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1701.07493v1_34

http://arxiv.org/abs/1701.07493v1

and sub-diffusive expansion, a clear trend towards arrested transport (γ∼ 0) is found for Δ/t ≫ 1. Combined with the observation of exponential localization of the site populations in Fig. FIG:fig2(b,iv) and Fig. FIG:fig2(d), these observations are consistent with a crossover in our 21-site system from metallic behavior to quantum localization for Δ/t ≳ 2.Our observations of a crossover from ballistic expansion (γ∼ 2) to nearly diffusive transport (γ∼ 1) for randomly fluctuating tunneling phase

1701.07493v1_35

http://arxiv.org/abs/1701.07493v1

(γ∼ 1) for randomly fluctuating tunneling phase disorder are also summarized in Fig. FIG:fig3(e). In the experimentally-accessible regime of low to moderate effective thermal energies (k_B T / t ≲ 1), our experimental data points (blue squares) match up well with numerical simulation (open black circles). For the magnitude of tunneling energy used in these experiments, we are restricted from exploring higher effective temperatures (k_B T /t ≳ 1), as rapid variations of the tunneling phases

1701.07493v1_36

http://arxiv.org/abs/1701.07493v1

≳ 1), as rapid variations of the tunneling phases introduce spurious spectral components of the Bragg laser fields that could drive undesired transitions. Simulations in this high-temperature regime suggest that the expansion exponent should rise back up for increasing temperatures, saturating to a value γ∼ 2. This results from the fact that the time-averaged phase effectively vanishes when the timescale of pseudorandom phase variations is much shorter than the tunneling time.The demonstrated

1701.07493v1_37

http://arxiv.org/abs/1701.07493v1

shorter than the tunneling time.The demonstrated levels of local and time-dependent control over tunneling elements and site energies in our synthetic momentum-space lattice have allowed us to perform first-of-their-kind explorations of annealed disorder in an atomic system. Such an approach based on synthetic dimensions should enable myriad future explorations of engineered Floquet dynamics <cit.> and novel disordered lattices <cit.>. Furthermore, the realization of designer disorder in a

1701.07493v1_38

http://arxiv.org/abs/1701.07493v1

the realization of designer disorder in a system that supports nonlinear atomic interactions <cit.> should permit us to explore novel aspects of many-body localization <cit.>.52 fxundefined [1]ifx#1fnum [1]#1firstoftwosecondoftwo fx [1]#1firstoftwosecondoftwonoop [0]secondoftworef[1]@startlink#1@href href[1]#1@endlink anitize@url [0]` 12`$12`&12`#12`1̂2`_12`%12 startlink[1] endlink[0]rl [1]href #1 @bib@innerbibempty[Sanchez-Palencia and Lewenstein(2010)]Sanchez-Palencia-Lewenstein-NP-2010

1701.07493v1_39

http://arxiv.org/abs/1701.07493v1

author author L. Sanchez-Palencia and author M. Lewenstein, 10.1038/nphys1507 journal journal Nat. Phys. volume 6,pages 87 (year 2010)NoStop [Moore et al.(1995)Moore, Robinson, Bharucha, Sundaram, and Raizen]Moore-Qdeltakicked-1995 author author F. L. Moore, author J. C. Robinson, author C. F. Bharucha, author B. Sundaram,and author M. G. Raizen, 10.1103/PhysRevLett.75.4598 journal journal Phys. Rev. Lett. volume 75, pages 4598 (year 1995)NoStop [Chabé et al.(2008)Chabé, Lemarié, Grémaud,

1701.07493v1_40

http://arxiv.org/abs/1701.07493v1

[Chabé et al.(2008)Chabé, Lemarié, Grémaud, Delande, Szriftgiser, and Garreau]Chabe-AndersonMetal-2008 author author J. Chabé, author G. Lemarié, author B. Grémaud, author D. Delande, author P. Szriftgiser,and author J. C. Garreau, 10.1103/PhysRevLett.101.255702 journal journal Phys. Rev. Lett. volume 101, pages 255702 (year 2008)NoStop [Roati et al.(2008)Roati, D'Errico, Fallani, Fattori, Fort, Zaccanti, Modugno, Modugno, and Inguscio]Roati-AndersonLocalization-2008 author author G. Roati,

1701.07493v1_41

http://arxiv.org/abs/1701.07493v1

author author G. Roati, author C. D'Errico, author L. Fallani, author M. Fattori, author C. Fort, author M. Zaccanti, author G. Modugno, author M. Modugno,and author M. Inguscio, 10.1038/nature07071 journal journal Nature volume 453, pages 895 (year 2008)NoStop [Billy et al.(2008)Billy, Josse, Zuo, Bernard, Hambrecht, Lugan, Clément, Sanchez-Palencia, Bouyer,and Aspect]Billy-AndersonLocalization-2008 author author J. Billy, author V. Josse, author Z. Zuo, author A. Bernard, author B. Hambrecht,

1701.07493v1_42

http://arxiv.org/abs/1701.07493v1

Z. Zuo, author A. Bernard, author B. Hambrecht, author P. Lugan, author D. Clément, author L. Sanchez-Palencia, author P. Bouyer,and author A. Aspect, 10.1038/nature07000 journal journal Nature volume 453, pages 891 (year 2008)NoStop [Kondov et al.(2011)Kondov, McGehee, Zirbel, and DeMarco]KondovAnderson-2011 author author S. S. Kondov, author W. R. McGehee, author J. J. Zirbel,andauthor B. DeMarco, 10.1126/science.1209019 journal journal Science volume 334, pages 66 (year 2011)NoStop

1701.07493v1_43

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Science volume 334, pages 66 (year 2011)NoStop [Jendrzejewski et al.(2012)Jendrzejewski, Bernard, Müller, Cheinet, Josse, Piraud, Pezzé, Sanchez-Palencia, Aspect, and Bouyer]Jendre-3D-Anderson author author F. Jendrzejewski, author A. Bernard, author K. Müller, author P. Cheinet, author V. Josse, author M. Piraud, author L. Pezzé, author L. Sanchez-Palencia, author A. Aspect,and author P. Bouyer, 10.1038/nphys2256 journal journal Nat. Phys. volume 8, pages 398 (year 2012)NoStop [Semeghini

