Structures and representations used by 6th graders when working with quadratic functions

This study lies within the feld of early-age algebraic thinking and focuses on describing the functional thinking exhibited by six sixth-graders (11- to 12-year-olds) enrolled in a curricular enhancement program. To accomplish the goals of this research, the structures the students established and the representations they used to express the generalization of the functional relationship were analyzed. A questionnaire was designed with three geometric tasks involving the use of continuous variables in quadratic functions. The students were asked to calculate the areas of certain fgures for which some data were known, and subsequently to formulate the general rule. The results show that the participating students had difculties expressing structures involving quadratic functions. However, they displayed the potential to use diferent types of representations to establish the functional relationship. The originality of this study lies in the diferences observed in the process of generalization with discrete variables, since, in the case of continuous variables, students could recognize the general expression from analyzing the set of values that can be attributed to the variables in an interval.EDU2016-75771-P, PID2020-113601GB-I00 and PID2020-117395RB-I00 Spanish State Research Agenc

FVQA: Fact-based Visual Question Answering

Visual Question Answering (VQA) has attracted a lot of attention in both Computer Vision and Natural Language Processing communities, not least because it offers insight into the relationships between two important sources of information. Current datasets, and the models built upon them, have focused on questions which are answerable by direct analysis of the question and image alone. The set of such questions that require no external information to answer is interesting, but very limited. It excludes questions which require common sense, or basic factual knowledge to answer, for example. Here we introduce FVQA, a VQA dataset which requires, and supports, much deeper reasoning. FVQA only contains questions which require external information to answer. We thus extend a conventional visual question answering dataset, which contains image-question-answerg triplets, through additional image-question-answer-supporting fact tuples. The supporting fact is represented as a structural triplet, such as . We evaluate several baseline models on the FVQA dataset, and describe a novel model which is capable of reasoning about an image on the basis of supporting facts.Comment: 16 page