The Tools and Lenses of Mathematics Education Research

There are multiple theories of learning throughout education and within math education itself.  Some of the major theories of learning in mathematics proposed through research by Martin Simon (2009) are constructivism, activism, and socioculturalism.  Simon (2009) does not attempt to say these are all possible learning theories, that all learning can take place within these domains, or that any large consensus on theories has been conceived; but determines that “these [theories of learning] are major background theories adopted by researchers” (p. 478).  Simon (2009) goes on to discuss these theories as many times competing in research and attempting to discredit one another; however, he suggests that they should actually be used to build one another.  This building process should be created through not only through viewing learning by these constructs but viewing research through these different constructs.

            The focus of much research, when emphasizing a particular learning theory, many times excludes or delegitimizes other theories of learning (Simon, 2009).  This many times inflames situations more than serving as constructs in the academic world (Simon, 2009).  Simon (2009) advocates that researchers be proponents of different learning theories other than their own worldviews of philosophies and find use of other’s research.  This advocating process should be careful in considering that new theories of learning invalidate past research.  Just as lasers have changed the way doctors perform many surgeries, the scalpel is still useful and necessary for professionals in this arena.  Theories of learning take place in multifaceted ways and should be considered together rather than separately.

            Simon (2009) suggests mathematical learning theories be used in research as tools and lenses.  Using learning theories as tools emphasizes the fact that certain theories of learning may be more constructive than others in particular domains of use (Simon, 2009).  Just as computer use as tools for learning have changed the way learning takes place in the mathematical classroom, the use of pencil and paper still serves a necessary place even in the most technological capable classrooms.  Researchers are encouraged to use learning theories as a lens to observe particular phenomena that may be present or not present if focusing through the researchers frame of learning reference (Simon, 2009).  An example of this would be a researcher who is observing how cooperative grouping is affecting instruction purely from a sociocultarlistic view, but fails to look at this high leverage practice from the lenses of constructivism and activism.  It is fundamental that researchers combine theories of learning and understand how each play together in the overall learning of the student. 

            Attempting to view research from one particular construct “can unnecessarily limit the observations that are made and the types of explanations that can be generated”  (Simon, 2009, p. 484).  How these theories relate to one another are not as important as what relationship one wants to construct through a particular problem (Simon, 2009).  Recent research has sought to go farther than observing classrooms from a single learning construct and observing their ability to be complimentary (Simon, 2009).  Researchers and teacher educators are encouraged to have their students go farther than a single class in mathematical learning theory and approaches to educating future teachers that emphasize one particular construct (Simon, 2009).  Researchers should seek to understand the difference between what is being looked at and what is being looked with and seek to justify their research based on learning theories as a matter of choice (Simon, 2009)  Teacher educators should use and teach learning theories cohesively in programs making them complimentary of one another.

The mathematical teacher education program at Auburn has done an excellent job in helping students understand the interconnectedness of learning theories.  Older research in learning by Piaget, Dewey, Vygotsky, and others has not been totally predated by current research and still has meaning for current research and teacher use (Simon, 2009).  Researchers using these multiple theories to emphasize particular developments in learning are essential in making theories of learning progress and not devalue other constructs.  Working outside ones own worldview and philosophy will be challenging for new researchers, but sets a high stander for future work.






Simon, M. A. (2009). Amidst multiple theories of learning in mathematics

educationJournal for ResearchinMathematics Education, 40(5), 477–

490.  17.


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