ABSTRACT

DIFFERENTIATING MASS FROM DENSITY:

THE EFFECT OF MODELING AND STUDENT DIALOGUE

IN A SIXTH-GRADE CLASSROOM

Martha L. (Molly) Shaw

The concept of density can be difficult to learn. In the middle grades, students characteristically conflate mass and density, and even after instruction many students do not distinguish them consistently (Smith, Maclin, Grosslight, & Davis, 1997). Few develop a conceptualization of density that accounts for the implications of changing mass, volume, temperature, and/or state. My work looks specifically at how students make sense of the relationship between mass and volume as they refine their understanding of density.

The concept of density is challenging to teach. Traditional methods of teaching density in middle-school classrooms typically involve either the measurement of an object’s mass and volume and the subsequent calculation of the ratio of the two quantities, or the observation of different materials in water to learn about their buoyancy. Unfortunately, as Carol Smith and her colleagues have documented (1985, 1992, 1997), these approaches leave many students stuck in their “commonsense frameworks” that merge mass and density into one concept. Teachers need better ways to teach density.

Hence I designed an intervention to study the effects of some possibly more effective ways to teach density. I developed and taught a complex intervention (Brown, 1992) featuring student modeling, extensive student dialogue on data and data analyses, formative assessments, the substitution of hands-on inquiry for mathematical problem sets, and multiple thought experiments. The hallmarks of the intervention were modeling and student dialogue, and the research question I posed was: Does classroom practice that encourages modeling with open-ended discourse help students differentiate between the concepts of mass and density?

I patterned my research on a Smith study of density instruction in eighth grade (Smith, Maclin, Grosslight, & Davis, 1997), which had a quasiexperimental research design that compared the results of teaching density differently in two classrooms. I selected an intervention class and a comparison class from those I was teaching. The core of the density curriculum was similar in both classes. Instead of the intervention, though, the comparison class closely followed the lesson sequences provided by the classroom textbook, which tended to focus on formal and formulaic density instruction. I modified Smith’s assessments for sixth graders. After teaching one class the intervention curriculum and the other the textbook-based curriculum, I evaluated and compared the progress of research participants in both classrooms by means of a pre- and post-instruction clinical interview, a pre- and post-instruction written test, and the end-of-chapter test from the textbook used in the comparison classroom.

The results of my study were consistent: the intervention students outperformed and showed greater improvement on all assessments compared to the comparison students. In this study, modeling and student discourse were more effective ways to teach density than a standard textbook-based lesson sequence. The intervention helped students start to disrupt the conflation of mass and density, fostering both the comprehension of volume as a variable property of matter, and a nuanced understanding of density beyond formulaic reasoning.

This dissertation is a report of my study for two audiences—academics and science educators. For the latter, I include recommendations for improving density instruction that are informed by my research.

My dissertation research is designed to improve access to STEM content through the development of cosmology visualizations that support all learners as they engage in cosmological sense-making. To better understand how to design visualizations that

work toward breaking cycles of power and access in the sciences, I orient my work to following "meta-question": How might educators use visualizations to support diverse ways of knowing and learning in order to expand access to cosmology, and to science? In this dissertation, I address this meta-question from a pragmatic epistemological perspective, through a sociocultural lens, following three lines of

inquiry: experimental methods (Creswell, 2003) with a focus on basic visualization design, activity analysis (Wells, 1996; Ash, 2001; Rahm, 2012) with a focus on culturally and linguistically diverse learners, and case study (Creswell, 2000) with a focus on expansive learning at a planetarium (Engeström, 2001; Ash, 2014). My research questions are as follows, each of which corresponds to a self contained course of inquiry with its own design, data, analysis and results: 1) Can mediational cues like color affect the way learners interpret the content in a cosmology visualization? 2) How do cosmology visualizations support cosmological sense-making for diverse students? 3) What are the shared objects of dynamic networks of activity around visualization production and use in a large, urban planetarium and how do they affect learning? The result is a mixed-methods design (Sweetman, Badiee & Creswell, 2010) where both qualitative and quantitative data are used when appropriate to address my research goals. In the introduction I begin by establishing a theoretical framework for understanding visualizations within cultural historical activity theory (CHAT) and situating the chapters that follow within that framework. I also introduce the concept of cosmological literacy, which I define as the set of conceptual, semiotic and cognitive resources required to understand the scientific Universe on a cosmological scale. In the first chapter I use quantitative methods to investigate how 122 postsecondary learners relied on mediational cues like color to interpret dark matter in a cosmology visualization. My results show that color can have a profound effect on the way that audiences interpret a dynamic cosmology visualization, suggesting a closer look at learning activity. Thus in the second chapter I look at how the visualizations are used by small groups of community college students to make sense of cosmology visualizations. I present evidence that when we look past linguistic fluency, visualizations can scaffold cosmological sense-making, which I define as engaging in object-oriented learning activity mediated by concepts and practices associated with cosmological literacy. In the third chapter I present a case study of an urban planetarium trying to define its goals at a time of transition, during and after the development of a visualization-based planetarium show. My analysis reveals several historical contradictions that appear to impel a shift toward affective goals within the institution, and driving the implementation of visualizations, particularly in the context of immersive1 planetarium shows. I problematize this result by repositioning the shift toward affective goals in the context of equity and diversity. Finally in my conclusion I present broad recommendations for visualization design and implementation based on my findings.

