Discussion of Calculator Use in Elementary School Mathematics
Dr. Brian
E. Enright, author and founder of Algebraic Thinking,
in a 2007 meeting at CSSD11, said that it is not a question of if calculators
are used in elementary and middle school, but how and when. Dr. Frank Yang,
president of Saxon Publishers, said in 1999 that using calculators in
elementary school can be used in two main ways; illustrating concepts and in tedious
calculations. Dr. Yang advises caution and care in the use of calculators so
that students gain deeper understanding of the calculations they are being used
for. Calculator use in elementary school mathematics has at times been widely
misunderstood by some who are not involved in daily mathematics instruction.
After all, always allowing students to use calculators instead of their brains
to perform mathematical computations seems wrong. That particular use of
calculators is wrong! Calculator use in Everyday Mathematics, Houghton
Mifflin, Harcourt Brace, Scott Foresman/Addison
Wesley, MacMillan McGraw Hill, and other popular mathematics programs are not
involved with that practice in any way. Calculators are used very intentionally
rather than carelessly or without justifiable reason. Some of the many ways
calculators are used are listed by mathematical standard and then grade level
below:
3rd Grade Usage
Finding
complements, memory, place-value puzzles, repeat key, riddles, routines,
skills, skip counting, extending a pattern, skip counting by large numbers,
seeing relationships between values of each place, counting aloud by tenths.
4th Grade Usage
Divisibility,
fraction-decimal conversions, fraction-percent conversions, games,
multiplication checks, place value.
Everyday Math explanation of calculator usage,
Grade 4, Volume 1, Unit 3, p. 144:
Calculators
are used in this unit for games such as Beat the Calculator and Broken
Calculator. In Beat the Calculator, students quickly realize that their brains
are much more efficient than their calculators when finding a product like 7 *
3. In Broken Calculator, students pretend, for example that the minus keys on
their calculators are broken and then devise strategies to solve such problems
as 2,421 874 = n. Calculator usage is also encouraged as students work on the
World Tour project.
However, the no-calculator icon (see margin) does appear on many journal pages,
including those on solving number stories and Math Boxes pages in which the
intention is to encourage practice with algorithms for adding and subtracting
numbers. Teachers alert students to watch for the icon.
Note: If your students have Texas Instruments TI-15 calculators, they can use
them to practice math facts. When the TI-15 is put into Arithmetic Training
mode, it automatically generates problems for the user to answer. This feature
of the TI-15 is discussed in the calculator section of the teachers reference
Manual and on Math Masters, pages 476 and 477.
5th Grade Usage
Basic fact
games, divisibility checks, square root, exponents and scientific notation,
rounding decimals in statistical data, generate random numbers in Division Dash
game, interpret remainders in context, check answers in 1 to 100 game, adjust
for special needs learners, convert non-common fractions to decimals and
decimals to percents, decimal equivalents for fractions, finding percents from
a frequency table, negative numbers and order of operations, place value
puzzles, circumference and area of a circle, volume and surface area of a
prism, cone, and pyramid, represent rates with formulas, tables, and graphs,
probability and tree diagrams, ratio number stories, calculating heart rate for
1 hour, day and year (large numbers), calculating cardiac output (large
numbers).
