K-12 Calculator Usage
Guidance
Proposal
developed by
the
West Virginia Department of Education
Office of Instruction
and
supported by
the
West Virginia Higher Education Policy Commission
K-12 Calculator Usage Guidance
West Virginia Department of Education
Office of Instruction
Introduction ................................................................................................................................. 1
Calculator Usage in the Primary Grades ................................................................................... 3
Calculator Usage in the Intermediate Grades ............................................................................ 6
Calculator Usage in the Middle Grades ..................................................................................... 9
Calculator Usage in the Secondary Grades .............................................................................. 13
Impact on Higher Education ..................................................................................................... 20
Committee Members .................................................................................................................. 22
Bibliography .............................................................................................................................. 23
Introduction
According to the National Council of Teachers of Mathematics,
“School mathematics programs should provide students with a range of knowledge, skills,
and tools. Students need an understanding of number and operations, including the use of
computational procedures, estimation, mental mathematics, and the appropriate use of the
calculator. A balanced mathematics program develops students’ confidence and
understanding of when and how to use these skills and tools. Students need to develop their
basic mathematical understandings to solve problems both in and out of school.”
We concur that appropriate use of calculators in the mathematics classroom heightens the development of
mathematical understanding in students at all levels. We believe in the value of calculators as students
discover patterns, analyze data, represent problems in personally meaningful ways, make and test
conjectures, and study concepts that would otherwise be beyond their understanding. Additionally, the
use of calculators can aid in the development of computational fluency, encourage deeper student interest,
enable students with weak computational skills to move forward, and allow for more time to be used for
critical thinking skills. However, the use of calculators does not eliminate the need to master the basic
algorithmic skills and processes of mathematics. In particular, all students must have a mastery of
numerical skills including multiplication facts, fractions, and integer operations as they are essential
prerequisites to the study of algebra.
To ensure that these skills are utilized beyond the rote memorization level, they must continually be
reinforced in contextual problem solving situations. Some problems must be posed that do not require
laborious computation, making the use of the calculator inappropriate; while others must be posed that
require the appropriate use of the calculator. We believe that a successful 21st century mathematics
student must experience both approaches in engaging and practical situations.
Graphing calculators offer a variety of opportunities. They allow students to easily organize data in
multiple ways including numerical, algebraic and visual representations. Graphing calculators,
particularly when used in conjunction with data-collection devices, allow students to investigate real data
through simulations, modeling, and experimentation. Thus students can induce patterns and make
reasonable conjectures that can be tested for possible validity. Mathematics is a blend of inductive and
deductive reasoning with induction used to formulate conjectures and deduction to prove results or derive
formulas. Calculators are powerful tools in the inductive process, but have limited application in proofs
and derivations. In order to be fluent in mathematics, a student must have sufficient exposure to both
inductive and deductive methods. Both must be properly integrated into classroom instruction.
The Equity Principle as found in Principles and Standards for School Mathematics, published by the
National Council of Teachers of Mathematics (NCTM) states that mathematics can and must be learned
by all. The principle emphasizes that excellence in mathematics education requires equity – high
expectations and strong support for all students. Equity involves accommodation of differences to help
all students master content. Use of technology, including calculators, can help provide equity in the
classroom by giving additional learning opportunities to students. For students with special needs, use of
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technology may need to be more individualized. Since the mastery of arithmetic is an essential
prerequisite to the formal study of algebra, the calculator may be used as either a tool for teaching facts or
expanding the time the student has to master facts, but not as a substitute for computational fluency. In
order to ensure equal access for all students, it is recommended that educational leaders make acquisition
of classroom sets of calculators a high priority.
