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The Common Core State Standards for Mathematics emphasize the importance of developing students' conceptual understanding, mathematical reasoning, and problem solving skills. This is a shift from the traditional approach to teaching mathematics and many teachers rely on curriculum resources to help them meet these new standards and expectations. One of the biggest strands of understanding across the middle grades is proportional reasoning. There are limited studies on how U.S. textbooks promote proportional reasoning across the middle grades. There is also a lack of textbook analyses that investigate the contexts proportional reasoning tasks are set in. This study looks to analyze the development of proportional reasoning skills in both traditional and NSF-funded textbooks across grades 6-8. This analysis looks at how proportional reasoning tasks in curriculum materials are presented to students. A total of 24 textbooks were analyzed for alignment with the Common Core State Standards for Mathematics as well as the presence of six different characteristics (cognitive demand, problem solving, type of context, type of information, contextual algebraic tasks, and proportional perspectives). This analysis sheds light on the opportunities to learn proportional reasoning through tasks presented through different textbooks series across the middle grades and highlights differences and trends that exist. The results of this analysis show the failure of curriculum resources to address the Common Core State Standards for Mathematics related to proportional reasoning. Opportunities to learn proportional reasoning through problems posed in textbooks series were also limited; this analysis showed low levels of cognitive demand, limited promotion of problem solving skills, lack of variety of context types, low degrees of algebraic robustness, and a failure to promote the understanding of multiple perspectives in solving proportional reasoning problems. The analysis adds to the current literature and has implications on how to create and use problems posed in curriculum resources. It also lays the foundation for future research and supports further needs for change and reform. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]

Uncertainty is inherent to scientific methods and practices, yet is it rarely explicitly discussed in science classrooms. Ironically, science is often equated with "certainty" in these contexts. Uncertainties that arise in science deserve special attention, as they are increasingly a part of public discussions and are susceptible to manipulation. Clarifying what is meant by scientific uncertainty would include identifying sources of uncertainty in scientific practice, and would help provide an instructional framework for understanding how scientists use methods, data, and models to justify claims about the natural world. This research introduces both a general typology of scientific uncertainty informed by a review of literature from a variety of perspectives, and two additional typologies that emerged from qualitative studies examining student essays about scientific uncertainty in two disciplinary contexts: biological evolution and global climate change. These typologies aim to provide leverage for curricular discussions about scientific knowledge and practices, and to help instructors interested in integrating scientific uncertainty into teaching these subjects. In particular, a focus on uncertainties in data and models can illustrate their integral relationship and can spark critical discussions about methods used to collect empirical data and the models used to explain them and make predictions. This research builds a case for integrating scientific uncertainty into science teaching and emphasizing its importance for understanding the practice of science within particular disciplinary contexts. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]