# Table 2 Categories synthesized from literature to capture the sensemaking opportunities of mathematical equations in science classrooms

Dimension Category Short definition Selected references
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) Hansson et al., 2015; Hestenes, 2010; Izsák, 2004; Kuo et al., 2013; Quale, 2011; Redish & Kuo, 2015
Sci-Description Uses a mathematical equation to provide a quantifiable measure of a scientific phenomenon or object within the phenomenon. (e.g., equations for diversity index, the equation for speed) Bain, Rodriguez, & Towns, 2019b; Brahmia et al., 2016; Lehavi et al., 2017; Lehrer & Schauble, 2010
Sci-Pattern Emphasizes the 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) Baxter, Ruzicka, Beghetto, & Livelybrooks, 2014; Michelsen, 2015; Redish, 2017; Rodriguez et al., 2019
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) Etkina et al., 2006; Hestenes, 2010; Redish, 2017; Schuchardt & Schunn, 2016
Mathematics sensemaking Math-Procedure Emphasizes the predetermined steps or algorithms for problem-solving Hiebert & Lefevre, 1986; Hansson et al., 2015; Peled & Segalis, 2005
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) Bing & Redish, 2007; Hansson et al., 2015; Potgieter & Blignaut, 2017; Schuchardt & Schunn, 2016
Math-Structure Focuses on the form of the equation, the numbers and arrangement of symbols and operations (e.g., □ + □ as two components added together) Bain, Rodriguez, Moon, & Towns, 2019; McNeil & Alibali, 2004; Pospiech, 2019; Redish, 2017; Sherin, 2001
Math-Relation Emphasizes quantitative relationships between variables in the equations (e.g., v = 9.8m/sec2 ∗ t + v0 says that if v0 is 0, v will be 9.8 times bigger for every unit increase in t) Carlson, Jacobs, Coe, Larsen, & Hsu, 2002; Lehavi et al., 2017; Rodriguez, Santos-Diaz, Bain, & Towns, 2018; Sherin, 2001
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) Even, 1990; Hiebert & Lefevre, 1986; Peled & Segalis, 2005; Rittle-Johnson & Schneider, 2015