Our students continuously experience a profusion of personal technology devices. Many of these devices
have potential to improve mathematics education. In particular, calculators are currently available with
symbolic manipulators that can perform most of the computations learned by secondary mathematics
students. As a result, it may be advantageous for some skills to be de-emphasized; however, many of the
skills are abstracted and generalized in later mathematics and must be emphasized to strengthen students’
mathematical foundation. At all levels, the use of technology should never interfere with the acquisition
and maintenance of the basic skills that are essential to future mathematical development. The individual
educator may not be aware of the significant role that a particular mathematical skill or its generalization
will play in students’ future education. Thus, it is imperative that technological and curricular decisions
not be made in isolation, but must result from continual articulation among educators from kindergarten
through college.
2
Calculator Usage in the Primary Grades
In the primary grades, the calculator is used as a tool to aid exploration and to extend the set of numbers
on which students can perform operations. It can also stimulate children’s natural curiosity and
fascination with patterns by enhancing their ability to answer questions such as:


Start counting by fives from the number 2. How is the pattern similar when you start with the
number 5?
If a magic beanstalk is one inch tall and doubles in height every day, how tall will it be after ten
days?
As students learn about the properties of the number system, the calculator can help them generalize from
their work with small numbers. Students can explore and collect evidence to answer questions such as:


When adding two numbers, does it matter which is the starting number? What about when
subtracting? Use your calculator to test your thinking.
Are there fact families for larger numbers? How can you use your calculator to explore this
question?
Students in the primary grades develop an understanding of the meaning of the operations of addition and
subtraction. Using the calculator allows students to extend their knowledge of the operations to numbers
beyond those typically used in class. Problems do not have to be restricted to numbers they can count and,
thus, can be more relevant to real-world situations. They can solve problems such as:


How many students in our school are eating hot lunch today?
Which weighs more, an elephant or a humpback whale? How much more?
Solving problems like these also gives students an opportunity to examine the reasonableness of answers
found with the calculator. These reflections strengthen the developing number sense of students in the
primary grades.
By the end of second grade, students should have quick recall of the single digit addition facts and the
corresponding subtraction facts. This fluency with the basic facts forms the foundation for mental math,
work with larger numbers and algebraic concepts. Students enjoy activities where they show that the brain
is faster than the calculator when you know your facts. Two students can be given a basic fact; one enters
it in a calculator and calls out the answer, the other uses mental math to give the answer. This simple
activity builds student confidence and mental math skills that can carry over to work with larger numbers
in subsequent grades.
As students begin working with addition and subtraction of two-digit and three-digit numbers, the use of
the calculator can be one of the methods used to verify answers. Developing understanding of the
concepts and procedures involved must remain the focus of instruction; using the calculator to obtain
answers does not deepen understanding of the procedures that need to be mastered.
The calculator is a tool and should be available for students to use in the classroom like other tools such
as a ruler or a hundred chart. The teacher must use discretion about if and when the use of the calculator
should be restricted. Certainly if the teacher’s objective is to assess a student’s computational fluency or
ability to perform pencil and paper computation, use of a calculator is not appropriate.
3
Any basic four-function calculator is suitable for use in the primary grades. Although there are models
designed for use in the primary grades that include features like two-line displays and representations of
place value, these added features are not necessary.
4
Calculator Usage in the Primary Grades
Is calculator being used by
teacher or students?
Teacher
Students
Use an overhead or document
camera to model the keystrokes
for students to follow in a problem
solving situation
What is the purpose of
the activity?
Explore counting and number
patterns or solve problems
beyond counting range
Developing concepts of
counting and meaning of
number
Can students perform the
needed operations?
No Calculator
Yes
Calculator optional,
recommended for checking
work
No
Calculator suggested
5
Calculator Usage in the Intermediate Grades
Mastering basic facts and algorithms for the operations of multiplication and division is a major focus in
the intermediate grades. Students are expected to become proficient in whole number computation
procedures in all four operations. They must develop an understanding of how and why the algorithms
work, rather than just memorize the steps of a procedure. Mastery of efficient algorithms develops with
practice over time. While the calculator is a useful tool for checking the accuracy of answers, it cannot
replace the pencil and paper practice required to develop proficiency. Use of the calculator is certainly
appropriate when operating with multi-digit numbers.
