Related papers: Making mathematical claims
Mathematics enters the period of change unprecedented in its history, perhaps even a revolution: a switch to use of computers as assistants and checkers in production of proofs. This requires rethinking traditional approaches to mathematics…
Curriculum Learning - the idea of teaching by gradually exposing the learner to examples in a meaningful order, from easy to hard, has been investigated in the context of machine learning long ago. Although methods based on this concept…
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,…
This paper explores the pedagogical potential of "teacher pre-prompting" as a means of guiding student collaboration in programming education. In particular, we investigate how brief teacher-initiated questions posed before students engage…
In this paper, we consider the problem of learning a first-order theorem prover that uses a representation of beliefs in mathematical claims to construct proofs. The inspiration for doing so comes from the practices of human mathematicians…
This study aims to observe if the theorem prover Lean positively influences students' understanding of mathematical proving. To this end, we perform a pilot study concerning freshmen students at the University of Zurich (UZH). While doing…
The generally accepted wisdom in computational circles is that pure proof verification is a solved problem and that the computationally hard elements and fertile areas of study lie in proof discovery. This wisdom presumably does hold for…
Mathematics can serve many functions in physics. It can provide a computational system, reflect a physical idea, conveniently encode a rule, and so forth. A physics student thus has many different options for using mathematics in his…
Eugene Wigner famously argued for the "unreasonable effectiveness of mathematics" for describing physics and other natural sciences in his 1960 essay. That essay has now led to some 55 years of (sometimes anguished) soul searching ---…
Social computing is the study of how technology shapes human social interactions. This topic has become increasingly relevant to secondary school students (ages 11--18) as more of young people's everyday social experiences take place…
An age-old controversy in mathematics concerns the necessity and the possibility of constructive proofs. The controversy has been rekindled by recent advances which demonstrate the feasibility of a fully constructive mathematics. This…
Math is widely considered as a powerful tool and its strong appeal depends on the high level of abstraction it allows in modelling a huge number of heterogeneous phenomena and problems, spanning from the static of buildings to the flight of…
As robots and other intelligent agents move from simple environments and problems to more complex, unstructured settings, manually programming their behavior has become increasingly challenging and expensive. Often, it is easier for a…
Highly successful students, as measured by grades and by scores on the Force Concept Inventory, still struggle with fundamental concepts in mathematics and physics. These difficulties, which turn physics into parrot learning and include…
Our introductory classes in statistics and data science use too much mathematics. The key causal effect which our students want our classes to have is to improve their future performance and opportunities. The more professional their…
A learning algorithm based on primary school teaching and learning is presented. The methodology is to continuously evaluate a student and to give them training on the examples for which they repeatedly fail, until, they can correctly…
We commonly think of mathematics as bringing precision to application domains, but its relationship with computer science is more complex. This experience report on the use of Racket and Haskell to teach a required first university CS…
We discuss how a class of difficult kinematic problems can play an important role in an introductory course in stimulating students' reasoning on more complex physical situations. The problems presented here have an elementary analysis once…
This paper establishes grounds for deeper exploration into the question of dual nature of mathematics as an abstract discipline and as a concrete science. It is argued, as one of the consequences of the discussion, that the division into…
The ability to make decisions based on data, with its inherent uncertainties and variability, is a complex and vital skill in the modern world. The need for such quantitative critical thinking occurs in many different contexts, and while it…