1701.07493v1_44

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volume 8, pages 398 (year 2012)NoStop [Semeghini et al.(2015)Semeghini, Landini, Castilho, Roy, Spagnolli, Trenkwalder, Fattori, Inguscio, and Modugno]Ing-MobEdge author author G. Semeghini, author M. Landini, author P. Castilho, author S. Roy, author G. Spagnolli, author A. Trenkwalder, author M. Fattori, author M. Inguscio,and author G. Modugno, 10.1038/nphys3339 journal journal Nat. Phys. volume 11, pages 554 (year 2015)NoStop [Fallani et al.(2007)Fallani, Lye, Guarrera, Fort, and

1701.07493v1_45

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et al.(2007)Fallani, Lye, Guarrera, Fort, and Inguscio]Fallani-TowardsBG-2007 author author L. Fallani, author J. E. Lye, author V. Guarrera, author C. Fort,and author M. Inguscio, 10.1103/PhysRevLett.98.130404 journal journal Phys. Rev. Lett. volume 98, pages 130404 (year 2007)NoStop [White et al.(2009)White, Pasienski, McKay, Zhou, Ceperley, and DeMarco]White-SpeckleDisorder-2009 author author M. White, author M. Pasienski, author D. McKay, author S. Q. Zhou, author D. Ceperley,and author

1701.07493v1_46

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author S. Q. Zhou, author D. Ceperley,and author B. DeMarco, 10.1103/PhysRevLett.102.055301 journal journal Phys. Rev. Lett. volume 102, pages 055301 (year 2009)NoStop [Pasienski et al.(2010)Pasienski, McKay, White, andDeMarco]Pasienski-Disorder-2010 author author M. Pasienski, author D. McKay, author M. White,and author B. DeMarco, 10.1038/nphys1726 journal journal Nat. Phys.volume 6, pages 677 (year 2010)NoStop [Gadway et al.(2011)Gadway, Pertot, Reeves, Vogt, andSchneble]Gadway-11-PRL author

1701.07493v1_47

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Reeves, Vogt, andSchneble]Gadway-11-PRL author author B. Gadway, author D. Pertot, author J. Reeves, author M. Vogt,and author D. Schneble, 10.1103/PhysRevLett.107.145306 journal journal Phys. Rev. Lett. volume 107, pages 145306 (year 2011)NoStop [Meldgin et al.(2016)Meldgin, Ray, Russ, Chen, Ceperley, and DeMarco]Carrie-Ray-NatPhys author author C. Meldgin, author U. Ray, author P. Russ, author D. Chen, author D. M. Ceperley,and author B. DeMarco, 10.1038/nphys3695 journal journal Nat. Phys.

1701.07493v1_48

http://arxiv.org/abs/1701.07493v1

10.1038/nphys3695 journal journal Nat. Phys. volume 4, pages 945 (year 2016)NoStop [D'Errico et al.(2014)D'Errico, Lucioni, Tanzi, Gori, Roux, McCulloch, Giamarchi, Inguscio, and Modugno]DErrico-1D-Dis author author C. D'Errico, author E. Lucioni, author L. Tanzi, author L. Gori, author G. Roux, author I. P. McCulloch, author T. Giamarchi, author M. Inguscio,and author G. Modugno, 10.1103/PhysRevLett.113.095301 journal journal Phys. Rev. Lett. volume 113, pages 095301 (year 2014)NoStop [Kondov

1701.07493v1_49

http://arxiv.org/abs/1701.07493v1

113, pages 095301 (year 2014)NoStop [Kondov et al.(2015)Kondov, McGehee, Xu, and DeMarco]Kondov-MBL author author S. S. Kondov, author W. R. McGehee, author W. Xu,and author B. DeMarco, 10.1103/PhysRevLett.114.083002 journal journal Phys. Rev. Lett. volume 114, pages 083002 (year 2015)NoStop [Schreiber et al.(2015)Schreiber, Hodgman, Bordia, Lüschen, Fischer, Vosk, Altman, Schneider, and Bloch]Schreiber842 author author M. Schreiber, author S. S. Hodgman, author P. Bordia, author H. P. Lüschen,

1701.07493v1_50

http://arxiv.org/abs/1701.07493v1

Hodgman, author P. Bordia, author H. P. Lüschen, author M. H. Fischer, author R. Vosk, author E. Altman, author U. Schneider,and author I. Bloch, 10.1126/science.aaa7432 journal journal Science volume 349, pages 842 (year 2015)NoStop [Choi et al.(2016)Choi, Hild, Zeiher, Schauß, Rubio-Abadal, Yefsah, Khemani, Huse, Bloch, and Gross]MBL-Gross author author J.-y. Choi, author S. Hild, author J. Zeiher, author P. Schauß, author A. Rubio-Abadal, author T. Yefsah, author V. Khemani, author

1701.07493v1_51

http://arxiv.org/abs/1701.07493v1

author T. Yefsah, author V. Khemani, author D. A.Huse, author I. Bloch,and author C. Gross, 10.1126/science.aaf8834 journal journal Science volume 352, pages 1547 (year 2016)NoStop [Yan et al.(2016)Yan, Hui, Rigol, and Scarola]MBL-Vito author author M. Yan, author H.-Y. Hui, author M. Rigol,and author V. W. Scarola, @noop(year 2016), http://arxiv.org/abs/1606.03444 arXiv:1606.03444 NoStop [Celi et al.(2014)Celi, Massignan, Ruseckas, Goldman, Spielman, Juzeli u̅ūnas, and

1701.07493v1_52

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Ruseckas, Goldman, Spielman, Juzeli u̅ūnas, and Lewenstein]Celi-ArtificialDim author author A. Celi, author P. Massignan, author J. Ruseckas, author N. Goldman, author I. B. Spielman, author G. Juzeli u̅ūnas,and author M. Lewenstein, 10.1103/PhysRevLett.112.043001 journal journal Phys. Rev. Lett. volume 112, pages 043001 (year 2014)NoStop [Stuhl et al.(2015)Stuhl, Lu, Aycock, Genkina, andSpielman]Stuhl-Edge-2015 author author B. K. Stuhl, author H.-I. Lu, author L. M. Aycock, author

