math matters: a journalist's guide — published october 2009

Math Matters:A Journalist’s Guide

A H E C H I N G E R I N S T I T U T E P R I M E R F O R J O U R N A L I S T S

Math Matters: A Hechinger Institute Primer for Journalists

Contents:page 1

U.S. Math Education Is Broken – But How to Fix It?

page 5

How Reporters Should Cover the Math Wars

page 6

New Emphasis on Learning Algebra RaisesQuestions

page 8

Story Ideas About Algebra and Math in theWorkplace

page 9

Why Some Claims for High-Level Math Don’tCompute

page 11

Why Very Young Children Can – and Should – Learn Math

page 13

U.S. Math Education Has a “Ham Butt Problem”

page 16

Math Teachers: Shortage Eases, but Issues Remain

page 18

How an Education Reporter Schooled Herself in Math

page 20

How Calculators Are Changing the Math Classroom

page 22

Actress Danica McKellar Extols the Wonders ofMath to Girls

page 23

Experts on Mathematics

page 24

Resources on Math: Reports, Publications andWeb Sites

Credits:

Front cover . . . . . . . . . . . . . . . . . Brendan Smith, a seventh-grader at the Clinton Schoolfor Artists and Writers in New York City; photograph byJustin Snider

Back cover, page 16 . . . . . . . . . photographs courtesy of the Milken Family Foundationand page 21:Page 1 . . . . . . . . . . . . . . . . . . . . photograph by Ryan BrenizerPages 9 and 10 . . . . . . . . . . . . . photographs by Joe Mabel (permission granted under

the terms of the GNU Free Documentation License)Page 11 . . . . . . . . . . . . . . . . . . . . photograph courtesy of Herbert GinsburgPage 13 . . . . . . . . . . . . . . . . . . . . photograph by Renee Comet / courtesy of the National

Cancer InstitutePage 18 . . . . . . . . . . . . . . . . . . . . photograph courtesy of Michael Alison Chandler

Editors . . . . . . . . . . . . . . . . . . . . . Barbara Kantrowitz and Justin SniderCopyeditor . . . . . . . . . . . . . . . . . Melissa Payton

Design . . . . . . . . . . . . . . . . . . . . . Bruce Colthart Creative LLCPrinting . . . . . . . . . . . . . . . . . . . . Liberty Graphics Inc.

This publication was made possible by a grant from the Ewing Marion KauffmanFoundation. Additional support was provided by Texas Instruments.

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U.S. Math Education Is Broken – But How to Fix It?As American students fall further behind counterparts overseas, experts say change must come.

By Richard Lee Colvin

Math Matters: A Hechinger Institute Primer for Journalists 1

It is a hot September weekday a few days after the startof school in Paramus, N.J., and 30 or so students arehunched over rows of desks reviewing arithmetic: mul-tiplication, division and how to use those procedures inevaluating number sentences. Written on the white boardis this problem: “[92 x (6-4) ÷ 8] + [7 x (8-3)].” 1

The key to calculating what this phrase equals is tofigure out which operations to do first. New Jersey’sacademic standards say this should be taught beginningin the third grade. But the struggling students in this BergenCounty Community College classroom have all gradu-ated from highschool. They’rehere becausetheir scores onthe col lege’splacement examshowed thatthey couldn’t dobasic material.And now anequation that amiddle-schoolershould be ableto master hasbecome a majorobstacle to theirchances of get-ting a degree.

The remedial math class is just one of dozens at Bergen,New Jersey’s largest community college. And the strug-gles in Bergen’s classrooms are echoed around the coun-try, where 61 percent of all community college mathstudents are still studying elementary or middle schoolconcepts and skills. These classes are just one manifes-tation of what governors, business leaders, policymakersand mathematicians describe as a national math crisis. Poormath skills, these critics say, harm the nation’s compet-itiveness, weaken its technological prowess, exacerbateinequity, shut people out of jobs and threaten voters’ capac-ity to understand complex issues such as the cost ofhealth care or the size of the national debt.

Two decades of international math comparisons showthat the longer American students are in school, the fur-ther they fall behind their counterparts in other developednations. (See story, pages 13-15.) William Schmidt, a

Michigan State University professor who studies howU.S. students match up against those in other countries,says most American eighth-graders can’t do relativelysimple tasks – such as add fractions – that students in othercountries master by fourth grade. According to theNational Assessment of Educational Progress (NAEP), onlyhalf of U.S. eighth-graders could place three fractions –2⁄7, 1⁄2, 5⁄9 – on a number line in order of magnitude. “Thisis not mental Olympics,” Schmidt says. “It’s not about onecountry doing a little bit better than others. It’s really aboutour kids being able to function.”