Students in the intermediate grades are also building the foundation for work with fractions and decimals.
Conceptual understanding of equivalence, comparing and ordering fractions and decimals, and converting
between fractions and decimals are important components of the curriculum. Computational skill in the
addition and subtraction of fractions and decimals is developed in the intermediate grades. Increasing
efficiency and accuracy in these pencil and paper computational procedures requires scaffolded
instruction, distributed opportunities to practice, and periodic review, not calculator drill. Use of the
calculator to do these procedures cannot replace these elements of the curriculum. Without a solid
understanding of the computational procedures, students are likely to struggle when they begin to work
with integers and variables. Use of the calculator is certainly appropriate when working with multi-digit
decimal numbers and “unfriendly” fractions.
The calculator can be used to verify answers, but it can also be used to help students decide which
operation is called for to solve a given problem. Students can test their ideas and refine their thinking. The
calculator allows the student to focus on whether an answer makes sense without being slowed down by
multi-step procedures with multiple opportunities for errors. While the calculator performs the
computation efficiently, the student must still make important decisions about the answer displayed. This
ability to determine the reasonableness of an answer is a critical skill, whether the answer is reached with
a calculator or with pencil and paper.
The teacher must use discretion in deciding when calculator use is sensible. If the focus is on building
fluency in computational skills, use of the calculator should be limited. If the focus is on application of
skills in problem-solving situations, the calculator allows the student to concentrate on finding reasonable
solutions while limiting the risk of computational error leading to an incorrect solution.
In the end, students need to be able to judge for themselves which method is best to solve a particular
problem. There are situations when mental math is the quickest solution or when only an estimate is
needed. There are other situations when an adult would choose a calculator to solve a problem involving
cumbersome numbers or multiple steps; students should have this option as well.
In the intermediate grades, the number of students experiencing difficulty with mathematics, particularly
computation, tends to increase. More students become eligible to receive special education services in the
general education setting. In terms of calculator use, the ultimate goal for students with special needs is
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to assist in optimizing their abilities and ultimately contributing to the promotion of their independence.
There may be times when it is appropriate for some students to use a calculator while others do not.
Teachers need to make decisions on a case-by-case basis, referring to a student’s Individual Education
Plan (IEP) if applicable. If using a calculator makes it more likely that a student with special needs is
successful with grade level curriculum, it should be made available; however, consideration must be
given to the role the skills play in later mathematical development. For example, the abstractions of
algebra will be more difficult to master without the immediate recall of skills and facts.
Students typically enter the intermediate grades with some experience in using a basic four-function
calculator. They are ready to learn to use the constant and memory features. Before entering middle
school, students begin using the percent and square root keys as well. It is important that the calculators
used by students follow the order of operations rather than calculating in the order the operations were
entered. Although a basic four-function calculator is sufficient for students through the intermediate
grades, a fraction calculator can also be a useful tool at this level. The fraction calculator can reinforce,
verify, and extend students’ work with addition and subtraction of fractions and mixed numbers and
conversions between fractions, decimals, and percents.
In summary, the calculator in the intermediate grades is a useful tool for extending computational skills,
but it cannot take the place of building conceptual and procedural understanding. In terms of assessment,
if the objective is to measure students’ computational skills, the calculator should not be used. If the
objective is to measure the application of skills in a problem-solving situation, use of the calculator is
acceptable.
7
Calculator Usage in the Intermediate Grades
What is the focus of the
lesson?
Learning Procedures
with Whole Numbers,
Fractions, Decimals,
and Percents
Do Not Use
Calculator
Solving Application
Problems in Real-World
Contexts?
Computation with
Very Large or
Messy Numbers*
Is computation
the focus?