1701.07493v1_53

http://arxiv.org/abs/1701.07493v1

author H.-I. Lu, author L. M. Aycock, author D. Genkina,and author I. B. Spielman, 10.1126/science.aaa8515 journal journal Science volume 349, pages 1514 (year 2015)NoStop [Mancini et al.(2015)Mancini, Pagano, Cappellini, Livi, Rider, Catani, Sias, Zoller, Inguscio, Dalmonte,and Fallani]Fallani-chiral-2015 author author M. Mancini, author G. Pagano, author G. Cappellini, author L. Livi, author M. Rider, author J. Catani, author C. Sias, author P. Zoller, author M. Inguscio, author

1701.07493v1_54

http://arxiv.org/abs/1701.07493v1

author P. Zoller, author M. Inguscio, author M. Dalmonte,andauthor L. Fallani, 10.1126/science.aaa8736 journal journal Science volume 349, pages 1510 (year 2015)NoStop [Meier et al.(2016a)Meier, An, andGadway]Meier-AtomOptics author author E. J. Meier, author F. A. An, and author B. Gadway, 10.1103/PhysRevA.93.051602 journal journal Phys. Rev. A volume 93, pages 051602 (year 2016a)NoStop [Meier et al.(2016b)Meier, An, andGadway]Meier-SSH author author E. J. Meier, author F. A. An, and author

1701.07493v1_55

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author E. J. Meier, author F. A. An, and author B. Gadway, http://dx.doi.org/10.1038/ncomms13986 journal journal Nat. Commun. volume 7, pages 13986 (year 2016b)NoStop [An et al.(2016)An, Meier, and Gadway]An-FluxLadder author author F. A. An, author E. J. Meier, and author B. Gadway,@noop(year 2016), http://arxiv.org/abs/1609.09467 arXiv:1609.09467 NoStop [Wall et al.(2016)Wall, Koller, Li, Zhang, Cooper, Ye, and Rey]Wall-Synth author author M. L. Wall, author A. P. Koller, author S. Li, author

1701.07493v1_56

http://arxiv.org/abs/1701.07493v1

Wall, author A. P. Koller, author S. Li, author X. Zhang, author N. R. Cooper, author J. Ye,and author A. M.Rey, 10.1103/PhysRevLett.116.035301 journal journal Phys. Rev. Lett. volume 116, pages 035301 (year 2016)NoStop [Kolkowitz et al.(2016)Kolkowitz, Bromley, Bothwell, Wall, Marti, Koller, Zhang, Rey, and Ye]Kolkowitz-Synth author author S. Kolkowitz, author S. L. Bromley, author T. Bothwell, author M. L. Wall, author G. E. Marti, author A. P. Koller, author X. Zhang, author A. M. Rey,and

1701.07493v1_57

http://arxiv.org/abs/1701.07493v1

Koller, author X. Zhang, author A. M. Rey,and author J. Ye, http://dx.doi.org/10.1038/nature20811 journal journal Nature volume advance online publication (year 2016)NoStop [Livi et al.(2016)Livi, Cappellini, Diem, Franchi, Clivati, Frittelli, Levi, Calonico, Catani, Inguscio,and Fallani]Livi-Synth author author L. F. Livi, author G. Cappellini, author M. Diem, author L. Franchi, author C. Clivati, author M. Frittelli, author F. Levi, author D. Calonico, author J. Catani, author

1701.07493v1_58

http://arxiv.org/abs/1701.07493v1

author D. Calonico, author J. Catani, author M. Inguscio,andauthor L. Fallani, 10.1103/PhysRevLett.117.220401 journal journal Phys. Rev. Lett. volume 117, pages 220401 (year 2016)NoStop [Gadway(2015)]Gadway-KSPACE author author B. Gadway, 10.1103/PhysRevA.92.043606 journal journal Phys. Rev. A volume 92, pages 043606 (year 2015)NoStop [Amir et al.(2009)Amir, Lahini, and Perets]LahiniDiffusion author author A. Amir, author Y. Lahini,andauthor H. B. Perets, 10.1103/PhysRevE.79.050105 journal

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http://arxiv.org/abs/1701.07493v1

H. B. Perets, 10.1103/PhysRevE.79.050105 journal journal Phys. Rev. E volume 79, pages 050105 (year 2009)NoStop [Price et al.(2016)Price, Ozawa, and Goldman]NateGold-TrapShake author author H. M. Price, author T. Ozawa,andauthor N. Goldman, @noop(year 2016), http://arxiv.org/abs/1605.09310 arXiv:1605.09310 NoStop [Christodoulides et al.(2003)Christodoulides, Lederer, and Silberberg]Christ-NatRev author author D. N. Christodoulides, author F. Lederer,and author Y. Silberberg, 10.1038/nature01936

1701.07493v1_60

http://arxiv.org/abs/1701.07493v1

author Y. Silberberg, 10.1038/nature01936 journal journal Nature volume 424, pages 817 (year 2003)NoStop [Schwartz et al.(2007)Schwartz, Bartal, Fishman, andSegev]And-Light-Seg-07 author author T. Schwartz, author G. Bartal, author S. Fishman,andauthor M. Segev, 10.1038/nature05623 journal journal Nature volume 446, pages 52 (year 2007)NoStop [Szameit and Nolte(2010)]SzameitReview-2010 author author A. Szameit and author S. Nolte, 10.1088/0953-4075/43/16/163001 journal journal J. Phys. B volume

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journal journal J. Phys. B volume 43, pages 163001 (year 2010)NoStop [Segev et al.(2013)Segev, Silberberg, and Christodoulides]AndersonLight-Review author author M. Segev, author Y. Silberberg, and author D. N. Christodoulides, 10.1038/nphoton.2013.30 journal journal Nat. Photon. volume 7, pages 197 (year 2013)NoStop [Aspuru-Guzik and Walther(2012)]PhotRev-NatPhys-2012 author author A. Aspuru-Guzik and author P. Walther, doi:10.1038/nphys2253 journal journal Nat. Phys. volume 8,pages 285 (year

