Unit 1: What is Problem-Based Learning and Why is it Important?

Home Page: PBL in a Mathematics Classroom

Unit Objectives

1. The learner will describe Problem-Based Learning in his/her own words.

2. The learner will identify by naming characteristics of Problem-Based Learning.

3. The learner will state orally the need for Problem-Based Learning in the classroom.

4. The learner will classify by writing the roles of the teacher and student in a Problem-Based Learning environment.

5. The learner will identify differences between a Problem-Based Learning environment and a traditional classroom environment.

Why Math Needs to be Important to Our Students

♦ Watch the following YouTube video to help understand why students need to be motivated and interested in mathematics...Real Math

Think about the following questions while watching the video:

• Why is math important?

• How have I used math in my life outside of school?

• How will my students potentially use math once they graduate?

The Problem with Mathematics Classrooms Today

Many Students often lack the deep conceptual understanding necessary to solve new problems or make connections between mathematical ideas.

♦ Often, mathematics teachers present formulas before presenting information and problems to their students. Teachers walk their mathematics students through the step-by-step procedure to finding the solution to a simple problem after introducing them to the formula. This step-by-step procedure leads students to believe there is only one single answer to every mathematics problem. The practice of these problems drills the procedure into the students memory leaving them with the notion that every mathematics problem has one single answer. As mathematics educators, we know this is not true. One single answer leads students to believe there is only one process to finding a solution, causing rote memorization of this process, eliminating the development of critical thinking and transfer of knowledge between mathematical concepts.

♦ If mathematics educators seek to redefine the learning that takes place within their classrooms, to foster critical thinking, problem-solving, and collaboration skills, the lessons within their curriculum need to foster more opportunities for such skills.

Experiment

Choose one of the following problems to solve. Things to think about: Where do you begin? What information do you have? What do you need? How many solutions can you find?

1) Using four 4's and any operations, try to write equations that have the numbers from 0 to 50 as the answer. Example: (4+4+4)/4 = 3

2) What is the relationship of perimeter to area in any square?

3) Among grandfather's papers a bill was found: 72 turkeys $_67.9_ The first and last digit of the number that obviously represented the total price of those fowls are replaced here by blanks, for they are faded and are now illegible. What are the two faded digits and what was the price of one turkey?

Reflection In a journal, use the following questions as a guide to reflecting on the problem you worked on above:

1) Were you able to find more than one solution to the problem?

2) How is the problem different from a mathematics task a student usually encounters in the classroom?

3) How would your mathematics students benefit from this type of task?

4) What skills would these types of tasks foster?

Problem-Based Learning

Mathematics teachers must teach students not only to solve problems, but also to learn about mathematics through problem solving.

♦ Problem-Based Learning describes a learning environment where problems drive the learning. That is, learning begins with a problem to be solved, and the problem is posed in such a way that students need to gain new knowledge before they can solve the problem. Rather than seeking a single correct answer, students interpret the problem, gather needed information, identify possible solutions, evaluate options, and present conclusions (Roh, 2003).

♦ Read the following article, Five Ideas for 21st Century Math Classroom, to get a deeper understanding of why problem-based learning should be integrated into more classrooms. [A UAlbany ID is needed for this link. If this is not an option, please Google PBL in a Mathematics Classroom, and reflect upon what you found, focusing on the questions below, in your reflective journal.)

After reading the article, reflect on the following questions:

♦ What makes a problem a "good" problem?

♦ What are the five ideas that should be incorporated into a classroom to foster deeper understanding and collaboration between students?

♦ How does integrating problem-based instruction into a classroom relate to student-led solutions?

♦ Why is risk taking and collaboration important to the careers of 21st Century students?

What are the Roles of the Teacher and the Students?

The primary role of an instructor is to facilitate group process and learning, not to provide easy answers.

♦ With changes in the task itself and overall procedures in a problem-based learning environment, the roles of the teacher and the students must change from their original roles in a traditional-classroom setting.

♦ Beyond presenting mathematical knowledge to students, teachers in PBL environments must engage students in obtaining information and using their knowledge in applied settings.

♦ Teachers in a problem-based learning setting must:

• have a deep understanding of mathematics that enables them to guide students in applying knowledge in a variety of problem situations.

• know how to engage students in the processes of problem solving and applying knowledge to novel situations (Roh, 2003).

From a teacher's perspective:

• You have to allow the students to come forward - you have to do that. At the same time you have to provide some limits, but the most important is to be there for them. You have to keep an eye on the process that goes on (Dahlgren, 1998).

Why PBL?

♦ Read the short web-page, Why PBL?, for a quick insight into why problem-based learning is important to promote collaboration and critical thinking skill, skills needed by the 21st Century Learner.

♦ A problem-based learning environment provides students with opportunities to develop their abilities to adapt and change methods to fit new situations. Students have greater opportunity to learn mathematical processes associated with communication, representation, modeling, and reasoning in a problem-based learning environment (Roh, 2003).

Reflection

Now that problem-based learning has been introduced to you through various articles and videos, take a moment to reflect based on the following questions:

♦ What is problem-based learning? How is problem-based learning different from a traditional learning setting?

♦ Why is problem-based learning an learning path to be considered for your classroom?

♦ How could you benefit from problem-based learning in your classroom?

When you are finished reflecting, proceed to Unit 2: What is a Problematic Task?

Resources

Dahlgren, Madeleine A., Reinhold Castensson, and Lars O. Dalgren. "PBL From the Teachers' Perspective." Higher Education 36.4 (1998): 437-47. Education Full Text. Web. Sept. 2012. <http://www.cmmayo.com/d5mwearchives.november.html>.

Gasser, Kenneth W. "Five Ideas for 21st Century Math Classrooms." American Secondary Education 39.3 (2011): 108-16. Education Full Text. Web. Sept. 2012. <http://ehis.ebscohost.com.libproxy.albany.edu/ehost/pdfviewer/pdfviewer?sid=a8119d42-2a58-45a8-b05c-c63251ce3cdb%40sessionmgr104&vid=8&hid=5>.

MacMath, Sheryl, John Wallace, and Xiaohong Chi. "Problem-Based Learning in Mathematics." What Works? Research into Practcie. The Literacy and Numeracy Secretariat, Nov. 2009. Web. Sept. 2012. <http://www.edu.gov.on.ca/eng/literacynumeracy/inspire/research/WW_problem_based_math.pdf>.

Real Life. YouTube. Web. Oct. 2012. Retrieved from: <http://www.youtube.com/watch?v=Htq1IVN9bh8>.

Roh, Kyeong Ha. "Problem-Based Learning in Mathematics." ERIC Clearinghouse for Science Mathematics and Environmental Education (2003): n. pag. ERIC Digest. Web. Sept. 2012. <http://www.eric.ed.gov/PDFS/ED482725.pdf>

"Why PBL?" Problem-Based Learning at University of Delaware. Web. Sept 2012. <http://www.udel.edu/inst/why-pbl.html>.