Although calculators have not figured prominently in discussions of the
common-core math standards, it's likely the complementary tests will result in far greater uniformity in their use on state exams across the nation.
Policies emerging from the two state consortia developing common-core assessments would prohibit most students from using calculators on the grades 3-5 tests, for example. At grades 6 and above, they call for calculator "on" and "off" sections and set restrictions on what functionality is allowed. (Both consortia will provide online calculators for the computer-based tests.)
Those rules, especially in today's high-stakes-testing environment, are sure to influence regular classroom use of calculators, from the elementary ban to the ways increasingly sophisticated calculator use is assumed at the secondary level, many experts say.
State policies are all over the map for using calculators on large-scale assessments. At least a few states—including Arizona, California, and Nevada—prohibit most students from using calculators at all, even on high school exams. But that approach appears to be the exception. Meanwhile, some states, such as New York and Ohio, prohibit calculators only for elementary students.
There are other variations across states, too, including whether the exams have calculator-free sections (many do, including tests in Kentucky, Maryland, and Rhode Island), and the limits imposed on the type of device students may use at different grade levels, such as a basic four-function, scientific, or graphing calculator.
Reaction from math experts and educators to the PARCC policy since it was issued in July 2012 has been mixed. Although making the exams at grades 3-5 calculator-free has been welcomed in some quarters, others criticize the move.
"The old saw is, teach to the test, and that's the reality," said W. Gary Martin, a professor of math education at Auburn University in Auburn, Ala. "If [students] can't use a calculator on the test, it's effectively banished from the classroom."
On the other hand, Mr. Martin and others praised the PARCC guidelines for high school, which call for the use of an online graphing calculator with comparable functionality to a Texas Instruments TI-84, a popular calculator in high schools.
"It will be a step in the right direction," said Brad Findell, the associate director of math-teacher-education programs at Ohio State University. "It will encourage graphing-calculator use in high school, particularly among lower-achieving students for whom this may have been withheld."
Exactly how many states will ultimately use the PARCC and Smarter Balanced assessments is unknown. Recently, Georgia and Oklahoma have bowed out of the PARCC exams, for instance, though most states are planning to use one or the other testing system.
'Appropriate' Use
The use of calculators in schools has long been a divisive issue, with some critics seeing little place for them at the K-12 level, especially for younger students. But analysts suggest the debate has quieted down in recent years.
Today, with calculators widely used in schools, particularly at the secondary level, the real dilemma is when and how to use them, argues Kathryn B. Chval, an associate professor of math education at the University of Missouri in Columbia who has studied calculator policies.
"The debate should be: When do we use calculators? When do we not use calculators? What is the calculator going to help you teach?" she said.
"I personally see them as useful tools, but like all tools, they need to be used appropriately," said Patrick Honner, who teaches math at Brooklyn Technical High School in New York City. That, he said, includes explicit training for students.
The word "appropriate" is key to how calculators are discussed in the common core. The document explicitly references using technology, including calculators and other tools such as spreadsheets and even geometry software. The main guidepost, analysts say, comes in the Standards for Mathematical Practice. The fifth practice standard, Use Appropriate Tools Strategically, says that mathematically proficient students "are able to use technological tools to explore and deepen their understanding of concepts."
The PARCC and Smarter Balanced testing consortia have written policies for the online calculators to be used on their common-core exams. The Smarter Balanced policy is in draft form, subject to approval by member states.
Mr. Findell from Ohio State appreciates that emphasis.
"Under current practice, the words 'appropriate' and 'strategically' are too often absent from discussions of the use of calculators and other tools," he said, arguing that students often rely too heavily on them.
To that end, Mr. Findell praised plans for the common-core assessments to have calculator "on" and "off" sections at grades 6 and above, which would be a change for Illinois and some other states.
"The common core represents a reasonable middle ground that potentially, if we take it seriously enough, and assessment helps us enough, can bring us to a better place where students end up being thoughtful," he added.
In developing calculator-use policies, officials from both PARCC and Smarter Balanced said they considered several factors, including what the common standards say, current state policies, and how the issue is handled on other prominent assessments, such as national and international exams.
"We really spent time researching the standards and researching what the standards call for as technology," said Carrie Piper, a senior adviser for mathematics at Achieve, a Washington-based organization working on the PARCC assessments. "PARCC feels as though the calculator should be used as a tool for the student."
Ms. Piper also said PARCC consulted with Jason Zimba, one of the lead writers of the math standards.
The rules for national and international assessments vary. The Trends in International Mathematics and Science Study bans calculators for the grade 4 exam, but allows them at grade 8. But the National Assessment of Educational Progress permits calculators for some questions at grades 4, 8, and 12. On the SAT, scientific and graphing calculators are permitted.
