7,213 research outputs found
Carnap: an Open Framework for Formal Reasoning in the Browser
This paper presents an overview of Carnap, a free and open framework for the development of formal reasoning applications. Carnap’s design emphasizes flexibility, extensibility, and rapid prototyping. Carnap-based applications are written in Haskell, but can be compiled to JavaScript to run in standard web browsers. This combination of features makes Carnap ideally suited for educational applications, where ease-of-use is crucial for students and adaptability to different teaching strategies and classroom needs is crucial for instructors. The paper describes Carnap’s implementation, along with its current and projected pedagogical applications
The conjecturing process: perspectives in theory and implications in practice
[Abstract]: In this paper we analyze different types and stages of the conjecturing process. A classification of conjectures is discussed. A variety of problems that could lead to conjectures are considered from the didactical point of view. Results from a number of research studies are used to identify and investigate a number of questions related to the theoretical background of conjecturing as well as practical implications in the learning process
The conjecturing process: perspectives in theory and implications in practice
In this paper we analyze different types and stages of the conjecturing process. A classification of conjectures is discussed. A variety of problems that could lead to conjectures are considered from the didactical point of view. Results from a number of research studies are used to identify and investigate a number of questions related to the theoretical background of conjecturing as well as practical implications in the learning process
If Archimedes would have known functions
These are notes and slides from a Pecha-Kucha talk given on March 6, 2013.
The presentation tinkered with the question whether calculus on graphs could
have emerged by the time of Archimedes, if the concept of a function would have
been available 2300 years ago. The text first attempts to boil down discrete
single and multivariable calculus to one page each, then presents the slides
with additional remarks and finally includes 40 "calculus problems" in a
discrete or so-called 'quantum calculus' setting. We also added some sample
Mathematica code, gave a short overview over the emergence of the function
concept in calculus and included comments on the development of calculus
textbooks over time.Comment: 31 pages, 36 figure
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