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.