Standard curricula have children jump through a progression of hoops. True – they stop every so often to “review” content, but this is usually time wasted for top students and it is only tolerated in order to get struggling students “caught-up” with the rest of the class.
This is wrong. Here is the two-step solution.
1. Reviews (for the purpose of reacquainting struggling students with content) must be kept engaging for top students by embedding the old skill in a tough puzzle, problem, or game. Top students are deflected into hard problem solving. This is never a waste of time. Problem solving is the #1 reason we teach math.
This has been my standard mantra since MathPickle started in 2010, but it does not go far enough. The problem is that struggling students are never given time to just relax and focus on the #1 reason we teach math: problem solving. They are too focussed on new skill acquisition or on catching up with old skills. Therefore I encourage classrooms to experiment a few times a year:
2. Go far back in the curricula – not for the purpose of getting struggling students “caught-up” but in allowing the whole class to focus on tough problem solving. Guage the energy level of the class. The purpose here is (i) to get the struggling students a chance to focus on problem solving, and (ii) to give them an opportunity to re-engage with the bulk of the class.
This realization happened when I tried a new puzzle (Uncut Spaghetti) out at my 2015/2016 school: Rosedale. I first tried it out in grade 1, then grade 2. That was really where I thought the problem would have its home. My next class was grade 4. I apologetically told the teacher that I had a new puzzle that was beneath their grade level, but I was going to try it anyway. The result was electrifying. I’m used to getting high student engagement, but this was enthusiastic engagement beyond my norm. It was attained by giving a problem that no child was learning a skill – that they could all just focus on problem solving. They did so together – en masse. It was a joy.
This experience also reminded me that “engagement-level” is not the sole measure that you should use to judge the success of an activity. Most of the time you cannot do reviews of very old curriculum.