Exponential polynomials as solutions of certain nonlinear difference equations

Recently, C.-C. Yang and I. Laine have investigated finite order entire solutions f of nonlinear differential-difference equations of the form fn + L(z, f ) = h, where n ≥ 2 is an integer. In particular, it is known that the equation f(z)2 + q(z)f (z + 1) = p(z), where p(z), q(z) are polynomials, has no transcendental entire solutions of finite order. Assuming that Q(z) is also a polynomial and c ∈ C, equations of the form f(z)n + q(z)e Q(z) f(z + c) = p(z) do posses finite order entire solutions. A classification of these solutions in terms of growth and zero distribution will be given. In particular, it is shown that any exponential polynomial solution must reduce to a rather specific form. This reasoning relies on an earlier paper due to N. Steinmetz.     

Analysis of psychometric properties as part of an iterative adaptation process of MKT items for use in other countries

Researchers at the University of Michigan have developed sets of items that can be used to analyze teachers’ mathematical knowledge for teaching (MKT). In this paper, we consider what is required in the adaptation of a set of these items for use in a Norwegian context. We discuss how analysis of item difficulty and point–biserial correlation can be applied in combination with qualitative approaches to ensure a high-quality process of piloting adapted MKT items. Findings indicate that researchers who attempt to adapt MKT items for use in cultural contexts other than those for which they were designed need to use different methods to analyze all aspects of the adaptation process. The results from the different analyses conducted might then be used to inform other parts of the process, and this will mean that the process of adapting and piloting items becomes cyclic and iterative.