skip to main content

Title: Social Networks and Instructional Reform in STEM: The Teaching-Research Nexus

Instructional reform in STEM aims for the widespread adoption of evidence based instructional practices (EBIPS), practices that implement active learning. Research recognizes that faculty social networks regarding discussion or advice about teaching may matter to such efforts. But teaching is not the only priority for university faculty – meeting research expectations is at least as important and, often, more consequential for tenure and promotion decisions. We see value in understanding how research networks, based on discussion and advice about research matters, relate to teaching networks to see if and how such networks could advance instructional reform efforts. Our research examines data from three departments (biology, chemistry, and geosciences) at three universities that had recently received funding to enhance adoption of EBIPs in STEM fields. We evaluate exponential random graph models of the teaching network and find that (a) the existence of a research tie from one faculty member$$i$$ito another$$j$$jenhances the prospects of a teaching tie from$$i$$ito$$j$$j, but (b) even though faculty highly placed in the teaching network are more likely to be extensive EBIP users, faculty highly placed in the research network are not, dimming prospects for leveraging research networks to advance STEM instructional reforms.

; ; ; ; ; ; ; ; ; ; ; ; ; ;
Publication Date:
Journal Name:
Innovative Higher Education
Springer Science + Business Media
Sponsoring Org:
National Science Foundation
More Like this
  1. Abstract

    Let us fix a primepand a homogeneous system ofmlinear equations$$a_{j,1}x_1+\dots +a_{j,k}x_k=0$$aj,1x1++aj,kxk=0for$$j=1,\dots ,m$$j=1,,mwith coefficients$$a_{j,i}\in \mathbb {F}_p$$aj,iFp. Suppose that$$k\ge 3m$$k3m, that$$a_{j,1}+\dots +a_{j,k}=0$$aj,1++aj,k=0for$$j=1,\dots ,m$$j=1,,mand that every$$m\times m$$m×mminor of the$$m\times k$$m×kmatrix$$(a_{j,i})_{j,i}$$(aj,i)j,iis non-singular. Then we prove that for any (large)n, any subset$$A\subseteq \mathbb {F}_p^n$$AFpnof size$$|A|> C\cdot \Gamma ^n$$|A|>C·Γncontains a solution$$(x_1,\dots ,x_k)\in A^k$$(x1,,xk)Akto the given system of equations such that the vectors$$x_1,\dots ,x_k\in A$$x1,,xkAare all distinct. Here,Cand$$\Gamma $$Γare constants only depending onp,mandksuch that$$\Gamma Γ<p. The crucial point here is the condition for the vectors$$x_1,\dots ,x_k$$x1,,xkin the solution$$(x_1,\dots ,x_k)\in A^k$$(x1,,xk)Akto be distinct. If we relax this condition and only demand that$$x_1,\dots ,x_k$$x1,,xkare not all equal, then the statement would follow easily from Tao’s slice rank polynomial method. However, handling the distinctness condition is much harder, and requires a new approach. While all previous combinatorial applications of the slice rank polynomial method have relied on the slice rank of diagonal tensors, we use a slice rank argument for a non-diagonal tensor in combination with combinatorial and probabilistic arguments.

  2. Abstract

    Let$$X\rightarrow {{\mathbb {P}}}^1$$XP1be an elliptically fiberedK3 surface, admitting a sequence$$\omega _{i}$$ωiof Ricci-flat metrics collapsing the fibers. LetVbe a holomorphicSU(n) bundle overX, stable with respect to$$\omega _i$$ωi. Given the corresponding sequence$$\Xi _i$$Ξiof Hermitian–Yang–Mills connections onV, we prove that, ifEis a generic fiber, the restricted sequence$$\Xi _i|_{E}$$Ξi|Econverges to a flat connection$$A_0$$A0. Furthermore, if the restriction$$V|_E$$V|Eis of the form$$\oplus _{j=1}^n{\mathcal {O}}_E(q_j-0)$$j=1nOE(qj-0)forndistinct points$$q_j\in E$$qjE, then these points uniquely determine$$A_0$$A0.

