PART II Message 18 Faster Isnt Smarter 1Fr

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M E S S A G E

18Its a widespread belief that to be good at mathmeans to be fast at computation. But this belief mayin fact do more harm as good. Some of the worldsgreatest thinkers, scientists, and mathematicians havenot been fast at arithmetic, even though they weretremendously successful in working with higher-levelmathematics. Dr. Emma King has noted her poor per-formance on rote arithmetic computation, in spite ofher highly recognized work in the scientific field of cos-mology. Numerous scientists and scholars from aroundthe world could tell similar stories.

Certainly as part of a complete and balancedmathematics program it is useful to be able to add,subtract, multiply, and divide quickly, and it is impor-tant to know basic addition and multiplication factswithout having to figure them out or count on yourfingers. But asking students to demonstrate thisknowledge within an arbitrary time limit may actuallyinterfere with their learning. While computationalrecall is important, it is only part of a comprehensivemathematical background that includes more complexcomputation, an understanding of mathematical con-cepts, and the ability to think and reason to solveproblems. Measuring this one aspect of mathemat-icsfact recallusing timed tests is both flawed as anassessment approach and damaging to many studentsconfidence and willingness to tackle new problems.

A Classroom StoryThe pressure and potential damage of timed testsbecame especially evident to me several years agowhen a seventh-grade teacher invited me to visit herclass. It was September, and the teacher was spendingtwo weeks reviewing multiplication facts beforegoing on to seventh-grade material. The teacherexplained to me that each day she was testing a dif-ferent set of facts. The day I visited, the class was tak-ing a timed test on the four timeses. The studentsbecame increasingly anxious as the teacher passed

out short fact tests face down on their desks. All eyeswere watching the second hand on the clock; studentsknew that until it reached 12, they were safe. Thenthe second hand hit 12 and the teacher said, Begin!The boy I was sitting next to ground out a fewanswers. He was gripping his pencil so hard that itbroke in the process. It seemed an eternity, but finallythe three minutes were up. I looked at the boyspaper. He had not come close to finishing, and thefew answers he had so painstakingly attempted towrite were wrong. If his performance was similar toothers in the class, I had to conclude (as the teacherhad) that these seventh graders did not know theirfacts.

The teacher collected the papers and handed out apuzzle-type worksheet for the students to completewhile she graded the tests. The puzzle worksheet wason the same facts the students had just seen on the test.I sat quietly as the same boy now used his broken pen-cil to calmly and correctly complete all the facts on theworksheet. He got the correct answer to the puzzle,put down his pencil, and got out a book to read. A fewminutes later, the teacher read the names of the stu-dents who had passed the timed test. Of course, theboy seated next to me was not on the list.

The lessons from this story are obvious. Some stu-dents respond well to competitive and timed situa-tions, thriving on the pressure to bring out their best;others have quite a different reaction. This particularboy received a clear message that some students aregood at math and some are notand he knew whichgroup he was in. He also was prevented from finishingthe test, something that causes some students tremen-dous frustration. Furthermore, the teacher was led tobelieve, incorrectly, that this student did not know hismultiplication facts. Consequently, and perhaps worstof all, the boy was placed in a special group to receiveremediation on low-level arithmetic, robbing him ofthe opportunity to move into more interesting prob-lems and engaging work involving seventh-grademathematics.

Faster Isnt SmarterTHE TRAP OF TIMED TESTS

2 CATHY L. SEELEY Faster Isnt SmarterFrom

Faster Isnt Smarter

by Cathy L

. Seeley. 2009 M

ath Solutions. All rights reserved. Perm

ission granted to reproduce for nonprofit use in a classroom or sim

ilar place dedicated to face-to-face educational instruction.

Alternative ScenariosWhen I tell this story, sometimes teachers share otherapproaches to helping students develop speed in com-putation. For example, if a teacher or school chooses toinclude speed as a mathematics priority, the teachermight offer students the option to work toward theirbest time during a six- or nine-week grading period,designating a specified block of time one day a week forthis type of work. When a student is ready to try toimprove his previous time, he can request to take thetest. Students record their starting and ending times,doing their best to complete the test quickly and beattheir best time, but always finishing and competingagainst only themselves. This type of self-administeredassessment carries much less stress and allows each stu-dent to complete the test without competing againstother students.

