Problem solving in the primary school (K-2)

This article focuses on problem solving activities in a first grade classroom in a typical small community and school in Indiana. But, the teacher and the activities in this class were not at all typical of what goes on in most comparable classrooms; and, the issues that will be addressed are relevant and important for students from kindergarten through college. Can children really solve problems that involve concepts (or skills) that they have not yet been taught? Can children really create important mathematical concepts on their own – without a lot of guidance from teachers? What is the relationship between problem solving abilities and the mastery of skills that are widely regarded as being “prerequisites” to such tasks?Can primary school children (whose toolkits of skills are limited) engage productively in authentic simulations of “real life” problem solving situations? Can three-person teams of primary school children really work together collaboratively, and remain intensely engaged, on problem solving activities that require more than an hour to complete? Are the kinds of learning and problem solving experiences that are recommended (for example) in the USA’s Common Core State Curriculum Standards really representative of the kind that even young children encounter beyond school in the 21st century? … This article offers an existence proof showing why our answers to these questions are: Yes. Yes. Yes. Yes. Yes. Yes. And: No. … Even though the evidence we present is only intended to demonstrate what’s possible, not what’s likely to occur under any circumstances, there is no reason to expect that the things that our children accomplished could not be accomplished by average ability children in other schools and classrooms.

Modeling as a means for making powerful ideas accessible to children at an early age

The SimCalc Vision and Contributions Advances in Mathematics Education 2013, pp 419-436 Modeling as a Means for Making Powerful Ideas Accessible to Children at an Early Age Richard Lesh, Lyn English, Serife Sevis, Chanda Riggs … show all 4 hide » Look Inside » Get Access Abstract In modern societies in the 21st century, significant changes have been occurring in the kinds of “mathematical thinking” that are needed outside of school. Even in the case of primary school children (grades K-2), children not only encounter situations where numbers refer to sets of discrete objects that can be counted. Numbers also are used to describe situations that involve continuous quantities (inches, feet, pounds, etc.), signed quantities, quantities that have both magnitude and direction, locations (coordinates, or ordinal quantities), transformations (actions), accumulating quantities, continually changing quantities, and other kinds of mathematical objects. Furthermore, if we ask, what kind of situations can children use numbers to describe? rather than restricting attention to situations where children should be able to calculate correctly, then this study shows that average ability children in grades K-2 are (and need to be) able to productively mathematize situations that involve far more than simple counts. Similarly, whereas nearly the entire K-16 mathematics curriculum is restricted to situations that can be mathematized using a single input-output rule going in one direction, even the lives of primary school children are filled with situations that involve several interacting actions—and which involve feedback loops, second-order effects, and issues such as maximization, minimization, or stabilizations (which, many years ago, needed to be postponed until students had been introduced to calculus). …This brief paper demonstrates that, if children’s stories are used to introduce simulations of “real life” problem solving situations, then average ability primary school children are quite capable of dealing productively with 60-minute problems that involve (a) many kinds of quantities in addition to “counts,” (b) integrated collections of concepts associated with a variety of textbook topic areas, (c) interactions among several different actors, and (d) issues such as maximization, minimization, and stabilization.

Isolation and characterization of charge-tagged phenylperoxyl radicals in the gas phase : direct evidence for products and pathways in low temperature benzene oxidation

