Asked where does thinking take place, maybe we'd answer "in our heads" –– within the internal reaches of our minds.

But is this the full and true story? Or does it perhaps give too much credit to our mental prowess and powers? And too little acknowledgment of the many sorts of concrete support that our thinking gets from our physical environment and our ability to physically move and tinker with things?

Does thinking depend not just on how we play with ideas, or thoughts, but also on how we interplay with physical objects — concrete tangible things — existing out there in the world?

Deciding to tackle this very question, researchers in the United Kingdom and Denmark turned to what is well-known to problem-solving scholars as a pure insight challenge: the 17A problem. It's remarkably simple to state, but surprisingly tricky to solve: “How do you put 17 animals in four enclosures in such a way that there is an odd number of animals in each of the four pens?”

In the first experiment, 50 undergraduate and graduate students were given a pen and a blank sheet of paper and allowed three minutes to sketch out possible solutions to this problem. But no one solved the problem. Then, after completing some unrelated tests of working memory for about 25 minutes, the students were again given the question and allowed another 10 minutes to try to solve the problem.

During this 10 minutes, half of the students were given an electronic tablet and a stylus to work through their possible solutions. The remaining students were given a small pile of approximately 20 pieces of pipe cleaners, some short and some long, and a separate pile of 17 "zebra paper clips" representing the 17 animals — and were asked to use these materials to try to build a model of the solution.

None of the students equipped with the stylus-plus-tablet solved the problem. They all continued to doggedly work on the problem as though it required an arithmetic solution —trying repeatedly, as the researchers recounted, to discover " how an odd number could be split into 4 odd quantities, a mathematical impossibility with natural numbers." But the pipe cleaner and paper clip group avoided this trap. Significantly more of these students solved the problem: 26% solved the problem entirely, and an additional 17% offered partial solutions. So almost half of these students either solved the problem or were on the right track.

Why this difference in insight solution rates?

Were the students in the pipe cleaner-plus-zebras condition simply better problem solvers in general — perhaps enjoying puzzles or logical challenges more? Or did they have a higher working memory capacity or other reasoning abilities?

Additional data collected by the researchers showed that there was absolutely no evidence of such group differences. The students in the stylus-plus-tablet condition and the pipe-cleaner-plus-zebras condition scored nearly identically on several individual difference measures, such as questionnaires probing how much they enjoyed coming up with new ways to solve challenging problems. The two groups were also essentially equal in performance on two standardized measures of working memory capacity.

So why the difference between the two groups? Why did nearly half of the students given the pipe cleaners and "zebras" solve the problem, when no one in the tablet group could?

Perhaps the difference was just a chance fluke? But no: when the research team ran a new study, with a new group of forty-seven students, now given either a stylus-plus-tablet or a set of four metal hoops and 17 animal figurines, they found similar results. Conceptually replicating the first study, a mere 17% of the students in the tablet condition reached the solution, but just over half of the students (54%) in the hoops-plus-figurines model building condition found the solution to this difficult task.

These results suggest that the physical context in which the students worked — whether they were encouraged to actually touch and move about hoops and "animals" somehow boosted their ability to find and see the solution.

Thinking spaces/thinking places

So: what did the hoops or pipe cleaners help the students to see? The solution requires thinking of the problem not as an arithmetic problem (17 divided by 4) but, instead, as a problem of overlapping sets, where the animal pens can overlap like circles. Solving the problem requires noticing that the enclosures for the 17 animals might be allowed to overlap. Noticing this possibility could be sparked by physically interacting with actual objects such as hoops, pipe cleaners, and figurines.

One possible solution to the 17 animals in 4 pens problem.

Source: Jonathan Binks

The situational context in which we try to solve a problem is an integral part of our "thinking spaces." Physically interacting with objects, moving them about, looking at them, can help us to "see" possibilities that we otherwise may never find. Juggling ideas, and juggling objects may not be as different as we imagine.

Prompts and prods from our environment can point us — sometimes outside of our awareness — toward new insights. Our idea landscapes mingle with the world outside. As we note in Innovating Minds: Rethinking Creativity to Inspire Change, our environments enter into our thinking processes in multiple ways, not all of them expected.

The interplay of our environments with our idea landscapes.

Source: Innovating Minds: Rethinking Creativity to Inspire Change, Figure 2.6, Oxford University Press, 2015.

