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Investigations was developed between 1990 and 1998. It was just one of a number of reform mathematics curricula initially funded by a National Science Foundation grant. The goals of the project raised opposition to the curriculum from critics (both parents and mathematics teachers) who objected to the emphasis on conceptual learning instead of instruction in more recognized specific methods ...
They claim students learn to discern similarities and differences in the mathematics, and also that "through such rich mathematics classroom discourse, students develop and consolidate their understanding of the learning goal of the lesson in terms of making connections to prior knowledge and experiences and making generalizations". [3 ...
In classical real analysis, one way to define a real number is as an equivalence class of Cauchy sequences of rational numbers.. In constructive mathematics, one way to construct a real number is as a function ƒ that takes a positive integer and outputs a rational ƒ(n), together with a function g that takes a positive integer n and outputs a positive integer g(n) such that
A good way to understand the difference between learning and knowledge building is by considering mathematics and scientific contents as examples of public knowledge. Furthermore, Bereiter in his book on Education and Mind (2002) based his observation of the educational value of KB on Karl Popper's ontological analysis of our existence as made ...
The base logic of constructive analysis is intuitionistic logic, which means that the principle of excluded middle is not automatically assumed for every proposition.If a proposition . is provable, this exactly means that the non-existence claim . being provable would be absurd, and so the latter cannot also be provable in a consistent theory.
Experimentation: Students individually perform an experiment and then come together as a class to discuss the results. Research projects: Students research a topic and can present their findings to the class. Field trips: This allows students to put the concepts and ideas discussed in class in a real-world context. Field trips would often be ...
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