A study of grade three and five students' strategic use of spelling knowledge

Spelling is often a lightning rod in discussions on literacy. The general public, as well as educators, often judge the state of literacy by the occurrence of accurate, conventional spelling (Templeton & Morris, 1999). The purpose of this study was to reveal how students employ strategies in their spelling and how spelling strategies were being taught in their classrooms. This study also sought to uncover teachers’, parents’, and students’ perspectives and knowledge regarding spelling.Case studies of six elementary school students were conducted. Each student was interviewed, along with their teachers and one of their parents. Students also filled out a self-reflection form. Students and teachers were observed in their classroom setting.Findings indicated that students used a variety of strategies. The primary strategy articulated was sounding out; the better spellers also used analogy and visualization. Students knew and often used the strategies encouraged by their teachers and parents. The literature linked the processes of reading, spelling and writing. Most of the participants mentioned the connection between reading and spelling, but failed to recognize the importance of writing for spelling. A third finding was that the teachers had adopted new methods for teaching spelling but had not altered their role to provide for increased learning. Implications for practice include suggestions for combined methods for teaching spelling, explicit teaching of strategies for all students, and teacher education that includes “reflection and action” (Ritchie & Wilson, 2000, p. 88)

Recursive proof of the Bell-Kochen-Specker theorem in any dimension n>3n>3

We present a method to obtain sets of vectors proving the Bell-Kochen-Specker theorem in dimension $n$ from a similar set in dimension $d$ ($3\leq d<n\leq 2d$). As an application of the method we find the smallest proofs known in dimension five (29 vectors), six (31) and seven (34), and different sets matching the current record (36) in dimension eight.Comment: LaTeX, 7 page

A variant of Peres-Mermin proof for testing noncontextual realist models

For any state in four-dimensional system, the quantum violation of an inequality based on the Peres-Mermin proof for testing noncontextual realist models has experimentally been corroborated. In the Peres-Mermin proof, an array of nine holistic observables for two two-qubit system was used. We, in this letter, present a new symmetric set of observables for the same system which also provides a contradiction of quantum mechanics with noncontextual realist models in a state-independent way. The whole argument can also be cast in the form of a new inequality that can be empirically tested.Comment: 3 pages, To be published in Euro. Phys. Let

On small proofs of Bell-Kochen-Specker theorem for two, three and four qubits

The Bell-Kochen-Specker theorem (BKS) theorem rules out realistic {\it non-contextual} theories by resorting to impossible assignments of rays among a selected set of maximal orthogonal bases. We investigate the geometrical structure of small $v-l$ BKS-proofs involving $v$ real rays and $l$ $2n$-dimensional bases of $n$-qubits ($1< n < 5$). Specifically, we look at the parity proof 18-9 with two qubits (A. Cabello, 1996), the parity proof 36-11 with three qubits (M. Kernaghan & A. Peres, 1995 \cite{Kernaghan1965}) and a newly discovered non-parity proof 80-21 with four qubits (that improves work of P. K Aravind's group in 2008). The rays in question arise as real eigenstates shared by some maximal commuting sets (bases) of operators in the $n$-qubit Pauli group. One finds characteristic signatures of the distances between the bases, which carry various symmetries in their graphs.Comment: version to appear in European Physical Journal Plu

Kochen-Specker theorem for a single qubit using positive operator-valued measures

A proof of the Kochen-Specker theorem for a single two-level system is presented. It employs five eight-element positive operator-valued measures and a simple algebraic reasoning based on the geometry of the dodecahedron.Comment: REVTeX4, 4 pages, 2 figure

State-independent quantum violation of noncontextuality in four dimensional space using five observables and two settings

Recently, a striking experimental demonstration [G. Kirchmair \emph{et al.}, Nature, \textbf{460}, 494(2009)] of the state-independent quantum mechanical violation of non-contextual realist models has been reported for any two-qubit state using suitable choices of \emph{nine} product observables and \emph{six} different measurement setups. In this report, a considerable simplification of such a demonstration is achieved by formulating a scheme that requires only \emph{five} product observables and \emph{two} different measurement setups. It is also pointed out that the relevant empirical data already available in the experiment by Kirchmair \emph{et al.} corroborate the violation of the NCR models in accordance with our proof

Parity proofs of the Bell-Kochen-Specker theorem based on the 600-cell

The set of 60 real rays in four dimensions derived from the vertices of a 600-cell is shown to possess numerous subsets of rays and bases that provide basis-critical parity proofs of the Bell-Kochen-Specker (BKS) theorem (a basis-critical proof is one that fails if even a single basis is deleted from it). The proofs vary considerably in size, with the smallest having 26 rays and 13 bases and the largest 60 rays and 41 bases. There are at least 90 basic types of proofs, with each coming in a number of geometrically distinct varieties. The replicas of all the proofs under the symmetries of the 600-cell yield a total of almost a hundred million parity proofs of the BKS theorem. The proofs are all very transparent and take no more than simple counting to verify. A few of the proofs are exhibited, both in tabular form as well as in the form of MMP hypergraphs that assist in their visualization. A survey of the proofs is given, simple procedures for generating some of them are described and their applications are discussed. It is shown that all four-dimensional parity proofs of the BKS theorem can be turned into experimental disproofs of noncontextuality.Comment: 19 pages, 11 tables, 3 figures. Email address of first author has been corrected. Ref.[5] has been corrected, as has an error in Fig.3. Formatting error in Sec.4 has been corrected and the placement of tables and figures has been improved. A new paragraph has been added to Sec.4 and another new paragraph to the end of the Appendi

Observables have no value: a no-go theorem for position and momentum observables

A very simple illustration of the Bell-Kochen-Specker contradiction is presented using continuous observables in infinite dimensional Hilbert space. It is shown that the assumption of the \emph{existence} of putative values for position and momentum observables for one single particle is incompatible with quantum mechanics.Comment: 6 pages, 1 Latex figure small corrections, refference and comments adde

Parity proofs of the Kochen-Specker theorem based on the 24 rays of Peres

A diagrammatic representation is given of the 24 rays of Peres that makes it easy to pick out all the 512 parity proofs of the Kochen-Specker theorem contained in them. The origin of this representation in the four-dimensional geometry of the rays is pointed out.Comment: 14 pages, 6 figures and 3 tables. Three references have been added. Minor typos have been correcte

Proposed experimental tests of the Bell-Kochen-Specker theorem

For a two-particle two-state system, sets of compatible propositions exist for which quantum mechanics and noncontextual hidden-variable theories make conflicting predictions for every individual system whatever its quantum state. This permits a simple all-or-nothing state-independent experimental verification of the Bell-Kochen-Specker theorem.Comment: LaTeX, 8 page