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A well-ordering > on X ∗ is called a monomial ordering whenever it is compatible with the multiplication of words, that is, for all u, v ∈ X ∗ we have u > v ⇒ w 1 u w 2 > w 1 v w 2, for all w 1, w 2 ∈ X ∗.
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Based on the above SCK framework, we expect PTs to situate the teaching of AP of multiplication in word problem contexts, which can be unpacked through representation uses and explanations.
In particular, this research explores two questions: (1) How do PTs develop SCK for teaching the AP of multiplication through word problem contexts?
In all the diagnostic tests, the PTs were asked "How will you use the following word problem to teach the Associative Property of multiplication?" The word problems used in the tests were the mango, string, and cup tasks, respectively (see Table 1).
Neither intuition nor counting is of much use, and multiplication facts must be stored in the brain verbally, as strings of words.
Instead, he uses the multiplication of characters to suggest how adultery -- in a word -- adulterates, an issue raised when James and Jim consult the dictionary together.
Cain et al. [69] use the Schensted Knuth normal form (the set of (semistandard) Young tableaux) to prove that the multiplication table of column words, u v = u ′ v ′, forms a finite GS basis of the finitely generated plactic monoid.
In other words, the plastic deformation of the nanotwinned steel is mainly accommodated by glide and multiplication of dislocations.
A multiplication of accident.
Soon we're caught in a dizzying multiplication of texts.
This, in short order, led to a multiplication of the size of the federal budget deficit.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com