Conceptually driven and visually rich tasks in texts and teaching practice: the case of infinite series

The study we report here examines parts of what Chevallard calls the institutional dimension of the students’ learning experience of a relatively under-researched, yet crucial, concept in Analysis, the concept of infinite series. In particular, we examine how the concept is introduced to students in texts and in teaching practice. To this purpose, we employ Duval's Theory of Registers of Semiotic Representation towards the analysis of 22 texts used in Canada and UK post-compulsory courses. We also draw on interviews with in-service teachers and university lecturers in order to discuss briefly teaching practice and some of their teaching suggestions. Our analysis of the texts highlights that the presentation of the concept is largely a-historical, with few graphical representations, few opportunities to work across different registers (algebraic, graphical, verbal), few applications or intra-mathematical references to the concept's significance and few conceptually driven tasks that go beyond practising with the application of convergence tests and prepare students for the complex topics in which the concept of series is implicated. Our preliminary analysis of the teacher interviews suggests that pedagogical practice often reflects the tendencies in the texts. Furthermore, the interviews with the university lecturers point at the pedagogical potential of: illustrative examples and evocative visual representations in teaching; and, student engagement with systematic guesswork and writing explanatory accounts of their choices and applications of convergence tests

Aristotle's Platonic Response to the Problem of First Principles

how does one inquire into the truth of first principles? Where does one begin when deciding where to begin? Aristotle recognizes a series of difficulties when it comes to understanding the starting points of a scientific or philosophical system, and contemporary scholars have encountered their own difficulties in understanding his response. I will argue that Aristotle was aware of a Platonic solution that can help us uncover his own attitude toward the problem.Aristotle's central problem with first principles arises from the fact that they cannot be demonstrated in the same way as other propositions. Since demonstrations proceed from prior and better-known principles, if the principles themselves were in need of..

Scientific Argumentation as a Foundation for the Design of Inquiry-Based Science Instruction

Despite the attention that inquiry has received in science education research and policy, a coherent means for implementing inquiry in the classroom has been missing [1]. In recent research, scientific argumentation has received increasing attention for its role in science and in science education [2]. In this article, we propose that organizing a unit of instruction around building a scientific argument can bring inquiry practices together in the classroom in a coherent way. We outline a framework for argumentation, focusing on arguments that are central to science—arguments for the best explanation. We then use this framework as the basis for a set of design principles for developing a sequence of inquiry-based learning activities that support students in the construction of a scientific argument. We show that careful analysis of the argument that students are expected to build provides designers with a foundation for selecting resources and designing supports for scientific inquiry. Furthermore, we show that creating multiple opportunities for students to critique and refine their explanations through evidence-based argumentation fosters opportunities for critical thinking, while building science knowledge and knowledge of the nature of science

Integrating Authentic Digital Resources in Support of Deep, Meaningful Learning

"Integrating Authentic Digital Resources in Support of Deep, Meaningful Learning," a white paper prepared for the Smithsonian by Interactive Educational Systems Design Inc., describes instructional approaches that apply to successful teaching with the Smithsonian Learning Lab.After defining its use of terms such as deeper learning and authentic resources the authors review the research basis of three broad approaches that support integrating digital resources into the classroom:Project-based learningGuided exploration of concepts and principlesGuided development of academic skillsThese approaches find practical application in the last section of the paper, which includes seven case studies. Examples range from first-grade science, to middle-school English (including ELL strategy) to a high-school American government class. In each example, students study and analyze digital resources, going on to apply their knowledge and deepen their understanding of a range of topics and problems

Students\u27 Scientific Evaluations of Water Resources

Socially-relevant and controversial topics, such as water issues, are subject to differences in the explanations that scientists and the public (herein, students) find plausible. Students need to be more evaluative of the validity of explanations (e.g., explanatory models) based on evidence when addressing such topics. We compared two activities where students weighed connections between lines of evidence and explanations. In one activity, students were given four evidence statements and two models (one scientific and one non-scientific alternative); in the other, students chose four out of eight evidence statements and three models (two scientific and one non-scientific). Repeated measures analysis of variance (ANOVA) showed that both activities engaged students\u27 evaluations and differentially shifted students\u27 plausibility judgments and knowledge. A structural equation model suggested that students\u27 evaluation may influence post-instructional plausibility and knowledge; when students chose their lines of evidence and explanatory models, their evaluations were deeper, with stronger shifts toward a scientific stance and greater levels of post-instructional knowledge. The activities may help to develop students\u27 critical evaluation skills, a scientific practice that is key to understanding both scientific content and science as a process. Although effect sizes were modest, the results provided critical information for the final development and testing stage of these water resource instructional activities

Ethnography, education and on-line research

This paper is an attempt to establish the methodological basis for carrying out ethnographies of online education communities, in particular in the Continuing Professional Development VITAL project co-ordinated by the Faculty of Education and Language Studies at The Open University www.vital.ac.uk/ A much shorter earlier draft version of this paper was given at the Qualitative Research For Web 2.0/3.0: The Next Leap! 25 & 26 March 2010 in Berlin. Organised by Merlien. The arguments and references in this paper are almost all to be found in two books 'one authored and one edited – by Professor Christine Hine of Surrey University, UK (Hine 2000; Hine 2005)

A Path to Alignment: Connecting K-12 and Higher Education via the Common Core and the Degree Qualifications Profile

The Common Core State Standards (CCSS), which aim to assure competency in English/language arts and mathematics through the K-12 curriculum, define necessary but not sufficient preparedness for success in college. The Degree Qualifications Profile (DQP), which describes what a college degree should signify, regardless of major, offers useful but not sufficient guidance to high school students preparing for college study. A coordinated strategy to prepare students to succeed in college would align these two undertakings and thus bridge an unfortunate and harmful cultural chasm between the K-12 world and that of higher education. Chasms call for bridges, and the bridge proposed by this white paper could create a vital thoroughfare. The white paper begins with a description of the CCSS and an assessment of their significance. A following analysis then explains why the CCSS, while necessary, are not sufficient as a platform for college success. A corresponding explanation of the DQP clarifies the prompts that led to its development, describes its structure, and offers some guidance for interpreting the outcomes that it defines. Again, a following analysis considers the potential of the DQP and the limitations that must be addressed if that potential is to be more fully realized. The heart of the white paper lies in sections 5 and 6, which provide a crosswalk between the CCSS and the DQP. These sections show how alignments and differences between the two may point to a comprehensive preparedness strategy. They also offer a proposal for a multifaceted strategy to realize the potential synergy of the CCSS and the DQP for the benefit of high school and college educators and their students -- and the nation

Understanding the Role of Science-Specific Literacy Strategies in Supporting Science Teaching and Student Learning: A Case Study of Preservice Elementary Teachers in a Science Methods Course That Integrated a Disciplinary Literacy Framework

The shift to student engagement in scientific and engineering practices to learn science provides opportunities for science learning and language learning to occur in tandem. These opportunities also pose new challenges for elementary pre-service teachers (PSTs) since literacy methods courses have been presented separately from science methods courses. We integrated a disciplinary literacy framework in a science methods course to help elementary PSTs understand the synergistic connections between literacy and science teaching. The purpose of this study was to examine elementary PSTs’ understanding of the use of science-specific literacy strategies to support science teaching and learning through three points of observation. Findings from three data sources indicated that PSTs showed a developing understanding of the role of disciplinary literacy in supporting student engagement in science practices and learning disciplinary core ideas. Implications for future uses of a disciplinary literacy framework for teaching and learning science and elementary PSTs’ science preparation are presented