I think the phenomenon you're describing is definitely real, and definitely worth thinking about. There is signal in your poll about parity, but there's a lot o

I think the phenomenon you're describing is definitely real, and definitely worth thinking about. There is signal in your poll about parity, but there's a lot of noise there too. Figuring our what the signal is is very hard. You're writing isn't elitist here, but I think it moves very quickly up the ladder of stasis in an unjustified way (https://owl.purdue.edu/owl/general_writing/the_writing_process/stasis_theory/index.html https://owl.purdue.edu/owl/general_writing/the_writing_proce...). At my school we've been trying to sort out this phenomenon for about five years, and we're still wrangling at the stasis of definition, with understanding the nature of what we see in our students. An example: After I teach imaginary numbers, I give my students an (ungraded) assessment with these questions: 1. Please circle the imaginary numbers in this list. (about half imaginary) 2. Please perform the following multiplications. (mixed; about half imaginary x imaginary) 3. What is the definition of an imaginary number? 4. In your answers to question two, please circle all the products that are themselves imaginary numbers. 5. Is the product of two imaginary numbers imaginary? Why or why not? We've never explicitly discussed #5, but its answers flows necessarily from the previous answers. What I'm really interested in is whether the answer to #5 is coherent with the answers to the previous four questions. I'd say for about a third of students it is not. For example, a student correctly wrote that i * i = -1, and correctly identified -1 as not imaginary, but then said for #5, "Yes. Because when you multiply two imaginary numbers it doesn't become unimaginary." We see that play out in essentially every subject, and it's gotten much more prevalent in the last, say, ten years. It's especially noticeable in our 8th grade formal logic class, where a meaningful fraction of students appear unable to reason propositionally or syllogistically at all. We have some ideas about what's driving the change, but are still trying to figure out which of them are correct and what we can do about it. My personal theory is it's something to do with syntax and semantics, with some students not associating meaning with words in the way that one would expect. It's so hard to extract signal from the noise about that though.