**ERIC Identifier:** ED433219

**Publication Date:** 1999-05-00

**Author: **Lee, Hea-Jin

**Source: **ERIC Clearinghouse for
Science Mathematics and Environmental Education Columbus OH.

## Resources for Teaching and Learning about Probability and
Statistics. ERIC Digest.

As increased use of technology and the empirical sciences spreads throughout
the global community, the use of data and graphs to communicate information is
ever increasing. Daily decision making and discussions of social issues are
increasingly influenced by statistics and projected outcomes based on estimated
probabilities. Unfortunately, most high school graduates have little or no
background in the mathematics associated with calculating probabilities and
interpreting statistics. Therefore, in order for our students to be adequately
prepared to make informed decisions, schools need to provide greater attention
to probability and statistics in mathematics and other courses. Numerous
educators (NCTM, 1989; NRC, 1989; Shaughnessy, 1992) have recommend the
introduction of concepts related to probability and statistics throughout the
school years for all students, not just those students bound for college.

### KEY ISSUES

In spite of increased support for teaching
probability and statistics in schools, significant problems have been reported.

1.Absence
of probability and statistics lessons or courses in schools. (Barnett, 1988;
Shaughnessy, 1992): To date, very little probability and statistics have been
taught in our schools.

2.Teachers
are not prepared to teach probability and statistics. Historically, teacher
preparation programs have not systematically included probability and statistics
for prospective mathematics teachers (Shaughnessy, 1992).

3.Student
misconceptions and understanding. Conditional probability and the notion of
independent events are reported as particularly difficult concepts for students
to grasp (Falk, 1988).

4.Student
beliefs and attitudes. Statistics courses are some of the most rigorous and
anxiety evoking for college students. Because of this, researchers have
investigated techniques that may help to reduce anxiety and change negative
attitudes experienced by students taking such courses (Sgoutas-Emch &
Johnson, 1998).

### RECOMMENDATIONS

Educators have been endeavoring to overcome
the identified barriers to improving the teaching and learning of probability
and statistics. Following are suggestions from researchers (Falk, 1988; Friel,
1998; Shaughnessy, 1992) who have studied the teaching and learning of concepts
and applications of probability and statistics.

REGARDING
THE SCHOOL CURRICULUM:

*Include
a separate probability and statistics course in the main sequence of the
mathematics courses.

*Promote
increased awareness of the importance of probability and statistics in the
curriculum.

*Confront
students' and teachers' beliefs and concerns about probability and statistics.

REGARDING
TEACHERS:

*Teachers
must first confront their own misconceptions before they can be prepared to help
students overcome misconceptions.

*Teachers
must become familiar with students' preexisting conceptions related to
probability and statistics before they try to teach the concepts.

*Learning
statistics in elementary and middle schools involves building both conceptual
and procedural knowledge.

*Teachers
must use real world examples to help students understand concepts.

*Hands-on
materials must be used in teaching and learning probability and statistics.

*Computer
use of simulations enables students to investigate more realistic situations
than were previously possible. This strategy is strongly supported by numerous
studies.

Following is a listing of Internet and print resources for teaching and
learning about probability and statistics.

### WORLD WIDE WEB RESOURCES

Probability Computer Projects with
Mathematica http://www.wku.edu/~neal/probability/prob.html

Provides
interesting problems occurring in probability. This page includes "Monte Carlo
Approximation of Pi", "The Mystery of the Three Cards", "The Birthday Problem",
"The Gambling Boundary Problem", and others.

The Probability WEB

http://www.maths.uq.oz.au/~pkp/probweb/probweb.html

Contains
a collection of pages with the following headings: Probability links, Abstracts,
Listservers, Newsgroups, People, Jobs, Journals, Software, Books, Conferences,
Publishers and Miscellaneous.

Fun with Probability

http://lrs.ed.uiuc.edu/students/mcornell/cerealbox/index.html

Website
for a cooperative classroom project for grades K- 9. Students from five
countries and 19 of the U. S. states participated in this project.

Three Door Puzzle

http://www.intergalact.com/threedoor/threedoor.html

Includes
a simulation of the "Three Door Puzzle" of probability. Students can play an
interactive game as often as they wish.

Classroom materials for teachers and students

http://forum.swarthmore.edu/probstat/probstat.lessons.html

Provides
unit course materials and lesson plans, problems and puzzles, and reference
materials.

Software for Probability and Statistics

http://forum.swarthmore.edu/probstat/probstat.software.html

Contains
publicly available software and online publishers for probability and
statistics.

Internet project : Probability and Statistics

http://forum.swarthmore.edu/probstat/probstat.projects.html

Provides
fun and challenging activities for students.

