Proving Montessori: Identity and Dilemmas in a Montessori Teacher’s Lived Experience

This phenomenological case study was conducted to better understand the experience of a Montessori teacher in a leadership role. A veteran Montessori teacher, newly hired by an established Montessori preschool, was interviewed over the course of her first year in the position. A critical discourse analysis revealed multiple social identities that contributed to her desire, and ability, to be what she felt was an authentic Montessori educator. While some of these discourses and social identities aligned, some did not, creating ideational dilemmas that affected her work, relationships, and personal identity. The findings suggest that current Montessori discourse excludes important characteristics of the teacher-lived experience. Acknowledging and discussing the social challenges Montessori teachers face is a necessary addition to teacher preparation, teacher support systems, and Montessori leadership decisions

Higher Weak Derivatives and Reflexive Algebras of Operators

Let D be a self-adjoint operator on a Hilbert space H and x a bounded operator on H. We say that x is n-times weakly D-differentiable, if for any pair of vectors a, b from H the function is n-times differentiable. We give several characterizations of this property, among which one is original. The results are used to show, that for a von Neumann algebra M on H, the sub-algebra of n-times weakly D-differentiable operators has a representation as a reflexive algebra of operators on a bigger Hilbert space.Comment: This version acknowledges results from the litterature, which the first edition was unaware of. The result on the existence of a representation with a reflexive image is ne

Attachment, Forgiveness, and Generativity in Midlife

Current literature suggests secure attachment and forgiveness are positively correlated. However, to date, the relationship of adult attachment, forgiveness, and generativity has not been explored. In this current study, middle-aged adults, ages 45-80 from the George Fox University Alumni were surveyed to explore attachment (anxious and avoidant), generativity, and forgiveness. Since generativity is a prosocial trait, synonymous with altruism, suggesting one’s selfless service and concern for the well-being for others, it is predicted that generativity will have a positive relationship with forgiveness, and secure attachment. Further, multiple regression statistics were used to explore which of the independent variables (anxious attachment, avoidant attachment, and generativity) has the greatest effect on the dependent variable of trait forgiveness. Results indicated that there was a medium positive relationship between forgiveness and secure attachment, between generativity and secure attachment, and between forgiveness and generativity. Multiple regression found that each of the independent variables (anxious attachment, avoidant attachment, and generativity) were significant predictors of forgiveness with anxious attachment being the strongest predictor of forgiveness

Comment: Fisher Lecture: Dimension Reduction in Regression

Comment: Fisher Lecture: Dimension Reduction in Regression [arXiv:0708.3774]Comment: Published at http://dx.doi.org/10.1214/088342307000000041 in the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Finite von Neumann algebra factors with property Gamma

Techniques introduced by G. Pisier in his proof that finite von Neumann factors with property gamma have length at most 5 are modified to prove that the length is 3. It is proved that if such a factor is a complemented subspace of some larger C*-algebra then there exists a projection of norm one from the larger onto the smaller algebra. A new proof of the fact that the second continuous Hochschild cohomology group of such an algebra with coefficients in the algebra vanishes, is also included.Comment: 12 page

Nullspaces and frames

In this paper we give new characterizations of Riesz and conditional Riesz frames in terms of the properties of the nullspace of their synthesis operators. On the other hand, we also study the oblique dual frames whose coefficients in the reconstruction formula minimize different weighted norms.Comment: 16 page

Optimal decision under ambiguity for diffusion processes

In this paper we consider stochastic optimization problems for an ambiguity averse decision maker who is uncertain about the parameters of the underlying process. In a first part we consider problems of optimal stopping under drift ambiguity for one-dimensional diffusion processes. Analogously to the case of ordinary optimal stopping problems for one-dimensional Brownian motions we reduce the problem to the geometric problem of finding the smallest majorant of the reward function in a two-parameter function space. In a second part we solve optimal stopping problems when the underlying process may crash down. These problems are reduced to one optimal stopping problem and one Dynkin game. Examples are discussed