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2. Creative and productive sets - Wikipedia

   en.wikipedia.org/wiki/Creative_and_productive_sets

   The set of all provable sentences in an effective axiomatic system is always a recursively enumerable set.If the system is suitably complex, like first-order arithmetic, then the set T of Gödel numbers of true sentences in the system will be a productive set, which means that whenever W is a recursively enumerable set of true sentences, there is at least one true sentence that is not in W.

3. Center embedding - Wikipedia

   en.wikipedia.org/wiki/Center_embedding

   For example: The man who heard that the dog had been killed on the radio ran away. One can tell if a sentence is center embedded or edge embedded depending on where the brackets are located in the sentence. [Joe believes [Mary thinks [John is handsome.]]] The cat [that the dog [that the man hit] chased] meowed.

4. Principles and Standards for School Mathematics - Wikipedia

   en.wikipedia.org/wiki/Principles_and_Standards...

   The Principles and Standards for School Mathematics was developed by the NCTM. The NCTM's stated intent was to improve mathematics education. The contents were based on surveys of existing curriculum materials, curricula and policies from many countries, educational research publications, and government agencies such as the U.S. National Science Foundation. [3]

5. Worked-example effect - Wikipedia

   en.wikipedia.org/wiki/Worked-example_effect

   The worked-example effect is a learning effect predicted by cognitive load theory. [1] [full citation needed] Specifically, it refers to improved learning observed when worked examples are used as part of instruction, compared to other instructional techniques such as problem-solving [2] [page needed] and discovery learning.

6. Sentence (mathematical logic) - Wikipedia

   en.wikipedia.org/wiki/Sentence_(mathematical_logic)

   Sentences are then built up out of atomic sentences by applying connectives and quantifiers. A set of sentences is called a theory; thus, individual sentences may be called theorems. To properly evaluate the truth (or falsehood) of a sentence, one must make reference to an interpretation of the theory.

7. Language of mathematics - Wikipedia

   en.wikipedia.org/wiki/Language_of_mathematics

   The consequence of these features is that a mathematical text is generally not understandable without some prerequisite knowledge. For example, the sentence "a free module is a module that has a basis" is perfectly correct, although it appears only as a grammatically correct nonsense, when one does not know the definitions of basis, module, and free module.