Introduction – the rationale for reading about ‘chemical knowledge for teaching’

This study aims to develop and validate a new instrument for measuring chemistry teachers’ perceptions of Pedagogical Content Knowledge for teaching Chemistry Core Competencies (PCK_CCC) in the context of new Chinese chemistry curriculum reform. The five constructs and the initial 17 items in the new instrument were contextualized by the PCK pentagon model (Park S. and Oliver J. S., (2008), J. Res. Sci. Teach., 45(7), 812–834.) with the notions of the Senior High School Chemistry Curriculum Standards (Ministry of Education, P. R. China, 2017). 210 chemistry teachers from a University-Government-School initiative voluntarily participated in this study. The findings from item analysis, confirmatory factor analysis and correlation analysis provide sufficient empirical evidence to support the convergent and discriminant validity of the instrument. The concurrent validity of the instrument was confirmed by testing mean differences among teacher demographic groups. The high Cronbach's coefficient alpha values show good internal consistency reliability of the instrument. Integrating the evidence from theory and data, we documented a valid and reliable PCK_CCC instrument with five constructs consisting of 16 items. This study provides a thorough process for developing and validating instruments that address teacher perceptions of their PCK in a particular subject domain. The valid and reliable PCK_CCC instrument would be beneficial for teacher education researchers and teacher professional programs.

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What role does professional noticing play? Examining connections with affect and mathematical knowledge for teaching among preservice teachers

ZDM ◽

10.1007/s11858-020-01210-5 ◽

2021 ◽

Author(s):

Cindy Jong ◽

Edna O. Schack ◽

Molly H. Fisher ◽

Jonathan Thomas ◽

David Dueber

Keyword(s):

Preservice Teachers ◽

Mathematical Knowledge ◽

Mathematical Knowledge For Teaching ◽

Professional Noticing ◽

Knowledge For Teaching

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Reduction of the molecular hamiltonian matrix using quantum community detection

Scientific Reports ◽

10.1038/s41598-021-83561-x ◽

2021 ◽

Vol 11 (1) ◽

Author(s):

Susan M. Mniszewski ◽

Pavel A. Dub ◽

Sergei Tretiak ◽

Petr M. Anisimov ◽

Yu Zhang ◽

...

Keyword(s):

Community Detection ◽

Slater Determinant ◽

Hamiltonian Matrix ◽

Approximate Methods ◽

Molecular Systems ◽

Hartree Fock ◽

Molecular Hamiltonian ◽

Structure Problem ◽

Modularity Maximization ◽

Chemical Knowledge

AbstractQuantum chemistry is interested in calculating ground and excited states of molecular systems by solving the electronic Schrödinger equation. The exact numerical solution of this equation, frequently represented as an eigenvalue problem, remains unfeasible for most molecules and requires approximate methods. In this paper we introduce the use of Quantum Community Detection performed using the D-Wave quantum annealer to reduce the molecular Hamiltonian matrix in Slater determinant basis without chemical knowledge. Given a molecule represented by a matrix of Slater determinants, the connectivity between Slater determinants (as off-diagonal elements) is viewed as a graph adjacency matrix for determining multiple communities based on modularity maximization. A gauge metric based on perturbation theory is used to determine the lowest energy cluster. This cluster or sub-matrix of Slater determinants is used to calculate approximate ground state and excited state energies within chemical accuracy. The details of this method are described along with demonstrating its performance across multiple molecules of interest and bond dissociation cases. These examples provide proof-of-principle results for approximate solution of the electronic structure problem using quantum computing. This approach is general and shows potential to reduce the computational complexity of post-Hartree–Fock methods as future advances in quantum hardware become available.

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