Part of theblame shouldfall on succes-sive and oftenwildly contra-dictory waves ofreform over thelast half-century,from an empha-sis on preciseabstract con-cepts (the NewMath of the1960s) to thebasics of arith-metic and alge-bra (1970s and1980s) to a cel-

ebration of math exploration that eschews standard meth-ods for multiplying and dividing and downplays fractionsand long division (starting in 1990). Although math pro-grams based on those last ideas continue to be widely usedtoday – two of the most popular are Everyday Math andTERC: Investigations in Number, Data and Space –they are often unpopular with parents and criticized bymathematicians for failing to build the skills required tosucceed in algebra and beyond.

These wild swings in opinion set the stage for theso-called “math wars,” which continue today in schoolboard meetings and on YouTube. (See story, page 5.) It’sa debate that’s particularly frustrating to experts in math-ematics education because there is a broad consensus thatfast, accurate calculation goes hand in hand with under-standing the conceptual underpinnings of the proce-dures. Students also must be able continued on page 2

A remedial math class at Bronx CommunityCollege in New York City.

to apply what they know to solve problems, use logicalreasoning and see math as a useful tool that can belearned through effort.

The National Mathematics Advisory Panel, whichincluded experts with a diverse range of views on theseissues, concluded that math education in the UnitedStates “is broken and must be fixed. … This is not a con-

clusion about any single element of the system,” thepanel’s report said. “It is about how the many parts donot now work together to achieve a result worthy of thiscountry’s values and ambitions.”2

Francis “Skip” Fennell, a member of the advisory panelwho is former president of the National Council ofTeachers of Mathematics, agrees. “More and more of ourkids are taking algebra than ever in our history,” he says,“and yet we have high school performance that is eitherstagnant or declining, and we have too many kids mov-ing into higher education and having to immediately takeremedial classes. To me, that suggests a system that is morethan a little out of whack.”

STANDARDS

All 50 states now have standards for what students shouldbe able to do in order to be considered proficient.

Although those documents vary widely, experts agree thatthey are too voluminous, scattered and repetitive. TheNational Governors Association and the Council ofChief State Schools Officers released a draft of a com-mon set of improved standards for math and English inSeptember 2009. The standards are meant to be rigor-ous, emphasizing fewer topics and reflecting what highschool graduates need to know in order to be ready forcollege or work. “The idea here is less is more,” Fennellsays. “Let’s ensure we’re teaching what’s important andensure that kids really have it.”

Forty-eight states – as well as Washington, D.C., PuertoRico and the U.S. Virgin Islands – are participating in devel-oping the stan dards and, it is hoped, many will adopt themas their own. But getting diverse interest groups to agreeon what students should be expected to learn is a contentious,divisive process, so it may be hard to reach broad agree-ment. A potential danger is that the cost of getting manystates to sign on would be standards so watered-down thatthey don’t actually lead to any real change. Educators, pol-icymakers, politicians and parents all tend to favor highstandards in theory, but once they are enacted and theirconsequences become evident – higher drop-out rates andmore students repeating grades, for instance – people’s enthusiasm wanes.

CURRICULUM, TEXTBOOKS AND GRADUATION REQUIREMENTS

The purpose of standards is to send signals about whatshould be taught, but the signal sent by many sets of statestandards is not clear. U.S. math textbooks are typically700 to 1,000 pages long. Because they are unable tocover everything, teachers often sample the materialwithout a coherent plan.

The advisory panel report says that elementary andmiddle school curricula should prepare students to take aformal algebra class by eighth grade. (See story, pages 6-7.) Students need to understand whole numbers, fractions,measurement and geometry if they are to succeed in alge-bra. The panel’s survey of algebra teachers found that manyreported their students not only didn’t understand frac-tions or decimals but also didn’t know multiplication tablesor how to divide on paper. The teachers in the surveyblamed overuse of calculators – a finding that would res-onate in Bergen County, where community college reme-dial math teachers have banned calculators. But studentsare so dependent that some still sneak them into class ortry to use the calculators on their cell phones – until theyare caught by their teachers. (See story, pages 20-21.)Many states are raising the number of math courses stu-

Math Matters: A Hechinger Institute Primer for Journalists2

continued from page 1

A STUDENT WHO IS PROFICIENT INMATHEMATICS HAS ACQUIRED….

