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?

Transformers by Mary Kim SchreckMore than a few years ago I had the opportunity to dig deeper into the ideas of creativity and creative thinking thanks to the wonderful Mary Kim Schreck. She was thinking about, writing about, and sharing her ideas about creativity in her book, Transformers: Creative Teachers for the 21st Century. She had been thinking about creativity so much that she was about done with the book! But she asked me to contribute a chapter about technology in the creative classroom.

Don’t get me wrong, I’ve been thinking about creativity most of my career! I taught music and most people segregate musicians into a small, select group of “creatives,” that includes visual artists, actors, dancers, writers and a few others. But creativity is not the purview of the few. Everyone can be creative, and in fact, we need more people to be creative in their lives and in their work, now more than ever. I appreciate that Mary Kim gave me a reason to dig deeper into my own ideas about creativity and to compare them to others. It was a valuable experience and, luckily, I get to keep thinking about creativity.

The Value of Performance

I cringe a bit when I see or hear the directions “be creative” in an assignment, because usually this is followed up by using crayons, markers, or different backgrounds in a slide deck. Students are encouraged to “be creative” without ever teaching them what that means. And what does that mean in, say, science? Or math? It’s not the same as in my class. What few teachers realize is that we folks in the creative fields had content standards we had to address, and just like every other class, some of our standards promoted creative thinking, some did not. The important message here is, yes, science, math, and all the others have standards that promote creative thinking.

As a former high school band director I often reflect back on what was then a somewhat routine conversation that has turned out to have significant impact on my life. I had been through my annual observation with my principal, something all teachers go through. My principal, Dr. Barry Beers, was great to work with and full of ideas that pushed and stretched his teachers. I didn’t realize how valuable that was at the time. During our follow-up conference he said to me, “John, I really appreciate how you move from whole group, small group, to individuals, and back and forth whenever you need to. You’re customizing your instruction to the needs of each student.”

I replied to him, hopefully not too snarkily, something like, “Dr. Beers (I still have a hard time calling him Barry), I was just doing a rehearsal. That’s what musicians to do get ready for a performance. Nothing special.”

He tried to help me see the importance of what was going on, but I didn’t really understand his statement until later. Because everything my students did in my class eventually led to a performance, he tried to help me understand how a performance can only be successful when all of the students can play their part, literally. He reminded me that by working with all of the students individually and in groups during rehearsal that I knew who was ready and who still needed work. Then he challenged me.

Learning-Driven Schools by Barry BeersDr. Beers asked me to help teachers in other content areas understand how they can help their students learn how to “perform” their content. Whether math, science, English or whatever, Barry wanted me to help other teachers in other content areas understand how to help their students rehearse so they’d be better prepared to perform in a more authentic context. He enlisted all the Fine Arts staff, and I collaborated with a social studies teacher one year, English the next. It was a challenge, but it helped me to see connections I hadn’t seen before. So, thanks Barry, for thinking creatively about teaching and learning back then.

You can find out more about Barry’s work in his book Learning-Driven Schools: A Practical Guide for Teachers and Principals from ASCD.

Performance in All Classrooms

Recently, perhaps in reaction to the horribly mind-numbing compliance mentality promoted by federal education policy, the education community is once again seeing the value of performance. I saw this in the release of new college-and-career standards both at the national and state level. New standards in the core areas and the arts definitely push students to work towards levels of creative thinking in their domains. And now, in many states, students demonstrate higher levels of learning through performance.

The best performances are not compliance. They’re not mechanical. They’re not simply the replication of what someone has done before. They’re not multiple choice. The best performances give people a chance to be creative—to pull their knowledge and skills together—to address a real problem or situation in or across content domains.

In this way, creativity is a cumulative skill. I liken it to the top level of the revised Bloom’s Taxonomy. You can’t get to the top without working you’re way up. You have to have the foundational knowledge and skills of any domain you plan to be creative in—whether that’s writing, speaking, visual or performing arts, or science, or engineering, or even legislation. You have to know what the accepted strategies and processes are before you can change them. In other words, you have to know the rules before you can break them.You have to understand what work has come before and to analyze and evaluate information in order to provide a creative solution to address a problem.

Revised Bloom's Taxonomy

One interpretation of the cognitive process dimension from the revised Taxonomy of Learning by Anderson & Krathwohl (2001)

Ideas that don’t build on a foundation are not creative. They’re simply novelty. And novelty wears thin fast and falls apart. Creativity has weight, value, and lasting appeal.

The most creative ideas can live a long time—in an individual, a group, or society, but everyone can be creative as we are all faced with authentic problems that are routinely found in the real world. We need creative solutions for providing affordable housing to everyone no matter where they live. We need creative solutions on how to ensure our planet will be able to sustain us. We also need creative solutions to simply provide the best education to each generation of students.

Creativity: Imaginative processes with outcomes that are original and of value.

Sir Ken Robinson
“Out of Our Minds: Learning to be Creative” (2001)

What do you want to create today?

I’ve been given another chance to continue my musings about creativity. I’m very honored that Dell and Advanced Learning Partnerships have asked me to share my ideas and some of the work we’ve done in districts across the nation around promoting instruction and assessments that encourage creative thinking. Dell is calling these events, appropriately enough, “What do you want to create today?”

We’ll talk a bit about creativity and why it’s important, but the main plan is to co-create ideas of how creative thinking can be promoted in all classrooms—not just a few. We’ll explore performance tasks—something I’ve been immersed in for years (like this one a creative teacher from Lake Travis ISD just Tweeted out), but we’ll also explore how preparing kids to perform (in math, or English, or whatever) has deep implications for all curricula.

At these events I’m looking forward to hearing from district leaders from across the country who are promoting creative thinking in their own schools, and we’ll share ideas on how we can help every student in every classroom experience learning that helps them develop critical and creative thinking and perform what they’ve learned. I look forward to hearing your ideas whether you can attend one of these events or not.