Educational Psychology—Limitations and Possibilities

Educational Psychology on the Move 921
Let’s return to the example of the child learning to divide. In order to determine how a child
accomplishes the task of learning to divide double-digit numbers with single digits, for example,
the researcher looks at a variety of different factors. If the K-n diagram of Figure 105.3 represents
the research, the points on the graph are representative of the different interpretive lenses the
researcher places on the phenomenon. The investigation may begin with biography. What is the
child’s previous experience with division? The child who has experienced success in the past
will approach the task differently than the child who has struggled. What instruction outside the
classroom does the child receive? A child who receives tutorial help may have additional insights
into division that breed success, or may simply be confused because of contradictory instructions.
What is the family attitude toward mathematics? The child of parents who view division as a
daunting challenge has a different perspective than the child of mathematicians. Does the child
speak sufficient English to understand instructions? Language is an integral part of mathematics,
and facility with language affects acquisition. Other questions may be ethnographic in nature.
Did the child fight with a friend before class? Is this the day before a long weekend? The ability to
concentrate has a profound impact on attention to a learning task. A phenomenological approach
raises different questions. What experience with division does the child have in everyday life?
What is the lived experience of the child during the lesson? What is the lived experience of the
teacher?
This leads to an important contextual point: questions about the teacher might be considered
irrelevant in the CNB paradigm, but they are key in a post-CNB epistemology. What is the
classroom teacher’s attitude toward mathematics? The teacher who is a trained mathematician
has an approach different than the nonspecialist, and may have the ability to use a variety of
approaches. What tools are used in the lessons? A wealthy school may have the resources to
provide manipulatives and visual aids to supplement instruction or due to small class size, may
afford the teacher greater amounts of time to work with students on an individual basis. What
does the teacher believe are the child’s capabilities? Pedagogical decisions based on a teacher’s
expectations can have an enormous impact on classroom learning. The broader context is also
important. What is the prevailing societal attitude toward mathematics? A society that values
mathematical ability and achievement influences classroom instruction by providing funding,
and honoring individuals with demonstrated talent, whether they are students or teachers. These
questions and many, many more can affect the student’s ability to learn a mathematics task that is
apparently simple. Of course, it would be impossible to address all questions in order to come up
with the definitive answer to the question about a child’s learning. But what is most important is
not the answer, it is the questions, and the complexity of the process of attempting to discover the
answer leads to a sense of humility for the researcher. By acknowledging that any answers may
be dependent upon context, the researcher avoids the sweeping generalizations that have served
in the past to harm, not help, those being researched.
CONCLUSION
Clearly, the tendency exists to reduce epistemology to an easily digestible form, whether by
adherents to Cartesian–Newtonian–Baconian thought or by those who reject CNB entirely. Even
in describing the tendency, I delineate a tension between one side and another! Thus, by my own
example, binarisms exert a powerful pressure on the conceptualization of knowledge. It is best,
then, to keep in mind the dynamic qualities of the K-n graph of Figure 105.3. Is it possible to avoid
binarisms? It takes a concerted effort, and perhaps the question “What binarisms are evident in
what I just described?” becomes a useful question for the student of epistemology. The question
serves as one of the checks and balances enabling the creation of an epistemology that moves
more often than not toward dynamism instead of stoicism, expansion instead of contraction,