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College Students’ and Inservice Teachers’ Evoked Concept Images and Ways of Understanding Congruence

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Eleven years after being put into practice, the Common Core State Standards for Mathematics still take a back seat as traditional approaches drive many secondary geometry classrooms, specifically in regard to congruence. This thesis explores how university students reason about

Eleven years after being put into practice, the Common Core State Standards for Mathematics still take a back seat as traditional approaches drive many secondary geometry classrooms, specifically in regard to congruence. This thesis explores how university students reason about congruence based on their high school learning experience, as well as how in-service geometry teachers reason about and teach congruence. During the Summer of 2020, two distinct surveys were distributed to 33 undergraduate students at Arizona State University and two in-service geometry teachers in Arizona to characterize the ways they understand congruence and reflect on their experiences in secondary geometry classrooms. The results of the survey indicate that students who understood congruence either in terms of corresponding measurements or transformations were successful in identifying congruent shapes, while only students who understood congruence in terms of transformations were successful in constructing congruent shapes. Transformational reasoning was both the most productive and the least prominent way of understanding congruence among students. Their responses to activities and reflections on their experiences also suggested that deductive reasoning is not practiced or prioritized in many secondary geometry classrooms. Teacher understandings of congruence varied, and reflections suggested that development of materials and training that are aligned with the goals of CCSSM for both pre-service and in-service teachers would help teachers create an environment conducive to a transformational understanding of congruence and that promotes deductive reasoning.

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2020-12

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Nonwork role importance as a moderator to the congruence-satisfaction relation

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Individuals are attracted to occupational environments that align with their interests and personality characteristics (Holland, 1985, 1997). When an individual's attributes (i.e., needs, abilities, values and/or interests) align with the occupational environment's characteristics an individual is more satisfied. Past research

Individuals are attracted to occupational environments that align with their interests and personality characteristics (Holland, 1985, 1997). When an individual's attributes (i.e., needs, abilities, values and/or interests) align with the occupational environment's characteristics an individual is more satisfied. Past research suggests this relation is modest at best, hovering between .20 and .30 (Meyer et al., 2001, c.f. Wilkins & Tracey, 2014), with slightly higher estimates (ranging from .24 to .35) depending on how the variables of person and environment were measured (Kristof-Brown, Zimmerman, & Johnson, 2005). Several factors contribute to such low estimates, most notably the role of moderator variables in suppressing or exacerbating the true magnitude of this relation. A moderator that has yet to be explored is that of nonwork role priority, or the degree to which an individual's work identity is valued relative to other role identities. In the current study, three hypotheses were posited to investigate nonwork role priorities as a potential moderator to the congruence-satisfaction relation. Latent class analysis was used to apply a person-centered approach to understanding response patterns and differences in these roles. The sample was differentiated best by a two-class solution and the class variable in all three hierarchical regression models explained about five percent of the variance in job satisfaction, which suggests that work and nonwork role priority are meaningful to understanding individual career happiness. Class was not identified as a significant moderator to the congruence-satisfaction relation. Discussion of limitations to the current study and recommendations for future work in this area are presented.

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2016