All subjects were taught to apply the dot-notation method in the same way,
following the suggestions in the Touch Math manual. However, each subject altered the
method slightly to fit his or her own preferences. These adaptations were allowed because
they reflected the students’ attempts to make the material personally meaningful to them.
In other words, since these adaptations made it easier for the students to remember and
apply the method, they were allowed to deviate slightly from the recommended
procedure. For example, all subjects counted the dots in the same order in which they
were taught, following the pattern depicted in the Touch Math manual. The only
exception is that subject C insisted on counting the dots on the number 9 according to the
5 £''"(§), ,
following pattern: He stated that it was easier to remember that particular
All subjects were taught to apply the dot-notation method in the same way,following the suggestions in the Touch Math manual. However, each subject altered themethod slightly to fit his or her own preferences. These adaptations were allowed becausethey reflected the students’ attempts to make the material personally meaningful to them.In other words, since these adaptations made it easier for the students to remember andapply the method, they were allowed to deviate slightly from the recommendedprocedure. For example, all subjects counted the dots in the same order in which theywere taught, following the pattern depicted in the Touch Math manual. The onlyexception is that subject C insisted on counting the dots on the number 9 according to the5 £''"(§), ,following pattern: He stated that it was easier to remember that particular
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