A framework for the natures of negativity in introductory physics

Mathematical reasoning skills are a desired outcome of many introductory physics courses, particularly calculus-based physics courses. Positive and negative quantities are ubiquitous in physics, and the sign carries important and varied meanings. Novices can struggle to understand the many roles signed numbers play in physics contexts, and recent evidence shows that unresolved struggle can carry over to subsequent physics courses. The mathematics education research literature documents the cognitive challenge of conceptualizing negative numbers as mathematical objects--both for experts, historically, and for novices as they learn. We contribute to the small but growing body of research in physics contexts that examines student reasoning about signed quantities and reasoning about the use and interpretation of signs in mathematical models. In this paper we present a framework for categorizing various meanings and interpretations of the negative sign in physics contexts, inspired by established work in algebra contexts from the mathematics education research community. Such a framework can support innovation that can catalyze deeper mathematical conceptualizations of signed quantities in the introductory courses and beyond

Small dynamical heights for quadratic polynomials and rational functions

Let $f \in Q(z)$ be a polynomial or rational function of degree 2. A special case of Morton and Silverman's Dynamical Uniform Boundedness Conjecture states that the number of rational preperiodic points of $f$ is bounded above by an absolute constant. A related conjecture of Silverman states that the canonical height $\hat{h}_f(x)$ of a non-preperiodic rational point $x$ is bounded below by a uniform multiple of the height of $f$ itself. We provide support for these conjectures by computing the set of preperiodic and small height rational points for a set of degree 2 maps far beyond the range of previous searches.Comment: 19 page

Where does India end and Eurasia begin?

The Indus Suture Zone is defined as the plate boundary between India and Eurasia. Here we document geochronological data that suggest that Indian rocks outcrop to the north of this suture zone. The inherited age spectrum of zircons from mylonitic gneiss collected in the southern part of the Karakorum Batholith is similar to those obtained from the Himalayan Terrane, the Pamir and is apparently Gondwanan in its affinity. These data are taken to indicate that the Karakorum Terrane was once a component of Gondwana, or at least derived from the erosion of Gondwanan material. Several continental ribbons (including the Karakorum Terrane) were rifted from the northern margin of Gondwana and accreted to Eurasia prior to India-Eurasia collision. Many therefore consider the Karakorum Terrane is the southern margin of Eurasia. However, we do not know if rifting led to the creation of a new microplate(s) or simply attenuated crust between Gondwana and these continental ribbons. Thus there is a problem using inherited and detrital age data to distinguish what is "Indian" and what is "Eurasian" crust. These findings have implications for other detrital/inherited zircon studies where these data are used to draw inferences about the tectonic history of various terranes around the world

School trip photomarathons: engaging primary school visitors using a topic focused photo competition

The aim of this study was to explore the potential of photomarathons as a fun and engaging way to support students making connections between what they learn during a museum visit and what they learn in school or other contexts. Sixty primary school pupils aged between six and eleven took part in a photomarathon activity during their trip to the Roman Baths. The children were split into three groups. During their visit each group undertook three one-hour activities, namely: a photomarathon, a hands-on artefact exploration activity with a museum education officer, and a school-group handheld audio tour. For the photomarathon activity the children worked in subgroups of three and, for 15–20 minutes, took photos on three themes around the museum. At the end of the available time the children submitted a set of photos, one photo for each theme. Photo galleries for each theme were then generated and made available on a website for the pupils. The students voted for the best photo in each theme gallery, and a small prize was awarded to the members of each team that took the winning photo. A week after the visit the children were asked a number of questions concerning their visit. The photomarathon was spontaneously mentioned by 41% (23/56) of the children as the best activity in their visit to the Roman Baths, which was more than any other activity they engaged in during the visit. Overall, of the three activities the children liked the photomarathon the best. There were no age differences in how engaging the children found the photomarathon activity and all children regardless of age were able to take photographs

Framework for the natures of negativity in introductory physics

Mathematical reasoning skills are a desired outcome of many introductory physics courses, particularly calculus-based physics courses. Novices can struggle to understand the many roles signed numbers play in physics contexts, and recent evidence shows that unresolved struggle can carry over to subsequent physics courses. Positive and negative quantities are ubiquitous in physics, and the sign carries important and varied meanings. The mathematics education research literature documents the cognitive challenge of conceptualizing negative numbers as mathematical objects—both for experts, historically, and for novices as they learn. We contribute to the small but growing body of research in physics contexts that examines student reasoning about signed quantities and reasoning about the use and interpretation of signs in mathematical models. In this paper we present a framework for categorizing various meanings and interpretations of the negative sign in physics contexts, inspired by established work in algebraic contexts from the mathematics education research community. Such a framework can support innovation that can catalyze deeper mathematical conceptualizations of signed quantities in the introductory courses and beyond

Narrative and portfolio approaches to teacher professional standards

This paper analyses various uses of narrative in the exploration of teacher identity. It highlights the way many contemporary education writers use terminology such as &lsquo;storying lives&rsquo; and &lsquo;storied landscapes&rsquo; to describe teacher processes of reflection on practice. In this paper the authors discuss some recent approaches to narrative that incorporate or suggest systematic uses of narrative theory (Conle 2003, Kamler, 2001, Richardson, 2003). Consideration is also given to the links between critical ethnography and narrative in order to critique the use of teacher portfolios, as in a recent Australian initiative for the appraisal of beginning teachers. The authors conclude with an argument for the rehabilitation and refinement of narrative theory in the &lsquo;writing&rsquo; of teacher identity.<br /

Noticing a flow of networks

The world of the classroom is no less a &lsquo;flow of networks&rsquo; (Castells 1999) than the globalised world outside its doors. In this fluid context of the world outside and the inner world of identity, the linear and somewhat found understandings of reflective practice (Schon 1987) and observations of classroom practice may serve to limit rather than reveal. The authors of this paper have been engaging with the ways teachers shape personal and professional theory through a movement - oriented process of noticing (Moss et al 2004). Noticing,working at the elusive intersections of observation and construction, permits non-linear connections. Noticing theorised in this way draws on the physical (Mason 2002). The movement occurs between the seen and the seer &ndash; between beliefs, identity and responses. The movement of the eye in noticing touches the seen in various places &ndash; pulling in and out of focus that which is seen. The same movement brings in and out of focus the seer- the beliefs and values held and let go in the seeing. The focusing in the act requires convergence and divergence (&lsquo;Notitia&rsquo; being known -&lsquo;Middle English from Old French from Latin Notitia being known from notus past part. of noscere know&rsquo;). The paper will report on early data on the impact of implementing this theoretical model in mass teacher education at the University of Melbourne, Australia.<br /