✔ Conceptual understanding of key mathemati-cal ideas, operations, and relations

✔ Fluency with mathematical procedures andthe ability to use them flexibly, accurately, ef-ficiently, and appropriately

✔ Strategic competence, which means the abil-ity to formulate, represent, and solve mathe-matical problems

✔ Adaptive reasoning, which is the capacity tothink logically and reflectively and to explainand justify one’s thinking

✔ A productive disposition that sees mathemat-ics as sensible, useful, and worthwhile, andthat recognizes that diligence and effort willlead to results.

Source: adapted from Kilpatrick, J., Swafford, J., & Findell, B.(2001). Adding it up: Helping children learn mathematics.Washington, DC: National Academy Press. Page 116.


dents have to take to graduate. The percentage of highschool graduates taking either Algebra II or even moreadvanced math rose from 49 percent to 63 percentbetween 1990 and 2005. But SAT scores in math are flat,as the chart below shows, and enrollment in remediationclasses is on the rise.

TEACHING

One of the most notable findings of the advisory panelwas that researchers have no definitive answers about whatconstitutes good math teaching. The panel challengedclaims about the superiority of “student-centered” teach-ing or “teacher-directed” lessons. There is no high-qual-ity research supporting the exclusive use of either method.

The report also found limited benefit from learningmath using “real world” situations, as is commonly rec-ommended by math teachers today. Research says stu-dents taught that way do fine on test questions that dealwith “real world” situations. But students’ ability to cal-culate accurately, solve word problems or deal with equa-tions is not improved by such lessons.

What is clear, however, is that teachers must havedeep knowledge of the math they’re trying to teach andhow various math concepts and skills fit together. Thepanel called for more math content in teacher prepara-tion programs, more mentoring of early career teachers,and more opportunities for teachers to learn on the job.

PARENTS, CULTURE AND EXPECTATIONS

Perhaps one of the biggest barriers to increasing mathproficiency in the United States is cultural. In mostcountries, math literacy is expected, but in the United States,it is socially acceptable to say “I hate math” or “I was never

good at math.” “Imagine,” says Deborah Loewenberg Ball,dean of the University of Michigan School of Education,“if those same people said similar things about readingor writing: ‘I never could read.’”3

Many Americans also are complacent about math edu-cation. In a 2007 poll of Kansas and Missouri parents,

the nonpartisan polling organization PublicAgenda found that only 25 percent thoughttheir children should be studying more mathand science. About 70 percent said things “arefine as they are now.”4 A 2008 Associated Presspoll found that just over a third of parentsthought their children needed more mathinstruction.

The report of the math advisory panelis one of many that have been issued over theyears by smart educators and researcherscommitted to solving what virtually all agreeis a serious problem. However, for all that isknown about the problems and how to fixthem, math teaching remains stubbornlyfixed in place. Scholars of math education saythat classes today would seem familiar toAmericans who finished school decades ago.

But today’s graduates enter an adult world where the pricethey will pay for math deficiencies is far greater than thatpaid by their parents. Meanwhile, the cost to the nationis steep and growing steeper.

LOOKING BACK, LOOKING FORWARD

The 2008 documentary 2 Million Minutes attempted tostart a national discussion around such issues. The filmlooks closely at the lives and study habits of two high schoolstudents per country – one boy and one girl – in the UnitedStates, India and China. The film’s conclusion? Indianstudents, on average, spend about 40 percent more timein high school than American students. In China, whereboth the school day and year are considerably longer thanin the U.S., students spend about 90 percent more timein class than American kids. And these disparities onlywiden when one counts the number of hours spent study-ing outside of class. According to the film, 60 percent ofU.S. college-bound seniors do no more than one hourof homework per night and none on the weekends. Nosuch statistic is given for Chinese or Indian students, butthe clear implication is that their lives consist of little morethan studying. And they don’t eschew challenging mathand science classes like the average American student does.

