Implementation Strategies
Return to: Problem-Based_Learning_in_Mathematics
Lesson Objectives
By the end of this unit you will be able to do the following:
- Identify the steps necessary to foster an effective problem-based learning environment.
- Describe the stages of a problem-based lesson.
- Evaluate problem-based lessons.
- Choose various aspects from sample lessons that suit their classroom culture and teaching styles.
Introduction
In this lesson, you will learn how to develop and enforce an effective problem-based learning environment. When incorporating problem-based learning into your lessons, you are most likely venturing into uncharted waters. Making the transition from knowledge provider to facilitator of learning can be a challenge for you and for your students. When a child first learns to ride a bike, they often do not just jump on a two-wheeler bike without any support. Instead they begin with a balancing bike as a toddler, transition to training wheels, and finally try a full-fledged bike with help from a guardian. This also holds true for pedagogical instructional approaches.
As you learn about problem-based learning, it is important to look to experienced teachers for advice. According to Briggs:
“The reality is that learners who are new to PBL require significant instructional scaffolding to support the development of problem-solving skills, self-directed learning skills, and teamwork/collaboration skills to a level of self-sufficiency where the scaffolds can be removed” (2015).
Students will not grasp problem-based learning overnight. It will be necessary to give students time to understand the purpose of problem-based learning, process the change, and develop the skills needed for success.
Fostering an Effective Learning Environment
Before a problem-based learning approach can be implemented, you must develop a learning environment that is conducive to collaborative problem solving.
Set Clear Goals and Expectations:
Andreescu, T., Cordeiro, K., & Andreescu, A. (2020) suggest that teachers should begin the school year on the right note with a mission statement:
"Mission statements set top-level goals for the class, provide a cohesive team environment, and allow students to assess their contribution to the group."
The idea of offering a "mission statement" is modeled after successful business practices; businesses often have statements that explain what their company is all about. When teachers begin the year by stating the goals of the course and explaining the path to these goals, students can begin to see the bigger picture and gain an understanding of where their teacher's heart is. Therefore, by writing a mission statement for your class, you are exposing your students to what they may see in the future and setting the tone for your course. Mission statements can be written by the teacher or as a collaborative effort with students.
Activity: Write your own Mission Statement:
The following Google Doc has a sample mission statement written by the authors of Awesome Math. Read it over and write a mission statement for your own course. If you would like to share the statement you have written, please add it to the Google Doc.
Write your own Mission Statement
Scaffolding:
Problem-based learning requires students to draw upon skill sets that may not be fully developed. Therefore, it is crucial to have effective scaffolds in place.
- One scaffolding suggestion is to start off small and ease your students into problem-based learning. Begin the school year with 15-minute, lower-level problem-solving activities. During this time, introduce group work expectations, allow students time to get acquainted with the process, and provide a significant amount of support. As you progress through the year, slowly increase the level of difficultly and decrease the level of support.
- Provide a problem-solving template. Some students freeze at the start of a problem because they do not know where to begin. If given a specific outline to follow, students are more likely to participate in the activity.
Scaffolding Article: For more information on scaffolding techniques, read the following article:
Scaffolding for Optimal Challenge in K-12 PBL
Other Tips:
- Set and Model Clear Expectations: Arrange desks to support collaboration, enforce kindness and a growth mindset, & encourage risk taking and mistakes.
- Know Your Students: Understand what each student can bring to the table.
- Have a Plan: Design a clear road map for the year.
- Develop Your Style: Inspire your students to be better problem-solvers.
- Andreescu, T., Cordeiro, K., & Andreescu, A. (2020)
Basic Structure of a Problem-Based Learning Lesson
Problem-based learning lessons can take on many forms, but most follow this basic structure.
- Begin with a Problem: The lesson begins with a meaningful, relevant problem.
- Initial Brainstorm: Students work in small, collaborative groups to analyze the problem. In this step, students determine what they know and what they need to know.
- Learn a New Skill or Concept: At this stage, students have pinpointed any knowledge or skill deficiencies they may have. This is where the learning takes place. Students learn new mathematical skills and concepts, through research or with help from the facilitator, when it is necessary to use them.
- Application of New Knowledge: Students then apply their new knowledge and solve the problem.
- Present Strategies: After the problem has been solved, students present their strategies to their classmates using a chosen platform.
- Reflect: Finally, students reflect on their experience.
What is a Meaningful Problem?
Meaningful problems should play on the natural curiosity of kids and engage them in the solving process. Andreescu, T., Cordeiro, K., & Andreescu, A. (2020) claim that good problems should have at least two or three of the following characteristics:
- They take several steps to solve.
- More than one approach can be used to arrive at a complete solution.
- They lend themselves well to collaboration with peers.
- They require meaningful problem-solving that promotes flexibility of thought and innovation.
- Mathematical learning and reasoning are integral to the process of solving the problem.
- To solve the problems, students must work around obstacles to understand the unknown.
Sample Problem-Based Learning Lessons
In this section, you will fully immerse yourself into problem-based lessons. As you partake in the following activities, keep in mind the characteristics we discussed above. Think about what makes the featured problems “good problems.” While exploring these lesson plans and designing your own, think about the role of the students and the role of the teacher. What will you be doing while students are actively problem solving? Finally, take note of any common characteristics of the lessons.
Watch the following Youtube video for a "live action" project-based learning lesson. Although this video demonstrates project-based learning and not problem-based learning, the classroom environment and the lesson features are the same.
- Peruse the following website. It contains problem-based learning curriculum maps, sample problems, and lesson plans.
- For more information, read the following article:
Reflection
Now that you have had the opportunity to explore the structure of a problem-based learning lesson, take a few minutes and reflect on the following prompt.
- Describe the stages of a problem-based lesson and identify the steps you deem to be the most important to foster an effective problem-based learning environment.
After you have finished your reflection, you may proceed to Lesson #3: Assessments & Feedback
References and Resources
Ahamad, S. N., Li, H., Shahrill, M., & Prahmana, R. C. (2017). Implementation of problem-based learning in geometry lessons. Journal of Physics: Conference Series
Andreescu, T., Cordeiro, K., & Andreescu, A. (2020). Awesome math: teaching mathematics with problem-based learning. Hoboken, NJ: Jossey-Bass, a Wiley Brand.
Briggs, S. (2016). 10 Tips for Effective Problem-Based Learning: The Ultimate Instructional Solution. Retrieved from https://www.opencolleges.edu.au/informed/features/problem-based-learning/
ConnectEd (2014). Project-Based Learning: Beyond the Textbook. Retrieved from https://www.youtube.com/watch?v=DNppMPBtAK8
Kim, N. J., Belland, B. R., & Axelrod, D. (2018). Scaffolding for Optimal Challenge in K–12 Problem-Based Learning. Interdisciplinary Journal of Problem-Based Learning, 13(1). doi:10.7771/1541-5015.1712
Problem-Based Learning in Mathematics
Lesson #1: Features of Problem-Based Learning