The phenylperoxyl radical has long been accepted as a critical intermediate in the oxidation of benzene and an archetype for arylperoxyl radicals in combustion and atmospheric chemistry. Despite being central to many contemporary mechanisms underpinning these chemistries, reports of the direct detection or isolation of phenylperoxyl radicals are rare and there is little experimental evidence connecting this intermediate with expected product channels. We have prepared and isolated two charge-tagged phenyl radical models in the gas phase [i.e., 4-(N,N,N-trimethylammonium) phenyl radical cation and 4-carboxylatophenyl radical anion] and observed their reactions with dioxygen by ion-trap mass spectrometry. Measured reaction rates show good agreement with prior reports for the neutral system (k(2)[(Me3N+)C6H4 center dot + O-2] = 2.8 x 10(-11) cm(3) molecule(-1) s(-1), Phi = 4.9%; k(2)[(-O2C)C6H4 center dot + O-2] = 5.4 x 10(-1)1 cm(3) molecule(-1) s(-1), Phi = 9.2%) and the resulting mass spectra provide unequivocal evidence for the formation of phenylperoxyl radicals. Collisional activation of isolated phenylperoxyl radicals reveals unimolecular decomposition by three pathways: (i) loss of dioxygen to reform the initial phenyl radical; (ii) loss of atomic oxygen yielding a phenoxyl radical; and (iii) ejection of the formyl radical to give cyclopentadienone. Stable isotope labeling confirms these assignments. Quantum chemical calculations for both charge-tagged and neutral phenylperoxyl radicals confirm that loss of formyl radical is accessible both thermodynamically and entropically and competitive with direct loss of both hydrogen atom and carbon dioxide.

Multifractal analyses of daily rainfall time series in Pearl River basin of China

The multifractal properties of daily rainfall time series at the stations in Pearl River basin of China over periods of up to 45 years are examined using the universal multifractal approach based on the multiplicative cascade model and the multifractal detrended fluctuation analysis (MF-DFA). The results from these two kinds of multifractal analyses show that the daily rainfall time series in this basin have multifractal behavior in two different time scale ranges. It is found that the empirical multifractal moment function K(q)K(q) of the daily rainfall time series can be fitted very well by the universal multifractal model (UMM). The estimated values of the conservation parameter HH from UMM for these daily rainfall data are close to zero indicating that they correspond to conserved fields. After removing the seasonal trend in the rainfall data, the estimated values of the exponent h(2)h(2) from MF-DFA indicate that the daily rainfall time series in Pearl River basin exhibit no long-term correlations. It is also found that K(2)K(2) and elevation series are negatively correlated. It shows a relationship between topography and rainfall variability.

Infrared and Raman spectroscopic characterization of the phosphate mineral leucophosphite - K(Fe3+)2(PO4)2(OH)·2(H2O)

The phosphate mineral leucophosphite K(Fe2)3þ(PO4)2(OH) · 2H2O has been characterized by SEM-EDS, Raman, and infrared spectro- scopic measurements. The mineral is predominantly a K and Fe phosphate with some minor substitution of Al in the Fe3þ site. Raman bands at 994 and 1058 cm-1 are assigned to the symmetric stretching modes of PO3- and HPO2- units. The Raman bands at 1104, 1135, and 1177 cm-1 are assigned to the PO3- and HPO2- antisymmetric stretching modes. Raman and infrared spectra in the 2600–3800 cm-1 region show a complex set of overlapping bands, which may be resolved into the component bands. The Raman bands observed at 3325, 3355, and 3456 cm-1 are attributed to water stretching vibrations, and in the infrared spectrum, bands at 3237, 3317, and 3453 cm-1 are assigned to water stretching bands.

A vibrational spectroscopic study of the silicate mineral harmotome – (Ba,Na,K)1-2(Si,Al)8O16⋅6H2O – A natural zeolite

The mineral harmotome (Ba,Na,K)1-2(Si,Al)8O16⋅6H2O is a crystalline sodium calcium silicate which has the potential to be used in plaster boards and other industrial applications. It is a natural zeolite with catalytic potential. Raman bands at 1020 and 1102 cm−1 are assigned to the SiO stretching vibrations of three dimensional siloxane units. Raman bands at 428, 470 and 491 cm−1 are assigned to OSiO bending modes. The broad Raman bands at around 699, 728, 768 cm−1 are attributed to water librational modes. Intense Raman bands in the 3100 to 3800 cm−1 spectral range are assigned to OH stretching vibrations of water in harmotome. Infrared spectra are in harmony with the Raman spectra. A sharp infrared band at 3731 cm−1 is assigned to the OH stretching vibration of SiOH units. Raman spectroscopy with complimentary infrared spectroscopy enables the characterization of the silicate mineral harmotome.

