Archive for November, 2020

Thought: Are Jigsaw Puzzles Good for Training Divergent-Convergent Thinking and Creativity?

Tuesday, November 24th, 2020

One of my newest obsessive hobbies is now jigsaw puzzles. After completing about 10 puzzles in the past 3 months, I have begun to wonder whether jigsaw puzzles build creativity and are a good example of an activity that uses divergent-convergent thinking. Could a jigsaw puzzle exercise be designed for YCISL workshops just like how we have a Lego activity to demonstrate rapid team prototyping?

Putting together jigsaw puzzles involves creative energy because there are many solution paths and solution strategies. Also, there are multiple and switchable directions: finding a piece that fits a hole or edge(s), or finding a hole or edge that fits the piece you have picked up. There are trial-and-error methods as well as visualization methods that involve rapid eye movement. There is not only shape matching. One could involve color matching as hints. So even though the end result should be the same assembled puzzle (assuming you finish the puzzle), there is a creative element because of the variations that are essentially guaranteed; even if I were to solve the puzzle twice, it is improbable that the exact same solution path would be repeated – and think of the probability that the same time-based profile would be repeated.

Let us also consider how jigsaw puzzles would make a good model for training divergent-convergent thinking. Usually, the jigsaw puzzle pieces have some sort of distinguishable pattern based on the number and directionality of the tabs and slots. These are sortable features and are part of my strategy. So given a particular hole or edge waiting to be connected with a piece, there are certain piece patterns that could be fit and other patterns that could be deductively reasoned not to be a fit candidate. So we can select several candidates to fit a position – this would be the divergent thinking step. We could choose two or more candidates for a hole using the criteria of the moment. We would start our convergent step by selecting a candidate piece and trying to attach it. If there is a perfect fit, great! (but sometimes it is a fake fit), and if that piece was not the right fit, then we would go back to the pool of candidates or create a new pool of candidates (if we learned something from that non-fit attempt where we figured the pool was not going to work). The big bonus of using jigsaw puzzles to model divergent-convergent thinking is the fast thinking cycle aspect because the divergent-convergent thinking steps are usually repeated in clusters. These clusters could be sized by varying the time periods spent on finding matches.

With the creativity and divergent-convergent aspects confirmed, what fun ways might there be to make this worthy of a workshop workout? The first round might involve individual efforts establishing the time periods of sustainable puzzle solving (ie, how long before you need to take a break and rest the mind and eyes?) The next level might be a team effort to reflect interpersonal communication and group dynamics skills. A trick version might be to include a piece that doesn’t actually belong.

The jigsaw puzzle lessons would be compared to real world problems where the pieces may or may not be at our disposal, and we have to practice divergent-convergent thinking with an understanding that the final product may be quite different from what we expected at the start.

Fun. Can’t wait to try it. Now if only I can figure out a version of this that would work over Zoom.


NYT: Nine Nonobvious Ways to Have Deeper Conversations

Monday, November 23rd, 2020

I came across this article through LinkedIn today. The article lists various ways to re-engage with each other especially during this time of un-shakeable stress. “Nine Nonobvious Ways to Have Deeper Conversations” is an Opinion article by David Brooks dated November 29, 2020 on

The author’s suggestions make sense to me and I will undoubtedly be spending some time thinking how to turn these into YCISL workshop actions. But because I am currently engaged in a series of Popcorn with Colin discussions on creativity, in particular a tribute to Sir Ken Robinson’s epic TEDTalk “Do Schools Kill Creativity?” (originally titled “Schools Kill Creativity.”), I will dwell on the suggestion to “Ask Open-Ended Questions” and the timeliness of this for the online learning pivot.

This idea fits into the Divergent-Convergent Thinking and Asking Questions component of the YCISL Innovators Toolkit series. Open-ended questions (or problems which are inviting of innovative solutions) have the potential to stimulate and strengthen creativity. So the task is not to simply ask an open-ended question, but to frame a worldview that accommodates various perspectives and past experiences. We need to use design thinking in creating open-ended questions.

I haven’t had much practice at this, but let’s give it a few application attempts.

Here is a Physics homework problem I found on the web:

Gravitational Potential Energy GPE = mg∆h
12. A 5.0 kg mass is initially sitting on the floor when it is lifted onto a table 1.15 meters high at
a constant speed.
a. How much work will be done in lifting this mass onto the table?
b. What will be the gravitational potential energy of this mass, relative to the floor, once it is
placed on the table?
c. What was the initial gravitational potential energy, relative to the floor, of this mass while
sitting on the floor?

What if we changed this question to “Place a dumb bell (or other object) on the floor. Lift it onto a table at a constant speed. Use a scale and/or tape measure, if desired. It’s ok to estimate.”? Would this be too challenging? Could this be a more fun application-type question that helps the student use visualization as well as experimentation skills? Not all the questions would have to re-framed this way. But it does give a more first-person real world feel about how science applies to things we do on a daily basis.

And here is a Chemistry homework problem I found on the web:

Coffee cooling
A mug of coffee cools from 100 ℃ to room temperature, 20 ℃. The mass of the coffee is
m = 0.25 kg and its specific heat capacity may be assumed to be equal to that of water,
c = 4190 J. kg-1. K-1.
Calculate the change in entropy
(i) of the coffee
(ii) of the surroundings

What if we changed this question to “Your morning mug of coffee/tea/water cools to room temperature. Use a scale and/or thermometer, if available. Otherwise estimate.”? Hopefully, everyone has been aware at some point that a hot beverage gives off warmth and gradually cools. There is also the intrinsic motivation factor (that we are fond of in YCISL) where we involve mastery, autonomy and purpose (added through the use of another Innovator Toolkit skill: Filling & Crossing Gaps).

As another example, I require online seminar logs for a seminar course at Stanford. This is for proof of attendance. But instead of asking for a summary of the seminar presentation, the question is “Describe in 2-3 sentences how this talk connects with or relates to your interests, or your MS studies.” In general, most responses will be quite different reflecting perspectives and background. This makes it more interesting and informative for me. Note though that some students find this open-ended question challenging and defer to the seminar abstract as a basis for their thoughts – as opposed to internal stimulation and connections.

Re-reading the examples above, there is probably more fine-tuning possible to engage each other better. An example is to use the Positivity Innovator Toolkit skill and “garnish” the problems with emotionally positive words and uplifting expressions. “Your delicious morning mug of…

A good topic for future discussion.