(CV) 
Yvonne Lai's research aims to improve instruction of mathematical reasoning at all levels by identifying and preparing teachers in the mathematical knowledge for teaching (MKT) necessary for such instruction. In her work on MKT, she builds on the work of Ball and colleagues (e.g., Ball, Thames, and Phelps (2008)). She brings a mathematics background to her work in mathematics education, specializing in hyperbolic geometry and geometric group theory prior to her interest in mathematical knowledge for teaching and practices of proof and reasoning. Her current projects investigate the cognition of teaching mathematical claim making and proving in secondary mathematics; the role of mathematical knowledge across different time scales (with Ruth Heaton and Mary Alice Carlson); differences between secondary MKT and elementary MKT and implications for professional development, teacher education, and measuring teachers' knowledge (with Heather Howell and Geoffrey Phelps); and the impact of content rich mathematics preparation on teaching practice (in collaboration with Jim Lewis, Lorraine Males, Wendy Smith, and Steve Swidler). 
Research
Areas of interest: Funding:
Past project affiliations:
Dissertation:
An Effective Compactness Theorem
for Coxeter Groups. Geometriae Dedicata, Vol. 145, Issue 1 (2010), pp. 195217.
DOI 10.1007/s1071100994168.
(arXiv)
(journal)

TeachingUniversity of NebraskaLincolnFall 2015: Math 405: Discrete Mathematics for Secondary TeachingThe overarching goal of this course is to do mathematics that will help teachers experience mathematical practice. Mathematical contexts to experience practice include graph theory and group theory. The emphasis in graph theory is on Eulerian paths/circuits, colorability, and genus of graphs and surfaces. The emphasis in group theory will be on permutation groups, dihedral groups, and polyhedral groups. Spring 2015, Spring 2014: Math 407/807: Algebra for Secondary TeachingA course emphasizing connections between algebraic concepts. Special emphasis on conic sections and trigonometric functions and understanding why different characterizations (e.g., slices of cones, ``stretched'' circles, focidirectrixeccentricity, Ax^{2}+By^{2}+Cxy+Dx+Ey+F=0) indeed characterize the same class of objects. Fall 2014, Fall 2013: Math 408/808: Geometry for Secondary TeachingEuclidean geometry from a transformation perspective, with particular attention to proof, proving, and reasoning within this perspective. Emphasizes group theoretic properties of transformations, applying transformation perspective to topics in secondary geometry and algebra curricula. Coordinating course design with Sherry West, current mathematics department chair of Lincoln Southeast of Lincoln Public Schools. Canada/USA MathcampSince 2000, I have worked at the Canada/USA Mathcamp. It's a wonderful place where graduate students and faculty teach high school students about mathematics that has been personally inspiring. I have taught the Banach Tarski paradox, Dehn invariants, the Scissors Congruence Problem, Disrete Fourier Transforms, and various pieces of hyperbolic geometry and geometric group theory (such as a class on SL(2,Z).) At Mathcamp 2010, Ilya Grigoriev and I organized a viewing of Not Knot interspersed with a Q & A about the math. The film is visually beautiful, but can be frustrating to watch without a friend with whom to delve into the mathematics. It was great fun to examine the film with enthusiastic students and a fellow geometer. Algebra ProjectThroughout the academic year 20092010, I visited the Ypsilanti cohort of the Algebra Project and participated in the weekend planning sessions for the class. Here are some mathematical and nonmathematical highlights of the year. University of MichiganFall 2013: Education 413: Secondary Mathematics MethodsCourse for prospective teachers focusing on pedagogy for lower secondary and upper middle school mathematics; concurrent enrollment with field placement and practicum. Worked with field instructors Annick Rougee and Rachel Snider in designing the course.[course information from 2013] Winter 2009, 2010, 2011: Math 486:

Service

(Geometry, personified, as woman teaching geometric construction) 
Talks/Travel/Slides and handouts 20132014

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