The New Handshake: Where We Are Now

The internet has empowered consumers in new and exciting ways. It has opened more efficient avenues for consumers to buy just about anything. Want proof? Just pull out your smartphone, swipe your finger across the screen a few times, and presto – your collector’s edition Notorious RBG bobblehead is on its way from China. Unfortunately, however, the internet has not yet delivered on its promise to improve consumer protection

Commensurate Fluctuations in the Pseudogap and Incommensurate spin-Peierls Phases of TiOCl

X-ray scattering measurements on single crystals of TiOCl reveal the presence of commensurate dimerization peaks within both the incommensurate spin-Peierls phase and the so-called pseudogap phase above T_c2. This scattering is relatively narrow in Q-space indicating long correlation lengths exceeding ~ 100 A below T* ~ 130 K. It is also slightly shifted in Q relative to that of the commensurate long range ordered state at the lowest temperatures, and it coexists with the incommensurate Bragg peaks below T_c2. The integrated scattering over both commensurate and incommensurate positions evolves continuously with decreasing temperature for all temperatures below T* ~ 130 K.Comment: To appear in Physical Review B: Rapid Communications. 5 page

Algebra Rules Object Boxes as an Authentic Assessment Task of Preservice Elementary Teacher Learning in a Mathematics Methods Course

The purpose of this study was to describe elementary preservice teachers’ difficulties with understanding algebraic generalizations that were set in an authentic context. Fifty-eight preservice teachers enrolled in an elementary mathematics methods course participated in the study. These students explored and practiced with authentic, hands-on materials called “object boxes,” then created sets of their own object box materials. Each algebra rules object box contained materials to illustrate and describe four different algebraic generalizations, or “rules.” The variables “n” and “z” were used in each of the generalizations. For each generalization, there was a set of objects attached to a piece of mat board that showed three cases of the generalization for different values of “n.” Two sets of cards accompanied these objects, giving word problems, defining variables, stating equations, and explaining the algebraic generalizations. Students matched word problems to the object sets, defined variables and checked their work, then wrote algebraic generalizations for the object sets and used the reverse sides of the equation cards to check their work. Projects were graded with a rubric. Students were then surveyed about their difficulties. Results of the analysis showed that students were able to make an assortment of authentic materials in a variety of contexts and enjoyed the creative aspects of the project, but found the algebraic content challenging. The most common mathematical difficulties were being able to define the variable, and identify the pattern. Examples of effective student materials are provided

Intertidal reef communities of the Marmion & Shoalwater Islands marine parks

Intertidal platform reefs are a distinctive feature of the Perth coastline. Occurring adjacent to shoreline beaches and also as isolated offshore reefs, these limestone platforms have been formed by wave action over many centuries. Rising and falling tides exert a major influence on the structure of intertidal reef communities, and this influence typically results in a distinctive distribution of organisms based on their tolerance to being exposed to the air when the tide is low. Those inhabiting the highest part of the rocky shore, and therefore exposed more often and for longer periods, are typically hardy, desiccation-resistant species. Those living further seaward are more frequently submerged, although even these organisms may be exposed to the drying sun during particularly low tides, or can be periodically buried by the deposition of shifting beach sand. During winter storms, large waves may crash onto these reefs, stripping away algae and dislodging animals. Yet despite such harsh conditions, intertidal reefs can support a diverse assemblage of algae and invertebrates. Intertidal reefs are recognised as key ecological values of the Marmion and Shoalwater Islands marine parks that are located adjacent to the Perth metropolitan area. Between 2009 and 2012, marine scientists from DEC’s Marine Science Program and the WA Herbarium worked with local marine park staff to survey some of the numerous intertidal reefs in these marine parks to improve our understanding of the communities they support

The Gates Of Gladness : On The Road To Sunshine Land

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Preservice Elementary Teachers Use Drawings and Make Sets of Materials to Explain Multiplication and Division by Fractions

Background: Multiplication and division by fractions are among the most troublesome concepts in the elementary mathematics curriculum. Recent studies have shown that preservice elementary teachers in the United States do not have deep understandings of these concepts. Effective ways to improve preservice teachers\u27 conceptual understanding of these concepts need to be identified. Citation: Rule, A. C., & Hallagan, J., editors. (2006). Preservice elementary teachers use drawings and make sets of materials to explain multiplication and division by fractions. A research study presented at the 2nd Annual Preparing Mathematicians to Educate Teachers (PMET) Conference at Oswego, New York, June 6, 2006. Conclusions: The two activities increased student understandings of multiplication and division by fractions. Although students improved through the activities, many students\u27 understandings were still incomplete. More than two focused activities are needed to ensure deeper understanding of concepts. Preservice teachers need concrete experiences with these concepts in their mathematics classes as well as in mathematics education coursework. 2 Control or Comparison Group: Both the control group and the experimental group consisted of preservice teachers from several sections of the same instructor\u27s undergraduate mathematics methods courses and were matched on pretest scores. Both groups completed the homework assignment in which they used drawings to illustrate multiplication and division by fractions. The instructor did not present lessons on these concepts to the classes until after the posttest had been completed so that the effects of these activities would not be confounded. The experimental group completed the additional activity of making hands-on materials to model these concepts. The study examined the increase in preservice teachers\u27 conceptual understanding of multiplication and division by fractions through the two activities. Data Collection and Analysis: Both control and experimental groups were assessed with identical pretest/ posttest instruments constructed by the investigators to determine both procedural knowledge of solving equations involving multiplication and division by fractions and conceptual knowledge of writing equations for story problems and using drawings to illustrate concepts. Posttest scores, student work on the assessments, drawing assignment, and hands-on materials were examined along with student comments on a survey that asked what subjects learned from participating in the intervention activity. Findings: The two activities improved preservice teachers\u27 understandings of these concepts as revealed by the change in scores from pretest to posttest (50.8% on pretest to 67.5% and 71.4%). Those who completed both assignments scored somewhat higher (71.4% compared to 67.5%) than those who only completed the drawing assignment, but this difference was not statistically significant. Preservice teachers reported that their understandings of these concepts improved through the activities. Intervention: Both control group and experimental group participated in composing story problems with drawings to illustrate multiplication and division by fractions. The experimental group completed the additional activity of making hands-on materials with accompanying story problems to model multiplication and division by fractions. Purpose: The purpose of the study was threefold: 1) to investigate the effectiveness of two activities in helping preservice teachers develop deeper understandings of multiplication and division by fractions; 2) to identify typical errors preservice teachers make and identify difficulties they encounter while learning these concepts; and 3) to provide examples of drawings and hands-on materials that effectively model multiplication and division by fractions for others to use in learning and teaching. Research Design: The study was a pretest - intervention - posttest design with control and experimental groups. Because lower-performing students tended to volunteer for the extra-credit activity (the intervention for the experimental group), blindly matched groups were formed on pretest scores. Setting: Preservice teachers from three mathematics methods classes of college students majoring in elementary education at a mid-sized college in central New York State during the spring semester of 2006. Study Sample: Forty-two white preservice elementary teachers enrolled in a mathematics methods course. The experimental group consisted of 18 females and 3 males; the control group consisted of 16 females and 5 males