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Topic: Calculator Information
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Ken Blystone

Posts: 15
Registered: 12/6/04
Calculator Information
Posted: Mar 20, 1995 7:32 AM
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APRIL 1992


Calculators and Computers

NAEPFacts are brief reports that extract the results of data on a
single topic from the National Assessment of Educational Progress
(NAEP); they are intended for elementary and secondary school
teachers and principals. NAEPFacts describe what educators,
researchers, and policymakers have to say about effective
practice; provide information from NAEP about what actually takes
place in schools; and conclude with questions for discussion.
They are not meant to promote or prove any educational theory.

This issue of NAEPFacts is concerned with the use of calculators
and computer technology in the classroom. We hope that it will
promote conversations among teachers, principals, parents, and
other interested parties about effective education. Readers'
comments and suggestions are welcome.

Emerson J. Elliott

The 20th century has been marked by scientific advances that have
had a profound effect on American enterprises such as
manufacturing, business management, transportation, and
communications. We entered the century with a horse-drawn
carriage; we leave it with spacecraft probing the universe. We
entered the century with pencil and paper; we leave it with
computers able to figure thousands of times faster than the human

Technology has revolutionized the education needs of the workforce
as it has revolutionized the workplace. As a result, schools that
use only pencil and paper to teach mathematics, for example, are
as out of step with the times as those that would use a horse-
drawn carriage to teach auto mechanics.

Yet, there is little evidence that technology is used to full
advantage in the American schoolroom. In fact, teachers report
that 47 percent of 4th-graders and 22 percent of 8th-graders were
never asked to use a calculator in mathematics class. This was a
finding of the 1990 NAEP assessment in mathematics.

Technology in the Mathematics Classroom

The National Council of Teachers of Mathematics (NCTM), a
professional association of classroom teachers, supervisors,
educational researchers, teacher educators, and university
faculty, states that the very nature of the mathematics curriculum
must be changed to meet the needs of the next century.
Mathematics problems and the methods used for solving them have
changed with technological advances.

The understanding and competent use of technological tools are
indispensable to U.S. students, all of whom will have a role in
the nation's progress in the 21st century. Thus, NCTM recommends
expanded use of computers and calculators in schools.

MATHEMATICS, NCTM recommends that

o Appropriate calculators be available to all students at all

o Every classroom have a computer for demonstration purposes;

o Every student have access to a computer for individual and
group work; and

o All students learn to use the computer as a tool for
processing information and performing calculations to
investigate and solve problems.

Further, students' understanding of mathematics should equip them
to know when and how to use the various technologies for problem
solving. "Students should be able to decide when they need to
calculate and whether they require an exact or approximate
answer," NCTM says.

Use of Calculators in the Classroom

A calculator component has been a part of the NAEP mathematics
assessment since 1982; albeit a small part. To determine how and
to what extent calculators actually are used in classroom
practice, the component was expanded in the 1990 assessment.

Calculators were used in the 1990 national assessment of 4th-,
8th-, and 12th-grade public and private school students and in the
Trial State Assessment of 8th-grade public school students.
Fourth-graders had the use of four-function calculators and 8th-
and 12th-graders the use of scientific calculators for portions of
the assessment. Before they were tested, all of the students were
trained briefly in how to use the equipment.

NAEP collected information about whether students understood how
to use a calculator, as well as when to use one (see tables 1 and
2). NAEP also questioned and collected information from students,
teachers, and administrators about the availability and use of
calculators and computers in schools and about school policies
related to their use.

NAEP results show that NCTM's recommendations have not been
implemented. According to their teachers, only 3 percent of 4th-
graders and 19 percent of 8th-graders were permitted free and open
use of calculators; only 2 percent of 4th-graders and 34 percent
of 8th-graders were permitted to use calculators when taking
tests. And, as indicated earlier, teachers reported that 47
percent of 4th-graders and 22 percent of 8th-graders were never
asked to use a calculator in mathematics class.

Fourth-grade teachers tended to use calculators somewhat more
frequently in their high-ability classes; 8th-grade teachers said
they used them least frequently with their low-ability classes.
Although there are some exceptions, more-proficient students
appear to have more opportunities to use calculators than their
less-proficient peers.