Use Calculator
Yes
Do Not Use
Calculator
*Students with special needs may require
modifications including using the calculator when
performing multi-digit computation
8
No
Calculator
Optional
Calculator Usage in the Middle Grades
The National Council of Teachers of Mathematics’ Principles and Standards for School Mathematics
proposes “an ambitious and rich experience for middle-grades students that both prepares them to use
mathematics effectively to deal with quantitative situations in their lives outside school and lays a solid
foundation for their study of mathematics in high school. Students are expected to learn serious,
substantive mathematics in classrooms in which the emphasis is on thoughtful engagement and
meaningful learning.”
Mathematics in the middle grades begins with an emphasis on whole numbers, fractions, mixed numbers,
decimals and integers, with later study emphasizing preparations for Algebra I. Proportional reasoning,
working with rational numbers, data analysis, patterns in arithmetic and problem solving applications are
big ideas that prepare students for the study of Algebra I. The developmental level of middle grades
students must be considered when introducing a concept. To build their knowledge base, students must
be exposed to activities that allow them to develop the concept and understand the procedures involved.
After working with concrete examples, students should move to pencil and paper manipulation, referring
back to concrete activities as necessary, to establish and reinforce understanding. After students have
been exposed to a concept and any accompanying algorithms, a calculator enhances and extends student
learning.
Middle grade students must have a well-equipped mathematical toolbox and know when to apply the
appropriate tool for maximum effectiveness. The teacher must strike a balance among the tools within
the context of what is being taught. The use of the calculator affords several advantages. The most
obvious advantage is the ease of computation, particularly with uncontrived, real-world data.
Additionally, graphing calculators give a pictorial representation of linear functions (constant rate of
change, regression, etc.) as well as allowing fluent transition among multiple displays of data (tables,
plots, graphs, etc.). Calculators also promote equal access to the mathematics curriculum for all.
There are cautions that should be considered when using calculators in the classroom. One concern is that
students can develop a dependence on the calculator for even simple computations. Total reliance on
calculator usage can diminish a student’s ability to estimate and judge the reasonableness of the answer
on the calculator display. Finally, accessibility to calculators is not always equal among schools, grade
levels, classrooms, or individual students. Students may be able to access a calculator in math class but
not have one available for use in another classroom.
NUMBER AND OPERATIONS
As students acquire computational fluency with fractions, decimals and integers, teacher-led discussions
of problems in real-world contexts can allow students to develop their own strategies to compute in ways
that make sense to them. Student understanding of computations is enhanced by creating individual
strategies and sharing them with others. By explaining why their strategy works, students reinforce their
9
understanding of the traditional algorithm. As these foundations are established, calculator use can be
added to the mathematical toolbox to enrich instruction and learning, ensure accuracy and facilitate timely
- not tedious - investigations and explorations of mathematical concepts.
ALGEBRA
At the middle level, students explore patterns that involve a constant rate of change. Linear functions are
modeled using multiple representations. Students need to engage in problem solving activities using
tables, graphs, words and symbols to represent and analyze functions and patterns of change. As students
investigate real data, the graphing calculator can be used to support and extend understanding of linear
models. A commonly used example of this application is the comparison of cell phone plans. Students
make a table and graph the data as ordered pairs (minutes, cost). Use of the graphing calculator provides
opportunities and time for greater exploration of data, especially for experiments involving collection of
authentic data. Making conjectures, finding the line of best fit, and checking for reasonableness can be
more stimulating when data is not contrived. Consistent with recommendations throughout this
document, it is suggested that students have experience with graphing using pencil and paper before using
the graphing calculator. Pencil and paper skills should be reinforced periodically.
GEOMETRY
In the middle grades, the NCTM Geometry Standard states that “students investigate relationships by
drawing, measuring, visualizing, comparing, transforming and classifying geometric objects.” Students at
this level should be able to make mathematical arguments about geometric relationships. In addition to
the use of manipulatives, dynamic geometry software and graphing calculators can support student
understanding as they construct geometric figures to explore, generate, apply and test conjectures about
definitions and properties of these figures.