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journal Nat. Phys. volume 8,pages 285 (year 2012)NoStop [Lee and Fisher(1981)]Lee-Fisher-RandomFlux-1981 author author P. A. Lee and author D. S. Fisher, 10.1103/PhysRevLett.47.882 journal journal Phys. Rev. Lett. volume 47, pages 882 (year 1981)NoStop [Ludwig et al.(1994)Ludwig, Fisher, Shankar, and Grinstein]RandomField1 author author A. W. W.Ludwig, author M. P. A.Fisher, author R. Shankar,and author G. Grinstein, 10.1103/PhysRevB.50.7526 journal journal Phys. Rev. B volume 50, pages 7526

1701.07493v1_63

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journal Phys. Rev. B volume 50, pages 7526 (year 1994)NoStop [Chamon et al.(1996)Chamon, Mudry, and Wen]RandomField2 author author C. d. C.Chamon, author C. Mudry,and author X.-G. Wen, 10.1103/PhysRevLett.77.4194 journal journal Phys. Rev. Lett. volume 77,pages 4194 (year 1996)NoStop [Brun et al.(2003)Brun, Carteret, and Ambainis]QtoC-Theory-Decoh author author T. A. Brun, author H. A. Carteret,and author A. Ambainis,10.1103/PhysRevLett.91.130602 journal journal Phys. Rev. Lett. volume 91,pages

1701.07493v1_64

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journal journal Phys. Rev. Lett. volume 91,pages 130602 (year 2003)NoStop [Broome et al.(2010)Broome, Fedrizzi, Lanyon, Kassal, Aspuru-Guzik, and White]Broome-White-QtoC-Decoherence author author M. A. Broome, author A. Fedrizzi, author B. P. Lanyon, author I. Kassal, author A. Aspuru-Guzik,and author A. G. White, 10.1103/PhysRevLett.104.153602 journal journal Phys. Rev. Lett. volume 104, pages 153602 (year 2010)NoStop [Schreiber et al.(2011)Schreiber, Cassemiro, Potoček, Gábris, Jex, and

1701.07493v1_65

http://arxiv.org/abs/1701.07493v1

Cassemiro, Potoček, Gábris, Jex, and Silberhorn]Silberhorn-DisorderAndDecoherence author author A. Schreiber, author K. N. Cassemiro, author V. Potoček, author A. Gábris, author I. Jex, and author C. Silberhorn,10.1103/PhysRevLett.106.180403 journal journal Phys. Rev. Lett. volume 106,pages 180403 (year 2011)NoStop [Karski et al.(2009)Karski, Förster, Choi, Steffen, Alt, Meschede, and Widera]Karski174 author author M. Karski, author L. Förster, author J.-M. Choi, author A. Steffen, author

1701.07493v1_66

http://arxiv.org/abs/1701.07493v1

author J.-M. Choi, author A. Steffen, author W. Alt, author D. Meschede,and author A. Widera, 10.1126/science.1174436 journal journal Science volume 325, pages 174 (year 2009)NoStop [Fukuhara et al.(2013)Fukuhara, Kantian, Endres, Cheneau, Schauß, Hild, Bellem, Schollwöck, Giamarchi, Gross, Bloch, and Kuhr]fukuhara:quantum_2013 author author T. Fukuhara, author A. Kantian, author M. Endres, author M. Cheneau, author P. Schauß, author S. Hild, author D. Bellem, author U. Schollwöck, author

1701.07493v1_67

http://arxiv.org/abs/1701.07493v1

author D. Bellem, author U. Schollwöck, author T. Giamarchi, author C. Gross, author I. Bloch,and author S. Kuhr, 10.1038/nphys2561 journal journal Nat. Phys. volume 9, pages 235 (year 2013)NoStop [Osterloh et al.(2005)Osterloh, Baig, Santos, Zoller, and Lewenstein]Osterloh-NonAbel-2005PRL author author K. Osterloh, author M. Baig, author L. Santos, author P. Zoller,and author M. Lewenstein, 10.1103/PhysRevLett.95.010403 journal journal Phys. Rev. Lett. volume 95, pages 010403 (year 2005)NoStop

1701.07493v1_68

http://arxiv.org/abs/1701.07493v1

Lett. volume 95, pages 010403 (year 2005)NoStop [Rudner et al.(2013)Rudner, Lindner, Berg, and Levin]Rudner author author M. S. Rudner, author N. H. Lindner, author E. Berg,and author M. Levin, 10.1103/PhysRevX.3.031005 journal journal Phys. Rev. X volume 3, pages 031005 (year 2013)NoStop [Mukherjee et al.(2017)Mukherjee, Spracklen, Valiente, Andersson, Öhberg, Goldman, and Thomson]Goldman-Floq-And author author S. Mukherjee, author A. Spracklen, author M. Valiente, author E. Andersson, author

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http://arxiv.org/abs/1701.07493v1

author M. Valiente, author E. Andersson, author P. Öhberg, author N. Goldman,and author R. R. Thomson, 10.1038/ncomms13918 journal journal Nat. Commun. volume 8, pages 13918 (year 2017)NoStop [Maczewsky et al.(2017)Maczewsky, Zeuner, Nolte, andSzameit]Szameit-Floq-And author author L. J. Maczewsky, author J. M. Zeuner, author S. Nolte, and author A. Szameit, 10.1038/ncomms13756 journal journal Nat. Commun. volume 8, pages 13756 (year 2017)NoStop [Titum et al.(2016)Titum, Berg, Rudner, Refael,

