Abstract:

Arithmetic and calculation are the core contents of the Primary Education curriculum in Spain, whose students are from 6 to 12 years old, as well as the equivalent educational stages of other countries for their importance in acquisition of new mathematical knowledge. However, the methods used for teaching arithmetic are generally focused on activities that do not stimulate the development of mathematical competence, particularly with regard to problem solving, which has made them subject to criticism by several experts in Mathematics Education.

Given the need to have problems that encourage students to analyse, interpret and develop strategies, models and arguments about the arithmetic contents to solve them, cryptoarithmetic is proposed. This is a kind of mathematical problems that consists of discovering the figures of arithmetic operations (addition, subtraction, multiplication and division) that have been replaced by the characters of a code. Cryptarithmetic was born as a mathematical pastime and, since its popularization in the 1930s, it has been studied in Mathematics and has had applications in Engineering, whereas in Education it only appears in some materials as a game, and, in the most of cases, without a pedagogical proposal as background. Not in vain, research on implementation and treatment of cryptarithmetic puzzles in the classroom is scarce. In this regard, since the concept of game is inherent in cryptarithmetic, it is possible to believe that the treatment with video games, thanks to its contributions to learning and its recreational component, enhance the learning experience with this kind of mathematical problems.

This paper aims to describe and analyse the results of cryptarithmetic problem solving and discover what differences exist in the acquisition of arithmetic skills, depending on whether the problems are treated in a digital (video game) or non-digital (paper) medium. To achieve these objectives, a mixed research methodology is used, based on the triangulation of the qualitative data of the cryptarithmetic problem solving and the quantitative data provided by the instrument designed to evaluate the arithmetic competencies acquired in said problem solving, applied as a pre-test and post-test and elaborated from a didactic analysis of the cryptarithmetic puzzles proposed to the students. The sample consists of ninety sixth grade students (aged between 11-12 years), a size that is conditioned by the research methodology, and is divided into two groups (experimental and control) depending on whether the cryptoarithmetic puzzles are solved through a digital or non-digital medium, respectively. Both groups solve the cryptarithmetic puzzles in pairs or small groups. Results show inter and intragroup differences in relation to the overall score and the average score of the ten subjects of the instrument of evaluation of the arithmetic competencies, in conjunction with the qualitative study of cryptarithmetic problem solving.

Keywords:

Mathematics Education, Problem Solving, ICT, Game-Based Learning, Primary Education.