Browsing by Subject "Representations"

Now showing 1 - 3 of 3
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    Exploring the impact of a standards-based Mathematics and pedagogy class on preservice teachers' beliefs and subject matter knowledge.
    (2012-05) Stohlmann, Micah Stephen
    This case study explored the impact of a standards-based mathematics and pedagogy class on preservice elementary teachers' beliefs and conceptual subject matter knowledge of linear functions. The framework for the standards-based mathematics and pedagogy class in this study involved the National Council of Teachers of Mathematics Standards, the Lesh Translation Model, building algebra through the elementary grades, social constructivism, and research on childrens' mathematical thinking from the Rational Number Project. The rich description of the mathematics and pedagogy class in this study provides relevant information for properly structuring mathematics content classes to prepare elementary teachers to be able to help all students learn mathematics. Overall, the preservice teachers demonstrated the most developed understanding in the realistic, language, symbolic, and concrete representations; while the pictorial representation was often not as fully developed. They also showed the ability to provide reasoning and justification for their mathematical ideas. The preservice teachers' beliefs about the teaching and learning of mathematics became more inline with standards-based learning environments. The preservice teachers were especially impacted by the Rational Number Project research on fraction division and fraction multiplication to see the benefit of having conceptual understanding of concepts in different representations. However, there were a few areas where the preservice teachers showed little evidence of beliefs: that the teacher should let children do most of the thinking in a mathematics class and that mathematics is a web of interrelated concepts and procedures.
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    Pedagogical content knowledge and the gas laws: a multiple case study.
    (2010-07) Sande, Mary Elizabeth
    Pedagogical content knowledge (PCK) has been described as an assemblage of the most powerful analogies, demonstrations, examples and illustrations that make content knowledge understandable to students, together with an understanding of the preconceptions and alternate conceptions that students bring with them to the classroom (Shulman, 1986). In speaking of representations, Johnstone (1991) and Gabel (1993, 1998) suggest that there are three categories of representations in chemistry: the macroscopic, particulate, and symbolic. For the present study, a fourth category has been added, the graphic representation. In addition, Bell, Veal & Tippins (1998) proposed a hierarchy of PCK, a structure wherein the broadest concept (science PCK) is specified by discipline PCK (chemistry PCK) and finally by topic PCK (Gas Law PCK). The present study will investigate the apex of this hierarchy, the intersection of PCK and the specific topic of the Gas Laws. The Gas Law PCK Model was created to illustrate the intersection of subject matter knowledge for teaching and topic-specific PCK. Four chemistry teachers, each holding a degree in chemistry, who had taught high school chemistry for at least three years, and who had taught the Gas Laws during each of the last three years, were given an assessment of their subject matter knowledge for teaching regarding the Gas Laws. Two interviews were conducted to address Gas Law PCK, focusing on representations and student preconceptions and alternate conceptions. Findings of this multiple case study indicate that the participants' subject matter knowledge for teaching, ability to move among representations, i.e. representational competence, and understanding of student alternate conceptions regarding the Gas Laws and how to address those conceptions were limited. Possible influential factors of curricula and lesson planning were also explored. Recommendations for emphasis on specific subject matter knowledge for teaching representations, representational competence, students' alternate conceptions and how to address student alternate conceptions were explored for pre-service teachers and in-service teachers.
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    Systems of Cultural Representation: An Examination of Native American Identity and Cultural Representations Through Digital Stories
    (2020-08) Fish, Jillian
    Psychological research has demonstrated that Native peoples engage with shared meanings of cultural phenomena in their environments when forming their identities. These are referred to as cultural representations and are critical for Native peoples to form a coherent and meaningful sense of self. To date, empirical studies on cultural representations use experimental methods to measure the effect of media representations on identity-related outcomes among Native adolescents from reservations and in academic settings. These studies take a top-down approach that neglects the range of cultural representations and the intrapsychic processes Native peoples use to engage with them during identity formation, as well as well-known constructs from cultural psychology that have implications for individuals’ identities. The present study addresses these limitations through a bottom-up approach using narrative and digital storytelling strategies to answer the following research questions: 1) What cultural representations are present in narratives of urban Native peoples? 2) How do urban Native peoples internalize and resist the aforementioned cultural representations? And 3) How do well-known cultural psychology constructs relate to these cultural representations and narrative processes? To answer these questions, participants (n = 73) completed a questionnaire of cultural psychology constructs and open-ended story prompts, and attended a one-day workshop to create a digital story. For Research Question 1, thematic analysis was used to examine the content of the historical and cultural representations in Native peoples’ environments from their digital story narratives. To address Research Question 2, digital story narratives were examined for narrative processes to determine how Native peoples’ internalized and negotiated with historical and cultural representations when forming their identities. For Research Question 3, associations between historical and cultural representations, narrative processes, and well-known cultural psychology constructs were examined through correlations, independent samples t-tests, and chi-square analyses to further contextualize the findings. Results provide rich and descriptive information about historical and cultural representations salient to Native peoples’ identity development, which are discussed through Story Profiles. Implications for Native peoples as active co-constructors of their identities are discussed in relation to the current literature.