1701.07493v1_70

http://arxiv.org/abs/1701.07493v1

[Titum et al.(2016)Titum, Berg, Rudner, Refael, andLindner]Titum-Floq-And author author P. Titum, author E. Berg, author M. S. Rudner, author G. Refael,and author N. H. Lindner, 10.1103/PhysRevX.6.021013 journal journal Phys. Rev. X volume 6, pages 021013 (year 2016)NoStop [Kosior and Sacha(2017)]Kosior-RandomFractals author author A. Kosior and author K. Sacha,@noop(year 2017), http://arxiv.org/abs/1701.04274 arXiv:1701.04274 NoStop [Dunlap et al.(1990)Dunlap, Wu, and Phillips]Dunlap-1990

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et al.(1990)Dunlap, Wu, and Phillips]Dunlap-1990 author author D. H. Dunlap, author H.-L. Wu, and author P. W. Phillips,10.1103/PhysRevLett.65.88 journal journal Phys. Rev. Lett. volume 65, pages 88 (year 1990)NoStop [Rolston and Phillips(2002)]Rolston-NL-2002 author author S. L. Rolston and author W. D. Phillips, 10.1038/416219a journal journal Nature volume 416, pages 219 (year 2002)NoStop [Aleiner et al.(2010)Aleiner, Altshuler, and Shlyapnikov]aleiner:finite_temperature_disorder_2010 author

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http://arxiv.org/abs/1701.07493v1

author author I. L. Aleiner, author B. L. Altshuler,and author G. V. Shlyapnikov, 10.1038/nphys1758 journal journal Nat. Phys. volume 6,pages 900 (year 2010)NoStop

1701.07754v2_0

http://arxiv.org/abs/1701.07754v2

daniel.reinholz@sdsu.edu Department of Mathematics & Statistics, San Diego State University, San Diego, CA 92182, USADepartment of Physics, University of Colorado Boulder, Boulder, CO 80309, USA One way to foster a supportive culture in physics departments is for instructors to provide students with personal attention regarding their academic difficulties. To this end, we have developed the Guided Reflection Form (GRF), an online tool that facilitates student reflections and personalized

1701.07754v2_1

http://arxiv.org/abs/1701.07754v2

facilitates student reflections and personalized instructor responses. In the present work, we report on the experiences and practices of two instructors who used the GRF in an introductory physics lab course. Our analysis draws on two sources of data: (i) post-semester interviews with both instructors and (ii) the instructors' written responses to 134 student reflections. Interviews focused on the instructors' perceptions about the goals and framing of the GRF activity, and characteristics of

1701.07754v2_2

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of the GRF activity, and characteristics of good or bad feedback, and impacts of the GRF on the nature of teacher-student relationships. Their GRF responses were analyzed for the presence of up to six types of statement: encouraging statements, normalizing statements, empathizing statements, strategy suggestions, resource suggestions, and feedback to the student on the structure of their reflection. We find that both instructors used all six response types, and that they both perceived that the

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types, and that they both perceived that the GRF played an important role in the formation of meaningful connections with their studentsin alignment with their perceptions of what counts as good feedback. This exploratory qualitative investigation demonstrates that the GRF can serve as a mechanism for instructors to pay personal attention to their students. In addition, it opens the door to future work about the impact of the GRF on student-teacher relationshipsinteractions. Personalized

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relationshipsinteractions. Personalized instructor responses to guided student reflections: Analysis of two instructors' perspectives and practices Dimitri R. Dounas-Frazer December 30, 2023 ==========================================================================================================================§ INTRODUCTION Reflection is an important skill in learning physics,<cit.> and is a key part of learning more generally.<cit.> Previously we have described how structured reflection

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we have described how structured reflection activities can augment physics courses that focus on iterative improvement of models<cit.> and apparatuses.<cit.> We have also developed an online tool, the Guided Reflection Form (GRF), that facilitates student reflection and personalized instructor responses.<cit.>. The GRF was designed to support students in describing a past experience, setting a goal for improvement, and identifying specific steps for achieving that goal. In a study of the GRF,

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for achieving that goal. In a study of the GRF, we focused on the structure of students' reflections in a physics course for future teachers; students in that study successfully used the GRF to narrate specific experiences upon which they wanted to improve and articulate goals and/or action plans for improvement.<cit.> In this article, we explore the GRF activity in a different context and from a different perspective. Here, we focus on how the GRF was implemented in an introductory lab course,

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was implemented in an introductory lab course, and we characterize the types of feedback that the two instructors of that course provided in response to their students' reflections.Our analysis of instructors' responses to students' reflections is motivated by an overarching desire to cultivate a culture of support and inclusiveness in undergraduate physics courses. In particular, we aim to develop and implement research-based educational tools that may counter weed-out culture. We consider

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that may counter weed-out culture. We consider weed-out culture to be a set of traditional educational practices and beliefs aimed at sorting and selecting the students seen as most capable, while “weeding out" the rest (i.e. removing them from the system). In their landmark study of undergraduate student attrition from science, mathematics, and engineering majors, Seymour and Hewitt described the disproportionate impacts of this culture on marginalized groups:<cit.>The most serious criticisms

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groups:<cit.>The most serious criticisms of the weed-out system, however, focused on its disproportionate impact on men of color and on all women. Even well-prepared, these two groups tend to enter basic classes feeling uncertain about whether they `belong.' The loss of regular contact with high school teachers who encouraged them to believe in their ability to do science exposes the frailty of their self-confidence. Faculty who teach weed-out classes discourage the kind of personal contact and

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discourage the kind of personal contact and support which was an important part of high school learning. It is, as some students describe, a `weaning away' process by which faculty transmit the message that it is time to grow up, cast aside dependence on personally-significant adults and take responsibility for their own learning. This attitude is perceived by students in the reluctance of teachers to answer questions, brusqueness in response to `trivial' inquiries, failure to offer praise or

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`trivial' inquiries, failure to offer praise or encouragement, disinclination to discuss academic difficulties in a personal manner, carelessness in keeping office hours, and a `no excuses' stance on test results. The difficulty of getting personal attention was troubling to many students, but it was especially troubling to those whose presence in [science, mathematics and engineering] classes was the result of considerable personal attention and encouragement by particular high school