Use of Computers in the Classroom

Computers can be used in a variety of ways in the mathematics
classroom. Teachers can take full advantage of this technology by
using computers to teach such things as statistics, graphs,
spreadsheets, and proportions and to encourage students to
undertake extended investigations of mathematical ideas requiring
higher-order thinking skills and logic.

Computers give students an opportunity to use "hands-on"
techniques in problem solving. Perhaps more important, they help
students develop an understanding of the processes and reasoning
that are the heart of mathematical problem solving. Because
computers can be used in ways that parallel the application of
mathematics in the real world of business and industry, computer
technology in the classroom enhances practicality and students'

Computers are expensive and finding the resources to make them
available for the use of students can be a problem. NAEP asked
school administrators and teachers about the availability of
computers in mathematics classrooms (see table 3).

School administrators and teachers appear to agree that more 4th-
grade than 8th-grade mathematics classrooms have computers.
Teachers reported that, at grade 4, about one-third of students
had at least one computer in their classroom. Teachers and
administrators reported that, at grade 8 and again at grade 12,
about one-fifth of students had at least one computer in their
mathematics classrooms.

Many schools have computer laboratories, and school administrators
reported that--across the grades--more than half of students were
in schools where computers were available for classroom use when
needed. Fifty-six percent of students in grade 4, 61 percent of
students in grade 8, and 79 percent in grade 12 were in schools
with computer laboratories.

If computers are to have an impact on mathematics instruction and
achievement, students must have opportunities to use the
equipment. NAEP, therefore, asked teachers and administrators
about student use. Despite the availability of computers,
teacher reports indicated that access to them was more limited.

Teachers and administrators reported that computer access was
difficult for about half of the students at grades 4 and 8.
Teachers and students agreed that school use of computers was
greater at grade 4 than at grade 8, but usage in general was quite
limited. A positive overall relationship was seen to exist
between the availability of computers and average mathematics
proficiency at grade 4; this relationship tended to hold across
ability groupings at that grade level. At grade 8, however, there
appeared to be no relationship between the availability of
computers and mathematics performance.

Questions for Discussion

NAEP data reveal minimal use of computers and calculators in
mathematics instruction. In many cases, technology is not widely
available, accessible, or used to advance students' mathematical
thinking. The following questions are posed to stimulate
discussion among teachers, principals, administrators, parents,
and other interested citizens about the use of calculators and
computers in the classroom:

1. What are the pros and cons of allowing students to use
calculators only after they have proven their ability
to compute with pencil and paper? Does this policy
worsen the performance gap between higher- and lower-
performing students?

2. How can calculators be used to help students develop a
broader view of mathematics problem solving?

3. Can students be taught estimation techniques that will
help them recognize whether computer or calculator
results are reasonable? If so, how?

4. How can computers be used to help students develop the
mathematical reasoning and problem-solving concepts
required in the real world?

5. How can computers be used in mathematics programs to
simulate problem-solving situations and applications?

6. Does electronic mail have a role in mathematics


Hembree, Ray, and Donald J. Dessart,
"Effects of Hand-Held Calculators in Precollege Mathematics
Education: A Meta-Analysis" in the Journal for Research in
Mathematics Education (Vol. 17, no.2, March 1988, pp.

Mathematical Sciences Education Board
and National Research Council, Reshaping School Mathematics:
A Philosophy and Framework for Curriculum (National Academy
Press, Washington, D.C.: 1990).

National Council of Teachers of
Mathematics, An agenda for Action:
Recommendations for School Mathematics of the 1980s (Reston,
VA: 1989).

Curriculum and Evaluation Standards for School Mathematics

National Governors Association, The
Governors' 1991 Report on Education, Results in Education:
1990 (Washington, D.C.: 1990).

National Research Council, Everybody
Counts: A Report to the Nation on the Future of Mathematics
Education, ed. Lynn Steen. (National Academy Press,
Washington, D.C.: 1989).

U.S. Department of Education, The
State of Mathematics Achievement: NAEP's 1990 Assessment of
the Nation and the Trial Assessment of the States
(Washington, D.C.: 1991).

