frustrated by the lack of rigid structure and be very needy.

Here's how I organized the task process in my room.
  1. I presented the concept of a mathematical task as different from a BCR (the style of constructed response used on MD state testing which is quite formulaic) and explained to them that there are so many correct ways to answer a task that they should answer a task in the way that makes the most sense to them mathematically.  I stressed that I was not going to be answering lots of questions during this task, so they were to rely on their group and "figure it out."  (I still coached a minimal amount when groups were quite astray, but I wanted them to feel independent.)
  2. I assigned groups of four, making sure each group had at least one or two strong math students and a mix of boys and girls.  (Side note: I use pocket charts for grouping and it has been a breath of fresh air this year.  Something about this system, perhaps the groups being on the wall when kids enter the room, has kept the whining/eye rolling/ugliness entirely at bay this year.  I so much as mention the word "group" and their little heads spin to the back wall to check out who they'll be with, but they don't complain!)    
  3. I presented the task they were responsible for, indicated the variety of materials available, and set them to work.  
  4. After 30 minutes the first day, none of the groups were even close to fully answering the question.  Most had talked for 90% of their time and written very little.  All the groups stayed on topic and remained focused during that time frame.  
  5. The next day, I made some general comments about the task and gave a small insight or two into the problem to give a few hints related to common misconceptions.  The groups reconvened and were charged with finishing their answer. 
  6. We did a jigsaw grouping to share out.  Two students stayed put and presented their group's work to two students who came from a different group.  We rotated again so all students had a chance to present and a chance to review another group's work.  
  7. The original groups had some time to debrief about what they would change after getting input from other classmates.
  8. Homework was to write a reflection on the process. 
The tasks I'm using this year are from the Dana Center.  This is a great PDF resource to download if you teach Algebra I or II, or possibly even pre-Algebra with motivated students.  You can scaffold more or less depending on your group of students and the relative difficulty of the task.  This week, students worked in groups of four on the "Extracurricular Activities" task, part B.  The task gave students a scenario and asked them to write a function to model the scenario and find its domain and range.  From my description, I'm sure you're wondering why I needed to devote even 15 minutes to this problem.  We actually spent nearly 90 minutes in class spread over two days plus one night's homework on this task.  Here's why: 
  • The problem is embedded into the task in a way that students must make meaning of the situation.  Since the meaning wasn't immediately clear to the students, most every group restarted or made significant revisions to their work during the process.  (Make sense of problems and persevere in solving them.)
  • Students have various ideas about the meaning of the problem and how to go about solving it, so they have rich discussions. My students were holding each other accountable for their ideas, asking pertinent questions to better understand their classmates' points of view.  (Construct viable arguments and critique the reasoning of others.)
  • Students were able to use any of the materials in the room, so some groups gravitated toward calculators, while others preferred to sketch a graph by hand or write out a table.   (Use appropriate tools strategically.)
  • The real world context leveled the playing field in an unexpected way in at least one group.  I overheard one student who is a weak math student leading his group through this task at the beginning because he was the only one with the real-world background knowledge to understand the problem.  His more "book smart" teammates were lost without his guidance.   He was more engaged in this task than I've seen him since school started. 
I was very proud of my students this week.  I wasn't really looking for their work as the final product.  I was hoping to see them demonstrate the eight Standards for Mathematical Practice.   I highlighted a few above, but I can honestly say that I saw all 8 standards in play during this process. 

Some students were already asking to do more tasks on Tuesday before we finished our first task.  They loved the interaction and I loved how involved they felt in solving the problem.  

Thursday, September 6, 2012

Why my job is awesome

a.k.a. I'm going to show off a little and tell you about one of my wonderful students. 

Last year, I taught a very nice, smart, and motivated class of students.  I once joked that I could assign them the entire textbook, leave the room, come back hours later, and find them in the same place I left them, apologizing to me because they weren't able to complete the entire assignment in that amount of time.  They were literally that amazing of a group of kids! 

One of the standout personalities in that class was a student whose math confidence wasn't very high.  While very smart, this student never felt comfortable with math as quickly as most students in the group.  This student worked very hard to understand the material throughout the year. 

Today, I checked my mailbox in the afternoon and found a very fat envelope.  Inside was a letter, a piece of chocolate, and a bottle of wite-out. 

The letter was touching.  I won't repost the whole thing, but I will quote a few of my favorite sentences. 

I truly enjoyed being in your class.  Math, for me, is my least favorite subject.  It is so confusing, disorienting, scary, easy to get wrong, and a HUGE stressor/frustrator.  (Oh yeah, it's bad.  The night before 6th grade I had a minor freak out...over math class!)  Yet in your class, when I did figure it out, I felt on top of the world.  [...] And everything was so fun!  I looked forward to class.

This student include a "personal and used" bottle of wite-out signed on the bottom as a gag gift/inside joke.  I am a wite-out queen.  My kids are always poking fun at me for my obsessive use of wite-out.  I write in pen on any papers I project under the document camera because it shows up easier than pencil.  Unfortunately, if I don't write so neatly or I make a mistake, I can't erase it.  Therefore, I always have a supply of the wite-out runners and use them generously.  I got one from a girl in that same class for a Halloween present last year.  :)

I'm adding the letter and wite-out to my teaching keepsake box.  Letters like this one, while few and far between, are what keeps me going as a teacher.  What keeps you motivated? 

Tuesday, September 4, 2012

Update: Storage pouches

Before school started, I posted about the storage pouches I was planning to use for my kids' desks this year.  As a middle school teacher, I see several groups of students throughout the day, so I wanted to have an easy supply set-up that wouldn't require materials to be passed out and collected each class period.  I also wanted a system that would be quiet and easy to operate.

So far, the storage pouches are doing their job nicely.  I did have three come off of the desk when the fabric loop unraveled.  Because they were all together and the same color, I'm going to blame that on faulty craftsmanship, not my kids.

Students have already accessed most of the materials in the pouches.  They are able to get what they need without leaving their seats or dumping the materials onto the floor, my two main worries prior to trying this out.  They're even doing a fairly good job remembering to put away what they've used and I'm doing a good job reminding them to do so.  I've only caught one runaway protractor on the floor in a week, so I think we're doing well. 

If you're looking for a way to organize supplies at student desks (and you aren't terribly worried about theft), I would recommend this method!  This wouldn't be a good method to use if you can't trust your students to return their materials when you ask them to do so.  I'm lucky to have a fairly trustworthy group most years, so I don't have too many materials walk.  Most of the materials that walk eventually find their way back because they've been accidentally liberated.  ;-)