Cold Spring Harbor Central School District and Cold Spring Harbor Teachers Association

In the matter of the fact-finding between Cold Spring Harbor Central School District, employer, and the Cold Spring Harbor Teachers Association, union. PERB case no. M2012-330. Before: Thomas J. Linden, fact finder

Uniondale Union Free School District and United Public Service Employees Union (UPSEU)

In the matter of the fact-finding between the Uniondale Union Free School DIstrict, employer, and the United Public Service Employees Union (UPSEU), union. PERB case no. M2015-096. Before: Thomas J. Linden, fact finder

Northport-East Northport Union Free School District and United Public Service Employees Union (UPSEU)

In the matter of the fact-finding between the Northport-East Northport Union Free School District, employer, and the United Public Service Employees Union (UPSEU), union. PERB case no. M2014-056. Before: Thomas J. Linden, fact finder

Criterion-referenced measurement: Its main applications, problems and findings

The need for criterion-referenced measurements has mainly arisen from the introduction of instructional programs organized according to modern principles from educational technology. Some of these programs are discussed, and it is indicated for what purposes criterion-referenced measurements are used. Three main problems of criterion-referenced measurement are distinguished: The problem of criterion-referenced scoring and score interpretation, the problem of criterion-referenced item and test analysis, and the problem of mastery testing. For each of these problems a variety of solutions of the paper to provide an overview of these and to introduce the reader to the original literature

Passing score and length of a mastery test

A classical problem in mastery testing is the choice of passing score and test length so that the mastery decisions are optimal. Thsi problem has been addressed several times from a variety of view-points. In this paper the usual indifference zone approach is adopted with a new criterion for optimizing the passing score. It appears that, under the assumption of the binomial error model, this yields a linear relationship between optimal passing score and test length, which subsequently can be used in a simple procedure for optimizing the test length. It is indicated how different losses for both decision errors and a known base rate can be incorporated in the procedure, and how a correction for guessing can be applied. Finally, the results in this paper are related to results obtained in sequential testing and in the latent class approach to mastery testing

Spectra and eigenstates of spin chain Hamiltonians

We prove that translationally invariant Hamiltonians of a chain of $n$ qubits with nearest-neighbour interactions have two seemingly contradictory features. Firstly in the limit $n\rightarrow\infty$ we show that any translationally invariant Hamiltonian of a chain of $n$ qubits has an eigenbasis such that almost all eigenstates have maximal entanglement between fixed-size sub-blocks of qubits and the rest of the system; in this sense these eigenstates are like those of completely general Hamiltonians (i.e. Hamiltonians with interactions of all orders between arbitrary groups of qubits). Secondly in the limit $n\rightarrow\infty$ we show that any nearest-neighbour Hamiltonian of a chain of $n$ qubits has a Gaussian density of states; thus as far as the eigenvalues are concerned the system is like a non-interacting one. The comparison applies to chains of qubits with translationally invariant nearest-neighbour interactions, but we show that it is extendible to much more general systems (both in terms of the local dimension and the geometry of interaction). Numerical evidence is also presented which suggests that the translational invariance condition may be dropped in the case of nearest-neighbour chains.Comment: Updated figures, as accepted in 'Communications in Mathematical Physics' on 5 January 201

Random matrices and quantum spin chains

Random matrix ensembles are introduced that respect the local tensor structure of Hamiltonians describing a chain of $n$ distinguishable spin-half particles with nearest-neighbour interactions. We prove a central limit theorem for the density of states when $n \rightarrow\infty$, giving explicit bounds on the rate of approach to the limit. Universality within a class of probability measures and the extension to more general interaction geometries are established. The level spacing distributions of the Gaussian Orthogonal, Unitary and Symplectic Ensembles are observed numerically for the energy levels in these ensembles.Comment: Updated figures, as accepted in 'Markov Processes and Related Fields' on 3 March 201

Matching bias in syllogistic reasoning: Evidence for a dual-process account from response times and confidence ratings

We examined matching bias in syllogistic reasoning by analysing response times, confidence ratings, and individual differences. Roberts’ (2005) “negations paradigm” was used to generate conflict between the surface features of problems and the logical status of conclusions. The experiment replicated matching bias effects in conclusion evaluation (Stupple & Waterhouse, 2009), revealing increased processing times for matching/logic “conflict problems”. Results paralleled chronometric evidence from the belief bias paradigm indicating that logic/belief conflict problems take longer to process than non-conflict problems (Stupple, Ball, Evans, & Kamal-Smith, 2011). Individuals’ response times for conflict problems also showed patterns of association with the degree of overall normative responding. Acceptance rates, response times, metacognitive confidence judgements, and individual differences all converged in supporting dual-process theory. This is noteworthy because dual-process predictions about heuristic/analytic conflict in syllogistic reasoning generalised from the belief bias paradigm to a situation where matching features of conclusions, rather than beliefs, were set in opposition to logic