Comments - Week 6
Vygotsky, citing Levy-Bruhl, notes early in his discussion that
I am guilty, as are nearly all of my mathematics friends/colleagues, of requiring students to memorize certain things: derivative formulas, integral formulas, factoring formulas, etc. I think the idea here is that we wanted the students to become adept at using these formulas to such a degree that they no longer needed to reference the formulas themselves. Through practice and by providing problems that caused the students to reflect on and modify their understanding of the formulas, we hoped that the formulas would become internalized and eventually interiorized.
On the one hand, I think some memorization is important. For instance, students who have not memorized (or who have forgotten) perfect squares, unsurprisingly, tend to have difficulty applying the difference of squares factoring formula.
On the other hand, it is false to assume or to give students the impression that, if/when they have a job or future position in which such formulas are necessary to be used, they will not be able to reference the Internet and other resources. [But, again, I think there is something to be said for interiorization here... deep conceptual understanding cannot be replaced by sheer memorization or referencing the Internet.] On several occasions throughout middle school, there were lists and other things that I was required to memorize that I had extreme difficulty in memorizing (and have long forgotten): the list of all U.S. presidents, for instance.
Lastly, and largely unrelated to my previous comments, I took note of the following passage:
...in the psychology and behavior of primitive man memory plays a much greater role than in our mental life, because some of its former functions in our behavior have been transferred elsewhere and changed... The constant use of logical mechanisms and abstraction concepts has profoundly altered the functioning of our memory.He provides several examples of this being the case. This observation makes me wonder to what degree and in what ways current methods of teaching and learning still assume and depend on the memory capacity of primal humans.
I am guilty, as are nearly all of my mathematics friends/colleagues, of requiring students to memorize certain things: derivative formulas, integral formulas, factoring formulas, etc. I think the idea here is that we wanted the students to become adept at using these formulas to such a degree that they no longer needed to reference the formulas themselves. Through practice and by providing problems that caused the students to reflect on and modify their understanding of the formulas, we hoped that the formulas would become internalized and eventually interiorized.
On the one hand, I think some memorization is important. For instance, students who have not memorized (or who have forgotten) perfect squares, unsurprisingly, tend to have difficulty applying the difference of squares factoring formula.
On the other hand, it is false to assume or to give students the impression that, if/when they have a job or future position in which such formulas are necessary to be used, they will not be able to reference the Internet and other resources. [But, again, I think there is something to be said for interiorization here... deep conceptual understanding cannot be replaced by sheer memorization or referencing the Internet.] On several occasions throughout middle school, there were lists and other things that I was required to memorize that I had extreme difficulty in memorizing (and have long forgotten): the list of all U.S. presidents, for instance.
Lastly, and largely unrelated to my previous comments, I took note of the following passage:
In the words of Engels that we have quoted earlier, man uses it but does not dominate it. Indeed, this type of memory dominates him, by suggesting to him unreal fictions, and imaginary images and constructions. It leads him to establish mythologies that often impede the development of his experience, by screening the objective picture of the world behnid subjective structures.Later, Vygotsky notes
The historical development of memory begins from the point at which man first shifts from using memory, as a natural force, to dominating it. This dominion, like any dominion over a natural force, simply means that at a certain stage of his development man accumulates sufficient experience -- and sufficient knowledge of the laws governing the operation of memory, and then shifts to the actual use of those laws.I wonder how this affects children. I wonder if there are aspects of children's memory, mingled with imagination, that lead them to be uncertain as to what is "real" and what is "imaginative" (to the extent that any of us can be certain). I wonder if certain fears that linger into adulthood might be traced back to this.
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