Counterfactual conditional sentences (e.g., "If giraffes had fins, they would swim") involve an antecedent (e.g., "If giraffes had fins") which is false in the actual world. They also involve a consequent (e.g., "they would swim"), expressing a possibility given the antecedent. Reasoning about counterfactual…

The ideas of measurement and measurement comparisons (e.g., fractions, ratios, quotients) are introduced to students in elementary school. However, studies report that students of all ages have difficulty comparing two quantities in terms of their relative size. Students often understand fractions such as 3/7 as part-whole relationships or…

Reading is a fascinating cognitive process through which individuals perceive arbitrary symbols on a page and turn them into vivid mental representations of text. Most available evidence supports an embodied explanation for how readers are capable of such representations--they recruit supralinguistic brain regions in order to mentally simulate the…

Covariational reasoning is a cognitive activity that attends to two or more varying quantities and how their changes are related to each other. Previous studies indicate that covariational reasoning seems to have levels. Content analysis was used to examine the pedagogy and development of covariational reasoning levels in the sections that…

Research has shown the majority of students who have completed a university calculus course reason about the definite integral primarily in terms of prototypical imagery or in purely algorithmic and non-quantitative ways. This dissertation draws on the framework of Emergent Quantitative Models to identify how calculus students might develop a…

This qualitative descriptive study aimed to explore how community college students describe their motivations and reasoning when learning about controversial science topics at a southwestern community college. Anti-science attitudes have been increasing globally, but is not fully understood. Two research questions were developed using the theory…

Chemistry is considered a difficult subject by most students. Its difficulty lies in Chemistry's complex and abstract nature. This highly abstract nature requires constant interplay and coordination between the macroscopic, particulate, and symbolic representations. Experts can successfully navigate the various representations without overloading…

Adaptive reasoning is one of five components students use to develop mathematical expertise and become mathematically proficient. When students adapt their reasoning they are logically thinking about the mathematical relationships between concepts and adapting their thinking to solve problems. Three Act Math Tasks are popular math problems used in…

One of the goals of science education is to help students make sense of the world around them. To that end, it is critical that students understand the central ideas in each discipline like, in chemistry, energy and interactions. These ideas are of particular importance because they are directly related to one another and are relevant across other…

Analogical reasoning has played a significant role in the development of modern mathematical concepts. Although some perspectives in mathematics education have argued against the use of analogies and analogical reasoning in instructional contexts, some attempts have been made to leverage the pedagogical power of analogies. I assert that with a…

Socioscientific issues (SSI) such as COVID-19 and climate change often highlight the inequalities that structural racism creates. If we ever wish to equitably solve these issues, we require a population that has the scientific literacy and the sociopolitical consciousness to do so. Yet, the push for culturally relevant education has had little…

This study examined middle and secondary mathematics teachers' knowledge structures, informal inferential reasoning (IIR), and pedagogical content knowledge (PCK) for statistics. Using task-based clinical interviews (Goldin, 1997) and cross-case analysis (Creswell, 2013), a stratified purposeful sample (Patton, 2002) of nine teachers responded to…

The periodic table is recognized as one of the most powerful tools in science. While it is included in virtually all high school and undergraduate general chemistry curricula, it remains a mystery to many chemistry students who find it impossible to decode. Students are often able to predict periodic trends concerning atomic radius, ionization…

This exploratory study uses the convergent design of mixed methods to integrate adaptive expertise theory to study how individual student participant from graphic design or non-graphic-design majors to solve a novel ideation problem in graphic design. Adaptive expertise includes six dimensions: metacognition, flexibility, dynamic knowledge,…

Socioscientific issues (SSIs) are used to guide science instruction by presenting scientific real-world problems as multifaceted, consisting of social as well as scientific components that must be considered when constructing solutions to the issues. Using SSIs in classrooms can support students in developing scientific literacy by enhancing their…