It wouldn't work. All the article seems to focus on "productivity", without defining what productivity is. What the goal of solving problems in a class? To solve problem? No, to goal is to learn something. Maybe to learn how to solve this problem, maybe to learn how to solve problems of this kind, maybe to learn some new words.
The goal is learning. Learning needs constant efforts applied. Not one time per month, but two-three times per week, or even every day efforts. It is how memory works. There is a forgetting curve[1], the forgetting begins when you learnt some new in a class. You need to rehearse material a few times, to move it into long-term memory. It is considered the most effective to rehearse material after three days. Effective in terms of minimizing efforts needed to move information into long-term memory. You could learn faster if learning sessions was placed each 2 days or even every day, but it would need more efforts per bit of long-term memorized information. At least theoretically so -- there are other factors which have their influence on a process of memorization.
So we need to have math lessons a few times per week. English lessons a few times per week. History lessons a few times per week. The most effective schedule would be 2-3 lessons per subject per week. It can be 1 lesson, but then we would need to add a homework assignment for student make a rehearsal of material between lessons, splitting a week by half. I can work great with highly motivated and conscientous students, but not all of students are highly motivated and conscientous. Therefore school creates schedule that forces students into the most effective learning experience. Or at least tries to do it.
