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Abstract Background Many students solving quantitative problems in science struggle to apply mathematical instruction they have received to novel problems. The few students who succeed often draw on both their mathematical understanding of the equation and their scientific understanding of the phenomenon. Understanding the sensemaking opportunities provided during instruction is necessary to develop strategies for improving student outcomes. However, few studies have examined the types of sensemaking opportunities provided during instruction of mathematical equations in science classrooms and whether they are organized in ways that facilitate integration of mathematical and scientific understanding. This study uses a multiple case study approach to examine the sensemaking opportunities provided by four different instructors when teaching the same biological phenomenon, population growth. Two questions are addressed: (1) What types of sensemaking opportunities are provided by instructors, and (2) How are those sensemaking opportunities organized? The Sci-Math Sensemaking Framework, previously developed by the authors, was used to identify the types of sensemaking. Types and organization of sensemaking opportunities were compared across the four instructors. Results The instructors provided different opportunities for sensemaking of equations, even though they were covering the same scientific phenomenon. Sensemaking opportunities were organized in three ways, blended (previously described in studies of student problem solving as integration of mathematics and science resources), and two novel patterns, coordinated and adjacent. In coordinated sensemaking, two types of sensemaking in the same dimension (either mathematics or science) are explicitly connected. In adjacent sensemaking, two different sensemaking opportunities are provided within the same activity but not explicitly connected. Adjacent sensemaking was observed in three instructors’ lessons, but only two instructors provided opportunities for students to engage in blended sensemaking. Conclusions Instructors provide different types of sensemaking opportunities when teaching the same biological phenomenon, making different resources available to students. The organization of sensemaking also differed with only two instructors providing blended sensemaking opportunities. This result may explain why few students engage in the successful strategy of integrating mathematics and science resources when solving quantitative problems. Documentation of these instructional differences in types and organization of sensemaking provides guidance for future studies investigating the effect of instruction on student sensemaking.

Abstract Scientific ideas are often expressed as mathematical equations. Understanding the ideas contained within these equations requires making sense of both the embedded mathematics knowledge and scientific knowledge. Students who can engage in this type of blended sensemaking are more successful at solving novel or more complex problems with these equations. However, students often tend to rely on algorithmic/procedural approaches and struggle to make sense of the underlying science. This deficit may partly be the fault of instruction that focuses on superficial connections with the science and mathematics knowledge such as defining variables in the equation and demonstrating step-by-step procedures for solving problems. Research into the types of sensemaking of mathematical equations in science contexts is hindered by the absence of a shared framework. Therefore, a review of the literature was completed to identify themes addressing sensemaking of mathematical equations in science. These themes were compiled into nine categories, four in the science sensemaking dimension and five in the mathematics sensemaking dimension. This framework will allow for comparison across studies on the teaching and learning of mathematical equations in science and thus help to advance our understanding of how students engage in sensemaking when solving quantitative problems as well as how instruction influences this sensemaking.

Teaching assistants (TAs) often lead courses using curricula they did not design. Therefore, examining how curriculum and professional development (PD) interact to influence TAs' teaching practices is critical. This study describes the effects of a curriculum and PD intervention in two contexts: when TAs are teaching curriculum that is explicitly linked to PD, and when teaching curriculum that is not linked to PD. The Intervention curriculum featured structured opportunities for reform-oriented teaching practices. The Intervention PD was situated in the context of these specific curriculum activities and modelled the desired teaching practices. TAs that participated in the intervention implemented more student-centered teaching practices than TAs that did not participate in the intervention, even when teaching curriculum that was not designed to be student-centered and was not linked to PD. A linear model of TAs' teaching practices that included PD type, task cognitive demand and curriculum type indicates that cognitive demand has the largest relationship with teaching practices, followed by PD type. These results have implications for policy. They suggest that investment in curriculum-linked TA PD can be effective even when teaching curricula that is not linked to PD. Additionally, investment in development of higher-cognitive-demand tasks may be an effective strategy to support implementation of student-centered practices.

Interdisciplinary research is the synergistic combination of two or more disciplines to achieve one research objective. Current research highlights the importance of interdisciplinary research in science education, particularly between educational experts within a particular science discipline (discipline-based education researchers) and those who study human learning in a more general sense (learning scientists). However, this type of interdisciplinary research is not common and little empirical evidence exists that identifies barriers and possible solutions. We hosted a pre-conference workshop for Discipline-Based Educational Researchers and Learning Scientists designed to support interdisciplinary collaborations. We collected evidence during our workshop regarding barriers to interdisciplinary collaborations in science education, perceptions of perceived cohesion in participants' home university departments and professional communities, and the impact of our workshop on fostering new connections. Based on participants' responses, we identified three categories of barriers, Disciplinary Differences, Professional Integration, and Collaborative Practice. Using a post-conference survey, we found an inverse pattern in perceived cohesion to home departments compared to self-identified professional communities. Additionally, we found that after the workshop participants reported increased connections across disciplines. Our results provide empirical evidence regarding challenges to interdisciplinary research in science education and suggest that small professional development workshops have the potential for facilitating durable interdisciplinary networks where participants feel a sense of belonging not always available in their home departments.

ABSTRACT Biologists consider variability during biological investigations. A robust quantitative understanding of variability is particularly important during data analysis, where statistics are used to quantify variation and draw conclusions about phenomena while accounting for variation. Many students struggle to correctly apply a quantitative understanding of variation to statistically analyze data. We present quantitative and qualitative analyses of introductory biology students’ responses on two pairs of multiple-choice questions querying two concepts related to the quantitative analysis of variation. More students correctly identify a mathematical expression of variation than correctly interpret it. Many students correctly interpret a nonsignificant p-value in the context of a very small sample size, but fewer students do so in the context of a large sample size. These results imply that many students have an incomplete quantitative understanding of variation. These findings suggest that instruction focusing on conceptual understanding, not procedural problem solving, may elevate students’ quantitative understanding of variation.

Variation is an important concept that underlies experimental design and data analysis. Incomplete understanding of variation can preclude students from designing experiments that adequately manage organismal and experimental variation, and from accurately conducting and interpreting statistical analyses of data. Because of the lack of assessment instruments that measure students' ideas about variation in the context of biological investigations, we developed the Biological Variation in Experimental Design and Analysis (BioVEDA) assessment. Psychometric analyses indicate that BioVEDA assessment scores are reliable/precise. We provide evidence that the BioVEDA instrument can be used to evaluate students' understanding of biological variation in the context of experimental design and analysis relative to other students and to their prior scores.