  3. Abstract

    We continue the program of proving circuit lower bounds via circuit satisfiability algorithms. So far, this program has yielded several concrete results, proving that functions in$\mathsf {Quasi}\text {-}\mathsf {NP} = \mathsf {NTIME}[n^{(\log n)^{O(1)}}]$Quasi-NP=NTIME[n(logn)O(1)]and other complexity classes do not have small circuits (in the worst case and/or on average) from various circuit classes$\mathcal { C}$C, by showing that$\mathcal { C}$Cadmits non-trivial satisfiability and/or#SAT algorithms which beat exhaustive search by a minor amount. In this paper, we present a new strong lower bound consequence of having a non-trivial#SAT algorithm for a circuit class${\mathcal C}$C. Say that a symmetric Boolean functionf(x1,…,xn) issparseif it outputs 1 onO(1) values of${\sum }_{i} x_{i}$ixi. We show that for every sparsef, and for all “typical”$\mathcal { C}$C, faster#SAT algorithms for$\mathcal { C}$Ccircuits imply lower bounds against the circuit class$f \circ \mathcal { C}$fC, which may bestrongerthan$\mathcal { C}$Citself. In particular:

    #SAT algorithms fornk-size$\mathcal { C}$C-circuits running in 2n/nktime (for allk) implyNEXPdoes not have$(f \circ \mathcal { C})$(fC)-circuits of polynomial size.

    #SAT algorithms for$2^{n^{{\varepsilon }}}$2nε-size$\mathcal { C}$C-circuits running in$2^{n-n^{{\varepsilon }}}$2nnεtime (for someε> 0) implyQuasi-NPdoes not have$(f \circ \mathcal { C})$(fC)-circuits of polynomial size.

    Applying#SAT algorithms from the literature, one immediate corollary of our results is thatQuasi-NPdoes not haveEMAJACC0THRcircuits of polynomialmore »size, whereEMAJis the “exact majority” function, improving previous lower bounds againstACC0[Williams JACM’14] andACC0THR[Williams STOC’14], [Murray-Williams STOC’18]. This is the first nontrivial lower bound against such a circuit class.

    « less
  4. Abstract

    Sequence mappability is an important task in genome resequencing. In the (km)-mappability problem, for a given sequenceTof lengthn, the goal is to compute a table whoseith entry is the number of indices$$j \ne i$$jisuch that the length-msubstrings ofTstarting at positionsiandjhave at mostkmismatches. Previous works on this problem focused on heuristics computing a rough approximation of the result or on the case of$$k=1$$k=1. We present several efficient algorithms for the general case of the problem. Our main result is an algorithm that, for$$k=O(1)$$k=O(1), works in$$O(n)$$O(n)space and, with high probability, in$$O(n \cdot \min \{m^k,\log ^k n\})$$O(n·min{mk,logkn})time. Our algorithm requires a careful adaptation of thek-errata trees of Cole et al. [STOC 2004] to avoid multiple counting of pairs of substrings. Our technique can also be applied to solve the all-pairs Hamming distance problem introduced by Crochemore et al. [WABI 2017]. We further develop$$O(n^2)$$O(n2)-time algorithms to computeall(km)-mappability tables for a fixedmand all$$k\in \{0,\ldots ,m\}$$k{0,,m}or a fixedkand all$$m\in \{k,\ldots ,n\}$$m{k,,n}. Finally, we show that, for$$k,m = \Theta (\log n)$$k,m=Θ(logn), the (km)-mappability problem cannot be solved in strongly subquadratic time unless the Strong Exponential Time Hypothesis fails. This is an improved and extended version of a paper presented at SPIRE 2018.

  5. Abstract

    In this paper we disprove part of a conjecture of Lieb and Thirring concerning the best constant in their eponymous inequality. We prove that the best Lieb–Thirring constant when the eigenvalues of a Schrödinger operator$$-\Delta +V(x)$$-Δ+V(x)are raised to the power$$\kappa $$κis never given by the one-bound state case when$$\kappa >\max (0,2-d/2)$$κ>max(0,2-d/2)in space dimension$$d\ge 1$$d1. When in addition$$\kappa \ge 1$$κ1we prove that this best constant is never attained for a potential having finitely many eigenvalues. The method to obtain the first result is to carefully compute the exponentially small interaction between two Gagliardo–Nirenberg optimisers placed far away. For the second result, we study the dual version of the Lieb–Thirring inequality, in the same spirit as in Part I of this work Gontier et al. (The nonlinear Schrödinger equation for orthonormal functions I. Existence of ground states. Arch. Rat. Mech. Anal, 2021. In a different but related direction, we also show that the cubic nonlinear Schrödinger equation admits no orthonormal ground state in 1D, for more than one function.