Magnetic field splitting of the spin-resonance in CeCoIn5

Neutron scattering in strong magnetic fields is used to show the spin-resonance in superconducting CeCoIn5 (Tc=2.3 K) is a doublet. The underdamped resonance (\hbar \Gamma=0.069 \pm 0.019 meV) Zeeman splits into two modes at E_{\pm}=\hbar \Omega_{0}\pm g\mu_{B} \mu_{0}H with g=0.96 \pm 0.05. A linear extrapolation of the lower peak reaches zero energy at 11.2 \pm 0.5 T, near the critical field for the incommensurate "Q-phase" indicating that the Q-phase is a bose condensate of spin excitons.Comment: 5 pages, 4 figure

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

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

Suppression of the commensurate spin-Peierls state in Sc-doped TiOCl

We have performed x-ray scattering measurements on single crystals of the doped spin-Peierls compound Ti(1-x)Sc(x)OCl (x = 0, 0.01, 0.03). These measurements reveal that the presence of non-magnetic dopants has a profound effect on the unconventional spin-Peierls behavior of this system, even at concentrations as low as 1%. Sc-doping suppresses commensurate fluctuations in the pseudogap and incommensurate spin-Peierls phases of TiOCl, and prevents the formation of a long-range ordered spin-Peierls state. Broad incommensurate scattering develops in the doped compounds near Tc2 ~ 93 K, and persists down to base temperature (~ 7 K) with no evidence of a lock-in transition. The width of the incommensurate dimerization peaks indicates short correlation lengths on the order of ~ 12 angstroms below Tc2. The intensity of the incommensurate scattering is significantly reduced at higher Sc concentrations, indicating that the size of the associated lattice displacement decreases rapidly as a function of doping.Comment: 7 pages, 5 figure

Hands-on Materials for Teaching about Global Climate Change through Graph Interpretation

Teachers need to address global climate change with students in their classrooms as evidence for consequences from these environmental changes mounts. One way to approach global climate change is through examination of authentic data. Mathematics and science may be integrated by interpreting graphs from the professional literature. This study examined the types of errors 72 preservice elementary teachers made in producing hands-on materials for teaching graph interpretation skills through graphed evidence of global climate change from the literature. The teaching materials consisted of a graph electronically manipulated on a colored background and enhanced with clip art related to the graph’s topic that was then printed and mounted on colored cardboard. The graph was accompanied by six graph interpretation statements printed on cards that were to be sorted as true or false. Additionally, a topic-related object was provided for each graph for an initial activity that focused student attention and aroused interest. Four graphs with their accompanying statements and four related objects were combined into one box of materials to be used by a small group of students. Preservice teachers practiced with example sets of materials made by the course instructor and then worked to each create a new, unique set. An appendix of many sets of correct materials is provided in this ERIC document. About half of the teaching materials produced were errorfree. The most common errors preservice teachers made were misuse of vocabulary and over generalizing a graph’s information. Other frequent errors included not supplying enough specific information in a statement to allow its verification and misinterpreting a major trend on a graph. These problems can be attributed to preservice teachers’ lack of sufficient experience in graph interpretation. Therefore, the authors conclude that the materials-making exercise was beneficial to preservice teachers and the resulting materials (with any errors corrected) can effectively be used with upper elementary and secondary students. [1 Table, 1 Appendix containing 18 graphs accompanied by interpretation statements.

Environmental Print Activities for Teaching Mathematics and Content Areas

Twenty-three mathematics activities that use environmental print materials are presented, along with two activities that focus on music education, one that highlights history concepts, and five science activities. The environmental print materials are words and images cut from food or other product packaging and mounted on mat board cards. Instructions for teachers regarding material preparation are given, along with directions for students to engage in each activity. Example layouts and labels for materials boxes are given for each activity. Mathematical topics include: more and less; numeration; addition and subtraction; time words; forming patterns; writing equations; story problems; chart coordinates; percents; fractions; measurement abbreviations; coins; liquid measurement; symmetry designs; Venn diagrams; volume and area of geometric solids; factors; permutations; and probability. The two music activities focus on rhythm. The history activity discusses ideas and items related to the taxation of the thirteen colonies. The five science activities include the following concepts: living versus nonliving; ecology food pyramid; distinguishing proteins, carbohydrates, and lipids; potential versus kinetic energy; and fossils in geologic time. (Author

Structural Fluctuations in the Spin Liquid State of Tb2Ti2O7

High resolution X-ray scattering measurements on single crystal Tb2Ti2O7 reveal finite structural correlations at low temperatures. This geometrically frustrated pyrochlore is known to exhibit a spin liquid, or cooperative paramagnetic state, at temperatures below ~ 20 K. Parametric studies of structural Bragg peaks appropriate to the Fd$\bar{3}$m space group of Tb2Ti2O7 reveal substantial broadening and peak intensity reduction in the temperature regime 20 K to 300 mK. We also observe a small, anomalous lattice expansion on cooling below a density maximum at ~ 18 K. These measurements are consistent with the development of fluctuations above a cooperative Jahn-Teller, cubic-tetragonal phase transition at very low temperatures.Comment: 5 pages, 4 figures, submitted for publicatio

Critical X-ray Scattering Studies of Jahn-Teller Phase Transitions in TbV1−x_{1-x}Asx_{x}O4_{4}

The critical behaviour associated with cooperative Jahn-Teller phase transitions in TbV$_{1-x}$As$_{x}$O$_{4}$ (where \textit{x} = 0, 0.17, 1) single crystals have been studied using high resolution x-ray scattering. These materials undergo continuous tetragonal $\to$ orthorhombic structural phase transitions driven by Jahn-Teller physics at T$_C$ = 33.26(2) K, 30.32(2) K and 27.30(2) K for \textit{x} = 0, 0.17 and 1 respectively. The orthorhombic strain was measured close to the phase transition and is shown to display mean field behavior in all three samples. Pronounced fluctuation effects are manifest in the longitudinal width of the Bragg scattering, which diverges as a power law, with an exponent given by $x=0.45 \pm 0.04$, on approaching the transition from either above or below. All samples exhibited twinning; however the disordered x = 0.17 sample showed a broad distribution of twins which were stable to relatively low temperatures, well below T$_C$. This indicates that while the orthorhombic strain continues to develop in a conventional mean field manner in the presence of disorder, twin domains are easily pinned by the quenched impurities and their associated random strains.Comment: 8 pages, 6 figure