K-tree : large scale document clustering

We introduce K-tree in an information retrieval context. It is an efficient approximation of the k-means clustering algorithm. Unlike k-means it forms a hierarchy of clusters. It has been extended to address issues with sparse representations. We compare performance and quality to CLUTO using document collections. The K-tree has a low time complexity that is suitable for large document collections. This tree structure allows for efficient disk based implementations where space requirements exceed that of main memory.

The knowledge advantage (K-Adv): unleashing creativity and innovation

The K-Adv has been developed around the concept that it comprises an ICT enabling infrastructure that encompasses ICT hardware and software infrastructure facilities together with an enabling ICT support system; a leadership infrastructure support system that provides the vision for its implementation and the realisation capacity for the vision to be realised; and the necessary people infrastructure that includes the people capabilities and capacities supported by organisational processes that facilitates this resource to be mobilised.

Document clustering with K-tree

This paper describes the approach taken to the XML Mining track at INEX 2008 by a group at the Queensland University of Technology. We introduce the K-tree clustering algorithm in an Information Retrieval context by adapting it for document clustering. Many large scale problems exist in document clustering. K-tree scales well with large inputs due to its low complexity. It offers promising results both in terms of efficiency and quality. Document classification was completed using Support Vector Machines.

4-Chloroanilinium 2-carboxy-4,5-dichlorobenzoate

The structure of the 1:1 proton-transfer compound of 4-chloroaniline with 4,5-dichlorophthalic acid (DCPA), viz. C6H7ClN+ C8H3Cl2O4-, has been determined at 130 K. The non-planar hydrogen phthalate anions and the 4-chloroanilinium cations form two-dimensional O-H...O and N-H...O hydrogen-bonded substructures which have no peripheral extension. Between the sheets there are weak \p--\p associations between alternating cation--anion aromatic ring systems [shortest centroid separation, 3.735(4)A].

1,10-phenanthrolin-1-ium 2-carboxy-4,5-dichlorobenzoate

In the structure of the 1:1 proton-transfer compound of 1,10-phenanthroline with 4,5-dichlorophthalic acid, C12H9N2+ C8H3Cl2O4-, determined at 130 K, the 1,10-phenanthroline cation and the hydrogen 4,5-dichlorophthalate anion associate through a single N-H...O(carboxyl) hydrogen bond giving discrete units which have no extension except through a number of weak cation C-H...O(anion) associations and weak cation--anion aromatic ring pi-pi interactions [minimum centroid separation, 3.6815(12)A]. The anions are essentially planar [maximum deviation 0.214(1)A (a carboxyl O)] with the syn-related H atom of the carboxyl group forming a short intramolecular O-H...O(carboxyl) hydrogen bond.

Zero- one- and two-dimensional hydrogen-bonded structures in the 1:1 proton-transfer compounds of 4,5-dichlorophthalic acid with the monocyclic heteroaromatic Lewis bases 2-aminopyrimidine, nicotinamide and isonicotinamide

The structures of the anhydrous 1:1 proton-transfer compounds of 4,5-dichlorophthalic acid (DCPA) with the monocyclic heteroaromatic Lewis bases 2-aminopyrimidine, 3-(aminocarboxy) pyridine (nicotinamide) and 4-(aminocarbonyl) pyridine (isonicotinamide), namely 2-aminopyrimidinium 2-carboxy-4,5-dichlorobenzoate C4H6N3+ C8H3Cl2O4- (I), 3-(aminocarbonyl) pyridinium 2-carboxy-4,5-dichlorobenzoate C6H7N2O+ C8H3Cl2O4- (II) and the unusual salt adduct 4-(aminocarbonyl) pyridinium 2-carboxy-4,5-dichlorobenzoate 2-carboxymethyl-4,5-dichlorobenzoic acid (1/1/1) C6H7N2O+ C8H3Cl2O4-.C9H6Cl2O4 (III) have been determined at 130 K. Compound (I) forms discrete centrosymmetric hydrogen-bonded cyclic bis(cation--anion) units having both R2/2(8) and R2/1(4) N-H...O interactions. In compound (II) the primary N-H...O linked cation--anion units are extended into a two-dimensional sheet structure via amide-carboxyl and amide-carbonyl N-H...O interactions. The structure of (III) reveals the presence of an unusual and unexpected self-synthesized methyl monoester of the acid as an adduct molecule giving one-dimensional hydrogen-bonded chains. In all three structures the hydrogen phthalate anions are

