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.

What does your P stand for?

I’ve just returned from my final coaching visits with some great teachers in Evergreen Public Schools in Vancouver, WA. We’ve been exploring PBL together. They’ve been developing and implementing PBL units and we discuss what they’ve learned and how that will impact their practice in the future. This last visit was the third in a series of three, and I’m so proud of the work these teachers have done—and their administrators. This has been such a rewarding experience because not only have teachers taken risks and tried new things, but their administrators have supported and encouraged them. They’ve become learners themselves, and have explored PBL right along with their teachers, acknowledging they have questions and want to learn, as well.

Steve Doyle PBL

Steve Doyle connects history with current events through his PBL unit in his social studies class.

I was also fortunate to share some ideas with the full faculty of both schools—Legacy High School and Harmony Elementary. We explored some of the characteristics of PBL and what that might mean for their lessons. I also got to showcase the work and experiences of the great residency teachers I’ve been working with, who have really dug in and have the best stories to share.

You’ll notice I just use the term “PBL” and don’t elaborate. That’s because the P in PBL can mean different things to different people. Both in the textbook I’ve co-authored and in many schools where I’ve embarked down the PBL path with teachers, I like to acknowledge this. And often I ask people what they think the P should stand for?

For many, the P in PBL stands for project. I’m good with that. A really good project can be an engaging source of deeper learning—especially when that project requires students to develop new knowledge and skills that they can then demonstrate through that project. In this case, the project is the learning, and not just something students do at the end. It’s not that they won’t need some guidance, and even directed learning, as they work on their projects, but the project isn’t just something tacked on at the end of other learning. Teachers don’t have enough time to add on projects after the learning, so the best projects are the learning. But for me, simply engaging students in a project is not enough to make it good PBL.

With the changes in the summative assessment landscape over the past decade, some people also suggest that the P in PBL stands for performance. I like that one, too, partly because almost all of the learning my own students did led to some kind of a performance—a public performance. I was a band director. So whether it was Friday night on the football field, in a concert hall or cafeteria, or performances of soloists or small ensembles, my students engaged in PBL activities that led to a performance. My work in developing performance tasks is actually, in part, an attempt to accomplish what my last principal suggested I help him with. He asked me to help him figure out how to get other teachers, whether math, science, English—whatever—to get their students to “perform” their content. PBL can do that, but again, just adding a performance doesn’t get to the best PBL.

Laura Buno, Harmony Elementary

Principal, Laura Buno, explores PBL by visiting and learning with the faculty at Harmony Elementary.

For me, the one P that I think should be in every PBL unit is a problem. A real problem. A complex problem. Real-world problems help kids get to the level of strategic thinking unlike academic problems that can be fairly sanitized and yield only one correct answer. These are what Wiggins & McTighe would refer to as exercises, not problems. They’re important, because they help students develop knowledge and skills, but what for? To tackle real problems, of course, and so in my PBL, I try to ensure there’s some real-world problem students are investigating. You can have a project with a problem, and you can include a performance at the end of a project, but without a problem, your students are going to miss out on the greater benefits of PBL and not reach those higher levels of cognitive demand that lead to deeper learning and transfer. What does your P stand for?

When asked to reflect on what makes good learning memorable, some of the faculty and staff at Harmony Elementary reported that memorable learning is:

  • Authentic
  • Provides student choice
  • Builds on individual strengths
  • Promotes independence
  • Hands-on
  • Engaging
  • Not limited by time
  • Fun
  • Group-based
  • Thought provoking
  • Connected to things outside the classroom
  • Collaborative

Sounds like great PBL to me!