Another Take on Problem Based Learning for Math

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I have been wrestling with the marriage of Project Based Learning (PBL) and Math for nearly 8 years now.  A few years ago I moved towards Problem Based Learning (PrBL) instead of Project Based for math. It just seemed to make more sense.

With PrBL there are shorter time periods to complete a problem which, to a math teacher, frees up more time for "Math Skills." Of course a veteran math teacher, using inquiry-based teaching (PBL or PrBL fall into this niche), will find opportunities for practicing math skills.

Once a teacher decides to pursue PrBL, he or she will need to figure out which math units fit best. Or at least that is what I used to think. Now, after years of working with this, I realize that instead of figuring out which units and then what specific problems to work with, there is a better way.  Teachers need to start the planning process with great "Open-Ended Questions."

Now I use the term "open-ended" loosely because many of the problems I found with that label were actually closed problems.  The open-ended problems I am looking for may have multiple solutions but they may just have multiple paths that can be taken to get to an appropriate solution.

So here's a problem I found for middle school students (taken from the Math Forum):

I can see this being used as an introduction to area. During the first day's questioning I would hope there would be obvious questions about how to calculate area. But I would also hope to hear questions about whether the "whole number dimensions" have to be in feet. Could they be in "whole" inches? How about a question about whether "rectangular" means it has to be four sided - could it be a composite figure of rectangles? There might be a question that comes up that I would never think of.

The beauty of this is that the students can explore their specific questions to solve the problem going down a path of their choosing. At the end of the week the real question is: "Can the students solve a 4-sided, rectangular figure, with a length of L and a width of W?"

My big AHA! then was this - what if I found 20 or 30 or 50 great open-ended questions that represent content I want my students to learn during a school year?  I could then lay these questions alongside my district Year at a Glance or Pacing Guide to see where the questions would make sense on the calendar.

Now as a teacher gets to each unit they will already have 2 or 3 (or 5) open-ended questions that have been vetted. These will be the problems used in class to foster inquiry.  These problems will take 3 or 4 days from start to finish. There will be opportunities for questioning and brainstorming; creating drawings or other models; presentations; and reflections.

For example, the questioning and brainstorming might be completed on the first day. The modeling (along with the requisite critical thinking) might be on day two. On the third day there would be an opportunity for an informal presentation of how the groups solved their problems, followed by a reflection. On the last day of this PrBL there might be an assessment on the learning that was completed.

This all started from having a sound, content specific, question that fueled inquiry, questioning, and thinking. Using an open-ended question allowed students to go in different directions in pursuit of answers. Successful students ask questions, think critically, and defend their ideas. That is where deeper learning happens and that is how we help our students develop perseverance.

What is Essential For Successful PBL?

   

http://earthmosaic.org/index.html

This year the Buck Institute for Education (BIE.org), of which I am on the National Faculty, is re-examining the "Essential Elements" for PBL.

As I was thinking about it I remembered that I have posted about these elements a few times, over the years, and I came across this post from July of 2013.

So, in the essence of recycling, please read it again, or read it for the first time, so that you too can begin thinking about what the Gold Standard should be for PBL:


THE NINTH ESSENTIAL ELEMENT OF PBL(7/7/13) -  I am about to work in my last co-facilitation with the Buck Institute for Education (BIE.org) doing what they call a PBL 101. A basic, 3-day, course in the planning, managing and assessing of a PBL project.

Within a project most people can agree that there are certain items that make it successful and BIE has narrowed the list down to 8 items that they call the 8 Essential Elements of PBL (see the diagram to the left).

Anyone who has truly done PBL knows that there must some sort of significant content, there must have been a way to establish a desire for inquiry (in this case by having a driving question and by overtly discussing what it is the students will need to know), and there must be a public audience so students feel an added desire to do their best.