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and encouragement by particular high school teachers. (p. 132)The GRF was designed to provide avenues of communication through which instructors and students can engage in precisely those interactions that are discouraged by weed-out culture. As educators ourselves, the authors of the paper have used the GRF to this end in multiple contexts. In the current study, our goal was to understand the extent to which the GRF opens up such opportunities for other instructors, particularly those who were

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other instructors, particularly those who were not involved in the iterative design process through which the GRF was developed. Indeed, as we will show, both instructors in our study perceived the GRF as valuable for developing personally-significant relationships with their students, and both used itused the GRF to provide their students with personal attention and encouragement. When imagining how instructors might ideally use the GRF to foster supportive student-teacher

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use the GRF to foster supportive student-teacher relationshipsinteractions, Brown's metaphor of “sitting on the same side of the table"<cit.> is helpful. Brown drew on this metaphor to create a checklist for feedback that includes items like sitting “next to you rather than across from you," putting “the problem in front of us rather than between us (or sliding it toward you)," and modeling “the vulnerability and openness that I expect to see from you" (p. 204). After outlining her checklist,

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you" (p. 204). After outlining her checklist, she asked,How would education be different if students, teachers, and parents sat on the same side of the table? How would engagement change if leaders sat down next to folks and said, “Thank you for your contributions. Here's how you're making a difference. This issue is getting in the way of your growth, and I think we can tackle it together. What ideas do you have about moving forward? What role do you think I'm playing in the problem? What can I

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you think I'm playing in the problem? What can I do differently to support you?" (pp. 204–205)The image of two people sitting on the same side of the table inspires our vision for how the GRF could shape classroom practices in physics: instructors and students working side-by-side to tackle academic problems together, building meaningful student-teacher relationships along the way.We present a qualitative exploration of two instructors' implementations of the GRF in a lab course for

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implementations of the GRF in a lab course for first-semester undergraduate students interested in majoring in physics. The instructors were physics graduate students, and the course was designed and offered as part of a student-led diversity initiative in the instructors' physics department.We conducted hour-long post-semester interviews with both instructors, and we collected electronic copies of 134 student reflections and corresponding instructor responses that were generated via the GRF.

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responses that were generated via the GRF. Using these data, we construct a rich picture of each instructor's unique implementation.This paper is organized as follows. In Sec. <ref>, we describe the GRF activity and provide a brief overview of some of the literature on feedback. We describe the programmatic and course context for our study in Sec. <ref>, outline our research methods in Sec. <ref>, and present results from our analyses of instructors' interviews and GRF responses in

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of instructors' interviews and GRF responses in Sec. <ref>.Finally, in Sec. <ref>, we summarize our findings, discuss their implications, and identify potential future directions for research and development of the GRF.§ BACKGROUND We begin our discussion by describing the GRF and summarizing relevant literature about instructor feedback practices. When describing the GRF, we focus on how it has typically been used in other courses we have taught and/or studied. The instructors in the present

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and/or studied. The instructors in the present study deviated slightly from this typical usage, as discussed in Sec. <ref>.§.§ Guided Reflection FormThe GRF has been described in detail elsewhere,<cit.> so we provide only a brief overview here. The GRF is an online tool, similar to a survey, that provides questions and other prompts to guide student reflections about issues of resilience, collaboration, and organization. Once per week, students are tasked with submitting a reflection via the

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are tasked with submitting a reflection via the GRF. Reflections may focus on any aspect of the students' learning experience, whether or not it is directly related to the course in which the GRF is being implemented. Instructors then read the reflections and provide individualized responses to each student based on the content of their (the students') reflection. This cycle of reflection and feedback repeats, ideally facilitating an ongoing written dialogue between each student and the

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written dialogue between each student and the instructor.Student responses can be collected by having students complete an online survey or submit individual electronic documents. In the former case, instructors can export student reflections into a spreadsheet, write their responses in the spreadsheet, and then use a mail merge program to generate individual documents with student responses and corresponding instructor feedback. In the latter case, the instructor can write their feedback

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case, the instructor can write their feedback directly on the submitted document.Based on our own experiences using the GRF, responding to reflections takes about 3 to 5 min per student. Instructors in this study reported spending about 10 to 15 min per student responding to reflections. In large classes, the time required for an instructor to respond to each student individually can be prohibitively large; hence, this activity is most suitable for classes with 10 to 20 students per instructor

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for classes with 10 to 20 students per instructor or, in larger courses, per teaching or learning assistant. The GRF has been implemented in a variety of contexts, including high school-level computer science and upper-division quantum mechanics.When using the GRF, students are presented with a prompt instructing them to recall a scenarioan experience from the previous week upon which they would like to improve. Such experiences could include, for example, procrastinating on a long-term

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for example, procrastinating on a long-term project.<cit.> Next, they are asked to choose one of three focus areas for reflection: bouncing back from failure or other setbacks; building a network and developing collaboration skills; or becoming an organized, self-aware, and mindful person. For students who would prefer to write about a different topic, the GRF includes a fourth option for “something different." After students choose a topic for their reflection, the GRF presents a short

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for their reflection, the GRF presents a short paragraph describing the importance of the skills related to the topic. Regardless of topic, students are asked to write short responses to two reflection prompts: * Describe the specific experience from last week that you would like to improve upon.* Describe an aspect of this experience that you can improve in the future. (Provide at least one concrete strategy that you will use to become more successful.)The GRF prompts were designed with three

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GRF prompts were designed with three aspects of reflection in mind: students should (i) revisit a salient experience from the previous week, (ii) set a future goal for improvement, and (iii) articulate specific steps for achieving that goal. In a study of undergraduate students using the GRF in a pedagogy course for future physics teachers, we found that all students successfully used the GRF to engage in multiple aspects reflection.<cit.> In this article, we explore for the first time the ways

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article, we explore for the first time the ways that instructors use the GRF to provide feedback to their students.§.§ Feedback Providing feedback to students has a significant impact on their learning, but not all feedback is equally useful. For instance, there are a number of characteristics that make feedback effective, including specificity and timeliness.<cit.> Process-level feedback is particularly effective for enhancing learning; such feedback focuses on students' ability to strategize

