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Science sensemaking
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Sci-Label
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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)
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Hansson et al., 2015; Hestenes, 2010; Izsák, 2004; Kuo et al., 2013; Quale, 2011; Redish & Kuo, 2015
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Sci-Description
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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)
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Bain, Rodriguez, & Towns, 2019b; Brahmia et al., 2016; Lehavi et al., 2017; Lehrer & Schauble, 2010
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Sci-Pattern
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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)
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Baxter, Ruzicka, Beghetto, & Livelybrooks, 2014; Michelsen, 2015; Redish, 2017; Rodriguez et al., 2019
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Sci-Mechanism
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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)
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Etkina et al., 2006; Hestenes, 2010; Redish, 2017; Schuchardt & Schunn, 2016
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Mathematics sensemaking
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Math-Procedure
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Emphasizes the predetermined steps or algorithms for problem-solving
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Hiebert & Lefevre, 1986; Hansson et al., 2015; Peled & Segalis, 2005
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Math-Rule
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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)
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Bing & Redish, 2007; Hansson et al., 2015; Potgieter & Blignaut, 2017; Schuchardt & Schunn, 2016
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Math-Structure
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Focuses on the form of the equation, the numbers and arrangement of symbols and operations (e.g., □ + □ as two components added together)
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Bain, Rodriguez, Moon, & Towns, 2019; McNeil & Alibali, 2004; Pospiech, 2019; Redish, 2017; Sherin, 2001
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Math-Relation
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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)
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Carlson, Jacobs, Coe, Larsen, & Hsu, 2002; Lehavi et al., 2017; Rodriguez, Santos-Diaz, Bain, & Towns, 2018; Sherin, 2001
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Math-Concept
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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)
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Even, 1990; Hiebert & Lefevre, 1986; Peled & Segalis, 2005; Rittle-Johnson & Schneider, 2015
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