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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.