# 5. Selected publications

- McGowen, M. A., & Davis, G. E. (2022). A Numerical Indicator of Student Cognitive Engagement and Mathematical Growth.
*International Electronic Journal of Mathematics Education*,*17*(1). - McGowen, M.A. & Davis, G.E. (2021) Using the distribution of individual gain to assess student engagement and growth, and focused teaching of mathematics. In preparation.
- Davis, G. E. & McGowen, M.A (2021). A mathematics educator’s guide to the mathematical brain. Submitted for publication
- Davis, G. (2020) Level of the Calkin-Wilf tree in which the n-th convergent of the continued fraction for e appears.
*Online Encyclopedia of Integer Sequences*, A339267. - McGowen, M.A. & Davis, G.E. (2019) A tale of divergence: Spectral analysis of concept maps of two undergraduate mathematics students.
*Journal of**Mathematical Behavior*, 55, 100686. - Yan, D. & Davis, G.E. (2019) A first course in data science.
*Journal of Statistics Education*(to appear). - Yan, D. & Davis, G.E. (2018) The turtleback diagram for conditional probability.
*The Open Journal of Statistics*, 8(4), 84–705. - Davis, G. (2017) An Inequality in Integers: Alternative proof, illustration, and generalization.
*Cut The Knot*. - Chung J, Yan, D., Davis, G. (2017). The Effects of Early Adoption of Academic Electronic .Health Records System (EHRS) on Patient Outcome in Nursing. UMass Center for Clinical and Translational Science Research Retreat. https://doi.org/10.13028/gsfe-gs70. Retrieved from https://escholarship.umassmed.edu/cts_retreat/2017/posters/15
- Davis, G. E. & McGowen, M.A. (2014) Individual gain and engagement with mathematical understanding.
*Proceedings of the XVI Annual Meeting, North American Chapter of International Group for the Psychology of Mathematics Education*. Toronto, Canada, vol 1, pp. 333-341. - Chen, Y., Davis, G., Gottlieb, S., Hausknecht, A., Heryudono, A. & Kim, S. (2013) Transformation of a mathematics department’s teaching and research through a focus on computational science.
*Journal of Computational Science Education*, 4(1), 24-29. - Audycki, S.L., Audycki, R. A.. & Davis, G.E. (2012) The effect of oral antipschotic medications on intraocular pressure.
*Investigative Ophthalmology & Visual Science*, 53(14), 5061. - Warner, L. B., Schorr, R. Y., & Davis, G. E. (2009). Flexible use of symbolic tools for problem solving, generalization, and explanation.
*ZDM*, 41(5), 663-679. - Campbell, A.E., Davis, G.E. & Adams, V. M. (2007) Cognitive demands and second-language learners: A framework for analyzing mathematics instructional contexts.
*Mathematical Thinking & Learning*, 9(1), 3-30. - Davis, G. E., & McGowen, M. A. (2007). Formative feedback and the mindful teaching of mathematics.
*Australian Senior Mathematics Journal*,*21*(1), 19. - Davis, G.E. & McGowen, M.A. (2006) Formative feedback and the mindful teaching of undergraduate mathematics. In J. Novotna, H. Moraová, M. Krátká & N. Stehlíková (Eds.) Proceedings of the 30th Conference of the
*International Group for the Psychology of Mathematics Education*, vol 1, p. 241. Prague: Charles University. - Davis, G.E. & Pearn, C.A. (2006) Generative concept images. In J. Novotna, H. Moraová, M. Krátká & N. Stehlíková (Eds.) Proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education, vol 2, pp. 393-400. Prague: Charles University.
- Dalton, S, Davis, G. & Hegedus, S.(2006) Modeling mathematics teachers’ questioning. In J. Novotna, H. Moraová, M. Krátká & N. Stehlíková (Eds.) Proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education, vol 1, p. 377. Prague: Charles University.
- Hegedus, S., Dalton, S., Cambridge, L., & Davis, G. (2006, July). Patterns of participation in networked classrooms. In
*Proceedings of the 30th conference of the international group for the psychology of mathematics education*(Vol. 3, pp. 257-264). - Davis, G. E., & McGowen, M. A. (2004). A Rush of Connections and Insights, a Glorious Moment of Clarity.
*Networks: An Online Journal for Teacher Research*,*7*(2), 116-116. - Warner, L.B., Alcock, L. J., Coppolo Jr., J. & Davis, G. E. (2003). How does flexible mathematical thinking contribute to the growth of understanding? In N.A. Pateman, B.J. Dougherty & J. Zillox (eds.), Proceedings of the 27th Conference of theInternational Group for the Psychology of Mathematics Education held jointly with the25th Conference of PME-NA , July 13 – 18, 2003, Honolulu, Hawaii (Vol. 4, pp.371-378).