MEASUREMENT
Content standards in the measurement strand across the middle grades require students to approximate pi
using measurements and to develop and test hypotheses to determine formulas for area, circumference,
perimeter and volume. Students are further required to use the knowledge of these formulas to solve
application problems involving measurements. They also use the Pythagorean Theorem to determine
measurements and must be able to convert measurements among different units. As students work at
mastering tasks such as developing hypotheses, determining strategies, and selecting appropriate methods
to apply to solving a problem, the use of a calculator is not appropriate, or even helpful. However, tasks
such as testing hypotheses, implementing strategies and specific problem solving methods, approximating
pi using measurements, and using the Pythagorean Theorem to determine measurements all involve
calculations. Teachers should design instruction to include problems which are appropriate to solve with
pencil and paper or mental math calculations, but also include problems with relevant, real-world data
that make the use of a calculator appropriate. Designing a balance of these types of problems provides
students with experience to build their ability to make decisions about what tools are appropriate for use
in a given situation.
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DATA ANALYSIS and PROBABILITY
Calculators can be used to simulate random data (tossing of a coin, rolling of dice, etc.). Pencil and paper
methods are often best for conducting surveys and collecting real-life data. Calculators allow for timely
testing of hypotheses based upon changes in data values. Pencil and paper calculations can be
cumbersome and time consuming and have a greater probability of errors. With graphing calculators,
multiple representations are easily accessible and allow the user to choose which representation displays
data most appropriately. Pencil and paper methods are recommended for some assessment tasks such as:
understanding the parts of a graph (title, labels, appropriate scale, etc.), constructing a graph, or
promoting individual creativity.
In the Middle School grades, the West Virginia Content Standards and Objectives prescribe that
calculators are initially used to solve application problems. Gradually less emphasis is placed on pencil
and paper computations and calculators are emphasized for all mathematical tasks, including assessment.
The integration of learning skills, technology tools, and the content standards and objectives is the
responsibility of all West Virginia teachers, regardless of content area.
11
Operations with Rational Numbers
Does student background include the
development of conceptual
understandings of operations with
rational numbers?
No
Yes
Engage students in hands-on and
pencil and paper investigations to
develop conceptual
understandings.
Does the learning task involve
computation with tedious rational
numbers?
No
Yes
Can estimation or mental
math be used?
No
Use pencil and paper
computation
Yes
Use estimation or mental
math
Assess student
understanding
12
Use calculator
Calculator Usage in the Secondary Grades
At the secondary level, graphing technologies should be accessible to all students. Graphing technologies
may include calculators (with or without computer algebra systems), computer software, and other
technologies available today or at some point in the future. That being said, accessibility need not be
thought of as an inalienable right at all times. Classroom teachers have an obligation to consider the
pedagogical advantages and disadvantages of any technology. Today’s “cutting edge” technology may
soon go the way of the rotary dial telephone, four function calculator, or floppy-disk. Educators need to
ensure that students have had a variety of experiences with graphing technologies designed to develop
their proficiency in problem solving applications. They also bear the responsibility to add new
technological applications to their classroom repertoire and prepare students to be adaptable to new
technologies.
Students and teachers must regularly make choices as to whether or not to use technology in a problem
solving situation, and it is the responsibility of educators to guide students in these decisions. To that end,
calculators can enable the learner to make connections through multiple representations of algebraic,
tabular and graphical applications of mathematics. Although there is a learning curve, the speed and
accuracy at which students can analyze effects of varying parameters in authentic situations more than
compensates for the time invested in learning to use the calculator. However, the overreliance on
calculators may diminish the student’s understanding of the process, and may be detrimental to their
willingness to learn and maintain necessary skills.
