Push-Pull Block Puzzles are Hard

This paper proves that push-pull block puzzles in 3D are PSPACE-complete to solve, and push-pull block puzzles in 2D with thin walls are NP-hard to solve, settling an open question by Zubaran and Ritt. Push-pull block puzzles are a type of recreational motion planning problem, similar to Sokoban, that involve moving a `robot' on a square grid with $1 \times 1$ obstacles. The obstacles cannot be traversed by the robot, but some can be pushed and pulled by the robot into adjacent squares. Thin walls prevent movement between two adjacent squares. This work follows in a long line of algorithms and complexity work on similar problems. The 2D push-pull block puzzle shows up in the video games Pukoban as well as The Legend of Zelda: A Link to the Past, giving another proof of hardness for the latter. This variant of block-pushing puzzles is of particular interest because of its connections to reversibility, since any action (e.g., push or pull) can be inverted by another valid action (e.g., pull or push).Comment: Full version of CIAC 2017 paper. 17 page

District-Funded Common Core Collaboration Grants Used for Teacher Professional Development

With the adoption of the Common Core State Standards (CCSS) in English language arts and mathematics by the State of California in 2010, a shift in instructional practices along with the level of rigor and expectations for students began. As a result of these changes, a local school district sought a way through district-funded Common Core Collaboration Grants (CCCG) to provide professional development that supported 4th-6th grade teachers in their implementation of the CCSS. The purpose of this qualitative program evaluation case study was to examine teachers\u27 perceptions of the effectiveness of professional development funded by CCCG in supporting 4th-6th grade teachers in understanding and application of instructional strategies aligned with the CCSS. Weiss\u27s theory of change and Roy and Killion\u27s program evaluation framework guided the study. Data were collected from individual interviews of 7 teachers of 4th-6th grade who participated in the district CCCG professional development sessions. Interview data were coded and themes of choice, time, collaboration, and integration of the CCSS emerged. The results indicated that the use of CCCG for professional development is assisting teachers in successfully implementing the CCSS through increased collaboration and more opportunities to engage in learning within their own contexts. A program evaluation report and presentation to the district school board were developed. The results of this study may affect positive social change through suggestions of an alternative in the form of grants to schools and districts looking for innovative ways to support teachers and enhance student learning through professional development on the CCSS