- Davis, G.E. & McGowen, M.A. (2002) Function machines and flexible algebraic thought. In A. Cockburn (Ed.) International Group for the Psychology of Mathematics Education, Vol 2, pp. 273-280. Norwich, UK: University of Norwich.
- Davis, G. E., & Tall, D. O. (2002). What is a scheme?
*Intelligence, learning and understanding in mathematics: A tribute to Richard Skemp*, 131-150. - McGowen, M.A. and Davis, G.E. (2002) Growth and development of pre-service elementary teachers’ mathematical knowledge. In D. Mewborn (Ed.) International Group for the Psychology of Mathematics Education, North American Chapter, Vol , pp.1135-1144. Athens, GA: University of Georgia.
- Warner, L. B., Coppola Jr., J., & Davis, G. (2002). Flexible mathematical thought. Proceedings of PME 26 (Vol. IV, pp. 354–361). Norwich, UK.
- Warner, L. B., Davis, G. E., Alcock, L. J. & Coppolo, J., Jr. (2002). Flexible mathematical thinking and multiple representations in middle school mathematics.
*Mediterranean Journal for Research in Mathematics Education*, 37–61. - Davis, G.E. & McGowen, (2001) M.A. Jennifer’s Journey: Seeing and Remembering Mathematical Connections in a Pre-service Elementary Teachers Course. In M. van den Heuvel-Panhuizen (Ed.), Proceedings of the 25th Conference of the International Group for the Psychology of

Mathematics Education, Vol 2,pp. 305-312. Utrecht, The Netherlands - McGowen, M.A. & Davis, G.E. (2001) What mathematical knowledge do pre-service elementary teachers value and remember? In Speiser, R., Maher, C. A. & Walter, C. N.(Eds.) Proceedings of the Annual Meeting of the North American. Chapter of the International Group for the Psychology of Mathematics Education (Snowbird, Utah, October 18-21, Vol. 2, pp. 875-884.
- McGowen, M. A. and Davis, G. E. (2001). Changing pre-Service elementary teachers’ attitudes to algebra. In Chick, H., Stacey, K., Vincent, J. & Vincent, J (Eds.)
*Proceedings of the 12th ICMI Study on The Future of the Teaching and Learning of Algebra*. University of Melbourne, Australia: 2, 438-446. - Tall, D., Thomas, M., Davis, G., Gray, E., & Simpson, A. (1999). What is the object of the encapsulation of a process?
*The Journal of Mathematical Behavior*,*18*(2), 223-241. - Davis, G., Pearn, C., Price, G. & Smith, K. (1997) Connections between counting and reading,
*Proceedings of the International Symposium on Elementary Mathematics Teaching*, August 24-29, Prague, The Czech Republic. - Hunting, R. P., Davis, G., & Pearn, C. A. (1996). Engaging whole-number knowledge for rational-number learning using a computer-based tool.
*Journal for Research in Mathematics Education*, 354-379. - Davis, G., & Royle, P. (1996). A comparison of Australian university output using journal impact factors.
*Scientometrics*, 35(1), 45-58. - Royle, P.L. and Davis, G.E. (1995) Quality and Distribution of Australian Science Journal Publishing. In M.E.D. Koenig and A. Bookstein (eds.) Fifth
*International Conference of the International Society for Scientometrics & Informetrics*. Proceedings – 1995. pp. 475-484. Medford N.J.: Learned Information. - Cairns, G., Davis, G., Elton, D., Kolganova, A., & Perversi, P. (1995). Chaotic group actions.
*Enseignement Mathematique*, 41, 123-123. - Davis, G., Hunting, R., & Pearn, C. (1993). Iterates and relations: Elliot and Shannon’s fraction schemes. In 1993). Proceedings of the seventeenth conference of the international group of PME (Vol. 3, pp. 154-161).
- Banks, J., Brooks, J., Cairns, G., Davis, G., & Stacey, P. (1992). On Devaney’s definition of chaos.
*The American mathematical monthly*,*99*(4), 332-334. - Davis, G. E., & Pepper, K. L. (1992). Mathematical problem solving by pre-school children.
*Educational Studies in Mathematics*, 23, 397–415. - Hunting, R. P., & Davis, G. (Eds.). (1991).
*Early fraction learning*. Springer. - Davis, G. (1991). A fraction of epistemology. In R. P. Hunting & G. Davis (Eds.), Early fraction learning (pp. 225-236). New York: Springer-Verlag.
