12/2/2023 0 Comments Ia writer math equationsthe net force causes the acceleration) and together form a blended mental space that enables proper interpretation and application of this equation. For example, Newton’s second law of motion is often represented as \( \), the resources from mathematics (e.g., procedures of doing calculation, knowledge of multiplication, knowledge of the mathematics notation) can be blended with resources from science (e.g. Scientists use mathematical equations to formulate theories deduced from observations or experimentation or to represent patterns they observe (Brush, 2015 de Ataíde & Greca, 2013 De Berg, 1992 Ghosh, 2009 Pospiech, 2019 Steen, 2005 Wigner, 1960). Scientists use mathematical knowledge to represent ideas about scientific phenomenonĬanonical mathematical equations in science have been developed based on understanding of both scientific phenomena and mathematical concepts represented in the equations (Ghosh, 2009 Quale, 2011). This paper presents such a framework based on a review of the literature on instruction of mathematical equations in science and on students’ problem-solving using mathematical equations in a science context. However, a consistent and coherent framework of sensemaking of mathematical equations in science has not yet been developed. To successfully develop and understand the impact of providing different sensemaking opportunities, it is first necessary to understand the types of sensemaking that can occur. The reliance on algorithmic problem-solving strategies has been attributed to the different opportunities provided for sensemaking of mathematical equations in science during instruction (Bing & Redish, 2008 Lythcott, 1990 Schuchardt & Schunn, 2016). This tendency to solve problems algorithmically has been associated with a failure to transfer problem-solving techniques to novel contexts or more complex problems (Becker & Towns, 2012 Nakhleh, 1993 Ralph & Lewis, 2018 Schuchardt & Schunn, 2016 Stamovlasis, Tsaparlis, Kamilatos, Papaoikonomou, & Zarotiadou, 2005). However, studies on students solving quantitative problems show that they often solve problems by relying on algorithmic procedures without making connections between the mathematical equation and the scientific phenomenon (Bing & Redish, 2009 Stewart, 1983 Taasoobshirazi & Glynn, 2009 Tuminaro & Redish, 2007). Students are expected to be able to engage in sensemaking with these equations to interpret the mathematical and scientific meaning represented by the equation (Bialek & Botstein, 2004 Heisterkamp & Talanquer, 2015 Kuo, Hull, Gupta, & Elby, 2013 Sevian & Talanquer, 2014). Mathematical equations are used to represent scientific phenomenon and communicate scientific ideas (Bialek & Botstein, 2004 Brush, 2015 Gingras, 2001 Lazenby & Becker, 2019 Steen, 2005). This framework will allow for comparison across studies on the teaching and learning of mathematical equations in science and thus help to advance our understanding of how students engage in sensemaking when solving quantitative problems as well as how instruction influences this sensemaking. These themes were compiled into nine categories, four in the science sensemaking dimension and five in the mathematics sensemaking dimension. Therefore, a review of the literature was completed to identify themes addressing sensemaking of mathematical equations in science. Research into the types of sensemaking of mathematical equations in science contexts is hindered by the absence of a shared framework. This deficit may partly be the fault of instruction that focuses on superficial connections with the science and mathematics knowledge such as defining variables in the equation and demonstrating step-by-step procedures for solving problems. However, students often tend to rely on algorithmic/procedural approaches and struggle to make sense of the underlying science. Students who can engage in this type of blended sensemaking are more successful at solving novel or more complex problems with these equations. Understanding the ideas contained within these equations requires making sense of both the embedded mathematics knowledge and scientific knowledge. Scientific ideas are often expressed as mathematical equations.
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