Unit 1: What is problem-based learning & why is it beneficial?

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"For the things of this world cannot be made known without a knowledge of mathematics"
-Roger Bacon

Unit Objectives:

  • By the end of this unit you will be able to do the following:
  • When given a prompt you will be able to describe, identify, and explain important aspects of problem-based learning through a journal entry.
  • When given a question, you will be able to characterize the benefits of problem-based inquiry through a reflective journal entry.

The Problem:

Students are unable to recognize and solve problems, students lack critical thinking skills, and students rely heavily on the teacher for answers.

  • Many students believe that there is one single answer and one way to obtain that answer, when in reality there are multiple solution methods to any known problem. Thus, if educators want students to become critical problem solvers, ready to accept the challenge and tackle the problem, conventional practices in the math classroom need to change.
  • Watch the following YouTube Video (12 minutes in length) to help understand where the Math curriculum is and where it needs to be...The Math Curriculum by Dan Meyer. While watching the video think about the following questions: What is wrong with math instruction today and what does Dan Meyer suggest we do to improve math education?

Problem-Based Learning:

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  • Problem-based learning describes an environment where 'problems' drive learning. Or in other words learning begins when there is a problem to be solved and the learner must gain new knowledge in order to solve that problem. Learning is therefore driven by problematic mathematics rather than by the memorization of facts, formulas, and procedures. Students no longer seek single answers, but they instead gather information, pose and identify different solution methods, evaluate their options, and then present a solution. The ultimate goal of math education is to promote understanding and transfer; students understand mathematics when they invent and examine their own solutions for solving mathematical problems, which is what PBL strives to achieve. Thus, "problem-based learning is a classroom strategy that organizes mathematics instruction around problem solving activities and affords students more opportunities to think critically, present their own creative ideas, and communicate with peers mathematically" (Roh, 2003, p. 2).


  • Read the following article to see the importance of problem-based learning in the mathematics classroom. While reading the article think about the following questions: What defines a problem? How do students develop problem-solving skills and what inhibits students from learning such skills in the conventional classroom? What role should the teacher play if problem- solving skills are desired? Note: The link brings you to the homepage of the article, to view the article either download the PDF version or the HTML version, both are free ...Problem-Based Instruction in mathematics.
  • After reading the article, go back and look at the final results, what do they show? Should problem-based learning be used in the average math classroom? Why?

Benefits of Problem-Based Inquiry

  • Since problem-based learning begins with an actual problem, students gain important skills that not only help them in the math classroom but these skills transfer to other academic disciplines and into future careers. Students develop problem-solving, creative-thinking, and critical thinking skills while engaging in problematic mathematics. Students also learn the importance of collaboration, communication, and reflection. Instead of the teacher acting as the main source of mathematical information and the evaluator of “correctness” the students act as their own evaluators, checking themselves and their teammates through communication. The students therefore, learn how to determine correctness on their own, since mathematics should make logical sense. This therefore implies the development of metacognitive skills.


  • "...Participants in problem-based experiences generate more accurate hypotheses and more coherent explanations, are more able to support claims with well-reasoned arguments, and show larger gains in conceptual understanding in science” (Darling-Hammond, 2008, p. 45). In the realm of mathematics, students have an increased understanding of mathematical concepts, word problems, and planning capabilities. They also acquire positive attitudes toward mathematics in general and the teacher’s feedback (p. 45). Thus, students gain an in depth understanding of mathematics in a PBL environment. This approach allows students to change and adapt their thinking and methods to new situations. There is no longer a cookbook style recipe to follow where rules, exercises, formulas, and procedures occupy precious classroom time. Students in PBL environments have the opportunity to learn mathematical processes and skills that are associated with communication, representation, modeling, and reasoning.


  • For more information on the importance of problem-based inquiry and the correlating benefits, please visit the following Wiki Space: Problem-Based Learning in Math by Joanne Contreni


So what does this look like in a Math classroom?

Take a look at the following Youtube video and reflect on the benefits and importance of such inquiry Applying Math Skills to a Real-World Problem. While watching this video, think about the general definition of problem-based learning and then see how it fits into the math classroom. How did the teacher begin the initial lesson? What benefits do you see culminating from such inquiry? How and why are the students engaged in the mathematics?

Pencil.jpg Reflection:

Now that you have been introduced to problem-based learning, the correlating benefits, and have analyzed case study results, take a few minutes and reflect on the following prompt.

  1. How do PBL and traditional styled classrooms differ?
  2. Explain, in your own words, the important aspects of problem-based learning.
  3. How could PBL be beneficial to your classroom? Think about and incorporate the different aspects and benefits of problem based learning in your reflection.


After you are finished with the reflection, you may proceed to... Unit 2: Designing Problematic Tasks

References and Resources:

Darling-Hammond, ML. (2008). Powerful learning:what we know about teaching for understanding. San Francisco, CA: Jossey-Bass.

Reeder, E (Writer). (2010). Applying Math Skills to a real life problem [Web]. Available from http://www.youtube.com/watch?v=hxufdpcfpJY

Hiebert, J., Carpenter, T. P., Fennema, E., Fuson, K. C., Wearne, D. , Murray, H.,…Human, P.(1997). Making sense: Teaching and learning mathematics with understanding. Portsmouth, NH: Heinemann.

Meyer, D. (Videographer). (2010). TedxNYED [Web]. Available from http://www.youtube.com/watch?v=BlvKWEvKSi8

Problem-based instruction in mathematics and its impact on the cognitive results of the students and on affective-motivational aspects. (2009).Educational Studies, 35(3), Retrieved from http://www.informaworld.com/smpp/content~db=all?content=10.1080/03055690802648085

Roh, K, H. (2003). Problem-based learning in mathematics. ERIC Clearinghouse for Science Mathematics and Environmental Education, Retrieved from http://www.eric.ed.gov/PDFS/ED482725.pdf

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Return to Problematic Mathematics: PBL designed for the math classroom

Unit 1: What is problem-based learning & why is it beneficial?

Unit 2: Designing Problematic Tasks

Unit 3: Assessment & Feedback

Extended Resources (PBL in math)