This report concerns a method for computing a substitute inverse for linear programs with a staircase structure. The constraints of a staircase structure linear program are of the following form: A(1)x(1)=d(1); B(t-1)x(t-1)+A(t)x(t) = d(t); (t = 2 ..., T). Letting m(i) be the number of constraints in period i, the substitute inverse consists of the inverse of T matrices which are m(i) x m(i), i = 1 ..., T as opposed to the actual inverse which is m x m, m = Sum over i m(i). Hence the substitute inverse would require significantly less storage than the actual inverse. Two methods are presented for updating the substitute inverse, both of which consist of updating some, but not necessarily all of the T smaller inverses. The first, a pivoting method, requires appending one or more columns to the smaller inverse and pivoting on the appended columns. The second requires adding one to T dyad matrices to the smaller inverses. Computational efficiency of both methods can be tested to a large degree using standard linear programming codes. (Author).
The second requires adding one to T dyad matrices to the smaller inverses. Computational efficiency of both methods can be tested to a large degree using standard linear programming codes. (Author).
This study evaluates the outcomes of a ten-week elementary language arts curriculum designed to improve the writing achievement and experiences of children who speak African American Vernacular English (AAVE). The curriculum integrated sociolinguistic research with contemporary language arts pedagogy, using multicultural children's literature to teach about regional and social language variation, and incorporating dialect-based grammar instruction (contrastive analysis) into the writing process. Six upper-elementary teachers in an urban school district in Ohio participated in a workshop on sociolinguistic diversity and subsequently implemented the curriculum with 76 students. Student outcomes were compared with two groups of students in the same school district: three classes (41 students) that participated in a partial intervention and four classes (58 students) that received no intervention.
... Maddahian and Sandamela 2000; Taylor 1989), vernacular-based classroom
teaching techniques such as the use of call-and-response (Bohn 2003; Boone
2003; Foster 2001), or exploitation of culturally-based writing patterns and genres
...
