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Eficacia comparativa de métodos de aprendizaje mixto en la enseñanza de nuevos algoritmos a maestros en formación: estudio de un caso para la elaboración de directrices de diseño Comparative efficiency of blended learning methods for teaching new algorithms to future teachers: study of a successful case to stablish design guidelines

The traditional way of teaching mathematics generates significant learning difficulties in students that are reflected in their academic performance. In recent years, the number of teachers and researchers interested in finding innovative, flexible and comprehensible methodologies has increased. The main objective of this article has been to carry out a theoretical review of the methodologies for learning/teaching mathematics at school level. Central elements of international and national method initiatives have been highlighted. The empirical evidence on the Singapore method and the Algorithm Based on Numbers (ABN) method confirms the need to include innovative and manipulative strategies in the classroom. The Singapore method has been shown as a source that improves students′ problem solving skill, mathematical competence, boosting reasoning, and a higher motivation. Some studies focused on the effectiveness of the ABN method and its influence on mathematical cognition. The use of this methodology and learning in flipped classroom have obtained significant results in teacher training. These results could provide guidance about how to improve pre-service education in Primary Bachelor’s Degree. The findings presented in the manuscript could be a basis for opening new lines of quantitative research, with the aim of analysing problem solving and the use of manipulative materials in mathematics. Thus, future research should focus on analysing the cognitive processes involved in mathematical learning, carrying out empirical studies in schools. In addition, it is necessary to improve future teachers’ training, so that they can learn about new alternatives for mathematical teaching and the available resources to be able to put it into practice. Moreover, alternative methodologies are a necessary driver for the improvement of mathematical performance both inside and outside the classroom, and also for the technological and economic development of countries.

Currently mathematics difficulties in schools are a major problem due to several factors. Some research suggest that mathematics teaching-learning methodology could be one of the causes. As a result, alternative teaching methods to the traditional approach (ciphers-based closed algorithm [CBC]) have emerged, such as numbers-based open algorithm (ABN) method. Some research about this new approach has emerged, including neuropsychological studies. The current study aims to analyze performance and potential cognitive differences in solving a computerized task linked to eye-tracking device, comparing CBC and ABN approaches. 18 5th & 6th graders participants were evaluated through a computerized mental arithmetic task. Nine participants learned mathematics with CBC, and nine with ABN approach. Participants were distributed according to his/her mathematical performance rate in three sub-groups, three students per sub-group: low, medium, and high. The ABN method group obtained a higher overall score in the computerized task (mean [M]_CBC=16.22; M_ABN=17.11), but the differences were not statistically significant (p=.690). However, significant differences have been found in two eye-tracking measures. ABN method group obtained a lower number of fixations average in areas of interest [AOIs]) (M_CBC=5.01; M_ABN=3.85; p=.001), and a lower pupil diameter average in AOIs (M_CBC=4.07; M_ABN=3.91; p=.001). This occurred regardless of the participants’ mathematical performance. These results suggest that differences between groups were not in task performance, but in cognitive effort spent in solving the task.