When I was teaching undergraduate economics, I found a great gap between how the students seemingly went about things and how I go about my own learning. While I could readily identify factors that explain this disparity - generational, locational, parental, etc. - and drill down on each of these, thereby developing an abstract argument to explain what I was observing, in my gut that abstract argument never held sway. Over time you get quite accustomed to your own patterns of thought, which are then a kind of habit. Those patterns seem normal to me and my gut tells me they should be a commonplace with everyone else as well. That it is not so, I will admit. But why it is not so remains a puzzle to me, one I haven't solved. This post is a kind of wishing that it were otherwise.
The other confession is that I'm completely out of it, having retired in summer of 2010, teaching one course a year after that for the most part through fall 2019, with Covid putting an end to that. I stopped teaching before AI entered the vernacular and have no experience with it on which to base my arguments. For many readers, that will disqualify what I have to say, giving them a legitimate reason to stop reading right here.
But it does make it easier for me to maintain that the elements of thinking, problem solving in a situation which has not previously been resolved, where some creativity is expressed in finding a solution, my belief is that these things are within us and don't change much at all over time, even if the technological environment changes enormously. In my ideal, this should provide the focus for teaching and learning, from grade school through college and thereafter as well.
Near to when I retired I started to write a book based on the idea that there must be joy associated with creative problem solving, with that joy emerging from a spark of intuition, the prelude to the Aha moment. Yet that intuition itself couldn't provide the right answer for certain. Indeed, it might lead one astray. At best it was a guess as to to right answer. I called the book Guessing Games. I thought the first several chapters went reasonably well, but then my inclination to lecture took over. The argument became overly pedantic and I got frustrated with the writing. That's why I stopped. But there is enough there that might pique the interest of others.
I recently reread a chapter I had long since ignored called Assessment. The first half has perhaps too much recounting of the economics we were taught during my first year of graduate school at Northwestern. But the second half makes a rather compelling argument in the support of embedded assessment which happens mainly via an ongoing conversation with the student, where each particular item to be assessed is done in a low-stakes environment. We have inadvertently made school anti-democratic with our emphasis on high-stakes testing. The very good students become the elite, receiving a variety of privileges from that, including that we professors teach as if they are the norm. The rest become the riffraff and develop the emotional scars associated with that determination.
I began to wonder whether one could teach a full course with only embedded assessment and how that might be done. I should note that during the teaching I did in retirement, I had students write weekly blog posts, which I would comment on. And I relied on portfolio grading - individual posts didn't receive a grade. Instead, I gave one grade for the posts during the first half of the course and another grade for the posts during the remainder of the course. But the economics department still wanted me to give exams, so I complied with that, though I did so unenthusiastically.
I suspect that AI would obliterate the benefits from the blogging approach I used. Plus, reading each post and commenting on it is time consuming. That was no problem for me, as a retiree, but it might otherwise make the approach unattractive to other instructors. And even so, it really would only work in small classes, the type you see in upper-level courses. Something else would be needed for larger classes. For now, I'll leave that something else to still be determined. Here, I only want to propose a framework, nothing more.
And with that, let me report that nowadays I spend an inordinate amount of time on puzzles, mainly word puzzles from the NY Times, also a lot of Sudoku. For Wordle, those without a subscription can access the puzzle. For Spelling Bee, those without a subscription can solve a few words in the puzzle before access to the rest is denied. But my favorite puzzle is Letter Boxed, which can only be accessed with a subscription, so I will illustrate with a screen shot from today's puzzle. I believe that the process of solving this puzzle is very much in the spirt of the problem solving that one does in an open-ended situation. The steps that one goes through can then be generalized, which I will do at the conclusion of the post.
The puzzle has 12 distinct letters arrayed around the box, with 3 letters on each side of the box. To make a word the next letter in the word must be on a different side of the box from the previous letter. This rules out words with double letters and it rules out a lot of letter combinations as well that might occur to you while trying to solve the puzzle, for example "er." You hit the Enter button when you want to enter a word. The next word then starts with the last letter of the previous word. Letters can be used as many times as you need to solve the puzzle. The goal is to use up all the letters and do so in as few words as possible.
Some years back I surprised myself when for the first time I solved the puzzle in only two words. I then wondered whether there always was a two-word solution and to convince myself of that I started to record my solutions at this site. I subsequently found another site that generates such solutions and later that the NY Times has a site with their solution. So now, each day I try for a two-word solution. I don't always find one, but I will spend quite a while looking before I give up. It's what one goes through in that search which I consider below.
Step 1: Familiarize yourself with what's there.
This seems so obvious, on the one hand, yet I believe that students often expect to find an answer to a problem on their homework or to an exam question before getting sufficiently familiar with what is being asked. In this case, I first look at the vowels, there is no "a" in this puzzle, as well as what vowels are on the same side of the box, so can't be used in combination. Then I look for the "hard letters," which in this case I take as "q" and "v." I'll want to find words which have at least one of these, unless I've found another words that already uses both. Regarding the latter, you might initially try "quiver" but then note that the "er" combination is not allowed. If you give up on finding a word with both of the hard letters, a different approach is needed.
Step 2: Frame the problem to admit a solvable subproblem.
In this case, it means finding a first word that doesn't end in a hard letter but contains one of them and that uses at least 8 letters of the puzzle, so the second word isn't too hard to find.
Step 3: Guess at a solution to the subproblem.
Now I will admit that I use an online dictionary to help me solve the puzzle. One feature of these dictionaries is that you can search using a non-word and it will return possible alternative words that seem similar, so have many of the same letters. I prefer to try first without the dictionary, but I don't wait too long before I start to use it. In this case my original word, which I think is pretty immediate, is "question." If that is my first word, can I find a second that starts with "n" and also has "c," "d," "r," and "v?" It occurs to me to try "noncurved" and I check that in the dictionary, but it's not a word. So, anticipating the next step, we're not done yet.
Step 4: Are we done yet? If not, is there another subproblem to solve?
If we're done, great. If not and there is another subproblem to solve, return to Step 3. If you're not done but you can't find a suitable subproblem to solve, you're stuck. Then go back either to Step 1 or Step 2 to get unstuck, but try something else this time around.
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Whether puzzles of this sort could be constructed for a variety of different subject matter, I leave as food for thought, as I really don't know whether that's possible or not. But if it were possible and if students developed the yen for solving such puzzles, it would address the mystery of intrinsic motivation and these students would really learn. Wouldn't that be nice?
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