A conference about uncertainty which might also be about the left-overs after problem-solving.
I have spent the week watching my youngest do two types of ‘problem solving.’ I got her one of those ‘daily calendars’ at Christmas – one of the ones that has a puzzle to solve everyday. She’s getting better at them, and while I was waiting to get asked to help with one… she really didn’t need it. She’s got the trick to doing them. The second kind of problem solving she was doing was quadratic equations. She does pretty well with it, but sometimes gets caught up in one method (her teacher has very specific methods) and then takes a few minutes to see that the textbook has just switched the problem around. She’s mostly got the trick of it.
ChatGPTo, it turns out, mostly has the trick of both of them. The algorithm is amazing at the puzzles and… mostly reliable for the word problems. (it got some of the variables mixed up… I asked it why, it said it just got ‘confused’)
Problem solving, it seems, is something we can get the trick of. It’s also something that new GenAI systems are doing extremely well. As I explained to a Social Psych grad student last week, employers are not going to need as many ‘problem solvers’ going forward. If a problem can actually be solved, an algorithm is probably going to be able to do it.
Turns out, if we follow work done at RAND and by the folks below, our method of problem solving was learned FROM early digital tools.
A little history of the kind of ‘problem solving’ I’m talking about?
In their 1958 article, Newell, Shaw and Simon suggest that we need a theory of problem solving so that we can “explain how human problem solving takes place.” They’re looking to describe a method that they’ve learned from digital computers (in this case RAND JOHNNIAC) because the digital thing can “be induced to execute the same sequences of information processes that humans execute when they are solving problems” (p.153).
The problem solving literature that comes out of this thread still has a long history. Simon and Newell’s thoughts about ‘well-structured problems’ (1970) and their obsession with using chess as an exemplar for ‘problem solving’ (Ensmenger, 2011) keep showing up in the literature. How can we solve the problem faster? How can we solve the problem more reliably? How can we beat the chess player/machine? How can we think more like a chess player?
In their ‘impacts on education’ section of that same 1970 article, S&N claim that they know very well that there are two kinds of learning – rote learning and meaningful learning. They suggest that we have known for a long time that there’s a real difference, but we’ve never been able to talk about ‘meaningful learning’ before. They propose, as you might expect, problem solving as meaningful learning.
What does it mean to ‘solve’ a problem?
In his 1973 article, Simon describes a ‘well-structured problem’ as one where the question, the process to solve the problem and the solution are known or knowable. Solving the problem, then, is to
- take the question that has been given to you
- Use the process for problem solving you’ve been taught
- Check if you’ve got the right answer against the answer that the person who has ‘structured’ that problem has for you. (back of the textbook, in my daughter’s case)
This is the standard trope of problem solving in the education system. It’s also the thing that many people like to study in educational research. “Did the kid get the right answer?” It can only be the ‘right answer’ if someone else has cleaned up all the messy stuff. Someone built a problem to solve, someone made a puzzle, someone developed the formula…
Isn’t that the hard work already done?
Newell and Simon address this issue. When asked whether the solving of a problem is implicit in the designing of a problem, their response is simple and direct. “Observation of subjects’ behavior over a sequence of chess problems, cryptarithmetic puzzles, or theorem-finding problems shows the argument to be empirically false.” (1970)
You can have solvable problems and puzzles and theorem finding, I’ll take the ‘left overs’
In 2001 Simon (yup, same guy – he won a Nobel Prize along the way) said that Ill-structured problems are what’s ‘left over’ from well-structured problem. They are the things that don’t fit into the nice categories of question/process/solution. This conference is about the leftovers. It’s about the things in life/learning that aren’t tidy. The ones that no one can confirm are right (there are many ways to confirm that an answer is wrong).
A well-structured problem almost never happens to me in real life. At work, as a parent, as a partner, as a citizen I am almost never in a position where I’m given a clear question that isn’t messy in some way, a process that I can follow, and a way for someone to say ‘yeah, you did that exactly right’. And when I am, I can mostly just use a GenAI tool to get there.
The things that are meaningful, to me, are about real life. They aren’t about chess, they aren’t about puzzles, they are about how each of us faces the uncertainty around us. With all these GenAI discussions swirling around I’m even more interested in how we learn when things are uncertain.
This conference is about how we teach and learn in that uncertainty.
References
Ensmenger, N. (2011). Is chess the drosophila of artificial intelligence? A social history of an algorithm: Social Studies of Science. https://doi.org/10.1177/0306312711424596
Newell, A., Shaw, J. C., & Simon, H. A. (1958). Elements of a theory of human problem solving. Psychological Review, 65(3), 151–166. https://doi.org/10.1037/h0048495
Simon, H. (2001). Problem Solving. In The MIT Encyclopedia of the Cognitive Sciences (MITECS) | MIT CogNet. The MIT press. http://cognet.mit.edu/erefs/mit-encyclopedia-of-cognitive-sciences-mitecs
Simon, H. A. (1973). The Structure of Ill Structured Problems. Artificial Intelligence, 21.
Simon, H. A., & Newell, A. (1970). Human problem solving: The state of the theory in 1970. American Psychologist, 26(2), 145. https://doi.org/10.1037/h0030806
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