framing words

e simply take whatever comes between the “either” and the “or” and call that one disjunct

translate “Either A or B

capture the fact that it’s a “neither-nor” statement

“not both” statements as: ¬(N ∧ G)

We translate “neither-nor” statements as “not or”:

Getting an A in participation is necessary for getting an A in the class

Necessary conditions go to the right of an arrow. Sufficient conditions go to the left of an arrow.

if the antecedent (left) happens, then the consequent (right) will happen

hree separate conditional phrases that indicate different conditional relationships

1. A Negation is not a connective and a connective must have 2 “arguments” or formulas on either side

Table 7.2.1

The first part of a conditional—what comes before the arrow/horseshoe—is called the “antecedent” and the second part is called the “consequent.”

There’s a conditional relationship between them.

a disjunction means that “at least one of the disjuncts is true”.

Or Unless

OR

ogical negation is when a statement is being denied.

We might read this “not R”. It means something like “It’s not the case that the simple proposition R is true.”

Sentence Letter—an upper-case letter that stands in as a variable for any simple proposition.

And But However Yet

If either of those statements ends up being false, then the whole statement above is false.

“and”

make one unified a claim about the world that might be true and might be false.

And Not Or If...then... If and only if...will...

focuses on the relations between different entities: propositions or statements

relations between categories, hence the name “Categorical Logic.”

Logic

virtue of form. Any statement with the logical form: If A, then B

stronger claim is a claim that is “harder to make true” in the sense that the world has to be one particular way to conform to that claim

disjunction or “or” statement since you’d have a higher change of winning. This is what we mean by “stronger claim” and “weaker claim”

Either Franklin is a student at Butte College or Franklin is a student at De Anza College”, then you’d know that one of two worlds must be the real world

Logic is the science of logical consequences: these relationships between statements such that if one is true, then the other must be true.

African American students from dialectally diverse backgrounds bring to school

teachers lack the linguistic training

In 2002, her firstyear of implementing code-switching strategies, she closed the achievement gap in herclassroom; on standardized state assessments, African American students did as well aswhite students in English and history and outperformed white students in math and science.

code-switch — to assess the needs of the setting (the time, place,audience, and communicative purpose) and intentionally choose the appropriate languagestyle for that setting.

metacognition, which is knowledge about one's own thinking processes.

A linguistically informed teacher understands that these usages are not errors, but rathergrammar patterns from the community dialect transferred into student writing (Wheeler,2005).

Students using vernacularlanguage are not making errors, but instead are speaking or writing correctly following thelanguage patterns of their community (

Further, research has found strong connections among teachers' negative attitudes aboutstigmatized dialects, lower teacher expectations for students who speak these dialects, andlower academic achievement (Godley et al., 2006; Nieto, 2000)

"demands a new way of looking at teaching that is grounded in anunderstanding of the role of culture and language in learning" (Villegas & Lucas, 2007, p. 29).

teacher education and professional development programs fail toequip teachers to respond adequately to the needs of many African American learners.

teachers routinelyunderrate the language knowledge and the reading and writing performance of AfricanAmerican students (Cazden, 2001; Ferguson, 1998; Godley, Sweetland, Wheeler, Minnici, &rCarpenter, 2006; Scott & Smitherman, 1985)