Educators and policymakers alike recognize that algebra is an important gatekeeper course, not only for college preparation but also for preparation for the world of work. To prepare students for future success, many school districts and state legislatures now make algebra a graduation requirement for all high school students. Of course, the burden for preparing all students in algebra falls on the shoulders of the classroom teacher. Whether an algebrafor-all initiative is school-, district-, or state-based, a teacher faces the difficult challenge of teaching a high-standards course to a classroom of students whose beginning knowledge may range from far below to far above the course prerequisites.
In many American legislative election systems incumbents have a good chance of returning and seats tend to be retained by a party even when the incumbent fails to return. Because of this, even should a minor party reach competitive parity with the dominant party, a significant increase in elected representation will not result in the short term (five elections). Further, small amounts of bias either for or against the minor party will not appreciably influence short-term elected representation. Thus, what has long been considered one party dominated American states might better be thought of as incumbent dominated. These points are demonstrated in a formal model which is applied to Republican candidates in Oklahoma state legislative elections.
In [8] a necessary and sufficient condition was given for determining the equivalence of two asymptotic boundary paths for an analytic function w = f(p) on a Riemann surface F. In this paper we give a necessary and sufficient condition for determining the nonequivalence of two asymptotic boundary paths for f(z) analytic in |z| < R, 0 < R ≤ + ∞. We shall, also, illustrate some applications of the main result and examine a class of functions introduced by Valiron.
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