The following ‘characterization’ of knowledge is from the paper A contemporary analysis of the six ‘‘Theories of Mathematics Education’’ theses of Hans-Georg Steiner by Gunter Torner and Bharath Sriraman published in ZDM Mathematics Education (2007) 39:155–163.
- Knowledge is an objective, definite, and organized body of facts that constitute the truth about a subject, to be distinguished from opinion, which is subject and cannot be proven as true. (in port)
- Knowledge consists of facts, principles, axioms, etc. that can be proved, although it may be difficult to carry out the proof. Overcoming this difficulty is the expert’s challenge, and some are more expert than others. (‘in safe harbor’)
- Knowledge consists of facts, principles, axioms, etc. that can be proved, although it may be difficult to carry out the proof. The coherence and completeness of the system may vary across disciplines, some being more advanced than others. (‘crossing the bar’)
- Knowledge is not secure but is any person’s organization and interpretation of available information. One interpretation is as good as another. But people with power can assert their interpretations over those of others. (‘entering the open’ and ‘losing sight of the shore’)
- Knowledge can be shared but not ‘‘measured’’ or counted upon to remain the same. (‘entering rough waters’)
- Knowledge is not something that is external and definite but something that each individual constructs according to his/her experience, background, etc. (‘Weathering storms; losing bearings’)
- Knowledge is the world view one has constructed from learning and experience, along with the ethical implications of this view, synthesized into a consistent philosophy. (‘Getting back one’s bearings; navigating successfully’)
- Knowledge is a creative resolution between uncertainty and the need to act, which makes it a dynamic means of transaction between the self the environment, requiring both stability and flexibility. (‘Progressing into new regions’)
- Knowledge is the evolution of awareness, best expressed as ascending levels of consciousness, in which the individual must break through to new perspectives and discard those no longer useful. (‘Discovering anticipated and unforeseen destinations or destinies‘)
, Paul Ernest gave a brief synthesis of four major learning theories in mathematics education in his article Reflections on Theories of learning. He calls them theories of learning but he also acknowledges that they are more appropriately called philosophies of math education. I’m sticking to learning theories. It’s less scary and makes me conscious that they are for framing teaching and learning studies and practice. In summarizing the ‘learning theories’ Paul Ernest in fact described each in the context of practice and research.