Singapore math focuses on teaching every concept by first manipulating physical objects, then manipulating pictures, then manipulating abstract symbols. Encouraging children to draw connections between these.
It also spreads each concept over time so that you keep revisiting the same ideas to ensure it gets fully integrated. And mixes them. So grade 1 kids may be doing "multiplication" by arranging blocks in a grid before they've fully mastered the + sign.
The USA gives a much more cursory pass through operational actions and goes straight to the abstract representation. We also do a lot more of one concept at a time, only to move on to the next while kids forget the first. The result is that kids learn to blindly follow poorly learned procedures, hoping to do it well enough to pass the test before forgetting the concept. And then the following year do it all over again, having forgot the material from last year.
Yeah, yeah, we have an official curriculum, sequencing, and there is lots of verbiage in official documents about how and when kids are supposed to get reminded, etc. But I described what ACTUALLY tends to happen. And you only have to glance at test scores to realize that the official narrative about what is learned is more myth than reality.
That sounds similar to how I learned math in Montessori in Grades 1-6.
Every math concept had physical "materials" that we had to manipulate to get to the answer (e.g. for square root, you place N beads on a grid in a square form and count how many are on the side). Often, tricks to get quickly at the answer were discouraged early on to promote a proper "grasp" on what the operations entail.
btilly|2 years ago
It also spreads each concept over time so that you keep revisiting the same ideas to ensure it gets fully integrated. And mixes them. So grade 1 kids may be doing "multiplication" by arranging blocks in a grid before they've fully mastered the + sign.
The USA gives a much more cursory pass through operational actions and goes straight to the abstract representation. We also do a lot more of one concept at a time, only to move on to the next while kids forget the first. The result is that kids learn to blindly follow poorly learned procedures, hoping to do it well enough to pass the test before forgetting the concept. And then the following year do it all over again, having forgot the material from last year.
Yeah, yeah, we have an official curriculum, sequencing, and there is lots of verbiage in official documents about how and when kids are supposed to get reminded, etc. But I described what ACTUALLY tends to happen. And you only have to glance at test scores to realize that the official narrative about what is learned is more myth than reality.
huevosabio|2 years ago
Every math concept had physical "materials" that we had to manipulate to get to the answer (e.g. for square root, you place N beads on a grid in a square form and count how many are on the side). Often, tricks to get quickly at the answer were discouraged early on to promote a proper "grasp" on what the operations entail.