The two Indian students in the documentary, RohitSridharan and Apoorva Uppala, envision futures in

480485490495500505510515520525

20082006

20042002

20001998

19961994

19921990

19881986

19841982

19801978

19761974

1972

509

492

520

515

Mean SAT Math Scores, 1972-2008*

*Source: the College Board. Accessible online at http://tinyurl.com/maz6b8.

continued on page 4

engineering because it’s a “safe” career choice – one inwhich there is no shortage of demand, in part becauseso few students in other English-speaking countries pur-sue engineering and related fields. As the charts belowreveal, only one of out every 100 U.S. college graduatesin 2005-06 majored in mathematics or statistics. The U.S.now produces only about half as many math and statis-tics majors as it did in the early 1970s, a fact that is allthe more striking when one recalls that many more peo-ple attend and graduate from college now than fourdecades ago.

Vivek Wadhwa, an adjunct professor at DukeUniversity who researches globalization’s impact on theengineering profession, sounds the alarm in 2 MillionMinutes: “Unless the U.S. wakes up and realizes the newthreat, realizes the fact that we’re competing with any-one anywhere in the world, we’re going to lose, we’re notgoing to be the leaders in the next 30 years or so.”

That so many U.S. college students steer clear of mathis perplexing, especially given the healthy job market for

those with strong math skills. A 2009 ranking of 200 different jobs by Careercast.com, for instance, found thatAmerica’s top three jobs were: 1) mathematician; 2) actu-ary; and 3) statistician. The five criteria used to evaluatejobs were: stress, work environment, physical demands,income and employment outlook.

No doubt part of the reason so few U.S. studentsmajor in math or statistics is that they leave high schoolwith neither the desire nor the foundation necessary todo higher-level math. In order for that to change, thereneed to be radical shifts in U.S. thinking about math, itsimportance in everyday life and to our economy, and howthe subject is taught in elementary, middle and highschools across the country. Only then might a simple prob-lem involving the order of operations be readily solvedby students everywhere.1 The correct answer is 58.2 United States Department of Education. (2008). “Foundations for Success: The

Final Report of the National Mathematics Advisory Panel.” Accessible online athttp://tinyurl.com/yopzor.

3 D.L. Ball. (2001). “Developing a mathematically proficient public: What are theproblems, what do we know about them, and what would it take to solve them?”Paper prepared for the Aspen Institute congressional conference on “PromotingExcellence in the New Economy: the Challenges to National Policy,” St.Petersburg, Florida, February 16–19, 2001.

4 Kadlec, A. & Friedman, W. (2007). “Important, But Not for Me: Parents andStudents in Kansas and Missouri Talk About Math, Science and TechnologyEducation.” A Report from Public Agenda, with support from the Ewing MarionKauffman Foundation. Accessible online at http://tinyurl.com/kr9egt.


0.5

1

1.5

2

2.5

3

2005-06

2000-01

1995-96

1990-91

1985-86

1980-81

1975-76

1970-71

2.95%

1.73%

1.18%1.63%

1.31%1.09%

0.897% 0.994%

Undergraduate Degrees in Mathematics and Statistics as % of Total Awarded

2005-06

2000-01

1995-96

1990-91

1985-86

1980-81

1975-76

1970-71

5000

10,000

15,000

20,000

25,000

30,000 24,8

01

15,9

84

11,0

78 16,1

22

14,3

93

12,7

13

11,1

71 14,7

70

Number of Undergraduate Mathematics and Statistics Majors Per Year, 1970-2006

THE BEST

1. Mathematician

2. Actuary

3. Statistician

4. Biologist

5. Software Engineer

6. Computer SystemsAnalyst

7. Historian

8. Sociologist

9. Industrial Designer

10. Accountant

11. Economist

12. Philosopher

13. Physicist

14. Parole Officer

15. Meteorologist

THE WORST

200. Lumberjack

199. Dairy Farmer

198. Taxi Driver

197. Seaman

196. EMT

195. Roofer

194. Garbage Collector

193. Welder

192. Roustabout

191. Ironworker

190. Construction Worker

189. Mail Carrier

188. Sheet Metal Worker

187. Auto Mechanic

186. Butcher

Source: from a 2009 ranking of 200 different jobs by Careercast.com, accessibleonline at http://www.careercast.com/jobs/content/JobsRated_Top200Jobs.

THE TOP 15 BEST AND WORST JOBS IN AMERICA



� Put the debate in context. Let your readersknow that the same arguments have playedout in hundreds and hundreds of otherplaces in the past two decades.

