Experiment 1

Today was a strange day.  During the homework portion of 3rd hour, the class was silent.  Just dead silent.  Everyone was sitting, working, and quiet.  This unusual occurrence was creepy enough for me to remark "I don't want to ruin this, but why are you so quiet?" to the students sitting near me.  My hypothesis was that, like crickets, students communicate less as temperature drops.  As today was the coldest day of the year so far, it seemed plausible, but I was really shocked when one student said "cold!"  Weird. 

Anyway, on to serious stuff: the same student who remarked "cold!" had some questions about hyperbolas and inverse-square functions today (who doesn't?!) that I volunteered to help with.  After we talked about it for a bit and class proceeded, she threw her arms up "I get it now!"  When I told her that she now has a responsibility to help her friends get it, I don't think she thought I was being serious.  =)

During lunch, Mrs. Colwell and I discussed the plan for our experiment with 4th hour.  Here's what we decided on:

• let students self-select groups of 3-5 students
• students work in teams to solve problems on the board
• groups that finish early should disband and help other groups

Here is what happened:

• Students seemed excited to try something new
• Group formation was hectic (Mrs. Colwell predicted this)
• Some students didn't want to join any groups (Mrs. Colwell predicted this)
• Eventually the room settled down (maybe after 10 minutes) and groups were hard at work
• Mrs. Colwell and I circulated the room answering questions, and adopted lone students into the Mrs. Colwell, Eric, etc group.
• Only one group started throwing things at another group
• A couple groups finished early and helped out their peers!!

Here are some student responses to "what did you think of today's class?":

• "Thanks for doing this.  I actually learned today"
• "I don't know... maybe I like regular class more?"
• "This helped a lot, thanks."
• "It was loud at the beginning but I think it was good.  Are we going to do this more?  I liked it."
• "I learned a lot today."
• "This was good."
• "It was helpful!"

 Here is my analysis of their work:

• Group 1:  Drew good graphs of 1/x and 2/x^2.  Got domain and range for both
• Group 2: Good graphs, didn't finish
• Group 3: Good graphs, eventually
• Group 4: good graphs, figured out what happens to k/x when k<0>
• Group 5: Everything good except for the names of the functions
• Group 6: Good graphs, figured out how things change when k<0
• Group 7: One good graph, the only group to find the function names we were looking for (rectangular hyperbola and inverse square function)
• Group 8: Good graphs, couple of domain and range questions

Some commonalities: Pretty much everyone was able to draw good graphs and called 1/x an inverse relation when we were looking for "rectangular hyperbola."  I think most people are confused about asymptotes.  The answers that were most commonly wrong were those that dealt with vocabulary.  The answers that were the most commonly right were those that involved playing with a function.  Incidentally, I happened upon this article about playing in math and science today.  

One thing I really liked about this format was the fact that I got to work with more students one-on-one, but with others looking over our shoulder.  Working in this way, it's easier to identify the specific concepts a particular student is struggling with and devise a problem approach that helps address it- and those with similar questions get automatic help.  When one of the backseat drivers has a question, they chime in and it helps guide the discussion so everyone's questions get answered.  One large group that seemed very skeptical of this format at the beginning was able to take advantage of the over-the-shoulder learning.  I helped them draw a graph of 1/x and mentioned "boy, this looks different from the one you guys drew.  why's that?  How would it look if it was -1 on top?  What about if we square the denominator?  Draw those, and I'll be back."  When I came back and we talked some more about Domains, Ranges, and Asymptotes, this once-skeptical group seemed to really like this.  I should note that 10 minutes into the activity, their paper was blank and when I asked how they were doing they said "we give up."  At the end, the "Thanks for doing this.  I really learned today" comment came from this group. 

Two other students today also had problems creating graphs of 1/x.  Sitting down and talking with them, it became apparent that the concept of "plugging in a value" for x was completely foreign.  Well, this is a pretty crucial thing in algebra! While we didn't get to the concepts of asymptotes, these students did get some extra personal attention with the functions and ended up creating some decent graphs.  In situations like these, I don't care if we don't cover all the material: going back and building the foundation is more important.  I'm glad we got the chance to do a little of that today.  Also, I think the ability to find these gaps in foundation are good: I wouldn't be able to do this from looking at the quizzes, but it was easy once we started talking.  Noticing that dialogue was so helpful, I really pushed tutoring on a lot of students today, and they seemed excited to go.

While from the above two paragraphs you might get the impression that I think this was the best thing ever, there are a bunch of areas for improvement.  One problem was having the two kids with the worst attitudes in the same group.  They were off-task and loud, but fortunately they were the exception.  On another day (perhaps a warmer one) this whole class has loud and rowdy potential.  Choosing groups beforehand will help with this, and also help us pair over-achievers with those that need more attention.  Also, I acknowledge that not all students learn better in this format.  At least one girl mentioned "I think I like regular class better," so this format certainly can't supplant traditional lectures.  The thing I was most happy about was the fact that almost everyone seemed to be engaged with the material and that there was a good amount of positive feedback.

As Mrs. Colwell mentioned, the real metric of success will be on the test!  I hope they perform well on their upcoming quizzes!

PS:  Guess who got her books and backpack back, and guess who had them?  BOOYAH!