Hoffman/Brahier response

I enjoy problem solving. It's a useful tool in any classroom. Again, by saying it is a tool, I suppose that I limit it from being a way of teaching. There were two scenarios of which I was reminded in this article. I will name two.

The first scenario was when I worked at a math camp over the summer. One of the students in the class did well with rote learning and practice (e.g. learning how to simplify exponential expressions). However, he acted out often, he would distract other students, and he created a challenging learning environment. I found the "remedy" for this was to bring out University of Waterloo math contest problems for him to do. He devoured each and every one of them. He went through any puzzle books I brought in, as well. 

The other side was when I took Math 414 at UBC, where I would travel to certain high schools in Vancouver and conduct math workshops. The layout of the workshop involved students being given a certain list of problems to solve in groups, then they would present the solutions to the class. Most students would work on the set of problems they were given, but they wouldn't really pay attention to those presenting alternate solutions. The students presenting were also very hesitant to come up to the board, and in some cases, students would quietly call each other "stupid" or "slow", which I found absolutely vulgar. 

I love any puzzle, it's always a delight for me to complete puzzles, especially ones like Kenken (which, if I have my own classroom, I would love to use in a grade eight classroom on the first day in order to gauge how students understand logical thinking and how their basic math facts are). I feel like I could fill up a whole year with nothing but problems. However, would this not require a readjustment of curriculum? One of the IRPs for grade 10, for example, under "Relations and Functions" is that a student must be able to express an equation in slope-point form, slope-intercept form, an general form. So there would still be a need for "arbitrary learning" as was mentioned in the other article. I was unclear as to how these things are balanced in Japan. How is new material introduced in a Japanese classroom? Do students find additional information elsewhere (e.g. online), or do they still have an instructional portion to their classes?