Table 1 Categories in the Sci-Math Sensemaking Framework (Zhao & Schuchardt, 2021)

Science sensemaking

Sci-Label

Connects variables or operators in mathematical equations to quantifiable characteristics of objects or processes in the scientific phenomenon, i.e., the definition or scientific meaning of the variable (e.g., m = mass)

Sci-Description

Uses a mathematical equation to provide a quantifiable measure of a parameter of a scientific phenomenon or an object within the phenomenon (e.g., equations for diversity index, the equation for density)

Sci-Pattern

Emphasizes the qualitive trend or pattern among variables in the mathematical equation situated within the scientific phenomenon (e.g., in the equation F = ma, acceleration is proportional to the force on an object)

Sci-Mechanism

Emphasizes connections to a mechanism that explains how or why a scientific phenomenon occurs (e.g., for the equation \( \overrightarrow{a}={\overrightarrow{F}}_{\mathrm{net}}/m \) , the net force distributed over mass causes the acceleration of an object in the same direction)

Mathematics sensemaking

Math-Procedure

Emphasizes the predetermined steps or algorithms for problem solving

Math-Rule

Focuses on generalizable statements that guide calculation (e.g., the probability of two events occurring simultaneously is equal to the product of the individual probabilities)

Math-Structure

Focuses on the form of the equation, the numbers and arrangement of symbols and operations (e.g., ▯+▯ as two components adding together)

Math-Relation

Emphasizes quantitative relationships between variables in the equations (e.g., v = 9.8m/s² ∗ t + v₀ says that if v₀ is 0, v will be 9.8 times bigger for every unit increase in t

Math-Concept

Refers to a network of knowledge that enables explanation of the what, how and why of a mathematical idea (e.g., conceptually, probability is the proportion of desired events out of all possible events)