For more information you can contact:

Carol Sue Fromboluti
Room 304b
555 New Jersey Avenue, N.W.
Washington, D.C. 20208

Table 1.--Students' understanding of when to use a calculator

High Group* Other Group**
Percent of Average Percent of Average
students proficiency students proficiency
Grade 4 57(0.7) 221(0.7) 43(0.7) 209(0.9)
Grade 8 44(0.9) 275(1.3) 56(0.9) 258(1.1)
Grade 12 30(0.8) 310(1.3) 70(0.8) 289(1.1)

NOTE: The standard errors of the estimated percentages and
proficiencies appear in parentheses. It can be said with 95
percent certainty that for each population of interest, the value
for the whole population is within plus or minus two standard
errors of the estimate for the sample.


*High Group--Students who used the calculator appropriately (i.e.,
used it for the calculator-active items and did not use it for the
calculator-inactive items) at least 85 percent of the time and
indicated that they had used the calculator for at least half of
the calculator-active itmes they were presented.

**Other Group--Students who did not use the calculator
appropriately at least 85 percent of the time or indicated that
they had used a calculator for less than half of the
calculator-active items they were given.

Table 2.--Students' reports on ways they use a calculator

For mathemaucs class, how often do you use a calculator to do each
of the following?

Almost always Sometimes Never
Percent Average Percent Average Percent Average
of Profi- of Profi- of Profi-
Grade students ciency students ciency students ciency
Work problems in class

8 46(0.9) 257(1.1) 30(1.1) 271(1.6) 24(1.3) 275(1.2)
12 (All stu-
dents) 42(1.0) 301(1.1) 32(0.8) 298(1.4) 27(1.0) 285(1.6)
12 (Taking
math) 53(1.2) 306(1.3) 33(1.0) 308(1.5) 14(0.9 299(3.0)
Do problems at Home

8 30(1.0) 264(1.2) 52(0.8) 266(1.3) 19(0.7) 266(1.3)
12 (All stu-
dents) 38(0.9) 305(1.2) 38(0.7) 295(1.4) 24(0.8) 283(1.5)
12 (Taking
math) 46(1.0) 311(1.3) 41(1.0) 303(1.5) 13(0.6) 294(2.5)
Take tests or quizzes

8 25(0.9) 257(1.6) 43(1.2) 261(1.5) 32(1.3) 277(1.2)
12 (All stu-
dents 34(0.9) 303(1.2) 34(0.9) 298(1.4) 32(1.1) 277(1.2)
12 (Taking
math 43(1.3) 309(1.3) 38(1.2) 304(1.6) 19(1.1) 300(2.7)

NOTE: The standard errors of the estimated percentages and
proficiencies are in parentheses. It can he said with 95 percent
certainty that for each population of interest, the value for the
whole population is within plus or minus two standard errors of
the estimate for the sample.

SOURCES: The State of Mathematics Achievement: NAEP's 1990
Assessment of the Nationa and the Trial State Assessment of the

Table 3.--Schools' reports on the availability of computers

Yes, computers Yes, computer Yes, computers
available all grouped in a available
the time in laboratory to bring to
mathematics available to classroom
classroom mathematics classes when needed
Percent of Percent of Percent of
students students students

Grade 4 22(2.7) 56(2.9) 53(3.1)
Grade 8 10(2.6) 61 (4.4) 57(3.5)
Grade 12 10(2.6) 79(3.8) 64(3.7)

NOTE: The standard errors of the estimated percentages and
proficiencies appear in parentheses. It can he said with 95
percent certainty that that for each population of interest, the
value for the whole population is within plus or minus two
standard errors of the estimate for the sample.

SOURCE: The State of Mathematics Achievement: NAEP's 1990
Assessment of the Nationa and the Trial STate Assessment of the

This material is in the public domain. Authorization to reproduce
U.S. Department of Education material in whole or in part is
Ken Blystone, Educational Technologist
Ysleta Independent School District
9600 Sims
El Paso, Texas 79925
Voice: 915-595-5676
Fax: 915-595-5930
Data1: 915-594-3429 (The CyberSchool System)
Data2: 915-598-1987 (The K12 Network/Internet Link)
Data3: 915-595-6806 (Ysleta Educational Telecommunications)

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