How Reporters Should Cover the Math Wars

By Richard Lee Colvin

The so-called “math wars” have raged for decades. Conflicts arise over competing views of teaching methods, educational philosophy, cognitive science, equity, race, standards and even post-modernism. Typically, math professors are at odds with education professors and math teachers. And parents worried about their kids learning the basics do battle with teachers and administrators who tell them to relax. The debate makes head-lines when a school or district chooses new materials that downplay memorizing multiplication tables andteaching standard long division and fractions while relying on calculators in the early grades and substitutingcutting, sorting and pasting paper for practicing number facts.

I wrote my first story about the math wars in California in 1994. I’ve written and read many stories on thetopic since then. Here are some suggestions about what to do and what to avoid in your coverage.

� Don’t pit memorization and computa-tional efficiency against conceptual un-derstanding and using math to solvereal problems. It is not a zero-sumgame. All of these skills are important.

� No matter what the method or curriculum,look at whether students in the classroomsyou visit are engaged in the lesson. JeremyKilpatrick of the University of Georgia, aleading math education expert, says: “Arestudents following what’s going on? If kidsare going to be learning math, they need tobe working on math in the class, and if theyare not, then they are just pushing pencils,and that is really unfortunate.”

� Acknowledge that different teaching meth-ods are appropriate for learning differentskills and concepts. In some, the teachertalks more. In others, kids work in groupsand talk with each other. Research has notanswered definitively which methods workbest and when. “I would be interested inwhether the content is being developed inways that make sense,” Kilpatrick says.“What is critical is whether skills and con-cepts are being developed with some care.”

� Reach out to national experts, such as some of thoselisted in this publication. They can put the local eventsinto a larger context and help you sort out the issues.And they will be seen as neutral because they aren’tcaught up in local controversies.

� Avoid using “traditional” and “reform” asshorthand labels for the two sides. The im-plication is that the traditionalists are tryingto hold back progress. In fact, there’s wide-spread agreement that math education mustimprove.

� Whenever someone starts a sentence with “Researchsays …” ask what specific research is being cited. Lots ofstudies are sponsored by textbook companies. Keep inmind that it’s hard to prove that a program, in and of it-self, caused children to learn. Many factors are at work.

� Talk to teachers (beyond those who are thestrongest advocates of a particular method).Do they feel comfortable teaching in a newway? Do they see success? How much train-ing have they had?


New Emphasis on Learning Algebra Raises QuestionsJournalists should check if teachers, students are getting help to meet tougher standards.

By Sean CavanaghFew academic topics are as highly regarded by policymakers– and as feared by students and the public at large – asalgebra. Across the country, state and local school officialsare asking students to take more courses in that subject,and to take them earlier in school. They say they are con-vinced that algebra is crucial preparation for more advancedmath, and a key to success in college and the workplace.

Two states, Minnesota and California, even requirestudents to take introductory algebra, or Algebra I, in eighthgrade, rather than waiting until high school – thoughCalifornia’s policy has been blocked in court. Nationwide,the percentage of eighth-graders now enrolled in alge-bra (31 percent) is nearly double what it was in 1990, accord-ing to a 2008 study by the Brookings Institution.1

Algebra standards are also being ratcheted up at thehigh school level. Twenty states, plus the District ofColumbia, require students to take Algebra II or its equiv-alent to graduate with a regular diploma, according toAchieve Inc., a Washington-based policy organization. Fouryears ago, only two states had that requirement. In addi-tion, 12 states are participating in a national test of AlgebraII skills, an effort that is being led by Achieve.

Despite these efforts, algebra remains a major stum-bling block for many middle- and high-school students.After cruising through more basic math, many studentsarrive woefully unprepared for their first full algebracourse and wind up having to repeat the class or scrap-ing by with little understanding of the subject.

The public perception of algebra probably doesn’t help.Many adults freely confess to having loathed algebra in school.A Web search reveals countless sites devoted to helpingstudents fight their way through the subject – or simplyallowing them to commiserate about how difficult it is.

As schools increase their expectations in algebra,education reporters have a number of questions toconsider. Perhaps the most obvious one: Why does thestudy of algebra – with its potentially bedeviling lan-guage of x and y, equations and polynomials – matter inschool, or in life? And, if it does matter, how can reportersdetermine whether schools are teaching the subject welland helping students who can’t keep up? What might schoolsbe doing better?