- Davis, G., & Pepper, K. L. (1991). Sharing by Dealing as Problem Solving. In
*Early Fraction Learning*(pp. 159-170). Springer, New York, NY. - Davis, G. E., & Hunting, R. P. (1990). Spontaneous partitioning: Preschoolers and discrete items.
*Educational Studies in Mathematics*, 21(2), 367–374. - Davis. G.E., and Pitkethly, A. (1990) Cognitive aspects of sharing,
*Journal for Research in Mathematics Education*. vol 21, no.2, 145-153. - Tierney, C., Boyd, C., and Davis, G.E. (1990) Prospective primary teachers’ conceptions of area. In G. Booker, P. Cobb, and T. N. de Mendicutti (Eds.)
*Proceedings of the Fourteenth PME Conference,*Vol II, pp. 307 – 314. Mexico City: Program Committee of the 14th PME Conference. - Davis, G.E. (1990) Reflections on dealing: An analysis of one child’s interpretations. In G.Booker, P. Cobb, and T. N. de Mendicutti (Eds.)
*Proceedings of the Fourteenth PME Conference,*vol III, pp. 11 – 18. Mexico City: Program Committee of the 14th PME Conference. - Davis, G.E. (1990) Children talking about children’s mathematics,
*Mathematics Education Research Journal*, vol 1, no. 2, 35 – 42 - Bigelow, J. C., Davis, G. E., & Hunting, R. P. (1989, April). Some remarks on the homology and dynamics of rational number learning. In
*Research Presession of the Sixty-Seventh Annual Meeting of the National Council of Teachers of Mathematics, Orlando*. - Davey, B.A., and Davis, G.E. (1986) Tensor products and entropic varieties,
*Algebra Universalis*, Vol 21, No. 1, 68-88. - Ball, R.B. and Davis, G.E. (1983) The α-completion of a lattice-ordered group.
*Czech Mathematics Journal*, 33 (108), 111 – 118. - Davis. G.E. (1982) Notes on zero-divisors and group presentations. In P. Schultz, C. Praeger and R. Sullivan (eds.)
*Algebraic Structures and Applications*. Lecture Notes in Pure and Applied Mathematics, vol 74. pp 3 – 14. New York: Marcel Dekker. - Davis, G.E. (1981) Permutation representation of groups with Boolean orthogonalities.
*Journal of the Australian Mathematical Society*(Series A), 30, 412 – 418 - Davis, G.E. and McCleary, S.H. (1981) The π-Full Tight Riesz Orders on A(Ω) .
*Canadian Mathematical Bulletin*, 24 (2), 137-151. - Davis, G.E. and McCleary, S.H. (1981) The lateral completion of a completely distributive lattice- ordered group (revisited).
*Journal of the Australian Mathematical Society (Series A)*, 31, 114 -128. - Davis, G.E. and Fox, C.D. (1977) Compatible tight Riesz orders on the automorphism group of an o-2-homogeneous set: Addendum.
*Canadian Journal of Mathematics*, 29, 664 – 665. - Colville, P.D., Davis, G.E., and Keimel, K. (1977) Positive derivations on f-rings.
*Journal of the Australian Mathematical Society (Series A)*, 23, 371 – 375. - Davis, G.E. and Fox, C.D. (1976) Compatible tight Riesz orders on the automorphism group of an o-2-homogeneous set.
*Canadian Journal of Mathematics*, 28, 1076-1081. - Davis, G.E. and Loci, E.S. (1976) Compatible tight Riesz orders on ordered permutation groups.
*Journal of the Australian Mathematical Society (Series A)*, 21, 317 – 333. - Davis, G.E. (1975) Automorphic compactifications and the fixed point lattice of a totally ordered set.
*Bulletin of the Australian Mathematical Society*, 12, 101 – 109 - Davis, G.E. (1975) Compatible tight Riesz orders on groups of integer valued functions,
*Bulletin of the Australian Mathematical Society*, 12, 383 – 390 - Davis, G.E. (1975) Orthogonality relations on abelian groups.
*Journal of the Australian Mathematical Society (Series A)*, 19, 173 – 179 - Davis, G.E. (1973) Representation and extension of semi-prime rings.
*Journal of the Australian Mathematical Society (Series A)*, 15, 353 -365 - Davis, G.E. (1971) Rings with orthogonality relations.
*Bulletin of the Australian Mathematical Society*, 4, (1971), 163 – 178 - Davis, G.E. (1970) Order topologies on ordered tensor products.
*Bulletin of the Australian Mathematical Society*, 3, 385 – 390