Meaningful Multiple Representations, MultipleSenses & Repetition (MMR-MSR) a systems approach to learning. (F Razo)

Following below is a summary of considerations suggested by widely accepted educational research theory and practices, to support the design and implementation of effective instructional materials and activities. The concepts, framed within a general systems function model, describes areas of cognitive ability which are similar to the main functional blocks of Luria’s Neurophysicological Theory (by A.R. Luria) including physical as well as virtual, computer-based materials and activities:

1.- MMR – Starting with Meaningfully focused context (M): The purpose and expectations of the learning exercise should be clear and meaningful to the learner, and unambiguously focused (minimal distractions) by the environments, materials, objects, activities. individual actions and timing in sequences introduced. These should be distinctively strong, understood and affectively embraced by the students in the context of their realities (Situated) as well as timely opportunities for action (affordances) for most effective, unencumbered (minimalist) learning – (contributing thinkers: J.J. Rousseau, J. Dewey, J. Bruner, M. Montessori, J. Lave, M.J. Wenger, J. Greeno, J.M. Carroll, D. A. Norman, J. J. Gibson,) reinforced by Multiple Representations (MR): These provide proper conceptual support and reinforcement from different , equivalent, comparable or surrogate representations, going from those that use realistic, concrete, clear explicit and faithful replicas and toys of observable reality, to those that use abstract, symbolic and implicit, coded objects and processes to suppot the more efficient processes of identification, storage and retrieval of information, and powerful development and mastery of knowledge, due to connected representations of real and relevant environments (Cognitive Science – H.A. Simon).
2.- MSR -- Multiple Senses (MS) involved in simultaneous interactive and repeated stimulation of the body and mind : The more senses involved in properly correlated strong, simultaneous, coordinated stimulation of the mind, the better for the students receiving and processing information within their complex brain structures (Perception and cognition – J.J. Gibson, R.E. Mayer, J. Piaget.) Allowing the learners to participate actively and interactively in the process reinforces their involvement, understanding and ownership (affective) of the knowledge (cognitive) targeted for learning (J. Dewey, J. Piaget, J. Bruner) , followed by (R) Repeated: Appropriate and effective repetition of pattern-developing experiences, so as to support the complex electrochemical and biological processes involved in the acquisition-generation and long-term retention of desired patterns of knowledge in the body and the brain (Behaviorism – J.B. Watson, B.F. Skinner)

References

Anderson, J. R., Reder, L. M., & Simon, H. A. (1996, May). Situated learning and education, Educational Researcher, 25(4), 5-11. Bruner, J. (1960). The Process of education. Cambridge, Mass.: Harvard University Press, 1960.

“A Brief History of American K-12 Education in the 20th Century.” Mathematics Cognition, 2013.
(http://www.csun.edu/~vcmth00m/AHistory.html). Accessed: December 12, 2013.

Bruner, J. The Culture of Education. 1997, Harvard University Press, Cambridge, MA.
Competent Children at 8: Families Early Education, and Schools., Wylie C., Thompson, J., New Zealand Council for Educational Research, Wellington, 1999.

Common Core State Mathematics Standards. http://www.corestandards.org/assets/CCSSI_Math%20Standards.pdf accessed December 13 2013.

Dewey, J. “Schools of Tomorrow”, 1915, New York. https://archive.org/details/schoolsoftomorro005826mbp
Accessed December 13, 2013

“Education in the United States Pose a National Security Threat”. Christian Science Monitor, March 12, 2012. http://www.csmonitor.com/USA/Education/2012/0320/Education-report-Shortcomings-of-US-schools-pose-national-security-threat. Accessed: December 12, 2013.

“Educate to Innovate” Initiative: President B. Obama, the White House”. http://www.whitehouse.gov/issues/education/k-12/educate-innovate. Accessed December 13, 2013.

Gibson, James, J.J. (1977), The Theory of Affordances. In: Perceiving, Acting, and Knowing, edited by Robert Shaw and John Bransford.

Knowing and Teaching Elementary Mathematics: Teacher Understanding of Fundamental Mathematics in China and the United States – Studies in Mathematics Thinking and Learning Series. Ma, L., 2010, Routledge, New York & London.

Lave, J. The culture of acquisition and the practice of understanding. In Kirshner D. & Whitson, J. (Eds.), Situated Cognition: Social, Semiotic and Psychological Perspectives (pp. 17-36). 1997, Mahwah, NJ: Lawrence Erlbaum Assoc. Pub.

Luria, Alexander Romanovich., Human Brain and Psychological Processes. Harper & Row, 1966

Greeno, J. G. (1988). Situations, mental models, and generative knowledge. In Klahr, D. and Kotovski, K. (Eds.), Complex information processing: The impact of Herbert Simon (pp. 285-318) Hillsdale, NJ: Lawrence Erlbaum Assoc.

Mayer, E. R. Thinking, problem solving, cognition – Second Edition. 1997. New York, NY: W. H. Freeman and Company.

Montessori, M. The absorbent mind. Translated from the Italian by Claude A. Claremont. 1964, India: Theosophical Publishing House.

New Generation Science Standards (NGSS) http://www.nextgenscience.org/next-generation-science-standards Accessed on December 13, 2013.

[21] Norman, Donald. “Things that Make Us Smart”, (1998). Addison Wesley, New York, NY.

“Over-100 Leading Tech Executives Urge President Oobama and Congress to Enact High-Skilled Immigration Reform”. http://www.technet.org/over-100-leading-tech-executives-urge-president-obama-and-congress-to-enact-high-skilled-immigration-reform/. Christian Science Monitor On Line. Accessed: December 12, 2013.

Piaget, J. The child's conception of the world. 1929 London: Routledge & K. Paul.

PISA, 2012 (Program for International Student Assessment, OECD) tests (http://www.oecd.org/pisa/ , http://www.oecd.org/pisa/keyfindings/pisa-2012-results.htm). Accessed: December 12, 2013.

Polya, G. How to Solve It: A New Aspect of Mathematical Method. Princeton University Press. Princeton, NJ., 1945.

Razo, F, Mathematics Learning ZigZag. Animath, 2004
http://www.animath.net/mathzigzag.html Accessed Jan 10, 2014

Razo, F, MMR-MSR Systems Model of Learning Animath, 2004
http://www.animath.net/MMR%20MSR.html Accessed Jan 10, 2014

Razo, F, Web STEMP Animation. Animath, 2004
http://www.animath.net/mathlrn11.htm Accessed Jan 30, 2014

Simon A. Herbert, John R. Anderson, Lynne M. Reder, Applications and Misapplications of Cognitive Psychology to Mathematics

Steps of the Scientific Method. Science Buddies. http://www.sciencebuddies.org/science-fair-projects/project_scientific_method.shtml Accessed on December 15, 2013.

TPACK,, Technological, Pedagogical, Area Content Knowledge. http://tpack.org/ Accessed Jan 10, 2014

Vygotski, L.. Mind in society: The development of higher psychological processes. Edited by Cole, M. et. al. Cambridge, MA: Harvard University Press, 1978.Who is Wired and Who is Not. Becker, H. J., The Future of Children – Children and Computers, University of California, Irvine, Ca., 2000.