Shelbi Cole, the math director for Smarter Balanced, said that for pilot testing conducted earlier this year, the consortium's policy was similar in many respects to PARCC's planned approach. But for the draft policy now awaiting action by the Smarter Balanced governing states, one notable change is to permit a scientific calculator at grade 7. PARCC restricts students in both grades 6 and 7 to a four-function calculator with square root.
Ms. Cole said the change came in response to feedback from educators in the field and a closer examination of the content to be tested in grade 7.
One of the eight Standards for Mathematical Practice in the common core, Use Appropriate Tools Strategically, explicitly discusses the use of calculators and other technology.
"Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful. … For example, mathematically proficient high school students analyze graphs of functions and solutions generated using a graphing calculator."
Smarter Balanced also plans some adjustments to the high school calculator functions based on feedback from educators, she said.
At high school, the draft policy says the online calculator will have scientific, regression, and graphing capabilities. In fact, it's already available online for anyone to use, though Ms. Cole said updates are being made prior to field testing—planned for early next year—to further refine it.
Smarter Balanced is still exploring how to handle calculator use for students with disabilities. PARCC's recently issued accommodations policy makes some allowances for students with disabilities on noncalculator sections.
In the draft policy, Smarter Balanced says it will not allow hand-held calculators for students who use the online test (unless explicitly allowed under the accommodations policy). PARCC will allow hand-held calculators for the first year of testing, but no decision has been made beyond that.
Ms. Cole said a key advantage of using online calculators is it levels the playing field to ensure all students, regardless of background or income level, use the same calculator on the test.
"The biggest benefit to me is the equity issue," she said.
But several educators said that while they like the idea of an online calculator for the exams, they still see reasons for concern, especially in high school.
"While everybody will have access to the same technology, not everybody will have the same background with that technology," said Cliff Bara, who teaches math and science at Troy Junior and Senior High School in Troy, Mont.
Mr. Bara also expressed concerns about the middle school restrictions in both consortia's policies.
"If the common core ... is moving a lot of the algebra down to grade 7 and especially 8th grade, for them not to allow a graphing calculator, at least at the 8th grade, seems to be a serious oversight," he said. Seventh and 8th graders at his school use them "all the time."
Chilling Effect?
The "no calculator" plan for grades 3-5 has generated considerable criticism. Some educators and experts who believe calculators have a valuable role at that level fear the policies will have a chilling effect on their use, and say it has implications for test questions.
"It's absolutely true that kids need to be able to compute without calculators, ... but that's only part of what they need," said Cathy Seeley, a senior fellow emeritus at the Charles A. Dana Center at the University of Texas at Austin. "To prohibit them [on the exams] in grades 3-5 even when there are very useful ways students would use them to get to higher-level thinking" is a mistake. "It constrains the depth of the [test] problems you provide."
In 2011, the National Council of Teachers of Mathematics, long an advocate for using calculators across grade levels,
issued a policy statement explicitly touting the benefits of "selective and strategic use" of calculators to support elementary math learning.
But a
2012 teacher survey
suggests calculators are not regularly used at that level. Four-function calculators are available in 58 percent of elementary classrooms, it reported, but they are used at least once a week in only 13 percent.
Linda Gojak, the president of the NCTM, said she's "not too troubled" by the grades 3-5 prohibition on tests, though she said "it's really hard to make a judgment without seeing more test items."
But Jennifer Barrett, a math-curriculum consultant for the 14,500-student Kenton County district in Kentucky, welcomes the restriction. (In Kentucky, calculators are now allowed for some elementary test items.)
"This gives teachers permission to spend time on the grade-level fluencies explicitly stated in the [common core], which in recent years have been de-emphasized," she said. "If calculators are used, how is [computational] fluency and number sense being supported?"
Ms. Piper said there was little debate in PARCC on the grades 3-5 policy. "Deciding not to include a calculator was a pretty easy [call]," she said, "because of students being able to build their number-sense skills, number sense, and fluency."
Linda Kaniecki, a math specialist at the Maryland education department who worked with PARCC on its policy, said that while the rules will be a shift for her state, there's no intention to send a no-calculator message to teachers.
"We're hoping that it's still used in instruction," she said.
Bushra Makiya, an 8th grade math teacher at a New York City public school, is upbeat about the PARCC rules, which she says are quite similar to how New York, a PARCC governing member, now approaches testing, except for the planned use of online calculators.
"Calculators are a really important tool for students, and if they're going to be used effectively in the classroom, it's important that they are also used on state tests," said Ms. Makiya, who teaches at the Leadership and Community Service Academy. "I don't see how good problems that really delve into the eight mathematical practices [in the common core] can be developed if calculators aren't allowed for at least some portion of the test."
One of her chief concerns, however, echoed by other teachers, is getting students used to the online calculator that will be embedded with the computer-based tests.
"While this may seem like a small detail, I could see it really throwing some students off if there's not adequate practice time," she said.
Vol. 33, Issue 01, Pages 1,12-13