Within the context of the secondary classroom, the graphing calculator (or graphing technology) can be
used as a tool for:
1. Discussion – A calculator demonstration can provide a springboard for discourse on
mathematical ideas and can help students clearly focus on key elements leading to deeper
understanding.
2. Exploration – Parameters can be varied and results can be investigated by individual students or
by students in a small group setting.
3. Generalization – Using inductive reasoning based on discoveries made during the exploration,
students can formulate conjectures.
4. Justification – Conclusions can be graphically or numerically supported to make abstract ideas
more concrete.
The role of the calculator is not to eliminate the deductive process that leads from conjecture to
conclusion. Rather, it should be used to enhance and establish connections among mathematical
concepts. It is the deductive process itself that bridges the gap from a conjecture to a conclusion.
In the secondary mathematics curriculum, calculators play different roles in different courses. For
instance, in an Algebra I class, calculators may not be appropriate for the introduction of polynomial
13
operations. In this course and later courses, however, when those same topics are expanded to include an
analysis of function families, transformations and operations, it may become important, or even critical, to
incorporate graphing calculators into the discussion. Because of these vertical implications, both teachers
and students need to internalize a decision making process as to when calculators are appropriate; a
process that should be encouraged and modeled by the teacher.
Though trigonometry offers many opportunities for calculator usage similar to the analysis of functions,
students need to be able to manually sketch graphs of basic trigonometric functions. In a statistics course,
calculators can be used to manipulate and analyze large amounts of data. In a geometry course, dynamic
geometric software can be used to make interactive geometric figures which allow students to induce
conjectures. Since geometry is the high school course that most embodies the deductive process of
mathematics, it is imperative that resulting theorems are formally proven setting the stage for proof in
future mathematics courses.
Formative and summative classroom assessment must include both calculator and non-calculator
components, with accommodations for students with special needs determined on an individual basis. It
is crucial that students and teachers realize that, though calculator fluency is an extremely valuable
addition to the mathematical toolbox, it is not a substitute for the ability to generate rich mathematical
thinking or to determine the reasonableness of solutions.
The process of determining when calculator usage is appropriate should become a “habit of mind” for
both students and teachers. Appropriate use of calculators often represents a dilemma, particularly for
novice teachers. Following are examples in a “flow chart” format of how the decision-making process
could play out in the teaching of several specific concepts.
14
Teaching Statistical Tools
Are you introducing a new
concept?
Yes
Can the skill/concept be
demonstrated with a small
amount of data?
Yes
Demonstrate the concept with
a small amount of easily
manipulated data using basic
operations.
No
No
Teach the students to do the
skill on a graphing calculator
using “real-world” data.
Do the students know how to
do the skill/concept on a
graphing calculator using “realworld” data
No
Yes
Do students demonstrate
understanding of the concept?
Yes
Assign homework problems
related to the concept.
Model problems with
and without a calculator.
No
Were the students successful
with the assigned problems?
Yes
Assess Student
Understanding
15
No
Teaching Polynomial and Rational Functions
16
Does student
background include an
understanding of yintercepts and zeros?
No
Yes
Graph with pencil/paper and
with calculators linear and
quadratic functions and observe
intercepts.
Graph with pencil/paper a few
easily factored varying degree
polynomial and rational functions
and discuss generalizations
No
Teach students to use graphing
calculators with functions
generated from “real-world” data.
No
Do students know how to
investigate polynomial and
rational functions on a graphing
calculator?
Yes
Can students demonstrate
understanding of the concept?
Yes
Assign some problems requiring sketches of graphs
and identifying intercepts and asymptotes and
some generated by “real-world” data situations
using graphing calculators for solutions.
Were assignments completed
successfully?
Teaching Logarithmic Functions as
17
No
Inverses of Exponential Functions
Does student background include
an understanding of exponential
functions?
No
Graph with pencil/paper and/or
calculator exponential functions
and identify graph characteristics.
Yes
Does student background include
an understanding of inverse
functions?
