0000000001331120
AUTHOR
David Arnau
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…
Domain-specific knowledge representation and inference engine for an intelligent tutoring system
One of the most challenging steps in learning algebra is the translation of word problems into symbolic notation. This paper describes an Intelligent Tutoring System (ITS) that focuses on this stage of the problem solving process. On the one hand, a domain specific inference engine and a knowledge representation mechanism are proposed. These are based on a description language based on hypergraphs, and the idea of using conceptual schemes to represent the student's knowledge. As a result, the system is able to simultaneously: (a) represent all potential algebraic solutions to a given word problem; (b) keep track of the student's actions; (c) univocally determine the current state of the res…
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…
Disposición del alumnado al uso de herramientas de comunicación síncrona en la docencia universitaria
[EN] In recent years there have been numerous innovative educational initiatives that have proposed the use of synchronous communication tools to support university teaching. These proposals have proven their worth in specific application contexts such as: virtual tutoring, internationalization and mobility in masters and doctorates. However, their sometimes limited scope often makes it difficult to generalize results to other contexts and, thus, to pass from pilots to consolidated solutions. Within the framework of 2015 being declared as the International Year of Evaluation, this paper presents the results of a survey aimed to obtain the opinion of students regarding the use of synchronous…
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…
Actuaciones de alumnos instruidos en la resolución algebraica de problemas en la hoja de cálculo y su relación con la competencia en el método cartesiano
Presentamos resultados de una investigación en la que, entre otros objetivos, se pretendía determinar cómo influía la enseñanza de la resolución algebraica de problemas en la hoja de cálculo en la competencia en el método cartesiano. La comparación de los cuestionarios administrados antes y después de la enseñanza puso de manifiesto un aumento del uso polisémico de la equis cuando se resolvía con lápiz y papel, y una disminución del uso del lenguaje del álgebra en los problemas de edades. Mostramos que estos resultados pueden atribuirse a la aparición de estrategias de resolución en la hoja de cálculo en las que las situaciones descritas en el enunciado se modelizaban mediante relaciones fu…
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.
Mathematical problem-solving in early school years with Bee-bot
Los entornos relacionados con la robótica y los lenguajes visuales de programación por bloques permiten plantear tareas que pueden ser entendidas como problemas con contenido matemático aptos para edades escolares tempranas. Estos entornos permiten proponer situaciones problemáticas en edades en las que el formalismo o el escaso conocimiento matemático impide a los estudiantes abordar problemas matemáticos más complejos. En este trabajo se da cuenta de cómo el robot programable Bee-bot constituye un dispositivo privilegiado donde poder observar cómo los estudiantes toman decisiones durante el proceso de resolución. The environments related to robotics and the visual block-based programming …
Gui-driven intelligent tutoring system with affective support to help learning the algebraic method
Despite many research efforts focused on the development of algebraic reasoning and the resolution of story problems, several investigations have reported that relatively advanced students experience serious difficulties in symbolizing certain meaningful relations by using algebraic equations. In this paper, we describe and justify the Graphical User Interface of an Intelligent Tutoring System that allows learning and practising the procedural aspects involved in translating the information contained in a story problem into a symbolic representation. The application design has been driven by cognitive findings from several previous investigations. First, the process of translating a word pr…
Some insights into the impact of affective information when delivering feedback to students
The relation between affect-driven feedback and engagement on a given task has been largely investigated. This relation can be used to make personalised instructional decisions and/or modif...
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…
On Incorporating Affective Support to an Intelligent Tutoring System: an Empirical Study
Previous research studies have reported strong evidence that the emotional state of students may have a considerable impact on their learning. In this paper, we present an empirical study that evidences that it is possible to influence the user’s affective state in a controlled way, by adapting the system’s response. As part of this paper, we have analyzed the affective impact of varying the level of help provided in an existing Intelligent Tutoring System. Results show that it is possible to use classification approaches to predict positive and negative variations in dominance, valence, arousal, and performance to a reasonable level of accuracy.
Filtering of Spontaneous and Low Intensity Emotions in Educational Contexts
Affect detection is a challenging problem, even more in educational contexts, where emotions are spontaneous and usually subtle. In this paper, we propose a two-stage detection approach based on an initial binary discretization followed by a specific emotion prediction stage. The binary classification method uses several distinct sources of information to detect and filter relevant time slots from an affective point of view. An accuracy close to 75% at detecting whether the learner has felt an educationally relevant emotion on 20 second time slots has been obtained. These slots can then be further analyzed by a second classifier, to determine the specific user emotion.
A Hypergraph Based Framework for Intelligent Tutoring of Algebraic Reasoning
The translation of word problems into equations is one of the major difficulties for students regarding problem solving. This paper describes both a domain-specific knowledge representation and an inference engine based on hypergraphs that permits intelligent student supervision of this stage of the solving process. The framework presented 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) determine the current state of the resolution process univocally. Starting from these ideas, we have designed an intelligent tutoring system (ITS). An experimental eva…
Relación entre complejidad y dificultad en tareas con patrones lineales reiterativos en estudiantes de 5 años
Una de las finalidades de la enseñanza de las matemáticas en Educación Infantil es fomentar el pensamiento lógico, la creatividad y la capacidad para resolver problemas de los estudiantes. Entre las actividades escolares propias de estas edades es habitual encontrar tareas de identificación y continuación de patrones lineales de repetición. Esta actividad puede ser estudiada desde un contexto de resolución de problemas en el que el estudiante debe discriminar la información superflua de aquella que le permite obtener la regla de generación de la serie y resolver la tarea. Diferentes variables como la longitud del núcleo de repetición, el número de descriptores, su naturaleza o la aparición …
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...
Análisis de las actuaciones de los estudiantes de secundaria cuando resuelven problemas verbales en el entorno de la hoja de cálculo
En este trabajo presentamos una división en pasos ideales del Método de Resolución de la Hoja Electrónica de Cálculo y analizamos las dificultades propias del método que su uso plantea al resolutor. También mostramos los resultados de un estudio exploratorio realizado con alumnos de primer curso de secundaria en el que pretendíamos observar cómo resolvían problemas en el entorno de la hoja de cálculo y cómo se enfrentaban a las dificultades propias del método.