He displays a CCSS modeling problem related to the notes on a keyboard and involving an exponential expression, and then states the following?
"We give students variable expressions like the exponential one above, which they had no hand in developing, and ask them to evaluate the expression with a number. The student says, ?Ohhh-kay,? and might do it but she doesn?t know what pianos have to do with exponential equations nor does she know where any of those parameters came from. She may regard the whole experience as one of those nonsensical rites of school math which she?ll forget about as soon as she?s legally allowed.?
He then goes on with an arithmetic exercise about a parking lot and throws a formula in at the end, a non exponential formula.
When I took algebra, we did derive the meaning of exponential expressions in various scenarios before we were given arbitrary and varied problems involving exponential expressions. And before that we tackled relational expressions, monomials, binomials, polynomials, and all of the *algebra* involved in that. And before we tackled algebra we were proficient in arithmetic and applying it to a variety of situations and word problems.
Dan obviously isn?t talking about that experience. In fact, he seems fixated on *variables* which is a notion that comes at least two years prior to these exponential expressions.
He is making these nonsensical comparisons because the students (and most of the teachers) are not prepared for the problems they are critiquing.
Some of the comments?
Grant Wiggins: We need to slow the learning process down (does that mean stop putting students in material far past their comprehension) katenerdypoo: Fantastic, i love it, it?s perfect for one of my classes (i bet it is) Howard Phillips: Brilliant, now for the keyboard, or a violin string. (how about now for algebra and exponential expressions) Joe Schwatz: I agree with grant, let?s slow down the learning process. Tom Schwartz: Very nice, I just did this in Real Life with 5 equally spaced posters (so much for exponential expressions) Laura: How can a student get this without a musical background? (you should see the drag equation for an airfoil, something I think most pilots don?t understand) Kyle Pearce: Students struggle with variables (then they are not ready for exponential expressions)
Honorable Mention? Mike Lawler: This (the parking lot) is a lesson for 10 year olds (I completely agree)
The obvious point here is that these students and teachers are stuck at variables. They are trying to get unstuck, but they are a year or two away from the exponential expression they started with. Why did they even start with that expression at all? It seems what they are saying is that their students are not ready for problems like that.