Difculties in semantically congruent translation of verbally and symbolically represented algebraic statements
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AuthorCastro Martínez, Encarnación; Cañadas Santiago, María Consuelo; Molina González, Marta; Rodríguez-Domingo, Susana
Algebraic statementsVerbal representationRepresentationAlgebraic symbolismTranslation
Castro, E., Cañadas, M.C., Molina, M. et al. Difficulties in semantically congruent translation of verbally and symbolically represented algebraic statements. Educ Stud Math (2021). [https://doi.org/10.1007/s10649-021-10088-3]
SponsorshipSpain’s National Research Agency (Spanish initials, AEI) and the European Regional Development Fund (ERDF) under projects EDU2016-75771-P and PID2020-113601GB-I00; Funding for open access charge: Universidad de Granada / CBUA.
This paper describes the difficulties faced by a group of middle school students (13- to 15-year-olds) attempting to translate algebraic statements written in verbal language into symbolic language and vice versa. The data used were drawn from their replies to a written quiz and semi-structured interviews. In the former, students were confronted with a series of algebraic statements and asked to choose the sole translation, of four proposed for each, that was semantically congruent with the original. The results show that most of the errors detected were due to arithmetic issues, especially around the distinction between product and exponent or sum and product in connection with the notions of perimeter and area. As a rule, the error distribution by type varied depending on the type of task involved.