Is the Unitarity of the quark-mixing-CKM-matrix violated in neutron β\beta-decay?

We report on a new measurement of neutron $\beta$-decay asymmetry. From the result \linebreak $A_0$ = -0.1189(7), we derive the ratio of the axial vector to the vector coupling constant $\lambda$ = ${\it g_A/g_V}$ = -1.2739(19). When included in the world average for the neutron lifetime $\tau$ = 885.7(7)s, this gives the first element of the Cabibbo-Kobayashi-Maskawa (CKM) matrix $V_{ud}$. With this value and the Particle Data Group values for $V_{us}$ and $V_{ub}$, we find a deviation from the unitarity condition for the first row of the CKM matrix of $\Delta$ = 0.0083(28), which is 3.0 times the stated error

Cattle chosen, the story of the first group settlement in Western Australia, 1829 to 1841,

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Resisting reductionism in mathematics pedagogy

Although breaking down a mathematical problem into smaller parts can often be an effective solution strategy, when the same reductionist approach is applied to mathematics pedagogy the effects are far from beneficial for students. Mathematics pedagogy in UK schools is gaining an increasingly reductionist flavour, as seen in an excessive focus on bite-sized learning objectives and a tendency for mathematics teachers to path-smooth their students’ learning. I argue that a reductionist mathematics pedagogy severely restricts students’ opportunities to engage in authentic mathematical thinking and deprives them of the enjoyment of solving richer, more worthwhile problems, which would forge connections across diverse areas of the subject. I attribute the rise of a reductionist mathematics pedagogy partly to an assessment-dominated curriculum and partly to a systemic de-professionalisation of teachers through a performative accountability culture in which they are constantly required to prove to non-specialist managers that they are effective. I argue that pedagogical reductionism in mathematics must be resisted in favour of a more holistic approach, in which students are able to bring a variety of mathematical knowledge and skills to bear on rich, challenging and non-routine mathematical tasks. Some principles for achieving this are outlined and some examples are given