Assessing mathematical problem solving using comparative judgement

There is an increasing demand from employers and universities for school leavers to be able to apply their mathematical knowledge to problem solving in varied and unfamiliar contexts. These aspects are however neglected in most examinations of mathematics and, consequentially, in classroom teaching. One barrier to the inclusion of mathematical problem solving in assessment is that the skills involved are difficult to define and assess objectively. We present two studies that test a method called comparative judgement (CJ) that might be well suited to assessing mathematical problem solving. CJ is an alternative to traditional scoring that is based on collective expert judgements of students’ work rather than item-by-item scoring schemes. In Study 1 we used CJ to assess traditional mathematics tests and found it performed validly and reliably. In Study 2 we used CJ to assess mathematical problem-solving tasks and again found it performed validly and reliably. We discuss the implications of the results for further research and the implications of CJ for the design of mathematical problem-solving tasks

The normal breast microenvironment of premenopausal women differentially influences the behavior of breast cancer cells in vitro and in vivo

<p>Abstract</p> <p>Background</p> <p>Breast cancer studies frequently focus on the role of the tumor microenvironment in the promotion of cancer; however, the influence of the normal breast microenvironment on cancer cells remains relatively unknown. To investigate the role of the normal breast microenvironment on breast cancer cell tumorigenicity, we examined whether extracellular matrix molecules (ECM) derived from premenopausal African-American (AA) or Caucasian-American (CAU) breast tissue would affect the tumorigenicity of cancer cells <it>in vitro </it>and <it>in vivo</it>. We chose these two populations because of the well documented predisposition of AA women to develop aggressive, highly metastatic breast cancer compared to CAU women.</p> <p>Methods</p> <p>The effects of primary breast fibroblasts on tumorigenicity were analyzed via real-time PCR arrays and mouse xenograft models. Whole breast ECM was isolated, analyzed via zymography, and its effects on breast cancer cell aggressiveness were tested <it>in vitro </it>via soft agar and invasion assays, and <it>in vivo </it>via xenograft models. Breast ECM and hormone metabolites were analyzed via mass spectrometry.</p> <p>Results</p> <p>Mouse mammary glands humanized with premenopausal CAU fibroblasts and injected with primary breast cancer cells developed significantly larger tumors compared to AA humanized glands. Examination of 164 ECM molecules and cytokines from CAU-derived fibroblasts demonstrated a differentially regulated set of ECM proteins and increased cytokine expression. Whole breast ECM was isolated; invasion and soft agar assays demonstrated that estrogen receptor (ER)^-, progesterone receptor (PR)/PR^-cells were significantly more aggressive when in contact with AA ECM, as were ER⁺/PR⁺cells with CAU ECM. Using zymography, protease activity was comparatively upregulated in CAU ECM. In xenograft models, CAU ECM significantly increased the tumorigenicity of ER⁺/PR⁺cells and enhanced metastases. Mass spectrometry analysis of ECM proteins showed that only 1,759 of approximately 8,000 identified were in common. In the AA dataset, proteins associated with breast cancer were primarily related to tumorigenesis/neoplasia, while CAU unique proteins were involved with growth/metastasis. Using a novel mass spectrometry method, 17 biologically active hormones were measured; estradiol, estriol and 2-methoxyestrone were significantly higher in CAU breast tissue.</p> <p>Conclusions</p> <p>This study details normal premenopausal breast tissue composition, delineates potential mechanisms for breast cancer development, and provides data for further investigation into the role of the microenvironment in cancer disparities.</p

H2A.Z Acidic Patch Couples Chromatin Dynamics to Regulation of Gene Expression Programs during ESC Differentiation

The histone H2A variant H2A.Z is essential for embryonic development and for proper control of developmental gene expression programs in embryonic stem cells (ESCs). Divergent regions of amino acid sequence of H2A.Z likely determine its functional specialization compared to core histone H2A. For example, H2A.Z contains three divergent residues in the essential C-terminal acidic patch that reside on the surface of the histone octamer as an uninterrupted acidic patch domain; however, we know little about how these residues contribute to chromatin structure and function. Here, we show that the divergent amino acids Gly92, Asp97, and Ser98 in the H2A.Z C-terminal acidic patch (H2A.Z[superscript AP3]) are critical for lineage commitment during ESC differentiation. H2A.Z is enriched at most H3K4me3 promoters in ESCs including poised, bivalent promoters that harbor both activating and repressive marks, H3K4me3 and H3K27me3 respectively. We found that while H2A.Z[superscript AP3] interacted with its deposition complex and displayed a highly similar distribution pattern compared to wild-type H2A.Z, its enrichment levels were reduced at target promoters. Further analysis revealed that H2A.Z[superscript AP3] was less tightly associated with chromatin, suggesting that the mutant is more dynamic. Notably, bivalent genes in H2A.Z[superscript AP3] ESCs displayed significant changes in expression compared to active genes. Moreover, bivalent genes in H2A.Z[superscript AP3] ESCs gained H3.3, a variant associated with higher nucleosome turnover, compared to wild-type H2A.Z. We next performed single cell imaging to measure H2A.Z dynamics. We found that H2A.Z[superscript AP3] displayed higher mobility in chromatin compared to wild-type H2A.Z by fluorescent recovery after photobleaching (FRAP). Moreover, ESCs treated with the transcriptional inhibitor flavopiridol resulted in a decrease in the H2A.Z[superscript AP3] mobile fraction and an increase in its occupancy at target genes indicating that the mutant can be properly incorporated into chromatin. Collectively, our work suggests that the divergent residues in the H2A.Z acidic patch comprise a unique domain that couples control of chromatin dynamics to the regulation of developmental gene expression patterns during lineage commitment.Massachusetts Life Sciences Center (David H. Koch Institute for Integrative Cancer Research at MIT Core Grant P30-CA14051)National Science Foundation (U.S.). Emergent Behaviors of Integrated Cellular Systems (Grant CBET-0939511)MIT Faculty Start-up FundMassachusetts Institute of Technology. Computational and Systems Biology Initiative (Merck & Co. Postdoctoral Fellowship

