Preservice Teachers' Analysis of Children's Work to Make Instructional Decisions

Teaching is an interactive process in which teachers gather information, analyze the results, and construct a response based on this diagnosis ( Cooney, 1988 ). Considering alternatives in constructing a response, that is, making an instructional decision, is of great importance in teaching. How might mathematics teacher educators provide experiences for preservice teachers to begin the development of this skill? In an attempt to determine how these experiences might reveal the level of understanding preservice teachers have in regards to children's mathematical thinking, a study was conducted over three semesters. During the mathematics methods course, preservice teachers were involved in analyzing children's work through the review and discussion of several samples. They were required to determine the error pattern, discuss what might have lead to this misconception, and suggest appropriate instructional strategies that might help this student. Although most preservice teachers could correctly identify the computational error patterns, they had difficulty in determining what might have led to the misconceptions and proposing effective instructional strategies.     

The effect of different representations on Years 3 to 5 students’ ability to generalise

Over the past 3 years, in our Early Algebra Thinking project, we have been studying Years 3 to 5 students’ ability to generalise in a variety of situations, namely, compensation principles in computation, the balance principle in equivalence and equations, change and inverse change rules with function machines, and pattern rules with growing patterns. In these studies, we have attempted to involve a variety of representations and to build students’ abilities to switch between them (in line with the theories of Dreyfus in Advanced mathematical thinking. Kluwer, Dordtrecht, pp. 25–41, 1991, and Duval in Proceedings of the 21st conference of the North American chapter of the international group for the psychology of mathematics education, vol. 1, pp. 3–26, 1999). The studies have shown the negative effect of closure on generalisation in symbolic representations, the predominance of single variance generalisation over covariant generalisation in tabular representations, and the reduced ability to readily identify commonalities and relationships in enactive and iconic representations. This presentation will use a variety of studies to explore the interrelation between verbal and visual comprehension of context and generalisation. The studies showed in a variety of contexts the importance of understanding and communicating aspects of representational forms which allowed commonalities to be seen across or between representations.     

Digital biomagnetism: Electrodeposited multilayer magnetic barcodes

A novel magnetic encoding technique for performing high-throughput biological assays is presented. Electrodeposited Ni/Cu and Co/Cu multilayer pillar structures with a diameter of 15 μm and a thickness up to 10 μm are presented as “magnetic barcodes”, where the number of unique codes possible increases exponentially with a linear increase in length. A gold cap facilitates the growth of self-assembled monolayers (SAMs), while microdrop printing allows efficient generation of large libraries of tagged probes. Coercivity-tuning techniques are used to exploit a non-proximity encoding methodology compatible with microfluidic flow.     

Coulomb excitation of radioactive 20, 21Na

The low-energy structures of the radioactive nuclei ^{20, 21}Na have been examined using Coulomb excitation at the TRIUMF-ISAC radioactive ion beam facility. Beams of ～ 5×10⁶ ions/s were accelerated to 1.7MeV/A and Coulomb excited in a 0.5mg/cm^2 ^natTi target. Two TIGRESS HPGe clover detectors perpendicular to the beam axis were used for $ \gamma$ -ray detection, while scattered nuclei were observed by the Si detector BAMBINO. For ²¹Na , Coulomb excitation from the 3/2⁺ ground state to the first excited 5/2⁺ state was observed, while for ²⁰Na , Coulomb excitation was observed from the 2⁺ ground state to the first excited 3⁺ and 4⁺ states. For both beams, B ( $ \lambda$ L) values were determined using the 2⁺ $ \rightarrow$ 0⁺ de-excitation in ⁴⁸Ti as a reference. The resulting B(E2) ↓ value for ²¹Na is 137±9 e^2fm^4, while the resulting B( $ \lambda$ L) ↓ values for ²⁰Na are 55±6 e^2fm^4 for the 3⁺ $ \rightarrow$ 2⁺ , 35.7±5.7 e^2 fm^4 for the 4⁺ $ \rightarrow$ 2⁺ , and 0.154±0.030 μ_N^2 for the 4⁺ $ \rightarrow$ 3⁺ transitions. This analysis significantly improves the measurement of the ²¹Na B(E2) value, and provides the first experimental determination of B( $ \lambda$ L) values for the proton dripline nucleus ²⁰Na .-1     

Plasmonic enhancement of the two photon absorption cross section of an organic chromophore using polyelectrolyte-coated gold nanorods

The effect of plasmonic enhancement on the two-photon absorption cross section of organic chromophores attached to polyelectrolyte-coated gold nanorods was investigated. The magnitudes of such enhancements were confirmed using single and two photon excitations of the chromophore molecules bound to polyelectrolyte-coated gold nanorods. By synthesizing two-, four-, six-, and eight-polyelectrolyte layer coated nanorods of a particular aspect ratio, the distance dependence of the evanescent electromagnetic field on molecular two-photon absorption was observed. Enhancements of 40-fold were observed for the chromophores nearest to the surface.     

