Problem Based Learning In Math

A Teacher's Guide To Problem Based Learning
Specific To Splash - or - You're All Wet!
For those New to PBL

Problem Based Learning (PBL) “problems” may be different from most of the math “problems” you have encountered in your teaching experience.

Rather than “teaching” knowledge and skills aligned to the common core, and then testing to see what students have been taught, in PBL we present the student(s) with a real world problematic situation that includes an outline of “the test”. In the case of Splash - or - You're All Wet!, the test is stated in the last paragraph of the introductory page:
“Your task is to consider all of the data gathered for the five city pools, and to consider the wishes of the citizens of the city, and then to make a recommendation to City Council concerning what, if anything to do about the city's swimming pools next summer.”

Implicit in the problematic situation and the “test”, is the need to be able to master many common core, math concepts things such as:
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
(Common Core – Mathematical Practices)

and
Represent and interpret data.
(Common Core – Standard - Grades 1-5)

The scope of things to be learned in this activity is fairly limited. This PBL activity is designed as a manageable introduction to PBL, both for your students and for you the facilitator. The activity is designed to last no more than a few days to a week or so, depending on whether you meet with your students every day, or see them only a couple of times per week, as do some teachers of the gifted. It can also be used as a math center activity for advanced students.

Students should find themselves struggling to LEARN what they need to know to do what the “test” asks them to do. Your role is less that of a teacher and more of a facilitator / mentor. You should avoid teaching anything about the representation and interpretation of data to your students. On the other hand you should provide multiple resources (This is the time consuming part of a full scale PBL activity) that the students can use on their own TO LEARN about the representation and interpretation of data. .

As students begin to come to conclusions about the pools in Capitol City, and what, if anything, should be done about them next summer, you must again refrain from expecting “one right answer”. In fact, as PBL facilitators, we really don't care what answer the individual or group decides to pursue –
AS LONG AS THEY CAN SUPPORT IT WITH THEIR
DATA REPRESENTATION AND INTERPRETATION.

Sometimes it is tough to “let go” and allow students to develop a plan, that is not what we would do, or what we really would like to see them do. However the goal is not a pristine student plan, but rather (in this case - quality data representation and interpretation) seeing students LEARN the content and then USE what THEY HAVE LEARNED.

In a nutshell – PBL emphasis is much less on teachers teaching, and much more on students learning (mostly on their own – with resources provided) and showing what they have learned in a real world or simulated real world setting.