The One Where Students Think

I thought I would share the way my students "do" math in my classroom.  I'll admit it is a teaching style that I'm learning as I go.

Growing up my math teachers would work three or four examples for the class and then we were expected to do twenty problems on our own.  Every math teacher I had taught this way.  Though I always made good grades in Math it was because I could copy what my teacher did.  It was never because I had a real understanding of the math.

A few years ago when I taught math for the first time I swore to myself that I would not be that kind of teacher.  I want my students to understand the math.  I want them to be problem solvers.

I'm not perfect at this teaching style, but I'm learning right along with my students.

When I want to introduce a new concept I present my students with a task.  For example we are studying fraction in 6th grade so last week I presented my students with this problem: 

Jason has 3 1/2 candy bars.  He wants to share the candy bars with his friends.  He gives as many of his friends as possible 3/4 of a candy bar.  He keeps the rest for himself.

Part A: How many friends can he give 3/4 of a candy bar to?  Show your work and write your answer in a complete sentence.

Part B: How much of the candy bar will Jason keep for himself?  Show your work and write your answer in a complete sentence.

The first thing my students do is spend some time with the problem by themselves.  We call it individual time.  During this time they know that I will not answer any questions.  They are not allowed to talk to a neighbor.  I just want them to think about the problem on their own.

For some of my students this is incredibly difficult.  They have never been asked to figure out a math problem by themselves.  Some of them get frustrated sometimes, but I believe learning comes through struggle.  I believe there is a good kind of struggle and that is what I want my students to experience.

After they have had time to work on it individually I then allow them to talk about the problem with a neighbor.  Depending on how my desks are arranged, sometimes they talk with one person and sometimes they talk with their table (4 students to a table).   During this time they are to discuss their answer and what strategy they used to arrive at that answer.  If there is any disagreement about what the answer is they are to work together to figure out the correct answer.  I'm walking around listening to these discussions.  It is a great informal assessment.  I'm also strategically selecting students for the next part.

The next step is for a few students to share their work with the class. I like to start with a student who used a simple strategy and work up to a student who used a more advanced strategy.  We have set norms on how it should look when students are sharing their work.

The student sharing walks us through his or her thinking while other students watch and listen.  Sometimes they work it out on the white board.  Other times I show their work using the Elmo.  After the student is finished explaining he or she then asks the class if they have any questions and calls on any student that has a question.

Ya'll this is when some of the best learning takes place in my room.  It is not when I'm standing up front teaching but when my students are teaching each other.  They can come up with questions that are harder than anything I would have asked.  It is also good for the student explaining to have to field these questions.  

Some of my favorite AHA moments are when I have a student who doesn't quite have the right answer.  Often they will discover their mistake on their own while they are explaining.

As you can imagine it is very difficult at times for me to just sit back and not say anything.  However it is well worth it to see my students discovering things on their own.