Case Study of Dominant Factors Which Appear to Improve State Vocational Administrations Among Selected State Vocational Systems

Occupational and Adult Educatio

Professional development for mathematics teacher education faculty: Need and design

The purpose of this report is to share a conceptual model useful in the design of professional learning about teaching for university mathematics faculty. The model is illustrated by examples from a particular design effort: the development of an online shortcourse for faculty new to teaching mathematics courses for prospective primary school teachers. How novice mathematics teacher educators grow as instructors is an emerging area of research and development in the United States. At the same time, it is well established that effective instructional design of any course, including a course for faculty, requires breadth first: understanding and anticipating the needs of the learner. Therefore, given the sparse knowledge base in the new arena of mathematics teacher educator professional growth, effective design requires leveraging the scant existing research while also exploring and iteratively refining broad goals and objectives for faculty learning. Only after a conceptual foundation is articulated for what is to be learned and what will constitute evidence of learning, can cycles of design productively examine and test-bed particular course features such as lesson content, structures (like scope and sequence), and processes (like communication and evaluation). In the example used in this report, several researchbased perspectives on learning in/for/about teaching guided design goals and short-course objectives. These valued perspectives informed creation and prioritization of principles for short-course design which, in turn, informed evaluation of faculty learning. With these conceptual foundations in place, design of lessons to realize the goals, principles, and objectives rapidly followed. The work reported here contributes to the knowledge base in two ways: (1) it addresses faculty professional development directly by describing and illustrating a model for supporting instructional improvement and (2) it provides metanarrative to scaffold the professional growth of those who design professional learning opportunities for post-secondary mathematics faculty

Developing a model of pedagogical content knowledge for secondary and post-secondary mathematics instruction

The accepted framing of mathematics pedagogical content knowledge (PCK) as part of mathematical knowledge for teaching has centered on the question: What mathematical reasoning, insight, understanding, and skills are required for a person to teach elementary mathematics? Many have worked to address this question in K-8 teaching. Yet, there remains a call for examples and theory in the context of teachers with greater mathematical preparation and older students with varied and complex experiences in learning mathematics. In this theory development report we offer background and examples for an extended model of PCK – as the interplay among conceptually-rich mathematical understandings, experience in and of teaching, and multiple culturally-mediated classroom interactions

Developing a model of pedagogical content knowledge for secondary and post-secondary mathematics instruction

The accepted framing of mathematics pedagogical content knowledge (PCK) as part of mathematical knowledge for teaching has centered on the question: What mathematical reasoning, insight, understanding, and skills are required for a person to teach elementary mathematics? Many have worked to address this question in K-8 teaching. Yet, there remains a call for examples and theory in the context of teachers with greater mathematical preparation and older students with varied and complex experiences in learning mathematics. In this theory development report we offer background and examples for an extended model of PCK – as the interplay among conceptually-rich mathematical understandings, experience in and of teaching, and multiple culturally-mediated classroom interactions

Quantifying fault interpretation uncertainties and their impact on fault seal and seismic hazard analysis

We would like to thank DugInsight for the provision of an academic license for their software package. We would like to thank Emma Miche and two anomalous reviewers for constructive feedback on the original version of the manuscipt.Peer reviewe

Controllability, Observability, Realizability, and Stability of Dynamic Linear Systems

We develop a linear systems theory that coincides with the existing theories for continuous and discrete dynamical systems, but that also extends to linear systems defined on nonuniform time domains. The approach here is based on generalized Laplace transform methods (e.g. shifts and convolution) from our recent work \cite{DaGrJaMaRa}. We study controllability in terms of the controllability Gramian and various rank conditions (including Kalman's) in both the time invariant and time varying settings and compare the results. We also explore observability in terms of both Gramian and rank conditions as well as realizability results. We conclude by applying this systems theory to connect exponential and BIBO stability problems in this general setting. Numerous examples are included to show the utility of these results.Comment: typos corrected; current form is as accepted in EJD

Justice and the Mathematics Classroom: Realizing the Goals of the AMTE Standards for Preparing Teachers of Mathematics

This chapter is an introduction to justice in the post-secondary context of mathematics courses for prospective teachers. The chapter is a research-to-practice report (i.e., it describes an aspect of instruction and discusses how it is informed by, connects to, or is illustrative of findings from research). While the reader might be any type of mathematics teacher educator, the focus here is supporting those who teach mathematics content courses for elementary school teacher candidates. In addition to having an effect on discipline-specific knowledge, college mathematics classes contribute to the ways candidates communicate in/with/through mathematics in working with children. The chapter includes discussion of the keys of mathematical literacy: mathematics for and of justice and examples of what the ideas look like in practice. The examples include information from research and a reference case presented as the accumulation of experiences for Kara Thomas and Dr. Rhodes. The case is a means for exemplifying issues such as equity, agency, and identity in the mathematics classroom