Below, we’re sharing an excerpt from Keith Sawyer’s latest book, The Creative Classroom.  This excerpt highlights strategies for teachers to incorporate creative knowledge strategies when teaching math and science.


In guided improvisation students engage in hands-on activities that they develop, and they apply these creative habits of mind to the subject-area knowledge that they’re learning. If you start out by teaching students shallow knowledge, and then later teach them these habits, it’s too late: The creative mindsets work best when they build on creative knowledge. Students need to learn subject-area knowledge and creative habits of mind through the same activities. That’s why in creative schools every subject is taught differently, leading students toward creative knowledge in each subject. Students learn the required content knowledge as creative knowledge, not shallow knowledge.

Creative Knowledge in Math

Bob Knight, a middle school teacher at Colter Bay Junior High School, teaches algebra by guiding students through an improvisational creative process. In his classrooms students can’t solve problems with a rote application of memorized formulas (Yinger, 1987, pp. 40–43). Instead, he gives them complex problems where they have to spend some time learning how to think about them. In fact, this is at the core of the Common Core State Standards in math, which emphasize learning to think mathematically, rather than simply learning formulas as shallow, memorized knowledge. When researcher Robert Yinger asked Mr. Knight why he taught using guided improvisation, he said it was the best way to teach the following aspects of mathematical thinking. It’s fascinating that these are the same creative habits of mind described earlier in this chapter:

  • Understanding the fundamentals
  • Looking for different approaches to problems
  • Knowing what approach to take when setting up a problem
  • Applying concepts and making connections between them
  • Making connections between concepts and processes learned in other units in the course

Mathematical creativity doesn’t result from applying the formulas that are memorized in instructionist classrooms; it requires creative knowledge of math. Paul Halmos, one of the most influential mathematicians of the 20th century, wrote the following in his essay “Mathematics as a Creative Art”:

Mathematics is a creative art because mathematicians create beautiful new concepts; it is a creative art because mathematicians live, act, and think like artists; and it is a creative art because mathematicians regard it so. (Halmos, 1968, p. 389)

Creativity in math requires improvisation: spontaneous, cooperative action. Creative knowledge in math supports reasoning and argumentation (Knudsen & Shechtman, 2017, pp. 177–178). It prepares learners to improvise using math knowledge, and to construct their own knowledge.

Creative Knowledge in Science

In 2009 the leading U.S. scientists got together to figure out why students weren’t learning science very well in school.4 Of course, the students were taking science classes, and the best students got near-perfect scores on standardized tests. But these were instructionist classrooms, and these were tests of shallow knowledge. The scientists quickly realized what the problem was: Shallow knowledge doesn’t help students understand science. If you learn by memorizing shallow knowledge, you don’t learn that science is a creative process through time, a process that’s based on creative knowledge, a process that is within anyone’s potential. When all that you learn is shallow knowledge of science, you think that scientific knowledge comes from somewhere else, that it’s true and unchanging. You think all that scientists do is observe the world and then write down what they see. You don’t learn how to think like a scientist, or how scientific inquiry works, or how a scientist could ever be creative.

Creative knowledge in science is big, deep, and connected. The Next Generation Science Standards (NGSS) emphasize creative knowledge (e.g., National Research Council, 2012; NGSS Lead States, 2013). They argue that the most important learning outcomes of science education should be these seven crosscutting concepts (National Research Council, 2012, pp. 83–102):

  1. Patterns
  2. Cause and effect
  3. Scale, proportion, and quantity
  4. Systems and system models
  5. Energy and matter in systems
  6. Structure and function
  7. Stability and change in systems

These seven concepts are deep, connected, and adaptable. This kind of creative knowledge supports a range of creative scientific activities, including the following:

  • Gathering and generating lots of data related to the problem (supported by divergent thinking)
  • Interpreting and analyzing data (associated with combinatorial thinking)
  • Forming concepts based on these data (based on imaginative thinking)
  • Applying of general principles to specific cases (dependent on adaptive expertise)

Paul Wyatt, chemistry professor at the University of Bristol in the United Kingdom, told me that understanding in chemistry requires creative knowledge (personal communication, 2018). Year after year, the top students in the United Kingdom—the ones with the highest marks on the challenging A level college entrance exams—enter his classes with confidence in their scientific knowledge. But Wyatt says that he can’t trust the A-level exam scores because they test only shallow knowledge. The tests don’t reveal that the students haven’t learned how to think creatively with that knowledge. After years of teaching these students, he knows that it’s because they’ve been in instructionist schools that teach only shallow knowledge. Because his students have learned only shallow knowledge, they can’t solve authentic chemistry problems. And even when they’re stumped, they’re still confident that they have the necessary knowledge to solve it; they just think that they haven’t applied it effectively. They think the problem is just like all of the other shallow-knowledge problems they’ve been taught—and that it requires just a bit more effort. But as they try harder and harder, they get more and more frustrated, because you can’t solve creative problems with shallow knowledge.

Wyatt’s experience is echoed by many studies of what high school students know. A 1994 study found that when high school graduates start college, they can solve well-structured problems that are just like the ones they worked on in school (King & Kitchener, 1994). But when they’re given an open-ended problem, one that’s ambiguous and doesn’t have an obvious answer or a clear solution path, they’re confused. Their only option is to use shallow knowledge that they’ve memorized, and they try to solve these problems as if they’re well-structured.

Wyatt thinks that their shallow knowledge actually blocks their ability to be creative in chemistry. He has to un-teach them. It takes some work because the students are understandably resistant to leaving behind strategies that have caused them to be successful in their instructionist high school. Professor Karen Spear sees the same thing in her college courses. Her students have done well in big lecture classes using instructionism, and they’ve become very good at transcribing, memorizing, and regurgitating their lectures. But then they’re lost when they get to the advanced courses, where they’re expected to ask original questions, or find novel solutions, or examine their own preconceptions. According to their professors, the students actively resist attempts “to get them to go beyond the information that we give them” (Spear, 1984, p.7).

Featured Image: Learning backdrop, public domain via Pixabay.