5th Grade Lessons
1.3*
optional used in game, Beat the Calculator
1.4*
optional - used in game, Beat the Calculator
1.5
checking for divisibility
1.6*
optional - used in game, Beat the Calculator
1.8
experimenting with the square root key on the calculator
1.9 -
exponents
2.1* -
optional - used in game, Beat the Calculator
2.5
rounding decimals in statistical data
4.1 used in
game, Division Dash to generate random numbers, NOT FOR CALCULATION
4.5*
optional interpret remainders in context
4.6 check
answers only in game, First to 100, NOT FOR
CALCULATION
4.7 same
as above lesson 4.6
5.1*
optional used to adjust activity for special needs students
5.7 find
decimal equivalents for fractions and discuss meaning
5.8 -
convert fractions to decimals, decimals to percents and discuss meaning
5.10*
optional for enrichment convert 17/28 to a decimal
5.11*
optional for enrichment finding decimal equivalents for sevenths and eighths,
converting bar graphs to circle graphs
6.1 for
adjusting the activity for large number enrichment with mean (average)
6.6 find
percents from a frequency table
7.3*
optional enrichment for scientific notation with large numbers
7.5*
optional teacher discretion re: order of operations
7.10
negative numbers on a calculator
8.4 using
the fraction operations on a calculator
8.6
writing calculator sequences to solve place-value puzzles
8.9* one
of several options taught in finding percent of discount
8.10*
optional same as above lesson 8.9
8.11*
optional examine populations on maps and charts, use percents to estimate
populations
9.3
explore negative numbers, decimals, and fractions on a calculator
9.7* -
optional weeklong project working with only 4s and any operation on the
calculator to create expressions for values from 1 100. (square
root, 4°, factorials, and order of operations)
10.4
represent rates with formulas, tables, and graphs
10.5
unclear usage, not mentioned or obvious in lesson
10.8
calculating circumference with pi
10.9
calculating area of a circle using a formula
10.10
assessment review
11.1
circumference and area review
11.3
finding volume of cylinders
11.4
finding volume of pyramids and cones
11.7
calculating surface area of prisms, cylinders, and pyramids
12.2
probability and tree diagrams
12.5
ratio number stories
12.6 calculating
heart rate for 1 hour, day and year (large numbers)
12.8
calculating cardiac output (large numbers)
12.9*
American Tour culmination; unclear use, must be optional calculator use
Key to
Symbols
|
HM =
Houghton Mifflin |
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HB =
Harcourt Brace |
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S = Saxon |
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SF/AW =
Scott Foresman/Addison Wesley |
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SF =
Scott Foresman |
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GwM = Growing with Mathematics |
Data on lessons including use of a calculator for the remaining textbooks is currently
being collected. Data will be included as it comes in.
Key
HM = Houghton Mifflin
HB = Harcourt Brace
S = Saxon
SF = Scott Foresman
SF/AW = Scott Foresman/Addison Wesley
GwM = Growing with Mathematics
EDM = Everyday Mathematics
Lessons Using Calculators Grade 3
Elementary Math
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Grade 3
Math Series |
Lesson # |
Lesson # |
Lesson # |
Lesson # |
Lesson # |
Lesson # |
Lesson # |
Lesson # |
Lesson # |
Lesson # |
Lesson # |
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EDM |
1.5 |
1.8 |
1.1 |
1.11* |
1.13* |
2.2 |
2.3 |
2.8* |
4.5 |
4.6 |
5.1* |
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HM |
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HB |
1.1 |
1.3 |
2.2 |
2.3 |
3.1 |
3.3 |
3.5 |
3.6 |
4.3 |
4.4 |
5.1 |
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S |
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SF/AW |
1.4* |
1.5* |
1.6 |
1.11* |
2.5* |
2.review |
3.1 |
3.3 |
3.8* |
3.10* |
3.16 |
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SF |
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GwM |
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EDM |
5.2* |
5.3* |
5.5* |
5.8* |
6.7* |
6.8* |
7.3 |
7.6* |
7.7 |
7.10* |
9.8 |
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HM |
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HB |
5.5 |
7.1 |
10.1 |
10.4 |
11.Tech |
11.2 |
20.4 |
20.5 |
21.1 |
21.3 |
22.3 |
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S |
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SF/AW |
3.17 |
4.2 |
4.2 |
4.12* |
4.13* |
4.16* |
5.1 |
5.7 |
5.9* |
5.10* |
5.review* |
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SF |
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GwM |
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EDM |
9.13* |
10.7 |
10.9 |
10.1 |
10.12 |