A Study of Staff Development and Teacher Efficacy in Implementing Standards-Based Grading at the Elementary Schools in a Rural School District in North Carolina

Standards-based grading is still in its infancy within North Carolina. At this time, only 12 of the 115 school districts have incorporated the standards-based form of grading into their system. As school districts across North Carolina look to implement different forms of grading to assess student learning, it will be important to look at the effectiveness of the professional development that accompanies the shift. The research questions that guided this work center around the support needed by teachers during the transition period and the impact of the professional development on their understanding of how to successfully implement standards-based grading. The study looked to analyze data taken from the 2017-2018 school year. The study was conducted in a rural school district within the state of North Carolina where standards-based grading has been implemented within the elementary schools. It looked to utilize these data to draw on teacher feelings and beliefs regarding the professional development. The study also looked to determine the effectiveness of the professional development and what future courses of action can be taken to strengthen future practices. Through the use of focus groups conducted with district principals and teachers and an interview with the district’s director of elementary curriculum and instruction, an understanding was gained about the views and opinions of the participants. Survey data were also collected in an effort to gain further insight among a wider population of fourth-grade teachers within the district. The researcher looked for emergent themes that began to form based on the responses of the participants. Central themes that emerged from the research included the importance of utilizing Professional Learning Communities and site-based staff within the school to support teachers in the practical application of standards-based grading. In addition, findings reflected that participants in the study felt the need for further support in working with parents. Participants also identified the importance of providing support through practical applications including rubrics and scoring practices. Positive shifts in formative assessment were another theme coinciding with the shift towards-standards based grading. A solid understanding of the different standards was a final theme that surfaced during the course of the research. These themes that developed will be offered as a means of providing information and support for future districts when planning and introducing the standards-based form of grading within their systems. Based upon the findings, recommendations for the district include the development of a professional development model to support the future implementation of standards-based grading. Recommendations also include the need for ongoing differentiated professional development to support teachers and their individual needs. It will be valuable to look at future research and studies into the implementation efforts of other districts that are experiencing success

Efficient Solution of Language Equations Using Partitioned Representations

A class of discrete event synthesis problems can be reduced to solving language equations f . X ⊆ S, where F is the fixed component and S the specification. Sequential synthesis deals with FSMs when the automata for F and S are prefix closed, and are naturally represented by multi-level networks with latches. For this special case, we present an efficient computation, using partitioned representations, of the most general prefix-closed solution of the above class of language equations. The transition and the output relations of the FSMs for F and S in their partitioned form are represented by the sets of output and next state functions of the corresponding networks. Experimentally, we show that using partitioned representations is much faster than using monolithic representations, as well as applicable to larger problem instances.Comment: Submitted on behalf of EDAA (http://www.edaa.com/

Fast generation of lexicographic satisfiable assignments: enabling canonicity in SAT-based applications

Lexicographic Boolean satisfiability (LEXSAT) is a variation of the Boolean satisfiability problem (SAT). Given a variable order, LEXSAT finds a satisfying assignment whose integer value under the given variable order is minimum (maximum) among all satisfiable assignments. If the formula has no satisfying assignments, LEXSAT proves it unsatisfiable, as does the traditional SAT. The paper proposes an efficient algorithm for LEXSAT by combining incremental SAT solving with binary search. It also proposes methods that use the lexicographic properties of the assignments to further improve the runtime when generating consecutive satisfying assignments in lexicographic order. The proposed algorithm outperforms the state-of-the-art LEXSAT algorithm—on average, it is 2.4 times faster when generating a single LEXSAT assignment, and it is 6.3 times faster when generating multiple consecutive assignments

Heuristic NPN classification for large functions using AIGs and LEXSAT

Two Boolean functions are NPN equivalent if one can be ob- tained from the other by negating inputs, permuting inputs, or negating the output. NPN equivalence is an equivalence relation and the number of equivalence classes is significantly smaller than the number of all Boolean functions. This property has been exploited successfully to in- crease the efficiency of various logic synthesis algorithms. Since computing the NPN representative of a Boolean function is not scalable, heuristics have been proposed that are not guaranteed to find the representative for all functions. So far, these heuristics have been implemented using the function’s truth table representation, and therefore do not scale for functions exceeding 16 variables. In this paper, we present a symbolic heuristic NPN classification using And-Inverter Graphs and Boolean satisfiability techniques. This allows us to heuristically compute NPN representatives for functions with much larger number of variables; our experiments contain benchmarks with up to 194 variables. A key technique of the symbolic implementation is SAT-based procedure LEXSAT, which finds the lexicographically smallest satisfiable assignment. To our knowledge, LEXSAT has never been used before in logic synthesis algorithms