But then, a few weeks later, the kids go back to ignoring the difference between 3-5 and 5-3. Furthermore, despite hours of explanation and practice, half the class seems to do no better than toss a coin to make the call on positive or negative slopes.
This seems like basic neurophysiology. Short-term memories and skills dissipate. It takes time to rewire the brain for permanent storage of a given isolated unconnected uninteresting memory. Maybe someone can find the links?
From my tutoring experience, it takes a lot longer than “hours” for rote memorization to take permanent hold. And rote is how math is usually taught, or at least how children with low math aptitude learn it. For an abstract concept like line slope, not related to anything intuitive, it would take about 1000 problems solved by such a student, with spaced repetition over several weeks, before the relevant memory decay rate increases from minutes or hours to months.
In contrast, a person with high aptitude for math will easily fit the new memory into her existing jig saw puzzle of other memories (“oh, this makes perfect sense, given A, B and C!”) and, in effect, has to memorize a lot less random data, so the required amount of repetition is probably an order of magnitude less.
This seems like basic neurophysiology. Short-term memories and skills dissipate. It takes time to rewire the brain for permanent storage of a given isolated unconnected uninteresting memory. Maybe someone can find the links?
From my tutoring experience, it takes a lot longer than “hours” for rote memorization to take permanent hold. And rote is how math is usually taught, or at least how children with low math aptitude learn it. For an abstract concept like line slope, not related to anything intuitive, it would take about 1000 problems solved by such a student, with spaced repetition over several weeks, before the relevant memory decay rate increases from minutes or hours to months.
In contrast, a person with high aptitude for math will easily fit the new memory into her existing jig saw puzzle of other memories (“oh, this makes perfect sense, given A, B and C!”) and, in effect, has to memorize a lot less random data, so the required amount of repetition is probably an order of magnitude less.