In one sense, algebra is important for very practicalreasons. Research has shown that students who take algebra,and take it relatively early, are more likely to move on toadvanced math in high school and succeed in college. Algebra

also is found in varying amounts on state tests and collegeentrance exams. There’s simply no avoiding it.

Even so, convincing people of the value of algebra is noteasy. Henry Kepner, the president of the National Councilof Teachers of Mathematics (NCTM), in Reston, Va., recallsencountering a business executive several years ago whomhe was going to ask to meet with K–12 teachers to discussmath and its uses in the workplace. When the executivesuggested that he rarely used algebra on the job, Kepnerresponded by pointing to the man’s computer screen, whichincluded spread sheets with axis and trend lines estimatingprofits and costs. “It took me a while to convince him,‘That’s all algebra,’ ” Kepner recalls.

Algebra is sometimes described as the study of relation-ships between numbers, in which numbers are representedas symbols. Some math experts call it the study of gen-eralized arithmetic. Arithmetic – addition, multiplicationand so on – allows you to solve a single problem.Algebra allows you to create a formula or process for solv-ing a host of problems. “If you are doing something once,you probably don’t need algebra,” wrote Zalman Usiskin,a textbook author and the director of the University ofChicago School Mathematics Project, in a 1995 essay. “Butif you are doing a process again and again, algebra providesa very simple language for doing what you are doing.”2

Algebra allows someone to consider multiple quan-tities and variables at once. To use an all-too-relevantexample from today’s headlines, an algebraic equationcan help someone calculate the monthly payments on ahome, factoring in the down payment, interest rate, lengthof the loan and loan adjustments over time.

In recent years, many business leaders have supportedtougher requirements in algebra, arguing that improvingstudent math skills is necessary to produce a more qual-ified workforce. Industry groups backed a controversial 2008decision by the California state board of education to phasein a requirement that all students take the state’s algebratest as eighth-graders. That policy, which the board describedas a response to a No Child Left Behind testing require-ment, was widely regarded as mandating that students takealgebra in eighth grade. The Association of CaliforniaSchool Administrators and others sued to stop the policy’simplementation, arguing that the policy was approved with-out public input and exceeded the state board’s author-ity. A judge blocked the policy from being implemented,and the state board is appealing that decision.


As states and districts raise expectations in algebra, howcan reporters judge the impact of such policies on schoolsand students? One obvious, if imperfect, method is to lookat test results. A few states, such as Florida, allow reportersand the public to compare students’ performance in algebraagainst other content areas of math, such as geometry orstatistics. While many factors can affect student test scores,this is at least a starting point for journalists consideringthe impact of algebra policies, says Elaine M. Allensworth,co-director for statistical analysis at the Chicago Consortiumon School Research, who led a recent study of algebrapolicies in that city’s schools. “At the minimum, youwould expect test scores to improve,” she says.

Reporters should also look at whether more studentsare being forced to repeat classes after algebra policies takeeffect. A recent study by Allensworth, for instance, foundthat a Chicago mandate requiring students to take AlgebraI by ninth grade had not led to test-score gains for citystudents in math. Nor had it led to significant increasesin the percentages of students taking more advancedmath later in school.

The most relevant question for journalists writing aboutincreased algebra requirements, or covering districtswhere large numbers of students are struggling, Allensworthargues, is: What are policymakers doing to improve stu-dent performance? Are they offering algebra teachersmore training? Are they providing students extendedtime in algebra? What’s the effect of these policies? “Justputting a standard in place does nothing,” Allensworth says.“What matters are the supports for the policy.”

Kepner agrees, arguing that reporters should examinewhether districts are providing time for teachers to planalgebra lessons together and discuss common problems.Encouraging high school and middle school teachers –who often complain about students arriving in their alge-bra classes with poor skills – to work with teachers fromearlier grades would be especially beneficial, he says.

At least one state, Arkansas, has sought to improvealgebra instruction by phasing in a requirement that mid-dle school teachers obtain an algebra-specific credentialif they want to teach that subject in middle school. Teachertraining matters, Allensworth says: As schools seek to enrollyounger students in algebra, teachers are likely to beasked to work with students from a much broader rangeof ability levels – not an easy task.

One recent strategy for increasing students’ chancesfor success in algebra is to revamp math instruction inearly grades. In 2006, the NCTM took a major step inthis area through its release of “Curriculum Focal Points,”3

a document that sought to provide clearer guidance to

preschool through eighth-grade teachers on the crucialmath all students should know.

