Making Math Problematic



"When will I ever use this?" is a question that many math teachers hear on a regular basis. Why do students have such a problem connecting mathematics to their own lives? Furthermore, why are students asking the question in the first place? Perhaps it is because of the traditional approach to mathematics that many teachers use: (1) introduce concept, (2) define key terms, (3) work out examples, (4) practice. This course seeks to engage teachers into adding additional approaches to their repertoire, more specifically authentic problem-based learning (PBL) activities. Participants will explore first the need for change in the mathematics classroom, then the general procedures of PBL, moving on to exploring authentic tasks, and finally assessment in PBL.

Course Objectives

Given a variety of tasks, participants will be able to determine if tasks are problematic in nature and furthermore which are authentically problematic.

Given a variety of mathematical standards, participants will be able to generate a variety of authentic problem-based learning tasks.

Given a problematic task, participants will be able to determine and design effective assessment procedures.


Unit 1 - A need for change focuses on the need for new approaches in the secondary mathematics classroom. One suggested approach involves learning math through authentically problematic situations arising in the real-world.

Unit 2 - Anatomy/Implementation of a Problem Based Lesson focuses on how problem based learning activities/approaches should be implemented within the classroom, by focusing on role-shifts, structure, and the nature of problems.

Unit 3 - Authentic Tasks provides examples of problematic tasks which are authentic in nature. It serves as a platform for instructional designers to develop their own problematic tasks, as well as a small archive of resources.

Unit 4 - Assessing Problem Based Learning Activities focuses on how best to assess and provide feedback in PBL. It is designed to offer examples of ways to assess.

Unit 5 - Additional Resources/Links begins as an incomplete wiki page, to be filled in by participants of this course. As you research your own methods, you will surely find resources of great value to you. Use this space to share those resources.


Ertmer, P., Simons, K. (n.d.) Scaffolding Teachers’ Efforts to Implement Problem-Based Learning. Purdue University. Retrieved from:
Gerdes, D. (2011) PBL Teaching and Learning Template. Illinois Mathematics and Science Academy. Retrieved from:
Kaitlyn King's Problematic Mathematics: PBL designed for the math classroom
Macdonald, R. (2005) ASSESSMENT STRATEGIES FOR ENQUIRY AND PROBLEM-BASED LEARNING. Sheffield Hallam University. Retrieved from:
Meyer, D. (May 2010). Math class needs a makeover [Video File]. Retrieved from
Roberts, N. (n.d.) PROBLEM-BASED LEARNING (PBL). Southern Illinois University. Retrieved from:
Problems with a Point
What I Would Do With This: Groceries
Zero Knowledge Proofs - A Billion Nickels

Wiki Links

Serafina Chinappi - Needs Assessment/Learner Analysis