### MATERIALS INTRODUCING ACTIVITIES FOR PROBABILITY AND STATISTICS LESSON

Freda, A. (1998). Roll the dice-an introduction to
probability. "Mathematics Teaching in the Middle School," 4(2), pp. 85-89.

A
dice game that introduces students to probability is described. Two students
roll the dice simultaneously and find the absolute value of the differences of
the numbers that they get. Students then present explanations of what they found
from this game.

Ruggles, J. & Slenger, B.S. (1998). The "measure me" doll. "Teaching
Children Mathematics," 5(1), pp. 40-44.

A
unit of work that engages Kindergarten and first-grade students in making dolls
to represent their birth statistics. The activities develop the children's
emergent understanding of mathematics concepts.

Young, P. G. (1998). Probability, matrices, and bugs in trees. Teacher's
guide and worksheets. "Mathematics Teacher," 91(5), pp. 402-406.

Outlines
activities that involve modeling the path of an insect between trees and
determining the spread of the insect population in the trees. The activities
involve the use of basic probability, simple random walks, matrices, and Markov
chains.

Scavo, T. R. & Petraroja, B. (1998). Adventures in statistics. "Teaching
Children Mathematics," 4, pp. 394-400.

An
activity on data analysis that engages fifth-grade students. The specific
elements of the activity include a primary measurement task, data graphing,
computation and interpretation of the average area, an analysis of area per
student, and presentation of results.

Kader, G. & Perry, M. (1998). Push-penny: what is your expected score?.
"Mathematics Teaching in the Middle School," 3, pp. 370-377.

Outlines
an activity that develops students' intuitive feeling for the consequences of
randomness. In addition to having the central statistical principle, the law of
large numbers, and probability distribution illustrated for students, this
activity enables students to develop their data handling skills and their skills
in constructing and using tables and graphs.

Greeley, N. & Offerman, T. R. (1998). Words, words, words; ancient
communication. "Mathematics Teaching in the Middle School," 3, pp. 358-364.

Three
activities that are based on newspaper articles are outlined: "Frequencies",
"Making the Words Fit", and "Check Out That Fog" activities. These activities
can be given to students for independent study, and each involves analyzing
newspaper articles for their clarity.

Perry, M. & Kader, G. (1998). Counting penguins. "Mathematics Teacher,"
91, pp. 110-116.

An
activity based on counting penguins is outlined. It can be used to illustrate
the nature of sampling variability, the effect of sample size on the quality of
estimation, and the role of the underlying population distribution.

Robinson, P. (1997). Probability, mortality and life assurance. "Mathematics
in School," 26, pp. 42-45.

This
activity involves generating expected values or probability values, and present
values, as well as applying discount factors and using mortality tables.

Brunner, R. B. (1997). Numbers, please! The telephone directory and
probability. "Mathematics Teacher," 90, pp. 704-705.

This
paper illustrates how students can use the telephone directory in collaborative
group assignments in their introductory probability and statistics class to help
them understand such concepts as Monte Carlo simulations.

### REFERENCES

Barnett, V. (1988). Statistical Consultancy-A
basis for teaching and research. In R. Davidson, & J. Swift (Eds.)., "The
proceedings of the second International Conference on Teaching Statistics." Victoria B.C.: University of Victoria.

National Research Council (1989). "Everybody Counts." Washington, D.C.:
National Academy Press.

Falk, R. (1988). Conditional Probabilities: Insight and difficulties. In R.
Davidson, & J.Swift (Eds.)., "The proceedings of the second International
Conference on Teaching Statistics." Victoria B.C.: University of Victoria.

Friel, S. N. (1998). Teaching statistics: What's average?. "Yearbook
(National Council of Teachers of Mathematics) v." 1998, pp. 208-217.

Jones, G. A., Langrall, C.W. & Thornton, C. A. (1997). A framework for
assessing and nurturing young children's thinking in probability. "Educational
Studies in Mathematics," 32(2), pp. 101-125.

National Council of Teachers of Mathematics (1989). "Curriculum and
evaluation standards for school mathematics." Reston, VA: Author.

Sgoutas-Emch, S. A. & Johnson, C. J. (1998). Is journal writing an
effective method of reducing anxiety towards statistics?. "Journal of
Instructional Psychology," 25, pp. 49-57.

Shaughnessy, J.M. (1992). Researches in probability and statistics:
Reflections and Directions. In Grouws, D.A. (Ed.). "Handbook of Research on
Mathematics Teaching and Learning (pp.465-494)." New York: Michigan Publishing
Company.