Molecular phylogeny and timing of diversification in Alpine Rhithrogena (Ephemeroptera: Heptageniidae).

BACKGROUND: Larvae of the Holarctic mayfly genus Rhithrogena Eaton, 1881 (Ephemeroptera, Heptageniidae) are a diverse and abundant member of stream and river communities and are routinely used as bio-indicators of water quality. Rhithrogena is well diversified in the European Alps, with a number of locally endemic species, and several cryptic species have been recently detected. While several informal species groups are morphologically well defined, a lack of reliable characters for species identification considerably hampers their study. Their relationships, origin, timing of speciation and mechanisms promoting their diversification in the Alps are unknown. RESULTS: Here we present a species-level phylogeny of Rhithrogena in Europe using two mitochondrial and three nuclear gene regions. To improve sampling in a genus with many cryptic species, individuals were selected for analysis according to a recent DNA-based taxonomy rather than traditional nomenclature. A coalescent-based species tree and a reconstruction based on a supermatrix approach supported five of the species groups as monophyletic. A molecular clock, mapped on the most resolved phylogeny and calibrated using published mitochondrial evolution rates for insects, suggested an origin of Alpine Rhithrogena in the Oligocene/Miocene boundary. A diversification analysis that included simulation of missing species indicated a constant speciation rate over time, rather than any pronounced periods of rapid speciation. Ancestral state reconstructions provided evidence for downstream diversification in at least two species groups. CONCLUSIONS: Our species-level analyses of five gene regions provide clearer definitions of species groups within European Rhithrogena. A constant speciation rate over time suggests that the paleoclimatic fluctuations, including the Pleistocene glaciations, did not significantly influence the tempo of diversification of Alpine species. A downstream diversification trend in the hybrida and alpestris species groups supports a previously proposed headwater origin hypothesis for aquatic insects

Physical mechanical and tablet formation properties of hydroxypropylcellulose: In pure form and in mixtures

The aim of the study was to analyze hydroxypropylcellulose (HPC) in pure form and in excipient mixtures and to relate its physical and chemical properties to tablet binder functionality. The materials used were Klucel hydroxypropylcellulose grades ranging from low to high molecular weight (80–1000 kDa) of regular particle size (250 µm mean size) and fine particle size (80 µm mean size). These were compared with microcrystalline cellulose, spray-dried lactose, and dicalcium phosphate dihydrate. Thermal behavior of HPC was analyzed by modulated temperature differential scanning calorimetry (MTDSC). Tablets of the pure materials and of dry blends with 4% low viscosity, fine particle HPC and 30% high viscosity, fine particle HPC were produced on an instrumented eccentric tableting machine at 3 relative humidities. The 3-dimensional (3-D) model with the parameters time plasticity d, pressure plasticity e, and the twisting angle ω, the inverse of fast elastic decompression was compared with the Heckel method for characterization of compaction. Elastic recovery and compactibility were also studied. The results show that HPC tablet formation is characterized by high plastic deformation. The d, e, and ω values were markedly higher as compared with the reference materials. Plasticity was highest for the fine particle size HPC types. Maximum compactibility was observed for low molecular weight, fine particle size HPC. Tableting of the mixtures showed deformation, which was strongly influenced by HPC. Plasticity and crushing force of formed tablets was increased. In conclusion, HPC is characterized by strong plastic deformation properties, which are molecular weight and particle size dependent

Linear redshift distortions: A review

Abstract. Redshift maps of galaxies in the Universe are distorted by the peculiar velocities of galaxies along the line of sight. The amplitude of the distortions on large, linear scales yields a measurement of the linear redshift distortion parameter, which is β ≈ Ω0.6 0 /b in standard cosmology with cosmological density Ω0 and light-to-mass bias b. All measurements of β from linear redshift distortions published up to mid 1997 are reviewed. The average and standard deviation of the reported values is βoptical = 0.52 ± 0.26 for optically selected galaxies, and βIRAS = 0.77 ± 0.22 for IRAS selected galaxies. The implied relative bias is boptical/bIRAS ≈ 1.5. If optical galaxies are unbiased, then Ω0 = 0.33 +0.32 −0.22 are unbiased, then Ω0 = 0.63 +0.3