## Practice 5: Using Mathematics and Computational Thinking

Applications of mathematics and computational thinking in science and engineering require flexible thinking in a variety of contexts. Instructional strategies that support students’ feelings of belonging cultivate a safe space for students to take chances with potentially unfamiliar types of mathematical or computational thinking across contexts. Strategies that support belonging also encourage students to develop a sense of being part of a community of scientists and engineers, which is especially important for students who may not have a well-developed science identity or who may feel alienated from science [see Motivation as a Tool for Equity]. As students begin to feel a greater sense of belonging within their science classroom community and within science and engineering communities, they may feel more inclined to engage in using mathematics and computational thinking as a practice.

## Strategies

Students may have little experience using mathematics and computational thinking to represent, model, and analyze variables and their relationships to make sense of phenomena or solve design problems. Students’ mathematical and computational thinking proficiency and, more importantly, their confidence in those abilities may vary widely. Ample examples, models, and opportunities for success are crucial to support students who may enter science class with lower confidence in these areas and for those students whose skills can be developed further. Informational feedback will help all students understand when they are progressing and, if they are not, what they can work on to improve.

## Strategies

- Guidelines for graphing: the parts of a graph; how to determine a good scale for the data they are graphing; what type of graph will be most useful for their purpose
- Spreadsheets for algorithms:
- Functions in Excel or Google Sheets (e.g., calculating the mean or sum of several numbers; looking up numbers or text in a data set)
- Examples can help demonstrate to students what an algorithm is

- Process charts for algorithms:
- Common logical structures (e.g., if, then, else; for loop; while loop)
- Examples of simple algorithms that can be used as building blocks or jumping off points

Mathematics and computational thinking are skills that scientists and engineers use to gain deeper understanding of the phenomenon or problem they are investigating. Supports for a learning orientation frame the purpose of this work as such, rather than as an activity to complete in and of itself, or with the purpose of obtaining the correct answer. Because of varying proficiency in mathematics and computational thinking, supporting students’ learning orientation can help to sustain motivation if or when students struggle with, for example, abstract thinking, logic, or algorithms so that they do not become discouraged by mistakes or incorrect answers. This support may be especially important for students who are concerned that their struggles are confirming negative stereotypes that others may hold about their mathematical and computational ability [see Motivation as a Tool for Equity]. A learning orientation can help students view their mistakes as part of the process of developing mathematics and computational thinking skills in the context of science and engineering.

## Strategies

Problems requiring the application of mathematics and computational thinking often have multiple possible solutions or multiple possible algorithms to reach the optimal solution. When feasible, students should be given the autonomy to choose how they will approach a problem and how they will calculate a solution. Autonomy can be undermined if students feel there is only one correct answer or that they are being asked to follow a predetermined set of steps.

## Strategies

Mathematics and computational thinking are an integral part of science and engineering. Framing the use of mathematics and application of computational thinking within a phenomenon or design problem that is of interest to students may help motivate them to work hard on tasks involving these skills. Encouraging students to connect mathematics and computational thinking to a broad range of situations that relate to their lives and home communities can make them more invested in the practice as something that can be leveraged to figure out phenomena or solve problems that feel relevant and important to them [see Motivation as a Tool for Equity]. Many students may be unfamiliar with or lack confidence in using mathematics to represent and relate physical variables and to make predictions, and in using computational thinking. Connecting the practice of using mathematics and computational thinking to the work of scientists and engineers in understanding phenomena or solving problems of interest may help encourage students to engage in this type of work despite their unfamiliarity or lack of confidence.

## Strategies

- Relate software programs to the work that contemporary scientists and engineers do (i.e., they log their data and share results in their teams through digital platforms)
- Introduce the connection between software programs used in class and other programs used for coding (and the cool things coders do!)