Convergent and Divergent Exercises

In Ken Robinson’s TED Talk on education, he gives this definition of divergent thinking¹:

Divergent thinking isn’t the same thing as creativity. I define creativity as the process of having original ideas that have value. Divergent thinking isn’t a synonym; it’s an essential capacity for creativity. It’s the ability to see lots of possible answers to a question, lots of possible ways of interpreting a question, to think laterally, to think not just in linear or convergent ways, to see multiple answers, not one…

There are tests for this. One cod example would be, “How many uses can you think of for a paper clip?” Most people might be able to come up with ten or fifteen. People who are good at this might come up with two hundred. And they do that by saying, “Well, could the paper clip be two hundred feet tall and made out of foam rubber?”

Our makerspace treats reading and writing as acts that require divergent thinking. Literature is, as this video puts it, “a tool to help us live and die with a little more wisdom, goodness, and sanity,” something we “prescribe in response to a range of ailments and classify according to the problems it might be best suited to addressing.” Writing, as probably best expressed by Paul Graham, is our tool for discovering truth and investigating what’s interesting about ourselves and the world around us. Our reading and writing makes up the vast majority of the divergent work we do.

The other kind of thinking that matters (in our classroom and in life) is convergent thinking, which is about finding the right answer to a problem that has only one or two right answers. You’ll find that some of the problems we attempt to solve, whether they come up in class or elsewhere, have a limited set of solutions. There might be a fairly strict set of boundaries, and it’s within those boundaries that you must think creatively and divergently. It’s also within the necessary step of metacognition that you must think creatively and divergently.

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The Exercises: Ordeals and Ditloids

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This is a two-day exercise in divergent and convergent thinking. It is also a two-day exercise in the following:

1. Reading flipped instruction in preparation for in-class work
2. Collaborating effectively during the class period
3. Analyzing an activity metacognitively
4. Using the resources of the Internet effectively

The last one is interesting. You could use Google (or Bing, bless its heart) to find the solutions to each of these exercises. You could find a dozen more examples of this kind of exercise, and for each of those, you could find the answers.

That’s entirely by design. At some point, you will always need to rely on someone to give you feedback — to help you when you’re stuck, to verify a correct answer, etc. — and the Internet is usually the proxy for that someone. That device you have gives you access to nearly limitless information, including the responses of any other teacher or student who has done this work.

That makes the divergent question metacognitive: When and why do you look for help? How much time do you give yourself to be frustrated? What are the best solutions to managing these resources, including your peers? How do you process this kind of exercise?

The assignment that will be posted to Google Classroom is straightforward: Submit a copy of some of that metacognitive writing. This is evidence of the most important GAP criteria, of course, but it also helps build the habit of always unpacking your experiences. You should always take a bit of time to reflect on what you’ve learned and to be metacognitive about your choices. As Neil Postman wrote, “[T]he most important thing one learns is always something about how one learns.”

You can do these exercises in any order. That, too, is part of the divergent decision-making process.

The first exercise: “Ordeal by Cheque”

The first exercise is about deductive reasoning. You must piece together a narrative from nothing but a series of scanned checks:

• Wuther Crue, “Ordeal by Cheque” [PDF, opens in Google Drive]

Crue’s story was first published in 1932 in Vanity Fair. It’s interesting that this edition comes from a teaching textbook, since that underscores how many answers you’re going to find online when you get to that step.

You’ll have a hard copy of these pages, and that’s actually where the deductive reasoning will begin. You will be strongly encouraged not to head online until you’ve worked collaboratively, with deductive tools like whiteboards and markers, on a solution. What can you accomplish with just your collaborative reasoning ability?

You won’t be satisfied with just telling the story to each other as you work. You’ll need to write it down. When you search online for other theories, you’ll find fully developed narratives. You’ll want your own for comparison.

The second exercise: 24 Hours in a Day

The second exercise is a ditloid, which is a type of word puzzle that relies on deductive reasoning. From a set of abbreviations, you must determine what common phrase or idiom fits. These exercises are commonly associated with Mensa, the high-IQ society, which I mention only to tell you that IQ scores are overrated in education. You can find many examples of ditloids on a wide variety of subjects. Here is one:

• Ditloid: 24 Hours in a Day [PDF, opens in Google Drive]

Again, the divergent questions are metacognitive in nature: Will you wait to look up the answers? Will you tackle these alone, or in groups? What are you learning about how you solve problems like these? At what point does your pattern recognition stall or speed up?

 

Use the comment section here to ask questions about the metacognitive component of this work, to share insights into what you and your peers have accomplished, or to post links to the answers you’ve found online. You can even share other ditloids or atypical narratives that were inspired by Crue’s “Ordeal,” if you find them.

Remember, too, that this is part of most student’s introduction to our makerspace, which means you might find yourself interacting well outside of your normal peer group — and that’s a very good thing.

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1. Note: The language has been edited a bit for readability. ↩