I spent Friday and Saturday this week at the Utah Council of Teachers of Mathematics (UCTM) conference. It was a great opportunity to learn about and be inspired about mathematics education. And I got to reconnect with some of my past students who are now also mathematics teachers!
I attended several great session, but one that stood out was on 3 Acts Math by Jessica Patterson. I've already referenced the 3 Acts math that Dan Meyer's does in a previous post. Part of what Jessica did was to compare 3 Acts problems to typical textbook word problems. Now, especially in secondary math, typical word problems are ridiculous. As Jo Boaler explains they answer questions that no one is asking. Dan Meyer's refers to the them as "pseudocontext" which meet two criteria 1) it asks a question that most people would not ask and 2) uses a method that most people would not use.
Another problem that Jessica brought out is that most textbook word problems identify the variables and (at least implicitly) the mathematical model (or equation, algorithm, etc.) that students should be using. In other words the meaningful thinking has been taken away from the students. This aligns well with something Jo Boaler explains in Mathematical Mindsets, "Mathematics has four stages: 1) Posting a question, 2) going from the real world to a mathematical model, 3) performing a calculation, and 4) going from the model back to the real world" (p. 27). Done properly 3 Acts problems do all of these while textbook problems do 2 (2 and 3) sometimes and usually just require calculation.