Year 2015, Volume 2, Issue 1, Pages 54 - 60 2015-01-21

Reflections on the Importance of Reference for Understanding Thinking

Reinhard Oldenburg [1]

237 542

An intentional form of the semantics of algebraic expressions in the tradition starting with Frege is popular in mathematics education. On the other hand, mathematical logic including predicate calculus and lambda calculus is dominated for more than 50 years by referential semantics. A third field of investigation is the semantics of mathematics as realized in programming languages and computer algebra systems. The paper explores the tension between these approaches and tries to clarify the role of reference both in he developed mathematics as well as in the learning process. Referential semantics simplifies theories but requires mental objects to be constructed to be useful. This links the topic to reification theory. A small collection of observations of learners’ behavior adds support to the claim that reference is of some importance in the learning process.

Semantics; algebra; variables;
Primary Language en
Journal Section Articles
Authors

Author: Reinhard Oldenburg

Dates

Publication Date: January 21, 2015

Bibtex @ { ijcer167821, journal = {International Journal of Contemporary Educational Research}, issn = {}, eissn = {2148-3868}, address = {Mustafa AYDIN}, year = {2015}, volume = {2}, pages = {54 - 60}, doi = {}, title = {Reflections on the Importance of Reference for Understanding Thinking}, key = {cite}, author = {Oldenburg, Reinhard} }
APA Oldenburg, R . (2015). Reflections on the Importance of Reference for Understanding Thinking. International Journal of Contemporary Educational Research, 2 (1), 54-60. Retrieved from http://ijcer.net/issue/16048/167821
MLA Oldenburg, R . "Reflections on the Importance of Reference for Understanding Thinking". International Journal of Contemporary Educational Research 2 (2015): 54-60 <http://ijcer.net/issue/16048/167821>
Chicago Oldenburg, R . "Reflections on the Importance of Reference for Understanding Thinking". International Journal of Contemporary Educational Research 2 (2015): 54-60
RIS TY - JOUR T1 - Reflections on the Importance of Reference for Understanding Thinking AU - Reinhard Oldenburg Y1 - 2015 PY - 2015 N1 - DO - T2 - International Journal of Contemporary Educational Research JF - Journal JO - JOR SP - 54 EP - 60 VL - 2 IS - 1 SN - -2148-3868 M3 - UR - Y2 - 2019 ER -
EndNote %0 International Journal of Contemporary Educational Research Reflections on the Importance of Reference for Understanding Thinking %A Reinhard Oldenburg %T Reflections on the Importance of Reference for Understanding Thinking %D 2015 %J International Journal of Contemporary Educational Research %P -2148-3868 %V 2 %N 1 %R %U
ISNAD Oldenburg, Reinhard . "Reflections on the Importance of Reference for Understanding Thinking". International Journal of Contemporary Educational Research 2 / 1 (January 2015): 54-60.
AMA Oldenburg R . Reflections on the Importance of Reference for Understanding Thinking. International Journal of Contemporary Educational Research. 2015; 2(1): 54-60.
Vancouver Oldenburg R . Reflections on the Importance of Reference for Understanding Thinking. International Journal of Contemporary Educational Research. 2015; 2(1): 60-54.