A Framework for All: Building Capacity for Service Delivery in Catholic Schools

The challenge to include students with disabilities in Catholic schools requires a comprehensive system of service delivery to meet student need and avoid pathologizing individuals as problems. The purpose of this article is to provide an overview of Multi-tiered Systems of Support (MTSS), a framework for organizing resources, delivering services, and measuring success that directly addresses the mission of Catholic Schools to truly serve all students. MTSS is a research-based and systematic service delivery model that provides tiered supports based on individual learner need. MTSS is defined and contextualized to address both academic and behavioral supports for all students. A brief review of evidence to support the framework is provided. Finally, specific features of the framework are presented with examples to illustrate how Catholic educators might implement across the entire school

Self-testing/correcting with applications to numerical problems

AbstractSuppose someone gives us an extremely fast program P that we can call as a black box to compute a function f. Should we trust that P works correctly? A self-testing/correcting pair for f allows us to: (1) estimate the probability that P(x) ≠ φ(x) when x is randomly chosen; (2) on any input x, compute f(x) correctly as long as P is not too faulty on average. Furthermore, both (1) and (2) take time only slightly more than the original running time of P. We present general techniques for constructing simple to program self-testing/correcting pairs for a variety of numerical functions, including integer multiplication, modular multiplication, matrix multiplication, inverting matrices, computing the determinant of a matrix, computing the rank of a matrix, integer division, modular exponentiation, and polynomial multiplication

Why Inclusion Isn’t Coming, It Is Already Here: Catholic Schools and Inclusive Special Education

Catholic school personnel are increasingly recognizing that many of their students, including students with disabilities, need and benefit from inclusive educational practices. These oftentimes ad hoc practices are motivated by the Catholic identity and mission of the school, as well as the diverse educational needs of students. This article responds to these recognized realities, arguing that Catholic Social Teaching (CST) and the practical reality of academically diverse students requires understanding disability as being unique to each student, though within categories recognized in the Individuals With Disabilities Act (IDEA) that serve as starting points for interventions. CST and the recognition of student needs necessitate that teachers be equipped with the appropriate intervention skills, and convincing school communities to embrace this responsibility. To this end, current educational terms are defined and explained, models of inclusion are summarized, and five common misperceptions about inclusion of students with disabilities in Catholic schools are debunked

Inclusion in Catholic Schools: An Introduction to the Special Issue

Introduction to the special issu

Distances on Rhombus Tilings

The rhombus tilings of a simply connected domain of the Euclidean plane are known to form a flip-connected space (a flip is the elementary operation on rhombus tilings which rotates 180{\deg} a hexagon made of three rhombi). Motivated by the study of a quasicrystal growth model, we are here interested in better understanding how "tight" rhombus tiling spaces are flip-connected. We introduce a lower bound (Hamming-distance) on the minimal number of flips to link two tilings (flip-distance), and we investigate whether it is sharp. The answer depends on the number n of different edge directions in the tiling: positive for n=3 (dimer tilings) or n=4 (octogonal tilings), but possibly negative for n=5 (decagonal tilings) or greater values of n. A standard proof is provided for the n=3 and n=4 cases, while the complexity of the n=5 case led to a computer-assisted proof (whose main result can however be easily checked by hand).Comment: 18 pages, 9 figures, submitted to Theoretical Computer Science (special issue of DGCI'09