7/28/2019 A Psycholinguistic Approach to Teaching or Learning
Mathematics
1/2
Algebraic Thinking Vol.2-161
A PSYCHOLINGUISTIC APPROACH TO TEACHING/LEARNING MATHEMATICS
BASED ON BRAIN PATTERN PROCESSING OPERATIONS
Victor Amezcua
La Catalina Natural Language School, Mexico
www.lacatalinaschool.comThe poster presents an emerging
framework on teaching/learning mathematics, grounded in a 10-year
project conducted as design-based research and in
education-research literature
(mathematics, Schoenfeld, 1992; 2nd
language acquisition, Krashen, 1995), and focusing on the
mathematical domain of algebra. The project was motivated by my
observations as aneducational practitioner and as founder/director
of a natural language school, and bears
implications for teaching, learning, and design. The framework
foregrounds cognitive andaffective factors contributing to or
hindering mathematics learning and connections between
these factors (see Schoenfeld, 1992). These factors, I
demonstrate, can be modeled as cohering
around the construct pattern that undergirds a heuristic model
of brain-pattern processing.
As mathematics is arguably the science of patterns (Devlin,
2003, Schoenfeld 1992) with a
language to deal with them (Esty, 1992), I discern structural,
functional, and developmentalcontinuity from simple
pattern-processing perceptual activity (e.g., recognition,
comparison,
matching) to learning language and basic mathematical skills
(Amezcua, 1999). Thus, similarpattern-processing cognitive
faculties are active in learning languages and mathematics. Much
of
naturalistic learning is the development of equivalence classes,
e.g., table. To the extent that
mathematics-learning shares with language-learning cognitive
faculties, students need ampleopportunity and supportive contexts
to recognize and construct equivalences. Algebra, though, is
particularly demanding, as equivalences, e.g., [123=102+2*10+3]
[x
2+2x+3], are stated but not
initially evident or intuitive to the learner. Abstraction is
based on the innate ability to recognize
equivalent classes, but observation strongly suggests that at
its natural level the skill isinsufficient to deal with mathematics
requirements. Strengthening this ability allows fluency in
the mathematical language to emerge making possible the
transferring of skills between one areato another via the
abstraction process.
The psycholinguistic approach to teaching/learning mathematics
that emerged from my study
offers tools for diagnosing learning problems and for designing
strategies for their resolution.
The framework deals with affective factors metacognitively.
Students are lead to recognize andassess their hidden beliefs by
showing them that their equivalence-class recognitions skills
in
daily activities are the same as those required in mathematical
endeavors. Through this, one can
remove learning blockages by replacing old beliefs with more
effective ones. Much of myresearch was done from a qualitative
perspective, but I am conducting new quantitative studies in
rural areas in Mexico where the difficulties are especially
challenging to ground the research.
References.Amezcua, V (1999)A heuristic model of brain pattern
processing. Unpublished Manuscript.
Devlin, K (2003)Mathematics: The science of patterns. New York:
Henry Holt & Co.Esty, W. (1992) Language concepts of
mathematics FOCUS on Learning Problems in
Mathematics 14.(4).
Krashen, S (1995) Principles & practice in 2nd
language acquisition. UK: Redwood.
_____________________________
Alatorre, S., Cortina, J.L., Siz, M., and Mndez, A.(Eds) (2006).
Proceedings of the 28th annual meeting of the
North American Chapter of the International Group for the
Psychology of Mathematics Education. Mrida, Mxico:
Universidad Pedaggica Nacional.
http://www.lacatalinaschool.com/http://www.lacatalinaschool.com/
