Separation of Variables and the Computation of Fourier Transforms on Finite Groups, II

We present a general diagrammatic approach to the construction of efficient algorithms for computing the Fourier transform of a function on a finite group. By extending work which connects Bratteli diagrams to the construction of Fast Fourier Transform algorithms %\cite{sovi}, we make explicit use of the path algebra connection to the construction of Gel'fand-Tsetlin bases and work in the setting of quivers. We relate this framework to the construction of a {\em configuration space} derived from a Bratteli diagram. In this setting the complexity of an algorithm for computing a Fourier transform reduces to the calculation of the dimension of the associated configuration space. Our methods give improved upper bounds for computing the Fourier transform for the general linear groups over finite fields, the classical Weyl groups, and homogeneous spaces of finite groups, while also recovering the best known algorithms for the symmetric group and compact Lie groups.Comment: 53 pages, 5 appendices, 34 figure

Exploring Professional Dispositions with Preservice Teachers Assignment Description

The dispositions needed to be an educator is vast. Some dispositions come naturally to teacher candidates and others are nurtured by teacher education programs. According to the National Council for Accreditation of Teacher Education (2008), professional dispositions expected of teacher candidates include “the ideal of fairness and the belief that all students can learn (p. 22). This assignment provides teacher candidates an opportunity to explore, analyze, and discuss various professional dispositions needed by educators using six examples of children’s literature, all of which by the author, Patricia Polacco.https://digitalcommons.pittstate.edu/oer-teaching/1002/thumbnail.jp

Creating a Gifted-Friendly Classroom

The goal of undergraduate teacher preparation programs is to equip future teachers to work with all learners. Gifted and talented learners are likely found in every classroom regardless of where they reside. According to Rinn et al. (2022), Kansas, Missouri, Oklahoma, Colorado, and Nebraska do not require undergraduate teacher candidates to take university coursework on gifted education. The goal of this presentation is to provide a general overview of gifted education specific to Kansas. This presentation aims to address myths and misconceptions about gifted education and gifted learners, characteristics of gifted learners, a basic overview of a general identification process, and strategies to create a gifted-friendly classroom.https://digitalcommons.pittstate.edu/oer-teaching/1001/thumbnail.jp

Utilizing Counter Narratives to Develop Culturally Sustaining, Critically Conscious Preservice Teacher Practitioners

The content areas that get most attention in an elementary classroom include mathematics and English/Language Arts (ELA), and little time is devoted to other content areas like social studies. Preservice elementary teachers can learn to maximize instructional time by integrating social studies content in the ELA block. Using counternarratives, preservice teachers can learn to use children’s literature to teach multiple perspectives to the dominant narrative in the textbooks. This article shares strategies to present counternarratives and examples of children’s literature that can be used in an elementary classroom

The Journey Box: Promoting Language Development while Exploring One’s Identity

A Journey Box allows students to explore and share their family’s historical narrative using primary sources like interviews and artifacts. Students explore different facets of their own family’s history and journey to America while engaging in a larger shared experience among classmates to understand different perspectives. The Journey Box develops oral and written language skills while supporting individual’s exploration of their culture and identity.https://digitalcommons.pittstate.edu/oer-teaching/1005/thumbnail.jp

Journey “Box” Assignment Description

The Journey “Box” allows preservice teachers to explore and share their own historical narrative as they different aspects of their own family’s journey to America. The Journey “Box” first asks preservice teachers to explore themes by reading children’s literature and then positions preservice teachers as interviewers as they seek out different facets of their family’s historical narrative from members of their family. Preservice teachers then use their experience with a Journey “Box” to design an inquiry that could be used in their field experience. The Journey “Box” integrates social studies standards and best practices with ELA standards.https://digitalcommons.pittstate.edu/oer-teaching/1004/thumbnail.jp

Retaining First-Generation College Students: Faculty and Staff Perceptions

Research showed faculty-student interactions impact student engagement and was a primary factor to student retention (Kuh & Hu, 2001; Means & Pyne, 2017; Swecker et al., 2013; Tinto, 1987). The literature revealed while retention may be an issue for many institutions, there is a greater need to address retention specifically related to first-generation college students (FGCS). Students often seek advice from faculty and staff when faced with questions about their academic progress. Faculty and staff voices need to be collected regarding their perceptions of the effectiveness of the support systems used within an institution that promote retention for FGCS. This dissertation study aimed to explore faculty and staff perceptions of the factors that influence retention with a qualitative-dominant explanatory sequential mixed-methods research design. In the first phase, twenty-three faculty and staff at a two-year community college in southeastern Minnesota participated in an online questionnaire. Key findings from Phase One included faculty and staff perceived Academic Integration, Academic Conscientiousness, Support Service Satisfaction, and Financial Strain as having a significant impact on retention of FGCS and they perceive themselves as slightly prepared to advise FGCS on topics related to Financial Strain. In the second phase, eight faculty and staff from the same institution participated in an interview. Key findings from Phase Two included 50% of faculty and staff commented that the institution’s support systems for FGCS were effective; of those, 66.6% of staff commented these support systems were effective whereas 40% of faculty perceived the supports as effective

Student with Twice-Exceptionalities IEP Meeting Assignment Description

General education teachers should remember that all students are general education students, first. We need to be prepared to work with students of all abilities in our classrooms. As general education teachers, we have an active role on a child’s IEP team and an active role during the IEP meeting. This assignment asked preservice teachers to develop a script of what they would say at an IEP meeting of one character from four different novels that would be considered a child with twice-exceptionalities.https://digitalcommons.pittstate.edu/oer-teaching/1000/thumbnail.jp

Revisioning the K-12 Teacher Tenure Process

Earning tenure is monumental in the professional journey of most educators. However, the most common means of earning tenure is through an evaluation process that is likely primarily based on a supervisor’s series of classroom observations. This article proposes a holistic approach when envisioning the K-12 evaluation process that mirrors one used by institutions of higher education, the Professional Development Plan (PDP)