Experiences preservice teachers (PTs) have in their preparation programs can directly impact their use of effective and just pedagogy in the classroom (Darling-Hammond, 2000; Tolbert, 2015; Stoddart, Pinal, Latzke, and Canaday, 2002; Bravo, Mosqueda, Solis and Stoddart, 2014). However, researchers in the field of Education have struggled to make sense of the impact that teacher preparation programs have on teachers and their practice, particularly with respect to issues of diversity, equity, and justice in instructional theory and practice (Cochran-Smith et. al, 2015; Tolbert, 2016; Ladson-Billings, 1999; Waghorn and Stevens, 1996). This dissertation addresses the field’s need for new analytics that can be used to gauge the actual, in-the-moment impact that equity-oriented teacher preparation activities have on preservice teachers’ orientations with respect to students and equitable science instructional practices. This study employs a longitudinal case study design and Critical Cultural Discourse Analysis to investigate in depth how hegemonic power is enacted, resisted, challenged, and transformed in an equity-oriented science teacher preparation program (Creswell, 2014; Moje and Lewis, 2007; Gee, 2015; Fairclough, 1992). The analysis is guided by a critical sociocultural framework. My purpose was to add to our growing understanding of how systemic, structural, historical, and ongoing harm is sustained in and through equity-oriented science teacher preparation. Findings from this study reveal some of the ways in which hegemonic power acts in and through science teacher preparation. Through my analysis of two classroom discussions, I highlight Discourses of power that were enacted in/through the activity system. The first discussion, presented as Vignette I, concerned learning theories and their applications in science classrooms, and my analysis highlights the competing ideological and ontoepistemic assumptions embedded in the learning theories and Discourses. The second discussion, presented as Vignette II, centered on two preservice science teachers’ reading of two articles on equitable science instruction. The PSTs’differing disciplinary discourse enactments engender a subtle tension, and the disciplinary literacy practices of western natural sciences enacted by one PST become an obstacle to sensemaking for the small group involved. My hope is that through building understanding of these issues, this study may generate new possibilities for reparation, care, and more just ways of being and learning in and beyond secondary science classrooms.

Equity in science education is a central goal for many educators, researchers, policymakers, learning institutions, community organizations, and more. Scholars are increasingly looking to critical, intersectional, transdisciplinary, and dialectical theories to better understand the tensions that promote or limit equitable science education (Stetsenko, 2016; Sharma, 2020; Higgins et al., 2017; Takeuchi et al., 2020; Strong et al., 2016). This dissertation explores one specific intersection of science education inequity: access to equitable field-based education (EFBE). Utilizing critical ethnography (Freire, 1970; Barton, 2001; Trueba,1999) and cultural-historical activity theory (CHAT) (Vygotsky, 1986; Engestrom, 1987; Cole, 1988; Leon’tev, 1978; Sannino, 2015), a patchworked theoretical framework I call critical ethnographic CHAT (CE-CHAT) (Higgins et al., 2017), this research aimed to understand how teachers, who were former participants of a professional development program for pre-service teachers that aimed to prepare them to teach EFBE in their future classrooms, took up the program goal of EFBE in their first year(s) teaching, in both theory and practice, exploring the overlapping systems constraining or expanding the process of hybridization. The findings from this study provide insight into the multiplicities of enactment (Buxton et al., 2015) and nuanced pathways that teachers took when trying to hybridize and enact EFBE in their classrooms and the tensions they faced. From these pathways, a story of resistance and expansion emerged, as all the teachers I spoke with, regardless of where they were on their pathway to EFBE, strongly believed in the goal of EFBE and saw it as something they could accomplish overtime.

To protect and conserve the Earth's biodiversity and ecosystem services, it is important not only to understand and conserve species and ecosystems, but also to instill an understanding and appreciation for biodiversity and ecosystem services in the next generations of both scientists and citizens. Thus, this dissertation combines research into the ecology and identity of large bivalves at Midway Atoll in the Northwestern Hawaiian Islands (NWHI) with research on pedagogical strategies for integrating mathematics into undergraduate biology education.

The NWHI is one of the few remaining large, mainly intact, predator-dominated coral reef ecosystems and one of the world's largest marine protected areas. Previous bivalve studies focused on the black-lipped pearl oyster, Pinctada margaritifera, which was heavily harvested in the late 1920s, has not recovered, and is now a candidate species for restoration.

First, I combined remote sensing, geographic information systems, SCUBA, and mathematical modeling to quantify the abundance, spatial distributions, and filtration capacity of large epifaunal bivalves at Midway Atoll. These bivalves are most abundant on the forereef outside the atoll, but densities are much lower than reported on other reefs, and Midway's bivalves are unlikely to affect plankton abundance and productivity inside the lagoon.

Second, I used molecular techniques and phylogenetic reconstructions to identify pearl oysters (Pinctada) from Midway Atoll as P. maculata, a species not previously reported in Hawaii. As a small morphologically cryptic species, P. maculata may be a native species that has not been collected previously, a native species that has been identified incorrectly as the morphologically similar P. radiata, or it may be a recent introduction or natural range extension from the western Pacific.

Finally, I review science education literature integrating mathematics into undergraduate biology curricula, and then present and evaluate a computer inquiry module using learner-centered teaching strategies to introduce structured population (matrix) models in an upper-division ecology course. Using pre- and post-test surveys and student interviews, I concluded that students accomplished the module's learning goals: to use matrix models to assess and protect populations and to better appreciate the importance and uses of mathematics in ecology and conservation.