Problem Based Learning

 

I once had an awesome curriculum specialist come and explain Problem Based Learning to me as it applies to math (I've heard of Project Based Learning as well, but this is a shorter math version.)  I'll try to summarize it in a way that it hopefully is understandable.  I was experiencing a real challenge teaching two-step and three-step problems to my students.  Is your experience similar with your students?  When in doubt, third graders just add everything, right?!  They just could not seem to grasp which steps to take because they weren't really understanding the problems.  They could do one-step problems pretty well, at least I had that to build on.  The technique is to present the class a "challenge problem."  I pull them up to the floor and tell them I am having difficulty solving a problem, and I really need their help.  I personalize it, and make it as real as possible (this is KEY).  I try to use each student's name in a problem before the year is over.  I keep the problems on my computer desktop and just change the names from the year before!  I might start off saying, "I have a problem and I need your help.  I am planning to do something special for the class and I need to figure out the cost.  I need each of you to help me think it through and come up with the answer.  Can you all help me with this?"  Of course they want to!  And...of course they want to know if we get to have a party.  I tell them that we will soon (followed by, "yessss," and giggles, and I follow up on as soon as I can!)  One of the problems was similar to this: 

We have 18 students in our class.  I want to have a party, but I'm not sure how much it will cost.  I want to buy some cupcakes and drinks for our party.  If cupcakes are $8.00 per dozen and drinks are $.50 each, how much will I spend on the party in order to have enough for every student?

Now we may never have one quite like this on a standardized test...but then again, we may!  I like this kind of problem for several reasons.  It first makes the students figure out how many packages of cupcakes they will need (must know how many in a dozen), then they have to calculate the costs of both cupcakes and drinks.  For the drinks, some groups will start to add .50 eighteen times!  Somewhere along the way, a student may come up with the idea of grouping $.50 into dollar sets.  Some others may attempt to multiply 18 x .50, and some other brilliant child might decide that the cost would be half of 18 since .50 is half of a dollar.  Who knows what brilliance is in your midst!?!  The beauty of Problem Based Learning is that there are several ways to arrive at the answer.  They just need lots of time to talk and think!

I put the students in groups of three (no less than three, no more than four.)  This is a great opportunity to mix up the usual groups. I post the problem several times (typed in a large font) spread out around the room for each group to have their own space.  I staple the problems to the wall near the floor where the kids are sitting so that each group has its own page.  Each student gets the problem on a clipboard for thinking and showing work.  They sit with their group of three and one of them re-reads the problem.  While you could assign jobs within the group, I find it works the best when they just all begin to talk about it.  I do have to teach them to listen to everyone in the group.  My part is to walk around the room and listen.  I don't help them, but I might ask a guided question here and there, or I might say, "What operation do you think you might start with?" or "Wow, Jerry, sounds like you are really thinking!"  This gets the group to listen to Jerry who is on the right track!  The conversations are fantastic.  Sometimes one student sounds like a little parrot, mimicking me, and I have to turn my head and not laugh!  They begin to solve the problem, step by step.  I hear them correcting each other and sharing ideas about what to do first.  Reminders of respect are part of my job as I walk around. When a group is finished, I hand them a sheet of construction paper and have them make a "final copy" of how the group solved the problem.   If I have an early finisher group, I ask them to extend the problem.  I might hand them a little strip of paper (after I have them make sure they all agree on the answer!) that has the extension question.  For the extension to this problem, I would ask them,  "would I had any cupcakes left over, and if so, how many?" or, "what if there were 24 students in the class?" If there is still time left, I hand them some flashcards or a quick center game to do until everyone is done.

I then take up the finished final copies and tape them to the main board.  I have a group come up and one or two of them explain the steps they used to solve the problem.  Of course some have incorrect final answers, but there is always something to brag about.  It might be a step they did exactly right, neatness, or just the way the group worked together.  This method has absolutely changed the way I teach the more difficult word problems.  Since I do Guided Math most days, this is great for Fridays.  It does take awhile, so block out about an hour or more.  The kids love it and do I!  I have done this activity for an evaluation.  I've had our a.p. come to observe me and she ended up sitting on the floor with a group and listening to the kids talk about the problem they were solving.  I loved that, and I got a great eval.!  I plan to offer my problems on TpT soon.  

I will take pictures to add to this post next time we do a PBL lesson in class.