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focuses on students' ability to strategize about their learning and to seek help when needed.<cit.> When students receive feedback about their learning strategies, it draws attention to the ways in which they can adapt to become more effective learners.<cit.> In contrast, praise can have unpredictable impacts—and can even inhibit learning, especially if it is perceived as undeserved—because it draws students' attention to themselves rather than the task at hand.<cit.>A popular way of

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than the task at hand.<cit.>A popular way of interpreting these findings is through the concept of mindset;<cit.> indeed, this concept informed the perspectives of one of the instructors in our study. Here, “mindset" refers to students' beliefs about the nature of intelligence. Mindset is commonly described using a fixed/growth dichotomy: in the extreme cases, people with a fixed mindset view intelligence as static and unchangeable beyond a predetermined level, whereas those with a growth

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predetermined level, whereas those with a growth mindset view intelligence as malleable and something that can be improved with effort.<cit.> Using the language of mindset, providing process-level feedback is consistent with a growth mindset.<cit.> In particular, feedback that emphasizes self-improvement can bolster students' beliefs in their own capability to succeed.<cit.> On the other hand, praising a student for being “smart" may reinforce a fixed mindset,<cit.> and feedback that

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a fixed mindset,<cit.> and feedback that communicates a lack of faith in a student's capabilities can undermine their confidence, motivation, and willingness to attempt challenging tasks.<cit.> From this literature, we infer two principles that could support instructors' effective use of the GRF: P1. Praise should should focus on students' efforts to improve, express confidence in their ability to improve, and be sincere.P2. Process-level feedback should identify specific areas for improvement

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should identify specific areas for improvement and suggest strategies that students can use to improve their learning.Each principle is also informed by a particular aspect of weed-out culture, as described by Seymour and Hewitt. <cit.> In particular, they identified instructors' “failure to offer praise" and “disinclination to discuss academic difficulties in a personal manner" as factors contributing to weed-out culture. However, because not all forms of praise support student perseverance,

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all forms of praise support student perseverance, P1 recommends a particular process for giving praise. Similarly, P2 can be thought of as a guideline for how instructors can discuss academic difficulties with students. Taken together, these two principles align with part of Brown's vision for students and teachers sitting on the same side of the table. <cit.> For example, should a teacher say to a student, “This issue is getting in the way of your growth, and I think we can tackle it

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way of your growth, and I think we can tackle it together," they would be identifying an area for improvement (P2) and expressing confidence in the student's ability to improve (P1). Importantly, feedback must be understood in the context of the learning environment in which it is given and received. For instance, feedback is more effective when instructors create classroom communities that normalize failure and value criticism. Students in these settings are better situated to receive and use

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settings are better situated to receive and use feedback.<cit.> Therefore, one way for instructors and students to sit on the “same side of the table" is to be embedded in a culture where students are in the habit of receiving timely, sincere, and critical feedback focused on their strategies for self-improvement. In the sections that follow, we describe a course in which the instructors aspired to foster such a culture, in part by using the GRF.§ CONTEXT Our study is an exploratory qualitative

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CONTEXT Our study is an exploratory qualitative investigation of two instructors' feedback practices. As Eisenhart argues,<cit.> such qualitative studies are responsible for “providing sufficient detail about the researched context for a person with intimate knowledge of a second context to judge the likelihood of transferability." (p. 56). Accordingly, we describe the context for our study at three grain sizes: organization, course, and activity. §.§ Organizational context The two instructors

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§.§ Organizational context The two instructors in our study—Emily and Taylor—were both physics graduate students at the University of Colorado Boulder (CU), a predominantly white public R1 university with a large physics program. Emily was a white woman and Taylor was a white man. They co-taught a course called Foundations of Scientific Investigation (hereafter “Foundations"). Foundations was designed as part of a student-led organization called CU-Prime. CU-Prime is a member of The Access

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CU-Prime. CU-Prime is a member of The Access Network (hereafter “Access").[The Access Network, <http://accessnetwork.org>] Access organizations—including The Berkeley Compass Project,<cit.> The Chi-Sci Scholars Program,<cit.> and several other organizations—are characterized by student leadership and a commitment to improving diversity in the physical sciences through community building. To achieve their goals, these organizations offer multiple services designed to support students from

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services designed to support students from underrepresented groups and raise awareness about issues of marginalization in physics. Examples of services include summer programs,<cit.> diversity workshops,<cit.> mentorship programs,<cit.> and courses with multi-week final projects.<cit.> Many of the courses designed and run by Access organizations use the GRF or similar tools to facilitate cycles of student reflection and instructor feedback. In this work, we focus on the implementation of the

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this work, we focus on the implementation of the GRF in Foundations. §.§ Course description Foundations was first designed and taught in 2014 and was subsequently refined and taught in 2015 and 2016. It is a 14-week, fall-semester course designed for first-year undergraduate students interested in majoring in physics. On average, 22 students enroll in Foundations each semester. Students from underrepresented and/or minority racial and gender groups are especially encouraged to participate in

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are especially encouraged to participate in the course; a demographic breakdown of students who completed the course is provided in Table <ref>. The overarching goals of Foundations are twofold: build community among students enrolled in the course, and introduce students to the practice of research. Two corresponding subgoals are for students to practice developing theoretical models of scientific phenomena, and to reflect on and refine their coursework in Foundations and other courses.Each

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coursework in Foundations and other courses.Each semester, the Foundations class met twice weekly for 75 minutes per meeting, and the course consisted of 2 successive 7-week halves. Consistent with the subgoals of the course, each half included both experimental activities that focused on building models as well as activities that engaged students in the practice of reflection.During the first half of the course, students worked in groups on a set of guided optics experiments. They also used

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set of guided optics experiments. They also used the GRF to reflect on their collaboration, organization, and resilience. During the second half, students worked in groups on multi-week final projects under the guidance of graduate student mentors; a similar approach to final projects has been described elsewhere.<cit.> In this part of the course, students used a tool similar to the GRF to reflect on goals, challenges, and successes related to their final projects.Since its inception,

