“Modeling problems have an element of being genuine problems, in the sense that students care about answering the question under consideration. In modeling, mathematics is used as a tool to answer questions that students really want answered. Students examine a problem and formulate a mathematical model (an equation, table, graph, etc.), compute an answer or rewrite their expression to reveal new information, interpret and validate the results, and report out. This is a new approach for many teachers and may be challenging to implement, but the effort should show students that mathematics is relevant to their lives. From a pedagogical perspective, modeling gives a concrete basis from which to abstract the mathematics and often serves to motivate students to become independent learners.”
(I can’t be sure, but the above passage sounds as if it were written by Phil Daro.)
I’ve seen this “make math relevant” and “problems that students really want answered” line of reasoning before from those who supposedly know what’s best for students. Out of the other sides of their mouths, they lament that math is not just about computation and push for problems that explore the relationship between perimeter and area of polygons and other concepts. Using the same logic about making math relevant one could then argue that students may not find such topics relevant to their lives. But people in the edu-establishment often have things both ways.
Extending this Phil Daro-ish logic that students only like to solve problems they really want answered, one would conclude that students do crossword puzzles and sudokus, because they really care about having them answered. Also breakout video games, Tetris and D&D.
In my experience and the experience of teachers who actually know what math is about and how to teach it, students care about problems if they’re able to solve them. Otherwise they write them off as irrelevant–sour grapes.
The problems that so-called math ed experts believe are so fascinating to students are generally one-off open-ended type problems which often involve gadgetry and ultimately number crunching. The fact that they don’t generalize to anything useful mathematically matters little to the people who write these frameworks.