Becoming
a Teacher of Statistics
Portfolio
by
Susan
Sexton
Probability and Statistics for Secondary
Teachers
STAT 6070
University of Georgia
Fall 2007
Instructor: Christine Franklin
Recommendation 1: Use real data.
Franklin, C. & Mulekar, M. (2004). Effect of prior information on string length estimates. Teaching Statistics, 26(3), 66–71.
Abstract:
This article describes an activity through which students collect data and explore ways to display them through graphs and charts. It also motivates various summary measures for location, spread and shape. Finally, it gives an introduction to concepts of validity, reliability and unbiasedness.
The authors describe an activity aimed at helping students collect and describe characteristics of meaningful data. Through the analysis of the data, the students are provided with opportunities to use technology that will help them Òvisualize [the] data through various graphs and charts, and to explore and compare different shapes of distributionsÓ (p. 66). Using real data in learning statistics is one of the six recommendations of the Guidelines for Assessment and Instruction in Statistics Education (GAISE).
In
the activity, students are provided with visuals of two strings of different
lengths. The students are shown the two strings one at a time and asked to
estimate the length of each string. The class is not given any information
about the length of the first string but told that the length of the second
string is at least 35 inches. The estimations were gathered, the instructors
facilitated discussions about the data, and the students used computer software
to help create various visuals of the data. The authors of the GAISE report call this type
of data as Òclassroom-generated dataÓ (GAISE, 2005, p. 9) and state:
ÒUsing real data sets of interest to students is also
a good way to engage them in thinking about the data and relevant statistical
conceptsÓ (GAISE, 2005, p.
9).
The
discussions the authors facilitated around the data included predicting the
shape, spread, and centers of the two string estimation distributions. The
students then used technology to aid their understanding of their collective
predictions and/or what the visuals actually displayed. The instructors used
key moments to introduce statistical ideas, concepts, and terminology. These
types of discussions and visualizations centered about an activity are avenues
for the students to enhance their statistical thinking and heighten their
statistical literacy as well as a means for the instructors to foster student
learning by actively engaging in discourse through analysis of the data.
Emphasizing statistical literacy, developing statistical thinking through
utilizing technology and fostering active learning are all teaching methods
recommended within the GAISE
report.
The
instructors used the opportunity to increase the studentsÕ statistical
knowledge and understanding by having them consider the concepts of validity,
reliability, and unbiasedness. Conceptual understanding of all three concepts
is enhanced through the use of a larger data set. Thus the instructors provided
the students with the numerical and visual summaries of similar data collected
from three other classes to compare with their own class data. This aligns with
the suggestion for teachers in the GAISE recommendation to: ÒGet
students to practice entering raw data using a small data set or a subset of
data, rather than spending time entering a large data set. Make larger data
sets available electronicallyÓ (GAISE,
2005, p. 9).
Overall
this activity is a great illustration of how statistical concepts can be
introduced without an emphasis of procedural knowledge (another GAISE recommendation).
Students have the opportunity to Òuse real data in teaching statistics, for
reasons of authenticity, for considering issues related to how and why the data
were produced or collected, and to relate the analysis to the problem contextÓ
(GAISE, 2005, p. 9).
Furthermore the activity incorporates 5 out of the 6 GAISE recommendations. The
instructors were mere facilitators of the activity, probing and asking
questions when necessary and introducing key statistical concepts, ideas, and
terminology when appropriate.
The
final GAISE recommendation
not explicitly addressed in the activity is that of assessment. However, the
instructorsÕ comments throughout the article on various misconceptions and how
they addressed them or planned to address them (perhaps through a different or
new activity) is a form of in-the-moment assessment that results in real-time
decision making on when to pursue such issues.
References
GAISE College Report. (2005). Guidelines for Assessment and Instruction in Statistical Education College Report. Alexandria, VA: American Statistical Association, http://www.amstat.org/education/gaise.
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