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to their final projects.Since its inception, Foundations has been divided into 2 parallel sections of about 10 students. Each section has been co-taught by 2 instructors, for a total of 4 instructors per semester. By design, each co-teaching pair has been mixed gender and has comprised one undergraduate student and one graduate student. Most instructors have only taught the course once, and former instructors meet with new instructors during the summer to discuss teaching strategies for the

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the summer to discuss teaching strategies for the upcoming fall semester.Emily and Taylor taught Foundations concurrently, but in different sections. Hence, each was a member of a co-teaching pair, but neither was the other's co-teacher. §.§ GRF activity We introduced Emily, Taylor, and their co-teachers to the GRF during the summer before they started teaching the course. Based on discussions between the authors and the instructors, the instructors' implementation of the GRF differed from that

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implementation of the GRF differed from that described in Sec. <ref> in two ways. First, the GRF was assigned only during the first half of the course. This choice was made because a different reflection tool was deemed more appropriate for the second half of the course. Second, GRF focus areas were assigned by the instructors. Reflections focused on collaboration during weeks 1 and 2, organization during weeks 3, 4, and 5, and resilience in weeks 6 and 7. This choice was informed in part by

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6 and 7. This choice was informed in part by the anticipated progression of student-to-student relationships in the course. Students would still be getting to know their group members during the first couple weeks of the semester, and they might not feel comfortable sharing about their experiences of failure with their instructors until several weeks had passed. This choice was also informed by the fact that many introductory courses have multiple midterms, making it important to develop good

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midterms, making it important to develop good time management practices as early as possible. Although students were not graded on the quality of their reflections, they were awarded a small amount of course credit for completing the GRF activity.At the start of the fall semester, we provided Emily and Taylor with guidelines for giving feedback.<cit.> The guidelines were based on our experiences with the GRF<cit.> and a precursor to the GRF,<cit.> and they emphasized the importance of

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GRF,<cit.> and they emphasized the importance of communicating the goal of the activity to students as well as providing feedback on both the structure and content of students' reflections. Based on the instructors' internal decisions about division of labor, Emily and Taylor were each solely responsible for responding to all the reflections written by students in their respective sections; their co-teachers did not provide any individualized written feedback to students via the GRF activity.

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feedback to students via the GRF activity. In this paper, we explore the ways that Emily and Taylor incorporated the GRF into their teaching. In doing so, we aim to provide clear examples of instructor feedback, as facilitated by the GRF. These examples could inform future instructors' use of the GRF in othercontexts.§ METHODS ThisThere are multiple ways in which the goals of the GRF, the Foundations course, and the CU-Prime organization are theoretically aligned. One line of reasoning is as

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aligned. One line of reasoning is as follows: Seymour and Hewitt noted that weed-out culture has a “disproportionate impact on men of color and all women;"<cit.> these populations are better represented in Foundations than in the CU Physics Department as a whole (Table <ref>); the GRF was designed to counter some aspects of weed-out culture; and, finally, the Foundations course was designed to support CU-Prime's commitment to improving diversity in physics. Thus, implementing the GRF in

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in physics. Thus, implementing the GRF in Foundations is in alignment with the diversity-oriented mission of CU-Prime. More narrowly, the GRF directly aligns with the course goal of engaging students in the practice of reflection. However, our present focus is not on student experiences or outcomes as they relate to improving diversity in physics. Rather, we are interested in teacher practices. Accordingly, this study is a qualitative exploration of the ways that Emily and Taylor implemented

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of the ways that Emily and Taylor implemented the GRF in the Foundations course.We conducted post-semester interviews with both Emily and Taylor, focusing on their goals for, perspectives on, and engagement with the GRF activity. To corroborate the instructors' self-reported response practices, we also collected and analyzed all instructor responses that were generated via the GRF. Thus, our study enables us to describe how Emily and Taylor implemented the GRF using their own words and

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implemented the GRF using their own words and authentic examples of the responses they provided to students. Our goal is not to make generalizable statements about either the GRF or instructors who use it, but rather to provide insight into the various ways that instructors might take up the GRF for use in their classrooms. In this section, we describe our data sources and analysis methods.§.§ Post-semester interviews At the end of the semester, we conducted semi-structured interviews with

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we conducted semi-structured interviews with Emily and Taylor to gain insight into their perspectives on the GRF and other aspects of the course. Emily and Taylor were interviewed separately, each for about an hour.Interviews focused in part on threetwo themes: the instructors' perceptions about the (i) goals and framing of the GRF activity, and (ii) characteristics of good or bad feedback, and (iii) impacts of the GRF on the nature of teacher-student relationships. We chose the first twothese

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relationships. We chose the first twothese themes because they give us insight into why and how the instructors were using the GRF. The third theme was chosen because it reflects a goal of the Foundations course that runs counter to weed-out culture: to foster supportive relationships among students and teachers.The first author transcribed both interviews, and the transcripts are the data that we analyzed. We collaboratively identified all excerpts that addressed the three themes that

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all excerpts that addressed the three themes that comprised the foci of our interviews. For each theme, we selected several representative excerpts and constructed two vignettes about the implementation of the GRF, one each for Emily and Taylor. These vignettes are presented in Sec. <ref>.§.§ GRF responses In total, 22 students were enrolled in Foundations: 10 in Emily's section and 12 in Taylor's. Each student was required to complete 7 reflections using the GRF. Of 154 possible GRF-based

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using the GRF. Of 154 possible GRF-based reflections, 135 were submitted. This corresponds to a completion rate of 88%, which is consistent with the GRF completion rate observed in another study.<cit.> The majority of students completed all or most reflections: 12 students completed all 7 reflections, 8 completed 5 or 6, and 2 completed 3 or 4. This distribution was roughly the same in both sections, resulting in similar completion rates for Emily's section (90%) and Taylor's section (86%).

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Emily's section (90%) and Taylor's section (86%). Each instructor responded only to reflections completed by students enrolled in their section. Almost every submitted reflection received a personalized response from either Emily or Taylor; only 1 reflection received no instructor response.We analyzed both instructors' GRF responses using an a priori coding scheme. This scheme was not directly informed by existing frameworks for effective feedback, such as those described in Sec. <ref>. Rather,