ERIC Identifier: ED464804
Publication Date: 2001-08-00
Author: Ozgun-Koca, S. Asli
Source: ERIC Clearinghouse for
Science Mathematics and Environmental Education Columbus OH.
The Graphing Skills of Students in Mathematics and Science
Education. ERIC Digest.
"Instructional programs from prekindergarten through grade 12 should enable
all students to:
create and use representations to organize, record, and communicate mathematical
select, apply, and translate among mathematical representations to solve
use representations to model and interpret physical, social, and mathematical
phenomena." (NCTM, 2000, p. 66)
The effective use of representations in mathematics and science education has
gained more importance as we enter the new millennium. National Council of
Teachers of Mathematics even added, Representation, to their four process
standards which "highlight ways of acquiring and using content knowledge" (NCTM,
2000, p.29) in their new reform document, "Principles and Standards for School
Mathematics". Even though all types of representations are being encouraged in
the teaching and learning of mathematics and science, graphical representations
play a special role.
Graphs can summarize very complex information or relationship very
effectively. Although graphs are explicitly taught in mathematics classrooms as
an end in themselves, many subject areas such as science or social studies
utilize graphs to represent and interpret relationships. So being able to
interpret or construct graphical representations is a crucial skill for every
student whether they want to pursue science or mathematics related careers.
However, many researchers detected that many students lack graphing skills.
Brasell and Rowe (1993) studied high school physics students' graphing skills
and they concluded that "[students] do not understand the fundamental properties
and functions of graphs in representing relationships among variables." Their
facility with graphs was generally superficial, grounded on a few, simplistic
algorithms such as plotting data points" (p. 69). Janvier was one of the first
mathematics educators to mention the problems that students have in interpreting
graphs (Bell & Janvier, 1981; Janvier, 1981). Mostly he argues how global
meanings of graphs and interpreting graphs are left out in mathematics
classrooms, while reading data and constructing and reading certain points on
graphs are emphasized.
WHAT RESEARCH SAYS ABOUT HOW TO IMPROVE STUDENTS GRAPHING
In this age of technology, many researchers advocate the use of
computers, calculators, Microcomputer-Based Laboratories (MBLs) or
Calculator-Based Laboratories (CBLs) in improving students' graphing skills.
Mokros & Tinker (1987) studied the effects of MBLs in students'
understandings about graphing. The use of an MBL or CBL allows student to
collect real-time physical data such as temperature, motion, light, or sound.
Then these data can be transferred into a computer or a calculator to be studied
through a variety of representations such as graphs or tables. They conclude
that "in three-month longitudinal study of MBL, students showed a significant
gain in understanding on 16 graphing items, although the instruction targeted
science topics, not graphing skills" (p. 369). They add that "MBL may also help
children develop graphing skills because it eliminates the drudgery of graph
production" (pp. 381-382).
Dugdale (1993) discusses the potentials for graphing software, such as Green
Globs, to enhance students' understanding of functional and graphical
relationships. Green Globs is a game where 13 "green globs" are randomly placed
on the grid. Players earn points by entering equations that pass through as many
green globs as possible. She argues that it is crucial to go beyond plotting and
reading points to interpret the graphs. Sivasubramaniam (1999) compares
students' graphing skills in a learning experiment with and without the use of
computers. The paper concludes that "the computer group improved significantly
more than the paper group in their graphing skills from the pretest to
Many educators went beyond teaching graphs as an end to themselves and used a
graphing approach to teach other mathematical or scientific subjects. Oakes
(1997) suggests an approach in teaching which combines the discovery method with
graphing skills in science instruction which "allows students to discover the
actual laws of nature rather than be given the equation and just plug in data"
(p. 35). Hollar and Norwood (1999) use graphing calculators in teaching algebra
with a graphing approach curriculum in which they could focus on real-world
situations. They concluded that the students in the graphing approach curriculum
showed better understanding of functions than the traditional students.
ELECTRONIC RESOURCES ON GRAPHING SKILLS
Representing, and Interpreting Data Using Spreadsheets and Graphing Software:
Collecting and Examining Weather Data
This site provides one of the electronic NCTM examples which are interactive
activities that support Principle and Standards for School Mathematics.
Spreadsheets and graphing software include tools for organizing,
representing, and comparing data. This activity illustrates how weather data can
be collected and examined using these tools. In the first part, Collecting and
Examining Weather Data, students organize and then examine data that has been
collected over a period of time in a spreadsheet. In the second part,
Representing and Interpreting Data, students use the graphing functions of a
spreadsheet to help them interpret data. Students learn to set up a simple
spreadsheet and use it in posing and solving problems, examining data, and
investigating patterns, as described in the Representation Standard.
NCTM's indexes for GRAPHS and GRAPHING list articles that have appeared in three
"Mathematics Teacher" (8-14 grade levels)
"Mathematics Teaching in the Middle School"
"Teaching Children Mathematics" (K-6 grade levels)
This site contains ideas for 18 graphing activities.
Graphing Equations From Software (SMILE)
Author: James Webb, Harlan High School
A lesson designed to reinforce previously learned equation-graphing skills;
and to develop new strategies (other than memorizing equations) for equation
graphing, using "Green Globs" software.
Author: Robert Bunge
Java applets for practicing equations, factoring, and graphing skills, with
multiple levels in each category.
Activities create real-time correlations between equations and graphs that
help students visualize and experiment with many of the major concepts from
elementary algebra through pre-calculus.
This site provides Shockwave (tm) interactive activities which offer
real-time correlations between equations and graphs that help students visualize
and experiment with many scientific concepts for grades K to 12.
Valentine Candy Count (CEC)
Author: Judy Dale; Bosque Farms Elementary, Bosque Farms, N.M.
This site offers an activity for grades 1-4 in which students observe, sort,
and predict by using Valentine candy. It uses a method through which children
can explore and internalize graphing skills.
Bell, A., & Janvier, C. (1981). The
interpretation of graphs representing situations. "For the Learning of
Mathematics," 2(1), 34-42.
Brasell, H. M., & Rowe, M. B. (1993). Graphing skills among high school
students. "School Science and Mathematics," 93(2), p. 63-70.
Dudgale, S. (1993). Functions and graphs-Perspectives on students thinking.
In T. A. Romberg, E. Fennema, & T. P. Carpenter (Eds.) "Integrating research
on the graphical representation of functions" (pp. 101-130). Hillsdale, NJ:
Janvier, C. (1981). Use of situations in mathematics education. "Educational
Studies in Mathematics," 12, 113-122.
Mokros, J. R., & Tinker, R. F. (1987). The impact of microcomputer-based
labs on children's ability to interpret graphs. "Journal of Research in Science
Teaching," 24(4), 369-383. NCTM (2000). "Principles and standards for school
mathematics." Reston, VA: Author.
Oakes, J. M. (1997). Discovery through graphing. "The Science Teacher,"
Sivasubramaniam, P. (1999). "Computers and graphing skills in the light of
learning theories." [Available online at