The influence of linguistic and musical experience on Cantonese word learning

Adult non-native speech perception is subject to influence from multiple factors, including linguistic and extralinguistic experience such as musical training. The present research examines how linguistic and musical factors influence non-native word identification and lexical tone perception. Groups of native tone language (Thai) and non-tone language listeners (English), each subdivided into musician and non-musician groups, engaged in Cantonese tone word training. Participants learned to identify words minimally distinguished by five Cantonese tones during training, also completing musical aptitude and phonemic tone identification tasks. First, the findings suggest that either musical experience or a tone language background leads to significantly better non-native word learning proficiency, as compared to those with neither musical training nor tone language experience. Moreover, the combination of tone language and musical experience did not provide an additional advantage for Thai musicians above and beyond either experience alone. Musicianship was found to be more advantageous than a tone language background for tone identification. Finally, tone identification and musical aptitude scores were significantly correlated with word learning success for English but not Thai listeners. These findings point to a dynamic influence of musical and linguistic experience, both at the tone dentification level and at the word learning stage.     

Spectroscopic structure-property relationships of a series of polyaromatic platinum acetylides

To develop a structure-spectroscopic property relationship in platinum acetylides having poly(aromatic hydrocarbon) ligands, we synthesized a series of chromophores with systematic variation in the number of fused aromatic rings (nFAR) and ligand topology (polyacene (L), polyphenanthrene (Z), or compact(C)). We measured ground-state absorption, fluorescence, and phosphorescence spectra. We also performed nanosecond and femtosecond transient absorption experiments. To extend the range of compounds in the structure-property relationship, we did DFT calculations on an expanded series of chromophores. Both the DFT results and experiments show that the S(1) and T(1) state energies are a function of both nFAR and the ligand topology. In the L chromophores, the S(1) and T(1) state energies decrease linearly with nFAR. In contrast, the S(1) and T(1) state energies of the Z chromophores oscillate around a fixed value with increasing nFAR. The C chromophores have behavior intermediate between the L and Z chromophores. A parallel series of calculations on the ligands shows the same behavior. The S(1)-S(n) energy obtained from ultrafast time-resolved spectra has a linear variation in nFAR. The rate constant for nonradiative decay, k(nr), was calculated from the S(1) state lifetime and decreases with an increasing number of π electrons in the aromatic ring. The result is consistent with the spin-orbit coupling caused by the central platinum heavy atom decreasing with larger nFAR. The present work shows that the framework developed for the analysis of poly(aromatic hydrocarbon) properties is useful for the understanding of the corresponding platinum acetylide complexes.     

Extending and interpreting Post’s programme

Computability theory concerns information with a causal-typically algorithmic-structure. As such, it provides a schematic analysis of many naturally occurring situations. Emil Post was the first to focus on the close relationship between information, coded as real numbers, and its algorithmic infrastructure. Having characterised the close connection between the quantifier type of a real and the Turing jump operation, he looked for more subtle ways in which information entails a particular causal context. Specifically, he wanted to find simple relations on reals which produced richness of local computability-theoretic structure. To this extent, he was not just interested in causal structure as an abstraction, but in the way in which this structure emerges in natural contexts. Post’s programme was the genesis of a more far reaching research project.In this article we will firstly review the history of Post’s programme, and look at two interesting developments of Post’s approach. The first of these developments concerns the extension of the core programme, initially restricted to the Turing structure of the computably enumerable sets of natural numbers, to the Ershov hierarchy of sets. The second looks at how new types of information coming from the recent growth of research into randomness, and the revealing of unexpected new computability-theoretic infrastructure. We will conclude by viewing Post’s programme from a more general perspective. We will look at how algorithmic structure does not just emerge mathematically from information, but how that emergent structure can model the emergence of very basic aspects of the real world.