Why Word Problems Aren’t Real-World Problems

O.K., I should have probably stated, “Why word problems usually aren’t real-world problems,” but that’s not as catchy a headline. As someone who works with a wide range of teachers across the country, I do often run into the misconception that the typical word problem—at least the ones I found used in many classrooms across the country—represent “real-world” problems. For some reason, using words to present problems about baking and fractions or making change tip the scale towards authenticity in many educators’ minds. My goal is to push their understanding of exactly what is meant by a real-world problem.

The primary limitation of simply representing a problem with a single known (and desired) solution with words rather than algebraically or graphically (or musically, or…?) is that changing the representation system somehow elevates it to a real-world problem. But it’s just a different way to represent an academic exercise, not a problem. When a word problem can easily be translated into a different representation system that all result in the same answer, the goal is to determine if a student can use a known algorithm. Real-world problems are usually not that simple, even when dividing pizzas and donuts.

Exercises Problems
Simplistic, well-structured
Distractions have been eliminated
Complex, ill-structured
May contain noise or detractors
Academic setting Real-world connection
One correct answer May be multiple correct answers
Focus is getting correct answer Focus is on the process and strength of evidence

Adapted from Wiggins, G., & McTighe, J. (2005). Understanding by design (expanded 2nd ed.). Alexandria, VA: Association for Supervision and Curriculum Development.

Grant Wiggins and Jay McTighe do an excellent job of comparing a real-world problem to an academic exercise in their foundational Understanding by Design instructional design model. The implication here is that a problem is complex; there are options. Using a real world context is not enough if the problem becomes routine and simplified. Real-world problems often have no single correct answer. Sometimes they don’t even have correct answers, but some answers can be better than others. Problems focus on the problem-solving processes students use to develop their solutions, not just a correct answer. In the real world we make decisions about real-world problems using the best information we have available and justifying our decisions with some kind of evidence (What kind of car can I afford? Is college really worth it? Should we clone dinosaurs?). That means my solution to a real-world problem can be different from yours, but both can be used to demonstrate the process we took to come up with our solutions.

I don’t want to imply that simplified word problems are bad. Students do need them to develop foundational knowledge and practice skills. These types of problems are those that fit squarely into what many educators understand as Depth of Knowledge Level 2, in which students apply and practice basic skills, often decontextualized. These problems can use any type of representation system. But if students are only presented with a word problem at the level of basic application, they are not exposed to the cognitive demand implied by encouraging the use of real-world problems—requirements of content standards in many grade levels. Real-world problems require students to draw upon a repertoire of knowledge and skills in order to address a non-routine problem, because whose real world is all that routine? These problems are often associated with Depth of Knowledge levels 3 (strategic thinking) and 4 (extended thinking), and that’s the intent of most content standards that include mention of real-world problems.

Designing Online Learning

As a coach with Advanced Learning Partnerships, I have the privilege of working school divisions participating in the Virginia is for Learners Innovative Network (#VA4LIN). If you live in Virginia you may have heard about this sweeping initiative launched by the Virginia Department of Education with support from VaSCL, JMU, and Ted Dintersmith. ALP coaches are working with the schools and divisions in the network who have identified their own priorities for promoting innovation.

One of the divisions I’m working with, Bedford County Public Schools, has already initiated efforts related to personalized learning prior to joining the network and asked for some support with developing online and blended learning. Division staff want to leverage online technologies to provide more personalized support for both learning opportunities for students and professional development for adults in the system. I met with a group of ITRTs (Instructional Technology Resource Teachers), library/media specialists, and others in Bedford County on May 9 to review instructional design for online and blended learning. Our goal was to develop design specifications for educators in Bedford County to refer to when designing their own learning materials.

Educators from Bedford County Public Schools discuss designing powerful online learning.

I provided access to materials based on my book, Online Professional Development, Design, Deliver, Succeed! and subsequent publications. We reviewed key instructional design principles, considered how staff are currently addressing them, and considered how these principles might be presented in the first draft of a design specifications document. The key ideas we reviewed include:

  1. Know your audience.
  2. Define your learning outcomes.
  3. Assess your learning outcomes.
  4. Consider your visual design.
  5. Match media to your outcomes.
  6. Evaluate your learning.

You can access the slide deck with links to handouts and templates on Google Drive. Let me know if it’s helpful. Next steps for the, the participants include returning to existing online professional learning to review what has already been developed and determine how the specifications might impact that work.

Considering implications of instructional design principles on practice.

What do you want to create today?

I had the great privilege of sharing some thoughts about promoting creativity and creative thinking with educators in Moreno Valley USD, California, on January 30, 2019. The following are links to resources that support my keynote presentation.

Slide Deck

Sir Ken Robinson’s website

How People Learn free download from the National Academies Press

What EXACTLY is Depth of Knowledge? (Hint: It’s NOT a Wheel!) article by Erik Francis for ASCD

Potential Basketball Learning Progression developed with Steven Doyle, Legacy H.S., Evergreen Public Schools, Vancouver, WA

Using Technology to Support At-Risk Students’ Learning (2014) by Linda Darling-Hammond, Molly B. Zielezinski, and Shelley Goldman

Performance tasks I’ve helped create with teachers from across the country.

The Visible Thinking website from Project Zero at Harvard

Mind Expanding: Teaching for Thinking and Creativity in Primary Education by Rupert Wegerif (free PDF download)

Literature Overview: Ideas of what students should be able to do to demonstrate creative thinking and strategies teachers can incorporate in their classrooms to encourage creative thinking.