The Spanish Ministry of Education has given our project the maximum qualification and financed it with resources and personnel. In this page, you can find more information about the ITS-MATHPS project.
A proficient human tutor characterizes learners according to the observed behaviour, and builds a mental abstraction of their most relevant abilities and weaknesses. Depending on the experience and skills of the tutor, the set of variables chosen to describe a student may be too generic, and lack the sufficient granularity to produce an adequate characterization of his/her abilities. In this project we aim to identify a relatively small set of variables that are sufficiently manageable and representative to be able to describe the student. These variables, among other aspects, should be able to identify and quantify the knowledge and skills related to arithmetical and algebraic word problem solving, and also describe affective characteristics and specific difficulties in the case of learners with special educational needs. We start from the hypothesis that success or failure at each problem step strongly depends on the learner’s proficiency at using the conceptual schemes that can be potentially applied to trigger a valid next action. The student model should hence include information about the student’s proficiency at using some key conceptual schemes, as well as specific difficulties. Finally, we will extend the data collection by adding affect-related information. First, we will use explicit emotional reports using well established tools, such as the SAM (Self-Assessment Manikin) designed by Bradley and Lang. Later, we will analyse the existing relations between the affective variables and other observable ones, with the final intention of building a computerised tool that is able to infer the emotional state without it being explicitly reported by the user.
When solving a word problem, the learner carries out analysis processes. In these analysis processes, learners bring conceptual schemes to their working memory, which allow them to identify relationships between quantities based on the information provided in the statement and other information implicitly evoked. The learners then explicitly state these relationships by using arithmetic or algebraic expressions. At some stages, the learner may need analysis processes that are supported by other previous analysis that are only present at the mental level. This need can overload the working memory of the learner and become a major difficulty to arrive to the correct solution. The above description reveals three major aspects that are related to the difficulty of solving a word problem: (a) the ability to retrieve appropriate conceptual schemes and use them properly to identify relationships between quantities; (b) the need to carry out simultaneous analysis processes while the results of other previous analysis are kept in the working memory; and (c) the expression of relationships in the language of algebra or arithmetic. We aim to identify relevant difficulties related to these three aspects, to advance in the diagnosis of misconceptions by observing the learner’s errors, taking into consideration that the same error made by different users may be due to different causes and using the student model defined in GO1 to identify the most likely source. We will also study whether the errors may serve as useful predictors of special educational needs. These studies will be supported by experiments that use our ITS to collect information about the errors and the specific situation in which they happened.
Phis objective is mainly aimed at contributing to key methodological aspects of the tutor's action (human or artificial) in the teaching of word problems solving. These are especially relevant in students with special needs, who can notably benefit from the adaptation of the instruction to their difficulties and other particularities. As part of this general objective, we will address the design of teaching sequences adapted to the singularities of each learner. For this, it is essential to be able to estimate the difficulty of each task for a student from the problem complexity and the student characteristics. However, the problem complexity will also depend on the solution path chosen by the student, which is only known during the solving process. Data recorded by HINTS can be used to predict the most likely resolution path, and facilitate the development of a complexity measure. This fact makes it possible to extend and implement dynamic models previously built by the research team, in such a way that the ITS could jointly consider both the task complexity and the student’s level of competence and affective state. As part of this general objective, we will also study of the so-called assistance dilemma, which is related to the amount of information that must be given or retained to achieve optimal learning. For example, when a learner faces some difficulty at solving a problem step, a more active role of the student may be encouraged by providing hints that do not completely reveal the actions required to solve the step. However, such aids may also have a negative effect if the student does not feel capable of solving the problem and decides to abandon it.