The “Problem” of Experience in Mathematics Teaching

Prior research has established that teachers' use of curriculum materials is affected by a range of factors, such as teachers' conceptions of mathematics teaching, and the nature and extent of their teaching experience. What is less clear, and far less examined, in prior research is the role that the teacher guide (TG) may play in mediating the influence of these and other factors on teachers' decisions and actions. Accordingly, this study examines how two 6th grade teachers use the TG from Connected Mathematics Project as a resource in making planning and enactment decisions, and factors associated with patterns of TG use. Through cross‐case analysis, the author found that these teachers seemed to draw largely from their previous experiences and their own conceptions of mathematics teaching and learning when making planning and enactment decisions related to mathematical tasks, and not particularly from the TG. For example, when faced with certain planning and instructional challenges, such as students struggling with the content, teachers tended to rely on their particular conceptions of mathematics teaching to address these challenges. Despite the fact that the TG provided suggestions for teachers as to how address such challenges, it was not extensively used as a resource by the teachers in this study in their planning and enactment of lessons.     

Erratum to the paper “An Integral Delay Inequality and its Applications to Boundary Value Problems”

We consider the infinitesimal generator of the time reversal of a time-homogeneous one-dimensional gap diffusion with state space [0, 1] given by the infinitesimal generator A^o = dD_s⁺ - dk / dm with nonlocal boundary conditions of Feller-Wentzell-type. This leads to an infinitesimal generator which belongs to a class of generators introduced in the earlier note [W1].     

On “bent” functions

Let P(x) be a function from GF(2ⁿ) to GF(2). P(x) is called “bent” if all Fourier coefficients of (−1)^P(x) are ±1. The polynomial degree of a bent function P(x) is studied, as are the properties of the Fourier transform of (−1)^P(x), and a connection with Hadamard matrices.