The Argument
When discussing a student's ability to learn, Shenk brings up the work of John Mighton. Mighton created a learning program called “Junior Undiscovered Math Prodigies.” He states that by breaking “down math concepts into the most easily digestible form […] a Grade 3 class could easily reach a Grade 6 or 7 level.” (152). Recall from earlier in the book that Shenk brings up Ericcson and Chase's study on a student initialed S.F. When posed with a series of numbers, S.F. was gradually able to remember long sequences by splitting the sequence into smaller sequences. What are the simlarities and differences between Mighton's method and the method S.F. used to memorize number sequences? Which method of memorizing and learning seems more effective? Relate your response to the types of learning behaviors explained in Ch. 51.2.
-Edward Wu (edwardwu0@gmail.com)
Both Mighton and Ericcson and Chase used small tidbits of information to learn a larger concept. Mighton’s method of learning is probably more effective because it focuses on skills, instead of rote memorization. Shenk explains that “countless numbers of math students get left behind at one point or another simply because they can’t quite grasp one small concept; then they quickly lose confidence in their ability to go forward, and they stagnate” (152). The point is, Mighton’s method helps kids understand certain math concepts that they continue to use and apply to further math problems. In the case of Ericcson and Chase’s study, however, S.F. mastered the skill of memorizing numbers, but could not apply the skill to memorizing anything else, even random letters.
ReplyDeleteS.F.’s failure to transfer his short-term memory from numbers to letters could be a form of habituation (Campbell 1125). Rather than waste time converting the memory gains into a useful strategy for memorization, S.F.’s brain became habituated to memorizing only numbers (1125). Though not mentioned specifically by Shenk, S.F. could also have exhibited operant conditioning, because Ericcson and Chase inevitably connected S.F.’s failure to remember a new digit to a decrease in the number of digits given (1127). S.F., conscious of the purpose and methods of the experiment, would acknowledge his own failure at remembering by recognizing the reduced length of the new number sequence. The desire to receive more numbers, because it is associated with success in the experiment, would be an example of operant conditioning through positive reinforcement, while the shame of forgetting a sequence and hearing fewer numbers was negative punishment (http://psychology.about.com/od/behavioralpsychology/a/introopcond.htm). S.F.’s natural desire to memorize more numbers could have created an operant conditioning model in which he would try to repeat his good behavior in order to know he was doing well in the experiment. S.F. definitely exhibited problem solving by devising his own way to remember numbers-regarding them as race times (1128).
Mackenzie Levy (GinnyFan@comcast.net)
Both Mighton's method and S.F.'s method involve associating the task/concept being learned with a previously known or experienced concept. S.F.'s method involved breaking the list of numbers into sequences of race times. Being a competitive runner, S.F. had previous experience with times (55); his strategy of memorizing times as opposed to numbers was associating the task at hand -- memorizing numbers -- with a previously known concept. Similarly, one of Mighton's basic methods for teaching multiplication involved counting in certain increments on the student's hands (341). Many children count on their hands; multiplication by counting in increments is expanding a task previously known by children. In both cases, by relating a potentially unrelated task to a task he or she already knew, both S.F. and the students are able to learn and eventually master (S.F. eventually got more than 80 digits, and the students' mathematics abilities became very advanced) the task.
ReplyDeleteA significant difference between S.F. and the students involves how they were able to expand upon their new strategy. S.F. was unable to expand memorizing sequences of numbers into sequences of letters, despite the similarities between the two tasks. S.F. could have employed a strategy of equating each letter a number or numbers, and then used his strategy for memorizing numbers (56). On the other hand, the students were able to to reach grade 6 or 7 level mathematics ability, which obviously involves more complex concepts than single-digit multiplication. Unlike S.F., the students were able to expand upon their previous method to learn a more complex concept.
One possible reason for this difference could have been in how meaningful the task was. In the case of S.F., his experience with competitive running allowed him to memorize a long series of digits by memorizing a corresponding time. However, memorizing letters did not have as much meaning to him as memorizing numbers (Letters cannot be directly translated into times), so he was unable to memorize letters. Meanwhile, the students' new tasks always expanded upon previous tasks, which gave each of the tasks being learned some meaning. Another study by Chase and Ericsson confirms that the meaning of the task directly corresponds with an ability to learn the task. In this study, Chase and Ericsson compared test subjects' abilities to memorize an "meaningful sentence of twenty or more words" to their abilities to memorize the sentences when the word order is scrambled. The test subjects had no difficulty in memorizing the organized, meaningful sentence; however, they could only memorize approximately six words of the rearranged sentence with less meaning. (http://www.psy.fsu.edu/faculty/ericsson/ericsson.mem.exp.html)
Essentially, Mackenzie's argument that S.F.'s failure to memorize letters is a form if habituation is the same as my argument that a sequence of letters was meaningless to S.F. Habituation is a loss of responsiveness to a meaningless stimulus; the task of memorizing letters was meaningless to S.F., so he stopped attempting to memorize the sequence. I disagree with Mackenzie's argument that S.F. experienced operant conditioning. While associations were being made with reward or punishment, S.F. was associating reward/punishment with a task, not a behavior. A behavior is defined as action in response to a stimulus (Campbell 1120). The main purpose behind a behavior is an increased ability to survive and reproduce; successfully memorizing a sequence of numbers has a very minuscule effect on S.F's fitness, if any.
Memorization techniques exhibit the biology theme of structure and function. The biology theme of structure and function describes how the structure of system relates to the system's function or how the way a process is organized relates to the process itself, and that, given the structure of a system or process, one can deduce the function and vice-versa. For example, plant leaves are thin and have a large surface area. This structure corresponds to the leaf's function of being the main photosynthetic organ in a plant (Campbell 741-742). In the case of memorization techniques, the organization (structure) of the memorization technique directly correlates to specifically what the technique is memorizing. For example, S.F.'s technique of converting numbers to race times directly correlated to the task at hand, which was memorizing a list of numbers. However, this did not work for memorizing letters; the structure of S.F.'s memorization technique of conversion of numbers to race times. did not match the task of memorizing letters. Moreover, Mighton's students' technique of assigning fingers consecutive multiples of a number matched its function: multiplying numbers. One can infer from looking at Mighton's diagram on p. 341 in the Evidence section of a hand with multiples of two above each finger that the specific function of the technique was to multiply numbers by two.
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