Related papers: Constructive mathematics and teaching
Mathematics is the language of science. Fluent and productive use of mathematics requires one to understand the meaning embodied in mathematical symbols, operators, syntax, etc., which can be a difficult task. For instance, in algebraic…
Understanding learners' understanding is a key requirement for an efficient design of teaching situations and learning environments, be they digital or not. This keynote outlines the modeling framework cK\cent (conception, knowing, concept)…
There are many ways we can not know. Even in systems that we created ourselves, as, for example, systems in mathematical logic, Go\"edel and Tarski's theorems impose limits on what we can know. As we try to speak of the real world, things…
Recent work has formulated the task for computational construction grammar as producing a constructicon given a corpus of usage. Previous work has evaluated these unsupervised grammars using both internal metrics (for example, Minimum…
In order to describe natural phenomena, science develops sophisticated models that use mathematical and formal languages which seem, and often are, very far from common experience. When a phenomenon is not accessible to our senses, its…
Constructivist philosophy and Hasok Chang's active scientific realism are used to argue that the idea of "truth" in cluster analysis depends on the context and the clustering aims. Different characteristics of clusterings are required in…
We examine various categorical structures that can and cannot be constructed. We show that total computable functions can be mimicked by constructible functors. More generally, whatever can be done by a Turing machine can be constructed by…
We study different notions of connected constructive metric spaces. They differ the types of connected components and how different components relate to each other. These notions are equivalent in classical point set topology but they give…
While motivation is of great interest to computing educators, relatively little work has been done on understanding faculty attitudes toward student motivation. Two previous qualitative studies of instructor attitudes found results…
In today's education systems, there is a deep concern about the importance of teaching code and computer programming in schools. Moving digital learning from a simple use of tools to understanding the processes of the internal functioning…
In order to work with mathematical content in computer systems, it is necessary to represent it in formal languages. Ideally, these are supported by tools that verify the correctness of the content, allow computing with it, and produce…
This paper has several purposes. We present through a critical review the results from already published papers on the constructive semigroup theory, and contribute to its further development by giving solutions to open problems. We also…
Probabilistic logic programs are logic programs where some facts hold with a specified probability. Here, we investigate these programs with a causal framework that allows counterfactual queries. Learning the program structure from…
We present a family of paraconsistent counterparts of the constructive modal logic CK. These logics aim to formalise reasoning about contradictory but non-trivial propositional attitudes like beliefs or obligations. We define their…
Mathematics has many useful properties for developing of complex software systems. One is that it can exactly describe a physical situation of the object or outcome of an action. Mathematics support abstraction and this is an excellent…
Since its existence, the computer tool has often supported mathematicians, whether it is to implement an approximation method (numerical calculation of a root, of an integral, ...) or to simulate a phenomenon (geometric in nature,…
The use of logical systems for problem-solving may be as diverse as in proving theorems in mathematics or in figuring out how to meet up with a friend. In either case, the problem solving activity is captured by the search for an…
The best empirical research in political science clearly defines substantive parameters of interest, presents a set of assumptions that guarantee its identification, and uses an appropriate estimator. We argue for the importance of…
Learning to create, use, and evaluate models is a central element of becoming a scientist. In physics, we often begin an analysis of a complex system with highly simplified or toy models. In introductory physics classes, we tend to use them…
With the increasing deployment of machine learning systems in practice, transparency and explainability have become serious issues. Contrastive explanations are considered to be useful and intuitive, in particular when it comes to…