No
Graph with pencil/paper, patty
paper, and/or calculator linear
and quadratic functions and
generalize results.
Yes
Graph simple exponential
functions such as y = 2x and y = 2-x
on a calculator and sketch their
inverses.
Explain the x and y reversals and
domain and range restrictions.
Define a logarithmic function as
the inverse of an exponential
function.
Do students recognize the graph
of a logarithmic function with a
particular base?
Yes
Assess student understanding.
18
No
Teaching Quadrilaterals
No
Do students understand the
definition of the quadrilateral?
Yes
Define the
quadrilateral
Students sketch samples of the
quadrilateral indicating definitive
characteristic
Provide the students with precisely drawn copies of
the quadrilateral. These may be distributed or
generated on their calculator as appropriate.
Use the copies to develop conjectures
related to the quadrilateral’s unique
properties
Prove or disprove conjectures
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Impact on Higher Education
There are two obvious areas of impact of the K-12 calculator usage guidelines on higher education.
First, the students in post secondary classrooms have expectations about calculator usage, and calculator
skills, based on their K-12 experiences. Whether their expectations are appropriate or not, their
experiences shape their attitudes about the mathematics being studied and their abilities to think
creatively. Calculator use affects a student's approach to problem solving and understanding of
mathematical proof.
The points made about calculator use in secondary schools are also applicable to higher education. A list
of appropriate calculator activities can be organized according to uses related to Discussion, Exploration,
Generalization, and Justification whether the course is at the foundation level, liberal arts mathematics,
college algebra, trigonometry, precalculus, calculus, or more advanced mathematics. Calculators can
make the first steps of conjecturing and modeling natural and easy. Many students are using calculators
and other technologies extensively in high school where they play a major role in how students represent
mathematics. Consequently, extensive restrictions on calculator use may impact the learning process of
the modern day learner. Calculators help students make sense of the mathematics they are attempting to
learn. For example, when working to understand a concept, make a conjecture, solve a problem, or make
a connection, a calculator makes moving among representations more transparent so that students can
concentrate on the key ideas. Here a calculator has a valuable role to play in exploring situations or
looking for patterns where the numbers involved are unwieldy (as they often are in applications), or when
data sets are too extensive to explore by hand.
Second, higher education has an obligation to incorporate activities in order that pre-service teachers use
calculators confidently and appropriately. Calculators (and technology in general) are ubiquitous and
inevitable. One purpose for this document is for faculty to make sense of the wealth of opportunities that
are available. College faculty can make pedagogical choices based on educational research and thereby
impact educational practice of pre-service teachers. Ultimately, college courses must equip in-service
teachers to be able to judge for themselves how and when technology should be used in the classroom and
which method is best to address a particular situation.
The instructor in a teacher preparation course models calculator use in ways that are grade level
appropriate. For example, in secondary schools the calculator is used in the teaching of the required
mathematics background through a variety of strategies that include demonstration, connecting multiple
representations, exploration, and forming and testing conjectures. At the same time, the instructor uses
calculators of different kinds to develop awareness of their features and capabilities, thereby helping preservice teachers make informed choices of which calculator is appropriate for specific grade levels and
purposes. Beyond teaching the mathematics, the instructor in the pre-service class can use calculators to
illustrate the connections between the mathematics studied in the college courses and the mathematics the
teachers will teach. The instructor in the pre-service class should explicitly model the process through
which teachers decide when to use calculators and when to avoid their use.
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Future educators need to be aware of the inappropriate uses of calculators, as well as their appropriate
usages in the classroom. Depending on the situation, there may be more effective strategies than
calculator use for developing understanding of basic concepts. These strategies may include the use
of manipulatives, paper folding, simulations, mental math, or the students' life experiences. The same is
true for the reinforcement of previously studied concepts or for the assessment of conceptual
understanding.
Calculator use often represents a higher level of abstraction than some students are initially able to attain.