What Can We Do?Even if we use other practices to evaluate speed, we needto weigh the importance of this aspect of mathematicswithin the entire program. Overemphasizing fast factrecall at the expense of problem solving and conceptualexperiences gives students a distorted idea of the nature

of mathematics and of their ability to do mathematics.Some students never survive this experience and theyturn away from mathematics for years, sometimes for-ever. Having experienced timed tests when they werestudents, many adults believe that accurate, fast compu-tation is the most significant part of mathematics. Whenpressed, many of these adults who dislike or fear math-ematics attribute these negative feelings to experiencesfrom their school years, especially the use of timed tests.In determining how much to value speed in arithmetic,we must consider the costs and benefits: If teachershighly value speed in mathematics, what are the poten-tial gains for student learning? The potential barriers?

For some students, their success at being fast atcomputation opens doors to allow them access tohigher-level mathematics. But as Marilyn Burns hasstated, Speed with arithmetic skills has little, if any-thing, to do with mathematical power (1989). We arenow discovering that being good mathematical thinkersor problem solvers is at least as important as being goodat computation and can also pave the way to higher-level mathematics. At a time when we want to helpevery student learn challenging, rigorous, and relevantmathematics, we must look for ways to tap into eachstudents strengths, not fall into the trap of believingthat timed tests are the way we identify our good math-ematics students.

Reflection and DiscussionFOR TEACHERS

What issues or challenges does this message raise foryou? In what ways do you agree with or disagreewith the main points of the message?

What value do you put on speed in your classroom,and how can you evaluate speed in positive waysthat support student learning?

If your school or district mandates timed tests, and ifyou disagree with this mandate, how can you workaggressively to change this practice?

How can you use a variety of assessments thatgo beyond timed computation or fact recall inorder to find out how well students are learningmathematics?

What questions or issues does this message raise foryou to discuss with your son or daughter, theteacher, or school leaders?

How can you help your daughter or son understandthat it is useful to be able to perform mathematicalprocedures efficiently, but that this is not the onlymeasure of success in mathematics?

Realizing that support at home can be tremendouslyuseful in fact recall, how can you help your sonor daughter learn, practice, and reinforce basicfacts and mental procedures so that these become automatic, without using timed tests or sending negative messages about mathematics that couldaffect his or her developing confidence as a learnerof mathematics?

FOR FAMILIES

PART II Message 18 Faster Isnt Smarter 3Fr

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How does this message reinforce or challenge policiesand decisions you have made or are considering?

In particular, if your school or district endorses,encourages, or mandates the use of timed computa-tion or fact recall tests, how might you redirect thispolicy?

How can you find out whether teachers support theuse of timed tests? How can you make teachers aware

of the potential negative consequences of using timedtests?

How can you help teachers develop a robust set ofassessment tools and strategies to inform their teach-ing and to find out what mathematics studentsknow?

FOR LEADERS AND POLICY MAKERS

RELATED MESSAGES

Message 16, Hard Arithmetic Isnt DeepMathematics, discusses what rigorous mathemat-ics looks like.

Message 24, Do It in Your Head, makes a casefor including the teaching of mental math as part ofa balanced mathematics program.

Message 35, Putting Testing in Perspective,looks at the types of assessments teachers can usein support of student learning.

FURTHER READING

The Need for Speed in Mathematics (Gilliland2001) looks at why timed skills tests may not behelpful for students.

About Teaching Mathematics: A K8 Resource(Burns 2007a) covers many aspects of school mathematics, including a discussion on misconceptions about the value of timed tests.

Overcoming Math Anxiety (Tobias 1995) looks atthe role of negative school experiences, includingtimed tests, in the development of math anxiety inadults.

The Family Resources page of the NationalCouncil of Teachers of Mathematics(www.nctm.org/resources/families) includes,among other resources, links to documents thatanswer questions about the changing nature ofmathematics today and the use of timed skillstests.

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