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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.

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.

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.

The National Research Council framework for science education and the Next Generation Science Standards have developed a need for additional research and development of curricula that is both technologically model-based and includes engineering practices. This is especially the case for biology education. This paper describes a quasi-experimental design study to test the effectiveness of a model-based curriculum focused on the concepts of natural selection and population ecology that makes use of Excel modeling tools (Modeling Instruction in Biology with Excel, MBI-E). The curriculum revolves around the bio-engineering practice of controlling an invasive species. The study takes place in the Midwest within ten high schools teaching a regular-level introductory biology class. A post-test was designed that targeted a number of common misconceptions in both concept areas as well as representational usage. The results of a post-test demonstrate that the MBI-E students significantly outperformed the traditional classes in both natural selection and population ecology concepts, thus overcoming a number of misconceptions. In addition, implementing students made use of more multiple representations as well as demonstrating greater fascination for science.

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.

Course-based undergraduate research experiences (CUREs) have the potential to improve undergraduate biology education by involving large numbers of students in research. CUREs can take a variety of forms with different affordances and constraints, complicating the evaluation of design features that might contribute to successful outcomes. In this study, we compared students’ responses to three different research experiences offered within the same course. One of the research experiences involved purely computational work, whereas the other two offerings were bench-based research experiences. We found that students who participated in computer-based research reported at least as much interest in their research projects, a higher sense of achievement, and a higher level of satisfaction with the course compared with students who did bench-based research projects. In open-ended comments, similar proportions of students in each research area expressed some sense of project ownership as contributing positively to their course experiences. Their comments also supported the finding that experiencing a sense of achievement was a predictor of course satisfaction. We conclude that both computer-based and bench-based CUREs can have positive impacts on students’ attitudes. Development of more computer-based CUREs might allow larger numbers of students to benefit from participating in a research experience.

Amid calls for integrating science, technology, engineering, and mathematics (iSTEM) in K–12 education, there is a pressing need to uncover productive methods of integration. Prior research has shown that increasing contextual linkages between science and mathematics is associated with student problem solving and conceptual understanding. However, few studies explicitly test the benefits of specific instructional mechanisms for fostering such linkages. We test the effect of students developing a modeled process mathematical equation of a scientific phenomenon. Links between mathematical variables and processes within the equation and fundamental entities and processes of the scientific phenomenon are embedded within the equation. These connections are made explicit as students participate in model development. Pre–post gains are tested in students from diverse high school classrooms studying inheritance. Students taught using this instructional approach are contrasted against students in matched classrooms implementing more traditional instruction (Study 1) or prior traditional instruction from the same teachers (Study 2). Students given modeled process instruction improved more in their ability to solve complex mathematical problems compared to traditionally instructed students. These modeled process students also show increased conceptual understanding of mathematically modeled processes. The observed effects are not due to differences in instructional time or teacher effects.

Prior studies have shown that students have difficulty understanding the role of mutation in evolution and genetics. However, little is known about unifying themes underlying students’ difficulty with mutation. In this study, we examined students’ written explanations about mutation from a cognitive science perspective. According to one cognitive perspective, scientific phenomena can be perceived as entities or processes, and the miscategorization of processes as entities can lead to noncanonical ideas about scientific phenomena that are difficult to change. Students’ incorrect categorization of processes as entities is well documented in physics but has not been studied in biology. Unlike other scientific phenomena that have been studied, the word “mutation” refers to both the process causing a change in the DNA and the entity, the altered DNA, making mutation a relevant concept for exploration and extension of this theory. In this study, we show that, even after instruction on mutation, the majority of students provided entity-focused descriptions of mutation in response to a question that prompted for a process-focused description in a lizard or a bacterial population. Students’ noncanonical ideas about mutation occurred in both entity- and process-focused descriptions. Implications for conceptual understanding and instruction are discussed.