Developing Intuitive Reasoning with Graphs to Support Science Arguments

By Grueber, David | Science Scope, September 2011 | Go to article overview

Developing Intuitive Reasoning with Graphs to Support Science Arguments


Grueber, David, Science Scope


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With all of the attention recently on the importance of students' ability to make scientific arguments (NRC 2007; Viadero 2009), have you wondered how to support them in doing so? Having the knowledge and skills to analyze and make claims about data is the heart of science literacy (Bybee 2007). Literacy broadly refers to the application of knowledge and skills. Science literacy more specifically means the ability to use scientific knowledge to identify questions and draw evidence-based conclusions to understand the natural world. Science literacy is necessary to making scientific arguments.

Graphs are important for supporting critical thinking and scientific argumentation because students can use them to reason, make judgments and decisions, and solve problems like a scientist (Connery 2007). Yet teaching students how to use math to actually think critically continues to be difficult for teachers.

Following are descriptions of two activities that teach students how to make a scientific argument and articulate a scientific claim (Driver, Newton, and Osborne 2000). First is a math activity that uses lemonade to teach students reasoning skills with graphs; what follows is a science activity with a basketball and pump that uses a discrepant event to make a claim about the nature of air.

Math and graphing

One key principle of a constructivist approach to teaching students how to use graphs is to connect the graph with students' experiences. A very effective way to do this is through tasting juice mixtures. The Rational Numbers Project (Behr et al. 2002) has produced a number of activities with juice mixtures to teach students math concepts, including how to express ratios as fractions; equivalent fractions; the relationship between the graph and the meaning of data points; the mechanics of data entry, such as determining the axis plotting and labeling points; and the intuitive underpinning of slope, because equivalent ratios lie on a single line of the graph.

In addition to understanding the mechanics of graphing, it is important for students to understand why graphs are a significant tool for reasoning in science (Hardy et al. 2005). X-Y scatter graphs are particularly useful to display relationships between variables with the slope of a line. The slope of the graph represents proportional concepts such as speed, density, or degree of concentration. In proportional situations, a relationship exists between the quantities that can be expressed through the algebraic rule of y = mx + b (Cramer and Post 1993). When students design an experiment, deciding what variables to record and where to plot variables on a graph is important for reasoning about the experiment.

The following activity, which is adapted from the Rational Numbers Project, teaches students about the relationship between slope and variables in an experiment Students begin by making mixtures of lemon juice and sugar, deciding for themselves how many spoonfuls of each to use. Next they taste and rate the resulting mixtures as one of the following: very sweet, sweet, neither sweet nor sour, or very sour. The class creates a data table to record student observations (see Figure 1). Next, the teacher plots on a graph students' data points (on the vertical axis, spoons of lemon juice; on the horizontal, spoons of sugar), labels each point with the student's name and taste rating, and connects the points with similar taste ratings. (Safety note: Because tasting food or drink in the science laboratory is not permitted, this activity should be performed in the consumer science classroom. Also, lemon juice is considered an acid, and chemical splash goggles should be worn at all times. Finally, check with students to make sure there are no food allergies to lemon juice or sugar.)

When students plot and label their taste ratings on the graph, they will see those ratings scattered all over the graph (Figure 2). …

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