The purpose of this study was to detail mathematical knowledge that supports the work of teaching proof and to investigate how such knowledge is evidenced in professional development (PD). To advance the construct of mathematical knowledge for teaching (MKT) in the context of proof, I developed a framework of MKT...
The Common Core State Standards for Mathematical Practice (SMPs) describe ways of thinking and doing mathematics that parallels how mathematicians engage with mathematics (National Governors Association for Best Practices, 2010). These standards reflect a broader goal in K-12 mathematics education focused on moving beyond K-12 learners acquiring knowledge of mathematical...
Teacher noticing is a necessary skill in order for teachers to elicit and respond to their
students' mathematical ideas and support the ambitious learning goals of school mathematics. The purpose of this dissertation is to investigate what teacher candidates noticed about their teaching as they were provided supports and opportunities...
As part of the continuing investigation of the thermal cis- 1, 3, 5-hexatriene to 1,3-cyclohexadiene rearrangement, four new trienes and a cross-conjugated pentaene have been prepared and their thermal reactions studied. A new route to the synthesis of highly substituted trienes has been developed. The synthesis of three of these...
Design in secondary mathematics teacher education must prepare teacher candidates to do the work of ambitious and equitable mathematics teaching with skill by situating development in the work of teaching and incorporating opportunities to investigate and enact teaching. Teacher education designs must also be responsive to the work that mathematics...
Policy and research have increased attention in K12 mathematics education on core mathematical practices such as argumentation, justification, and proof, that are central to students learning and doing mathematics. One reason for this increased focus is the empirical evidence that engaging students in mathematical practices provide more equitable opportunities for...
Issues of injustice in society (e.g. racism, classism, sexism, ableism) are perpetuated in and through educational opportunities, including mathematics learning (Freire, 1970/2000). Those that are committed to disrupting the interlocking systems that create disparities and oppression in mathematics education are considered to be “pursuing justice.” Pursuit of justice can involve...
Academic success is a salient domain of youth development and is related to positive lifelong outcomes among youth in foster care. However, youth in foster care experience compounding adversities, including maltreatment and foster care placement itself, which put them at risk of academic disengagement and underachievement. Despite these adversities, academic...
A model of an exhaust plume was developed and programmed
on a digital computer. The purpose of the model was to predict the
concentration and size distribution of ice particles produced from
automobile exhaust during arctic conditions. The model accounted
for the nucleation, growth, and freezing of the condensed water...
Steroid organoboranes have been found to be useful synthetic
intermediates. Attempted pyrolyses, based on simple trialkylborane
cyclizations, have not yielded C-19 or C-18 functionalized steroids,
but have produced isomerized systems not otherwise available.
Thus, hydroboration of cholesterol followed by pyrolysis at
215° gives 31% of 2-cholestene-6α-ol and 49% of a...