Through group work, research, and the inquiry process students end up having to do, what most people call, 21st century skills.  These skills include, but are not limited to, collaboration, critical thinking, communication (orally and in writing), and creativity. Finally, there must be a chance for students to have their work assessed. At that point, they must be allowed to revise their work and reflect on their assessment. This ensures the final product is something the students are proud of and the product demonstrates the knowledge that the students have gained during the project.

As I said, most people can agree that these 8 elements are key components of a classroom or school that uses PBL as the primary mode of instruction. But these elements are not as connected as the diagram might suggest. The glue that holds these 8 elements together is the classroom, school, or even district culture. Culture is the 9th Essential Element. Without a proper culture students might not be allowed to have voice and choice in the products they work on. Without a proper culture students might not be willing to do revisions of their work or they may not feel a need to reflect on their learning.

Even the 21st century skills can be restricted when there is not a culture of collaboration; students aren't encouraged to think critically; student communication is not allowed or shown as unimportant; or when students have no outlet to show their creative side. Each of these issues with students comes directly from the way teachers and administrators interact.  If the teachers don't collaborate, communicate, or get a chance to try creative things in the classroom then there is a shadow upon the entire school culture that can't be ignored.

So, teachers, as you finish your PBL 101,  your New Teacher training with the New Tech Network, or some other PBL training this summer, remember to work hard and stay positive. You can do this. But get your fellow teachers and administrators involved in what you are doing. Get the PTA or other parent organization involved too. It is time to work on the entire educational system so that you and, more importantly, your students can be successful pursuers of inquiry.

Make That Desert Project More PBL'y

http://goo.gl/XqZSjZ

Friend of mine had their son bring home a "project" to make a cell membrane.  I sighed. But then I thought about how the teacher could have done something with the same material.
And it hit me - science teachers need to see how to take that internet or youtube project and make it a PBL project.

So, I googled "make a cell membrane project," just now to simulate this process that the teacher might do.  Based upon 13 ratings it (the one I selected) had 4 stars (out of a possible 5) - so it has to be pretty darn good, right?

The Objectives of this project: (1) To build a model of a cell membrane and (2) to investigate how the cell membrane regulates what moves into and out of cells.

The "Research Questions" of this project: (1) What molecules of the cell membrane do the cotton swabs represent? -and- (2) If a molecule needs to enter or exit the cell and it cannot fit between the phospholipids, how can it cross the membrane?

Reading this made me think of the movie I enjoyed as a young boy: Fantastic Voyage. And I suddenly had a concept for the project. What if the students read the book or watched the movie and had to write their own chapter for the story where the crew had to move between cells in their craft.

http://goo.gl/1YsMlm

What if they had to create a cell and craft that were able to fit on a small table (for display)? What would they make the cell out of? What if they were required to explain how the craft moved through the cell walls?

Let's roll with this idea - Students are working for a toy company who will be working with a movie company creating an updated version of the movie "Fantastic Voyage." They are to create a mock up of a vehicle and a cell that would be scientifically accurate and will be sold to children ages 8 to 12. Their cell structure is to have an educational value and must be able to show the structure of a cell and must demonstrate the process of a molecule crossing a cell membrane. And, for this situation, the vehicle the crew will travel in must move like a molecule.

There you go. (Almost) the same project that I found on the internet. Except, in this case, the students are given the task of creating a cell structure that can demonstrate molecules crossing the cell membrane. They will have questions that will lead to inquiry (we can assume) which, in turn, will lead to a need for scaffolding (by the teacher or a guest lecturer) about how cells function.

And, if done right, students will have to interact with a book or a movie giving this project an additional literacy angle for a written product.

I'm not a science teacher but I'm betting your average science teacher could take what I suggested and run with an awesome (and fun) educational project that will help students understand the cell structure and the function of the various parts of a cell.

If you are a good science teacher tell us about this project by using the resources at BIE.org.  Start with the Project Planner.  Once you have it all planned out send me a link in the comments section and then I can share it out on Twitter to our science friends using #scichat.