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The prospective teachers responded that problem posing was difficult because of its nature (e.g., not knowing the steps of problem posing), their abilities (not being creative), or lack of mathematical knowledge (having difficulties understanding abstractions) although they were not novices but had been trained as teachers.
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Once again, at a time when so much of human knowledge had been cast into doubt, the idea of mathematical certainty was seductive.
Since a mathematical model requires a complete definition for all interactions, mostly fragmentary knowledge has to be completed by assumptions.
We discuss which prior knowledge has been used, how it is incorporated and how it modifies the mathematical properties of the underlying methods.
In the case of gravity, our knowledge has progressed from an abstract sense of a force causing things to drop, to a simple mathematical formula given by Newton, to a better understanding of quantum and relativistic effects of gravity.
Knowledge has mixed roots.
The main motivation behind this algorithm is to familiarize students and engineers having limited mathematical knowledge with the principles of system identification without adding more mathematical burdens.
To provide information to transform teaching practice through improved primary school mathematics teacher training (6-12 years), a tool to assess the mathematical knowledge for teaching didactic probability has been designed.
Facilitators' mathematical knowledge for professional development likely has a strong connection to their ability to enact a given PD program with fidelity.
The difference here (according to Field 1984) is not about having or lacking mathematical knowledge, but rather it is about logical knowledge: of knowing which mathematical theorems follow from certain mathematical principles, and which do not.
Students should have the opportunity to build their own mathematical knowledge through the teacher's guidance.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com