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Calculators and Connecticut's Eighth-Grade Mastery Test Author(s): Betsy Y. Carter and Steven J. Leinwand Source: The Arithmetic Teacher, Vol. 34, No. 6, FOCUS ISSUE: CALCULATORS (February 1987), pp. 55-56 Published by: National Council of Teachers of Mathematics Stable URL: http://www.jstor.org/stable/41193098 . Accessed: 12/06/2014 22:39 Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp . JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected]. . National Council of Teachers of Mathematics is collaborating with JSTOR to digitize, preserve and extend access to The Arithmetic Teacher. http://www.jstor.org This content downloaded from 188.72.126.41 on Thu, 12 Jun 2014 22:39:14 PM All use subject to JSTOR Terms and Conditions

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Calculators and Connecticut's Eighth-Grade Mastery TestAuthor(s): Betsy Y. Carter and Steven J. LeinwandSource: The Arithmetic Teacher, Vol. 34, No. 6, FOCUS ISSUE: CALCULATORS (February 1987),pp. 55-56Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/41193098 .

Accessed: 12/06/2014 22:39

Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at .http://www.jstor.org/page/info/about/policies/terms.jsp

.JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range ofcontent in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new formsof scholarship. For more information about JSTOR, please contact [email protected].

.

National Council of Teachers of Mathematics is collaborating with JSTOR to digitize, preserve and extendaccess to The Arithmetic Teacher.

http://www.jstor.org

This content downloaded from 188.72.126.41 on Thu, 12 Jun 2014 22:39:14 PMAll use subject to JSTOR Terms and Conditions

February 1987 55

Calculators and Connecticut's < Eighth-Grade M Mastery Test ̂

By Betsy Y. Carter and Steven J. Leinwand

An Agenda for Action (NCTM 1980) recommends that "mathematics ^ programs take full advantage of the power of calculators and computers at all grade levels" and that "the suc- cess of mathematics programs and student learning be evaluated by a wider range of measures than conven- tional testing."

On 8 January 1986, the Connecticut State Board of Education voted to endorse the use of calculators by stu- dents on parts of the state's new eighth-grade mastery test. In taking this action, the board took a critical step toward the improvement of math- ematics instruction by linking technol- ogy and testing.

The board's action allowed eighth- grade students to use calculators on the problem-solving-application and measurement-geometry items on the test beginning in October 1986. Stu- dents do not have access to calcula- tors on items assessing conceptual understanding or computational skills. The board also authorized the purchase and distribution of one cal- culator for each eighth-grade student for use on the test and in the class- room.

We are in the process of buying and distributing 35 000 TI- 1100 II battery- powered hand-held calculators, one for each eighth grader (bid price $3.25).

Betsy Carter and Steven Leinwand share re- sponsibilities in the Connecticut State Depart- ment of Education, Hartford, CT 06145 ', for the improvement ofK-12 mathematics programs.

The eighth-grade mastery test is the capstone of Connecticut's new pro- gram of statewide criterion-refe- renced tests for the fourth, sixth, and eighth grades. Each test contains four items for each objective and is de- signed to assess students' mastery of specific skills within the general areas of conceptual understanding, compu- tational skills, problem solving-ap- plications, and measurement-geom- etry. The board of education's decision was based, in part, on the following position paper. It is our hope that Connecticut's position pa- per will help other states to take sim- ilar steps.

Summary of Position Paper on Calculators and the Eighth-Grade Mastery Test Recognition is increasing that the fo- cus of mathematics instruction must shift toward critical thinking skills and problem solving and away from rote computation. One way to meet this goal is to encourage far greater use of calculators as computational tools in our classrooms.

The calculator in today's society The number of hand-held calculators

in use in the home and in the work- place has literally exploded in the last few years. The calculator is a very reliable and quite inexpensive tool that now rivals the automobile, televi- sion, and refrigerator in its availability and usefulness.

One survey of the mathematics skills used by the workforce revealed that calculators were used in 98 out of 100 jobs surveyed (Saunders 1980).

Data from the Connecticut Assess- ment of Educational Progress in Mathematics in 1979-80 showed that 85 percent of the nine-year-olds, 87 percent of thirteen-year-olds, and 93 percent of seventeen-year-olds an- swered "yes" to the question, "Do you or your family own a calculator?" Among the thirteen-year-olds (eighth graders), only 20 percent reported never having used a calculator. Un- doubtedly nearly every student will have access to a calculator in the late 1980s.

In light of such widespread use and availability, the calculator belongs in the mainstream of classroom activi- ties. Calculators can perform other- wise tedious, repetitious, and time- consuming computational operations rapidly and accurately while allowing users to focus on the collection and organization of data and on the selec- tion of strategies for problem solving.