Unusual hydrate stabilization in the two-dimensional layered structure of quinacrinium bis(2-carboxy-4,5-dichlorobenzoate) tetrahydrate, a proton-transfer compound of the drug quinacrine

The crystal structure of the hydrated proton-transfer compound of the drug quinacrine [rac-N'-(6-chloro-2-methoxyacridin-9-yl)-N,N-diethylpentane-1,4-diamine] with 4,5-dichlorophthalic acid, C23H32ClN3O2+ . 2(C8H3Cl2O4-).4H2O (I), has been determined at 200 K. The four labile water molecules of solvation form discrete ...O--H...O--H... hydrogen-bonded chains parallel to the quinacrine side chain, the two N--H groups of which act as hydrogen-bond donors for two of the water acceptor molecules. The other water molecules, as well as the acridinium H atom, also form hydrogen bonds with the two anion species and extend the structure into two-dimensional sheets. Between these sheets there are also weak cation--anion and anion--anion pi-pi aromatic ring interactions. This structure represents only the third example of a simple quinacrine derivative for which structural data are available but differs from the other two in that it is unstable in the X-ray beam due to efflorescence, probably associated with the destruction of the unusual four-membered water chain structures.

Proton-transfer versus nontransfer in compounds of the diazo-dye precursor 4-(phenyldiazenyl) aniline (aniline yellow) with strong organic acids: the 5-sulfosalicylate and the dichroic benzenesulfonate salts, and the 1:2 adduct with 3,5-dinitrobenzoic

The structures of two 1:1 proton-transfer red-black dye compounds formed by reaction of aniline yellow [4-(phenyldiazenyl)aniline] with 5-sulfosalicylic acid and benzenesulfonic acid, and a 1:2 nontransfer adduct compound with 3,5-dinitrobenzoic acid have been determined at either 130 or 200 K. The compounds are 2-(4-aminophenyl)-1-phenylhydrazin-1-ium 3-carboxy-4-hydroxybenzenesulfonate methanol solvate, C12H12N3+.C7H5O6S-.CH3OH (I), 2-(4-aminophenyl)-1-hydrazin-1-ium 4-(phenydiazinyl)anilinium bis(benzenesulfonate), 2C12H12N3+.2C6H5O3S-, (II) and 4-(phenyldiazenyl)aniline-3,5-dinitrobenzoic acid (1/2) C12H11N3.2C~7~H~4~N~2~O~6~, (III). In compound (I) the diaxenyl rather than the aniline group of aniline yellow is protonated and this group subsequently akes part in a primary hydrogen-bonding interaction with a sulfonate O-atom acceptor, producing overall a three-dimensional framework structure. A feature of the hydrogen bonding in (I) is a peripheral edge-on cation-anion association involving aromatic C--H...O hydrogen bonds, giving a conjoint R1/2(6)R1/2(7)R2/1(4)motif. In the dichroic crystals of (II), one of the two aniline yellow species in the asymmetric unit is diazenyl-group protonated while in the other the aniline group is protonated. Both of these groups form hydrogen bonds with sulfonate O-atom acceptors and thee, together with other associations give a one-dimensional chain structure. In compound (III), rather than proton-transfer, there is a preferential formation of a classic R2/2(8) cyclic head-to-head hydrogen-bonded carboxylic acid homodimer between the two 3,5-dinitrobenzoic acid molecules, which in association with the aniline yellow molecule that is disordered across a crystallographic inversion centre, result in an overall two-dimensional ribbon structure. This work has shown the correlation between structure and observed colour in crystalline aniline yellow compounds, illustrated graphically in the dichroic benzenesulfonate compound.