Problems of Understanding the Text and Symbolic Information in Teaching Mathematics

We posed the problem of understanding the text and symbol messages by students. We considered the interpretation of the concept of "understanding" in philosophy and psychology, presented psycholinguistic aspect of the concept in detail. We proposed a general classification of problems of perception of speech by students in teaching mathematics. We identified two broad categories of problems of understanding the language statements (direct problematic language codes perception and incorrect perception of the context). We introduce the concept of "reversible language constructs”, discuss the various types of reversible language constructs found in educational materials on math. The analogy is provided to demonstrate the similarity of reversible structures of natural language with constructs of algebraic material. The author presents the classification of reversible constructs. We substantiated the importance of the study of reversible structures decoding by students, identified properties of reversible constructs perception, the conditions for their understanding. We revealed the further ways to study how to create an effective technique for decoding reversible constructs (with the use of educational material on algebra).

1. Belyanin V.P.  Psikholingvistika [Psycholinguistics]. Moscow: Flinta, Moskovskiipsikhologo-sotsial'nyiinstitut, 2004. 232 p.
2. Gadamer G. G. Aktual'nost' prekrasnogo [The actuality of beauty]. Moscow: Iskusstvo, 1991.  367 p.
3. Gusserl' E. Idei k chistoifenomenologii [Ideas pertaining to a pure Phenomenology]. MikhailovaA.V. (ed.). Moscow: DIK, 1999. 311 p.
4. Zhinkin N. I. Mekhanizmyrechi [Mechanisms of speech]. Moscow: APN RSFSR, 1958.  378 p.
5. Znakov V.V. Ponimanie v poznanii i obshchenii [Understanding in cognition and communication]. Moscow: Institutpsikhologii RAN, 1998. 232 p.
6. Kravtsova N.A., Katasonova A.V. Neiropsikhologiyaformirovaniyadvigatel'nykhfunktsii i prostranstvennykhpredstavlenii u chastoboleyushchikhdeteimladshegoshkol'nogovozrasta [Neuropsychology  formation of motor functions and spatial representations in sickly children of primary school age]. Psikhologicheskayanauka i obrazovanie[Psychological Science and Education PSYEDU.ru], 2011, no. 2. Available at URL:http://www.psyedu.ru/authors/a2093.phtml (Accessed 12.06.2014
7. Luriya  L.R. Yazyk i soznanie [Language and cognition]. Rostov-on-Don: «Feniks», 1998. 416 p.
8. Statnikov A.I., Dragoi O.V., Bergel'son M.B., Iskra E.V., Mannova E.M., Skvortsov A.A. Osobennostiponimaniyalogiko-grammaticheskikhkonstruktsiiprirazlichnykhformakhafazii [Features of understanding of logical-grammatical constructions in various forms of aphasia]. Tezisykonferentsii “Kognitivnayanauka v Moskve: novyeissledovaniya” (g. Moskva, 16 iyunya 2011 g.) [Cognitive science in Moscow: new research] Moscow: BukiVedi, 2011, pp. 238–242.
9. Khaidegger M. Put' k yazyku [On the way to language]. Moscow: Respublika, 1993. 447 p. (In Russ.).
10. Shleiermakher F. Germenevtika [Hermeneutics]. Saint-Petersburg: Evropeiskii Dom, 2004. 242 p.(In Russ.).
11. Yaspers K. Obshchayapsikhopatologiya [General psychopatology]. Moscow: Praktika, 1997. 1056 p.(In Russ.).