A few questions to ponder:

Are you a little too reluctant to tinker with objects to find new creative directions? Are you trying too often to answer questions "just in your head"?

If you're struggling with a tough problem, what objects or things could you bring into interplay, to help you reach a fresh new view of what's possible?

What could act as your creative "hoops" or "pipe cleaners"?

Asked where does thinking take place, maybe we'd answer "in our heads" –– within the internal reaches of our minds.

But is this the full and true story? Or does it perhaps give too much credit to our mental prowess and powers? And too little acknowledgment of the many sorts of concrete support that our thinking gets from our physical environment and our ability to physically move and tinker with things?

Does thinking depend not just on how we play with ideas, or thoughts, but also on how we interplay with

physical objects— concrete tangible things — existing out there in the world?Deciding to tackle this very question, researchers in the United Kingdom and Denmark turned to what is well-known to problem-solving scholars as a pure insight challenge: the 17A problem. It's remarkably simple to state, but surprisingly tricky to solve: “How do you put 17 animals in four enclosures in such a way that there is an odd number of animals in each of the four pens?”

In the first experiment, 50 undergraduate and graduate students were given a pen and a blank sheet of paper and allowed three minutes to sketch out possible solutions to this problem. But no one solved the problem. Then, after completing some unrelated tests of working memory for about 25 minutes, the students were again given the question and allowed another 10 minutes to try to solve the problem.

During this 10 minutes, half of the students were given an electronic tablet and a stylus to work through their possible solutions. The remaining students were given a small pile of approximately 20 pieces of pipe cleaners, some short and some long, and a separate pile of 17 "zebra paper clips" representing the 17 animals — and were asked to use these materials to try to build a model of the solution.

None of the students equipped with the stylus-plus-tablet solved the problem. They all continued to doggedly work on the problem as though it required an arithmetic solution —trying repeatedly, as the researchers recounted, to discover " how an odd number could be split into 4 odd quantities, a mathematical impossibility with natural numbers." But the pipe cleaner and paper clip group avoided this trap. Significantly more of these students solved the problem: 26% solved the problem entirely, and an additional 17% offered partial solutions. So almost half of these students either solved the problem or were on the right track.

Why this difference in insight solution rates?Were the students in the pipe cleaner-plus-zebras condition simply better problem solvers in general — perhaps enjoying puzzles or logical challenges more? Or did they have a higher working memory capacity or other reasoning abilities?

Additional data collected by the researchers showed that there was absolutely no evidence of such group differences. The students in the stylus-plus-tablet condition and the pipe-cleaner-plus-zebras condition scored nearly identically on several individual difference measures, such as questionnaires probing how much they enjoyed coming up with new ways to solve challenging problems. The two groups were also essentially equal in performance on two standardized measures of working memory capacity.

So why the difference between the two groups? Why did nearly half of the students given the pipe cleaners and "zebras" solve the problem, when no one in the tablet group could?

Perhaps the difference was just a chance fluke? But no: when the research team ran a new study, with a new group of forty-seven students, now given either a stylus-plus-tablet or a set of four metal hoops and 17 animal figurines, they found similar results. Conceptually replicating the first study, a mere 17% of the students in the tablet condition reached the solution, but just over half of the students (54%) in the hoops-plus-figurines model building condition found the solution to this difficult task.

These results suggest that the physical context in which the students worked — whether they were encouraged to actually touch and move about hoops and "animals" somehow boosted their ability to find and see the solution.

Thinking spaces/thinking placesSo: what did the hoops or pipe cleaners help the students to see? The solution requires thinking of the problem not as an arithmetic problem (17 divided by 4) but, instead, as a problem of overlapping sets, where the animal pens can overlap like circles. Solving the problem requires noticing that the enclosures for the 17 animals might be allowed to overlap. Noticing this possibility could be sparked by physically interacting with actual objects such as hoops, pipe cleaners, and figurines.

The situational context in which we try to solve a problem is an integral part of our "thinking spaces." Physically interacting with objects, moving them about, looking at them, can help us to "see" possibilities that we otherwise may never find. Juggling ideas, and juggling objects may not be as different as we imagine.

Prompts and prods from our environment can point us — sometimes outside of our awareness — toward new insights. Our idea landscapes mingle with the world outside. As we note in Innovating Minds: Rethinking Creativity to Inspire Change, our environments enter into our thinking processes in multiple ways, not all of them expected.

A few questions to ponder: