El origen del error de inversión y las bases neuronales subyacentes
Una línea de investigación importante en la enseñanza-aprendizaje de las matemáticas, más concretamente en la resolución algebraica de problemas verbales, es la centrada en identificar los procesos cognitivos que se ponen en juego desde que un sujeto identifica una relación matemática en un problema hasta que la expresan mediante una expresión algebraica. Un caso en el que un número importante de estudiantes reconocen el esquema conceptual, pero no son capaces de plasmar una expresión matemática correcta sería el conocido como error de inversión. Este error aparece en los problemas en los que se plantean proposiciones verbales de comparación aditiva y multiplicativa. El nombre del error pro…
Emulating Human Supervision in an Intelligent Tutoring System for Arithmetical Problem Solving
This paper presents an intelligent tutoring system (ITS) for the learning of arithmetical problem solving. This is based on an analysis of a) the cognitive processes that take place during problem solving; and b) the usual tasks performed by a human when supervising a student in a one-to-one tutoring situation. The ITS is able to identify the solving strategy that the student is following and offer adaptive feedback that takes into account both the problem's constraints and the decisions previously made by the user. An observational study shows the ITS's accuracy at emulating expert human supervision, and a randomized experiment reveals that the ITS significantly improves students' learning…
Using System Dynamics to Model Student Performance in an Intelligent Tutoring System
One basic adaptation function of an Intelligent Tutoring System (ITS) consists of selecting the most appropriate next task to be offered to the learner. This decision can be based on estimates, such as the expected performance of the student, or the probability that the student successfully solves each particular task. However, the computation of these values is intrinsically difficult, as they may depend on other complex latent variables that also need to be estimated from observable quantities, e.g. the current student's ability. In this work, we have used system dynamics to model learning and predict the student's performance in a given exercise, in an existing ITS that was developed to …
Domain Specific Knowledge Representation for an Intelligent Tutoring System to Teach Algebraic Reasoning
Translation of word problems into symbolic notation is one of the most challenging steps in learning the algebraic method. This paper describes a domain-specific knowledge representation mechanism to support Intelligent Tutoring Systems (ITS) which focus on this stage of the problem solving process. The description language proposed is based on the concept of a hypergraph and makes it possible to simultaneously a) represent all potential algebraic solutions to a given word problem; b) keep track of the student's actions; c) provide automatic remediation; and d) unequivocally determine the current state of the resolution process. An experimental evaluation with students at a public school su…
Adding sensor-free intention-based affective support to an Intelligent Tutoring System
Abstract Emotional factors considerably influence learning and academic performance. In this paper, we validate the hypothesis that learning platforms can adjust their response to have an effect on the learner’s pleasure, arousal and/or dominance, without using a specific emotion detection system during operation. To this end, we have enriched an existing Intelligent Tutoring System (ITS) by designing a module that is able to regulate the level of help provided to maximize valence, arousal or autonomy as desired. The design of this module followed a two-stage methodology. In the first stage, the ITS was adapted to collect data from several groups of students in primary education, by providi…
Exploring the development of mental rotation and computational skills in elementary students through educational robotics
Abstract Interest in educational robotics has increased over the last decade. Through various approaches, robots are being used in the teaching and learning of different subjects at distinct education levels. The present study investigates the effects of an educational robotic intervention on the mental rotation and computational thinking assessment in a 3rd grade classroom. To this end, we carried out a quasi-experimental study involving 24 third-grade students. From an embodied approach, we have designed a two-hour intervention providing students with a physical environment to perform tangible programming on Bee-bot. The results revealed that this educational robotic proposal aimed at map…
Fundamentos de diseño de un entorno tecnológico para el estudio de las habilidades en resolución de problemas en primeras edades escolares
En este trabajo se presentan los fundamentos de diseno de un software capaz de monitorizar y registrar datos referentes a la gestion de procesos de resolucion de problemas matematicos. El software permite una recogida sistematica de las variables del proceso de resolucion a partir de las cuales es posible obtener diferentes metricas de aprendizaje del estudiante. Al no centrar la atencion exclusivamente en el resultado final del proceso de resolucion, es posible identificar tendencias cognitivas de los estudiantes. En este manuscrito describimos las caracteristicas de este entorno tecnologico junto con la base didactica que justifica el interes de la investigacion en niveles escolares en …
Predicting human performance in interactive tasks by using dynamic models
The selection of an appropriate sequence of activities is an essential task to keep student motivation and foster engagement. Usually, decisions in this respect are made by taking into account the difficulty of the activities, in relation to the student's level of competence. In this paper, we present a dynamic model that aims to predict the average performance of a group of students at solving a given series of maths problems. The system takes into account both student- and task-related features. This model was built and validated by using the data gathered in an experimental session that involved 64 participants solving a sequence of 26 arithmetic problems. The data collected from the fir…
Solving word problems algebraically in a spreadsheet environment in a primary school
This paper presents some results from an investigation into the teaching of the algebraic solving of word problems in a spreadsheet environment in the sixth grade of primary school in Spain (11-12 year old pupils). The main aim of the study was to investigate whether the spreadsheet could be a mediator to the teaching of algebraic problem solving. Through the analysis of excerpts from a case study, the core of the paper is focused on two different types of the difficulties that students showed when solving problems algebraically in a spreadsheet environment.
Fundamentals of the design and the operation of an intelligent tutoring system for the learning of the arithmetical and algebraic way of solving word problems
Designers of interactive learning environments with a focus on word problem solving usually have to compromise between the amount of resolution paths that a user is allowed to follow and the quality of the feedback provided. We have built an intelligent tutoring system (ITS) that is able to both track the user's actions and provide adequate supervision during the resolution. This is done without imposing any restriction on the resolution paths that are allowed. Instead, the system attempts to enforce metacognitive learning by requiring an appropriate definition of quantities before they are used. The program (a) supports both the arithmetical and algebraic way of solving problems; (b) allow…
The role of language on the reversal error. A study with bilingual Basque-Spanish students
The reversal error is a prevalent phenomenon that consists of reversing the relationship between two variables when writing equations from comparison in verbal language. A study with 169 Basque/Spa...