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10/29/2003 - Edwin P. Christmann
The National Council of Teachers of Mathematics Standards expect that all students in grades six through eight should be able to “formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them” (NCTM 2000). Likewise, as proposed in the National Science Education Standards (NRC 1996), middle school students engaged in inquiry are to use mathematics and technologies to gather, analyze, and interpret data. Subsequently, objectives from mathematics and science lessons can be met efficiently, especially when technological tools such as graphing calculators, PDAs, and/or statistical software packages are used as tools for data analyses.
The following activity is a practical example of how middle school students can use technology to analyze data. In this illustration, students will be expected to design and conduct a scientific investigation based on data collected from height and arm span measurements (see Content Standard A: Science as Inquiry). Subsequently, after students make accurate measurements, they can design and execute investigations, interpret data, and form logical explanations about the results of the investigation. Keep in mind, however, that the technology applications applied here for data analysis can be used across a variety of topics. For example, the Principles and Standards for School Mathematics (NCTM 2000) gives several examples that show how middle school teachers can provide learning experiences that involve the analysis of data (see Figure 1).
Figure 1. Sample data analysis problems.
Sample activity objectives
When you complete this lesson, you will be able to:
Activity
During a life science unit on the human body, a class of sixth grade students measured their height and arm span (see Figure 2). This activity can be adapted for middle schoolers’ of differing grade and ability levels. For example, middle school teachers who work with gifted students will be able to have their students compute a variety of statistics—perhaps even a correlation coefficient or a t-test (Lehman and Christmann 1999). To be realistic, however, having students compute descriptive statistics (e.g., mean, median, mode, standard deviation, and so on), and organizing the descriptive statistics with a statistical graph, such a scatter plot can be an excellent introduction to data analysis for most middle school students.
While students take the height and arm span measurements, the teacher can interface the TI-73 graphing calculator to an overhead projection panel to provide an audiovisual for the collection of data. Students can input their individual data quickly into the variables that the teacher has already designated in the data editor. The advantage in using a graphing calculator here instead of a spreadsheet program is the subsequent lesson’s emphasis on data manipulation and interpretation. As an extension activity, students could use the math functions within a spreadsheet application to develop their own analyses. In addition, students can modify or update the data entry and see the modified results. The statistical graphics and tables can be placed into a finished research report.
Figure 3. Box-and-whiskerplot for students' heights.
This box-and-whisker plot indicatesthe high, low, and median heights of the sixth grade students while dividing the data into four groups.
After taking the height and arm span measurements, the teacher can now lead a class discussion using a set of real-life data. Subsequently, the data can be organized in both table and plot formats in order to facilitate examination. For instance, a frequency table can be displayed and scanned for a minimum value, a maximum value, and a mode (if present). A box-and-whisker plot can be examined for outliers as well as for focusing on portions of the entire data set, namely quartiles (see Figure 3).
In addition to organizing data, data analysts generally summarize their data as well. Measures of central tendency (mean, median) and variability (range, standard deviation) are two of the descriptive statistics often used to “tell a story” about a set of data (see Figure 4).
Figure 4. Descriptive statistics for students' heights.
Again, computations like these can be performed on a single variable at a time or all variables simultaneously. Displaying all analyses or all raw data simultaneously can help students search for patterns among the computed statistics or raw data. For instance, students might detect that the lengths of height are longer than the lengths of arm span. In this example the arm span and height data appear to be similar. With the aid of the graphing calculator, the teacher can take such observations and have the class immediately examine them more quantitatively. For example, we can use the graphing calculator to draw a scatter plot showing the relationship between arm span and height (see Figure 5).
Figure 5. Scatter plot ofarm span and height.
In addition to analyzing entire data sets, scientists often examine subsets of data. If each student inputs his/her gender at the time of data entry, the analyses previously described can now be performed on each subset of the data. Moreover, these follow-up analyses can be used to illustrate the point that sometimes conclusions that are drawn for a set of data may be largely influenced by a subset of those data. In later science classes, students will hear how chemists describe properties of elements but at times may subdivide the set of elements into the subsets of metals and nonmetals to examine their properties more closely.
Conclusion
Without a doubt, the incorporation of data analysis activities into middle school science instruction can improve the critical thinking skills of middle school science students. Simultaneously, middle school students will find themselves making connections and applications through the integration of mathematics, science, and real-world problems. As middle school teachers look for ways to integrate mathematics and science instruction, data explorations can help meet this ongoing objective.
Edwin P. Christmann is a professor and graduate coordinator in the mathematics and science teaching program at Slippery Rock University in Slippery Rock, Pennsylvania.
References
Lehman, J.R. and E.P. Christmann.1999. Data explorations. New Mexico Middle School Journal 1(1), 26–28.National Council of Teachers of Mathematics (NCTM). 2000. Principles and Standards for School Mathematics. Reston, Va.: NCTM.National Research Council (NRC). 1996. National Science Education Standards. Washington, D.C.: National Academy Press.
I really like this video for bringing our attention to something that we see all the time, but don't pay close attention to. I also appreciate that the researchers are pointing out that just because we see something many times, that does not mean that we understand or can replicate it. Practice is an essential part of learning. YouTube link | Archive