Using the United States Census Data to Introduce Differential Equations

Abstract

This article describes a method for using the United States Census data to open a differential equations course. The question of finding a model for the United States population data gives students a first experience with creating a model using differential equations, and also understanding derivatives, what they mean, and how to calculate them in the context of real data. This model-building start motivates further exploration in many of the standard differential equations topics: the method of separation of variables, slope fields, autonomous equations, equilibria, and stability.     

New Challenges and Opportunities for Institutional Researchers in Assessment and Accreditation

Increased focus on assessment of student learning in the accreditation of higher education institutions offers new, challenging opportunities for institutional researchers. This article explores how institutional researchers can maximize these opportunities by offering methodological guidance in the assessment process and by designing new studies to produce assessment results. The article discusses the importance of methodological expertise, highlights the relevance of lessons learned from assessment literature, and provides a model for designing studies relevant for assessment.

     

Using Early Learning Standards to Provide High-Quality Education for All Children: The Early Learning Guidelines Toolkit

Today with the rise in the number of 3- to 6-year-old children enrolled in center-based early childhood programs, and a focus on program quality, it becomes imperative for educators to have a better understanding of the role research plays in establishing high-quality programs as these programs provide much of the foundation that supports early learning and development (Child Trends, 2014). Although psychology, and the role of child development research in particular, has always been integral to the field of early childhood education beginning with the seminal works of Piaget, Bronfenbrenner, Bruner, and others (Lickona,1971), the field had never fully embraced the use of research to inform practice, until the 1990s. This had been, in part, because the field of early childhood education originally viewed itself as a field of practitioners that provided for the everyday care and needs of young children, whereas it viewed child development researchers as scientists who paid little attention to the practical needs of classroom teaching (Takanishi, 1981 Takanishi, R. (1981). Early childhood education and research: The changing relationship. Theory into Practice, 20, 86–92.[Taylor & Francis Online] , [Google Scholar]). Although, today, there is no longer this ideological divide between the two areas, with the child development research being used to inform educational practice and policy (Center for the Developing Child, 2007), nevertheless there still remains a gap in the ability of educators to effectively implement evidence-based practices. Given the increased focus on providing young children with access to high-quality education, and the need for teachers to implement evidence-based practices the present paper attempts to bridge the gap by providing a brief overview of the science of early childhood development, its importance for development of early learning standards, and an overview of the Early Learning Toolkit which was developed to provide early learning educators guidance and resources to support the implementation of early learning standards within their own states as well as well across the nation. The goal of this article is to bridge theory and practice in early childhood education.     

Differential costs of curricula in Illinois public junior colleges: Some implications for the future

The purpose of this study was to determine and analyze the annual cost of operation including depreciation of movable capital equipment for educating one student in each curriculum of selected community colleges and to show the relationship of costs of vocational-technical curricula to the cost for common baccalaureate oriented curricula.A stratified sample of eight community colleges was drawn from those that had been in operation for at least five years.These data indicate that a majority of the courses offered in highly specialized curricula in both the occupational and baccalaureate categories were more expansive than those courses that were common to a wide variety of curricula.This study supports differential program funding to assure continued development of high quality vocational-technical programs in community colleges.     

Qualified Pedagogical Reflection as a Way to Improve Mathematics Education

All changes of the character of education and improvement of its quality depend, in our view, particularly on the teacher. To be able to do their work efficiently, teachers have to be equipped with professional skills and dispositions, with “teachers’ competence”. For their professional growth, we consider indispensable competence in reflection, which is aimed at the teacher’s activities with regard to aspects of pedagogy and/or subject-didactics. From the point of view of the goals and content of their teaching and the methods of work (and their realisation), the development of teachers’ conscious self-reflection on their own teaching and systematic pursuance of joint reflection with other teachers and/or researchers can promote the teacher’s professional growth. In this paper, we show how a selected group of elementary school teachers reflected on their competence in the course of preparing, carrying out and analysing several instruction experiments. The paper is based on samples of teachers’ reflections and their gradual development from mere simple conversations based on intuitive perceptions, through searching for effective teaching approaches, to the deep assessment of mathematics teaching from the point of view of topics and their didactic elaboration and to suggestions for the teachers’ own experiments. May the teacher know what he teaches. May the teacher know how to teach. May the teacher be sincerely interested in teaching. Comenius