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#2 Tips for Planning Successful Problem-Based Learning in Your Math Classroom

Written By: Julia Watson, Ph.D., Exemplars Consultant and Gifted and Talented Specialist

In her last post, Dr. Julia Watson provided an overview of Problem-Based Learning (PBL). In this segment, she offers suggestions on how teachers might go about incorporating this approach into their classrooms. You can access her first post here.

Where to begin?

(1) Think of your students, of their ages, maturity levels, and their interests. What school-level project possibilities might exist, just outside the classroom door? What local (community) issues or priorities could be integrated as a math challenge?

(2) Begin to map out your ideas in two sections, with Section I preceding Section II:

  •  Section I: Addresses preparation by a teacher/team.
  •  Section II: Deals with implementation for the unit in the classroom, either as a whole class or for a small team who may need this type of challenge.

What does it look like?

The following is an example of a possible PBL “experience” based on a local news article:

A recent proposal is being considered that may partially remediate Elm City’s budgetary crisis. At the last city council session, members suggested reducing the city debt by not funding the animal shelter for the next fiscal year. This recommendation is one of the possible cuts mentioned concerning the city budget. The suggestion caused immediate concern and debate among the citizens who attended the meeting. The suggestion has been tabled until the next meeting, in one month.

What are the steps?

(1) Define important questions for the unit.

  • What are the economic costs of having an animal shelter each year?
  • What is the impact on the city if there is no animal shelter to house stray and/or abandoned animals?
  • What information is needed and how can this information be presented to the city council so they are able to make a well-informed decision about the animal shelter?
  • What are some alternative solutions and costs for our community in order to provide for stray and abandoned animals?

(2) Select standards and learning outcomes to be developed during the PBL experience.

  • Based on your state standards and local curriculum, what mathematical possibilities exist within this problem?

(3) Integrate across content areas, making connections.

  • Brainstorm possible content area connections, network with other teachers/instructors to connect the learning possibilities.

(4) Define a possible problem statement.

  • What information about the possible closing of the animal shelter should we present to the city council so that they can make an informed decision that will be amenable to the community?

(5) Design assessments for the unit.

  •  Identify ongoing “check points” and formal/informal measures.

(6) Determine length of unit.

  •  Think of time frame and need to “be ready” for next session/end of unit. Set timeline, possibly working backwards.

 How do I implement the PBL experience with students?

(1) Meet the problem.

Sunflower City in Colorado has determined that in order to meet the city’s requirement for debt reduction by 20% the city has proposed a number of items to be cut from the budget. One of these is the support funding for the local animal shelter. Without this additional funding, the animal shelter cannot stay open. Concerned fourth graders have decided to present at the next city council meeting. The fourth graders job is to convince the council members to review alternative solutions and to convey the impact closing the shelter will have on the community. The meeting will be held next month.

(2) Construct “Know/Need to Know” statements.

  • We know Sunflower City’s proposal to cut the deficit.
  • We know some of the animal shelter needs.
  • We know students’ perceptions about what happens to abandon animals.
  • What are the operational costs for the animal shelter per month and year?
  • What are the donation and adoption monies received by the shelter per month and year?
  • What are the consequences for the closure for the city, the citizens, and the community?
  • How does this impact the city as a community?
  • What are alternative solutions?
  • What donations or sponsors can support the shelter?
  • What are the needs of the animals if they are left to roam the city untended?
  • What are the opinions of the community members for a place to house abandoned animals in the city?

To answer our “Need to Know” statements we need to:

  • Create a KWL chart.
  • Complete a cause and effect graphic organizer.
  • Determine flexible groups to research various solutions.
  • Obtain resources from multiple areas.
  • Create a financial fact sheet.
  • Create a list of questions for the animal shelter.

 (3) Class defines the problem statement.

How might we present accurate information regarding the effects on the community of not having a way to care for homeless animals in our city so that the council can make an informed decision about the management of the animal shelter?

(4) Students gather information.

Activity I: Making Connections.

  • Economics: Review alternative sources of funding including sponsors and grants and economic impacts on the community of the loss of the shelter.
  • Civics: Learn decision-making process of the council and gather multiple perspectives of the community.
  • Science: Investigate animal needs, such as food, water and shelter. What are the impacts if needs are not met?

Activity II: Financial Analysis Assignment. Each subgroup receives a financial fact sheet that answers the following financial questions:

  • How many animals are there on an average each month?
  • How many of each kind?
  • What does it cost to feed them?
  • What are the personnel and building costs?
  • What additional monies are donated and where are they from?
  • What are the costs of running the shelter per month and annually?
  • What would be the funds needed to replace the budget cut by the city?

Students use this information to create a balance sheet of funds coming into the shelter and shelter expenses per month. Next, they determine the costs annually. They calculate the income after the 20% reduction from the city and determine how much funding the shelter will lose if the cut occurs.

(5) Students share information with class.

(6) Students generate possible solutions to the problem.

(7) Students determine best-fit solution.

  • Which solution can be best prepared in time to present to the council?
  • Which solution will present the researched information most clearly to the council?
  • Which solution will most impact the decision-making process of the council?

(8) Solution is presented.

(9) As a class, debrief the PBL experience.

Discuss the effectiveness of the final presentation that was given to the city council and other members of the school and/or community. Think about:

  • What happened as a result of the presentation?
  • Were those the results you expected?
  • What are some other things you can do to support the shelter at this time?

Incorporating the 21st century skills of critical thinking, innovation and collaboration will empower our students to face challenges and problems, using their mathematical knowledge and skills. As educators, it is our task to help students develop skills to work with others to solve these future problems. Problem-based learning provides an effective instructional strategy for this purpose … and who knows, maybe Train A will never overtake Train B anyway …

What are some PBL opportunities that you have found effective with your students?

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