This TED talk by John Bennett raises an important question; why do we teach middle school and high school math?
I don’t know if using "puzzles" is a scalable solution for the problems in mathematics instruction in middle schools and high schools. It would probably work for many math teachers, but wouldn’t necessarily work for all math teachers. Puzzles and games are good for teaching analytical skills, provided you have someone around who models the use of analytical skills during the game. I’ve noticed, over many, many years of playing games, that many of my friends do not use much deductive reasoning during games. What I would support is much more use of puzzles and games during mathematics class than what is currently considered acceptable practice.
John’s argument that middle school and high school mathematics is unnecessary should actually be restated: our current middle school and high school mathematics curriculum is unnecessary. John is essentially arguing for a different curriculum, rather than discarding the practice of developing mathematical reasoning in students.
I think we need a variety of approaches. What we are doing right now works when students have a strong mathematics instructor, but isn’t working for every student. Instead of assuming that there is one solution to the mathematics education "problem", we should recognize that there are a variety of solutions. What works for John Bennett may not work for every mathematics teacher. I’d like to see these different solutions compete more with each other, and be able to do more research on the effectiveness of each of these approaches. We definitely need more flexibility in mathematics instruction, especially with regard to the curriculum outcomes.
I think we should be focusing less on curriculum outcomes, and more on the holistic goals of a mathematics education. I don’t think it matters if every student learns about the quadratic formula (for example), but all students would benefit from learning deductive and inductive reasoning, pattern finding, modelling of data, and problem formulation. Curriculum should be a vehicle for these goals, rather than the goal itself.