Search for: All records

Students exhibiting mature number sense make sense of numbers and operations, use reasoning to notice patterns, and flexibly select the most effective and efficient problem-solving strategies (McIntosh et al., 1997; Reys et al., 1999; Yang, 2005). Despite being highlighted in national standards and policy documents (CCSS, 2010; NCTM, 2000, 2014), students’ mature number sense and its nomological network are not yet well specified. For example, how does students’ mature number sense relate to their knowledge of fractions and their grade-level mathematics achievement? We analyzed 129 middle school students’ scores on measures of mature number sense, fraction and decimal computation, and grade-level mathematics achievement. We found mature number sense to be measurably distinct from their fraction and decimal knowledge and uniquely associated with students’ grade-level mathematics achievement. 

Abstract Adopting the Standard Halo Model (SHM) of an isotropic Maxwellian velocity distribution for dark matter (DM) particles in the Galaxy, the most stringent current constraints on their spin-dependent scattering cross-section with nucleons come from the IceCube neutrino observatory and the PICO-60 $$\hbox {C}_3\hbox {F}_8$$ C 3 F 8 superheated bubble chamber experiments. The former is sensitive to high energy neutrinos from the self-annihilation of DM particles captured in the Sun, while the latter looks for nuclear recoil events from DM scattering off nucleons. Although slower DM particles are more likely to be captured by the Sun, the faster ones are more likely to be detected by PICO. Recent N-body simulations suggest significant deviations from the SHM for the smooth halo component of the DM, while observations hint at a dominant fraction of the local DM being in substructures. We use the method of Ferrer et al. (JCAP 1509: 052, 2015) to exploit the complementarity between the two approaches and derive conservative constraints on DM-nucleon scattering. Our results constrain $$\sigma _{\mathrm{SD}} \lesssim 3 \times 10^{-39} \mathrm {cm}^2$$ σ SD ≲ 3 × 10 - 39 cm 2 ( $$6 \times 10^{-38} \mathrm {cm}^2$$ 6 × 10 - 38 cm 2 ) at $$\gtrsim 90\%$$ ≳ 90 % C.L. for a DM particle of mass 1 TeV annihilating into $$\tau ^+ \tau ^-$$ τ + τ - ( $$b\bar{b}$$ b b ¯ ) with a local density of $$\rho _{\mathrm{DM}} = 0.3~\mathrm {GeV/cm}^3$$ ρ DM = 0.3 GeV / cm 3 . The constraints scale inversely with $$\rho _{\mathrm{DM}}$$ ρ DM and are independent of the DM velocity distribution.