# 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/sec^{2} ∗ t + v_{0} says that if v_{0} 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 |