Modeling Scientific Processes With Mathematics Equations Enhances Student Qualitative Conceptual Understanding and Quantitative Problem Solving

Abstract

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.

How much professional development is needed with educative curriculum materials? It depends upon the intended student learning outcomes

“…Statistical significance and effect size details are presented for each planned contrast. The dotted line shows the mean pre–post change in each content area for a group of comparison teachers using a traditional curriculum (Schuchardt & Schunn, ). (B) Gains for each individual teacher's students by condition in open diamonds, and mean gain across teacher by condition in black squares…”

“…The description of the MCM unit contained here focuses on those details that illustrate how the MCM inheritance unit differed from traditional instruction in inheritance (see Schuchardt & Schunn, for details). This unit was designed to incorporate a type of insertion of mathematics into science that treated mathematics as a model.…”

“…The assessments were the same as used in Schuchardt and Schunn (), for comparability. The posttests had a mean KR‐20 (Kuder and Richardson Formula 20 test, (Kuder & Richardson, )) of 0.72 (mean discrimination = 0.46; mean difficulty = 0.50).…”

“…The posttests had a mean KR‐20 (Kuder and Richardson Formula 20 test, (Kuder & Richardson, )) of 0.72 (mean discrimination = 0.46; mean difficulty = 0.50). (See Schuchardt and Schunn () for additional details regarding test item sources, and on reliability and validity of the tests. )…”

“…This improved understanding would allow them to be better able to solve complex and novel quantitative problems and enhance their ability to apply their qualitative understanding of the biological process to make qualitative predictions. Schuchardt and Schunn () found that, compared to traditional instruction that used an algorithmic approach to mathematics (Figure B), this type of inclusion of mathematics in science instruction resulted in a five‐fold greater gain in students’ understanding of the mathematically‐modeled inheritance processes, and a four‐fold greater gain in students’ ability to solve complex inheritance problems. In other words, students were better able to make both qualitative predictions (e.g., what types of offspring) and quantitative predictions (e.g., the probability of each type of offspring) involving inheritance concepts.…”