They must first have an opportunity to grapple with the material in a more concrete way. For example,
students need to discuss the impact on answers of exact values, approximations, significant digits, and
rounding. Students also need to revisit the mathematical concepts that are taken for granted through the
use of the calculator, such as integer operations, determining extrema, intercepts, asymptotes, and
logarithmic values, so their later experience can help with mathematical sense-making.
Issues of calculator equity and access are different in higher education than in K-12. For example, there
is typically not a unique mathematics requirement for a college degree corresponding to the “algebra for
all” movement in secondary schools. Policies exist that if a calculator is listed as a requirement in the
syllabus, financial aid can be used to purchase the calculator as it would be used to purchase a solution
guide or other course ancillary.
21
Committee Members
This document was developed by:
Lynn Baker
Math Science Partnership Coordinator, WV Department of
Education
Susan Barrett
School Improvement Coordinator, Nicholas County Schools
Roger Bennett
Elementary Math Instructional Coach, Boone County Schools
Shirley Davis
Associate Professor of Mathematics, New River Community
and Technical College
John Ford
Title I Mathematics Coordinator, WV Department of Education
Michelle Hamrick
Learning Specialist, Clay County Middle School
Sheryl Hulmes
Mathematics Teacher, Eastern Greenbrier Middle School
Michael Mays
Director, Institute for Math Learning, WVU
Regina McCormick
Teacher, Madison Middle School
Karen Mitchell
Professor of Mathematics, Marshall University
Judy Pomeroy
Mathematics Coordinator, RESA 4
Anthony Pyzdrowski
Professor, Department of Mathematics, Computer Science and
Information Systems, California University of PA
Laura Pyzdrowski
WVU Pre-Collegiate Mathematics Coordinator
Lucie Refsland
Professor of Mathematics, New River Community &
Technical College
Matt Rhodes
Mathematics Teacher, Saint Albans High School
Debbie Seldomridge
Mathematics Teacher, Keyser High School
Cheryl D. Thomas
Mathematics Teacher, Clay County Middle School
Holly Woods
Math Facilitator/Trainer (K-12), Marshall County Schools
The project directors were
Jerry Pomeroy
Mathematics Teacher, Greenbrier West High School
Gary Seldomridge
Professor of Mathematics, Potomac State College of WVU
The committee was formed and supported by
Lou Maynus
Mathematics Coordinator, WV Department of Education
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Bibliography
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Teaching for the 21st Century, (2000) U.S. Department of Education.
Computation, Calculators, and Common Sense, (May 2005), National Council of Teachers of
Mathematics.
Ellington, A. J. (2003). A meta-analysis of the effects of calculators on students' achievement and attitude
levels in precollege mathematics classes. Journal for Research in Mathematics Education, 34(5), 433463.
Olson, J.F., Martin, M.O., & Mullis, I.V.S. (Editors). (2008). TIMSS 2007 Technical Report. TIMSS &
PIRLS International Study Center, Boston College.
Principles and Standards for School Mathematics (2000). National Council of Teachers of Mathematics.
Rittle-Johnson, Kmiclewycz, Alexander Oleksij (September 2008). When generating answers benefits
arithmetic skill: The importance of prior knowledge. Journal of Experimental Child Psychology, Volume
101, Issue 1, Pages 75-81.
The Final Report of the National Mathematics Advisory Panel, (January 2009). U.S. Department of
Education.
The Role of Technology in the Teaching and Learning of Mathematics (March 2008), National Council of
Teachers of Mathematics.
Thompson, A., & Sproule, S. (2000). Deciding when to use calculators. Mathematics Teaching in the
Middle School, 6, 126-29.
Usiskin, Zalman (Editor) (May/June 1999). Mathematics Education Dialogs - Groping and Hoping for
Consensus on Calculator Use.
West Virginia Content Standards and Objectives. West Virginia Department of Education.
http://wvde.state.wv.us/policies/csos.html
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