It is interesting to note that cur-

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rently calculators are used in several areas of the curriculum. It is unthink- able today to teach accounting or chemistry without calculators. Trigo- nometry and calculus students use them regularly. When calculations must be done, students and teachers turn to available technology, which parallels the situation in the real world. The calculator's place in the curriculum A major problem with mathematics instruction has been its overemphasis on rote pencil-and-paper skills. Much time is spent learning one standard algorithm for each arithmetic opera- tion and then repeating the algorithm with larger and larger numbers.

For example, in many seventh- grade mathematics textbooks, chapter 1 addresses addition and subtraction of whole numbers, chapter 2 covers addition and subtraction of decimals, chapter 3 concerns multiplication and division of whole numbers, and chap- ter 4 includes multiplication and divi- sion of decimals. Thus, many mathe- matics programs do not get far beyond pencil-and-paper computation until after the new calendar year has be- gun, leaving little time for the devel- opment of conceptual understanding and problem-solving abilities.

A growing body of research on cal- culator use reveals two major find- ings. First, although without calcula- tors students are able to complete an average of only ten problems in a class period, with calculators they complete twenty-five or more prob- lems in a class period. This finding means that students get more than twice as many opportunities to ask, "What should I do?" without having distracting computation to do. Sec- ond, research shows that calculators have no diminishing effect on test scores (including computational subtests) but often result in significant improvement of test scores.

One example is indicative of the current situation: A large proportion of eighth graders are capable of doing the problem 10.2V287. However, when these same students are asked about going 287 kilometers on 10.2 gallons of gasoline, a far smaller pro-

portion know that they must divide to determine kilometers a gallon, and even among these students, many will incorrectly try dividing 10.2 by 287.

Two test items from Connecticut's ninth-grade proficiency test also dem- onstrate the situation: Although 86 percent of the students correctly solve the problem 14V4872, only 50 percent correctly answer the far more practi- cal problem "Max drove 61 miles at an average speed of 29 miles an hour. About how many hours did the trip take?" Their skills of knowing when to divide, how to solve a problem, and how to determine the reasonableness of the answer are far weaker than the skill of simply knowing how to divide. This situation will continue unless we decrease attention on rote computa- tion and increase the time spent and emphasis placed on using mathemat- ics to solve real problems, in part by encouraging the use of calculators.

Used in this way, calculators do not replace the learning of basic facts or arithmetic processes. Similarly, de- spite commonly held myths, the cal- culator does not become a crutch or cause "brain atrophy." We must re- define computational skills to include facility with pencil-and-paper algo- rithms, mental computation with non- standard algorithms, estimation skills, and calculator skills. Permitting stu- dents to use calculators in testing sit- uations can rectify the present curric- ular imbalance and improve the overall quality of mathematics in- struction.

Strengthening mastery testing goals Connecticut's Guide to Curriculum Development in Mathematics recom- mends that "classroom sets of hand- held calculators should be available for student use in all schools and their use integrated into the mathematics curriculum." The availability of cal- culators for the mastery test will help implement this recommendation and allow testing goals to be set with higher standards and broader content. Without calculators , problem-solv- ing-application items must contain rather easy computations because we are trying to test problem-solving skills, not computational skills.

Equity of Instructional Tools An additional concern relates to eq- uity. Calculators abound in middle- and upper-class homes and are more readily supplied to students in wealth- ier school districts. As with comput- ers, an imbalance of opportunity ex- ists in urban and rural districts with respect to technology. To equalize educational advantages , calculators should be available to all students in all districts.

Conclusion Good testing practices help to drive the curriculum and concomitant in- struction in positive directions. By allowing students to use calculators on part of this statewide test, the state board of education sends a clear mes- sage about curricular and instruc- tional expectations to students, teach- ers, and the community. It is a decision that can and will help to improve the learning of mathematics.

To preclude the use of calculators would blur the message considerably. Given the overall importance of test scores, teachers would be unwilling to risk classroom time on calculator use from fear that it would negatively af- fect the scores. We would be left sending a contradictory message: en- couraging an updated, realistic curric- ulum, including calculators, but then outlawing their use on the test de- signed to assess the effectiveness of this curriculum.

Allowing students to use calcula- tors for the problem-solving-applic- ation and measurement-geometry items will result in a strong, sound, and consistent statement about what is important in mathematics instruc- tion and a stronger, more realistic, and responsive testing program.

References Connecticut State Board of Education. Sum-

mary and Interpretations of the Connecticut Assessment of Educational Progress, 1979-1980. Hartford: The Board, 1980.

National Council of Teachers of Mathematics. An Agenda for Action: Recommendations for School Mathematics of the 1980s. Reston, Va.: The Council, 1980.

Saunders, Hal. "When Are We Ever Gonna Have to Use This?" Mathematics Teacher 73 (January 1980):7-16. m

56 Arithmetic Teacher

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