Then last year, the National Mathematics AdvisoryPanel, a White House-commissioned group, released itsown recommendations for how to improve students’preparation for algebra. The panel’s report4 emphasizedgiving students in kindergarten through eighth grade amuch stronger grounding in whole numbers, fractions,geometry and measurement to provide them with aspringboard to algebra.

Reporters writing about eighth- or ninth-graders’ strug-gles in algebra need to look closely at how math is beingtaught in elementary schools, Kepner says, because schoolscan and should be attempting to introduce students to alge-braic thinking in elementary school. The early exposure,Kepner argues, prepares students for algebra, and makesthe topic seem relevant.

When using numbers in a relatively simple mathproblem, a student starts to ask, “What if the numberswere different?” Kepner says. “It helps students under-stand, ‘What does algebra do for me?’ ”

Some states are realizing that elementary teachers them-selves need stronger math skills if they are to teach thesubject effectively. Massachusetts, for example, nowrequires new elementary teachers to pass a separate mathproficiency exam as part of the certification process.Previously, new teachers could gain certification withoutanswering any math questions correctly because math waspart of a general exam and not scored separately. Would-be skeptics of the new policy will have a tough time argu-ing that it is unnecessary: Only 27 percent of aspiringelementary teachers who took the math proficiency examat its debut in March actually passed.

Reporters covering middle- and high-school mathinstruction should look at how district and state policiesshape both teacher training and the curriculum. Often whatis decided at the district and state level for elementary gradescan have profound effects on what happens in middle- andhigh-school classrooms.

Sean Cavanagh is a staff writer for Education Week. His beatsinclude the curriculum areas of math and science, adult edu-cation, vocational and school-to-work issues, and dropouts.He also covers the states of Alaska and Illinois.

1 “The Misplaced Math Student: Lost in Eighth-Grade Algebra.” http://www.brookings.edu/~/media/Files/rc/reports/2008/0922_education_love-less/0922_education_loveless.pdf

2 Zalman Usiskin, “Why Is Algebra Important to Learn?” American Educator,Spring 1995.

3 http://www.nctm.org/standards/content.aspx?id=270

4 http://www.ed.gov/about/bdscomm/list/mathpanel/report/final-report.pdf


� Is there a connection between a particular level ofmath achievement and pay levels that cuts acrossmany industries? Do you really need Algebra II toearn a middle-class salary?

� Journalists, admittedly not often math whizzes in theirown school careers, certainly can appreciate the real-world relevance of statistics, something they con-front almost daily in their own jobs. Yet, few schooldistricts offer courses in the basics of this importantsubject. Why is this the case? And why don’t moredistricts offer other clearly useful math-relatedcourses, such as how to manage personal finances?

� How does job-related math education in the UnitedStates compare to other countries? What do studentsin Germany, India or China learn and at what ages?

� How do companies compensate for the lack of mathskills in their employees? Is on-the-job remedialeducation effective?

� Does the rapidly changing technological landscape– with more and more tools available for doingquick and easy calculations – mean most workersneed fewer math skills?

STORY IDEAS

� What percentage of students is flunking or beingforced to retake algebra, compared to other mathcourses? If a state or district increases its require-ments, do more students drop out or repeatgrades?

� Members of the public are often at a loss to explainwhy studying algebra is important. Talk to employ-ers, mathematicians and college faculty, pressingthem to explain, in clear terms, why studentsshould care about algebra – other than that thesubject helps students on standardized tests.

� Many school districts are experimenting withcommercial “algebra readiness” programs aimed athelping students who fail algebra or have beenidentified as likely to struggle in that subject thefollowing academic year. What is the percentage ofstudents taking these “readiness” courses? Arethese students succeeding when they reachalgebra?

QUESTIONS TO ASK

� If a state or school district is raising its algebra re-quirements, what are administrators doing to makesure the policy is successful? Are they creating newprofessional development for teachers? Are theyadjusting the math curriculum at earlier grades?

� As algebra requirements increase, what’s the im-pact on student test scores on local and statetests? Are overall test scores increasing, and (if thedata are available) are students’ scores on algebra-specific questions improving?

� Who in a district or state is calling for increasedalgebra requirements, and why? If business leadersare asking for higher academic standards, how willtheir companies benefit from students’ improvedalgebra skills?

� How are parents and community members reactingto increased algebra requirements? Do they sup-port higher standards, even if it means that chil-dren who struggle with math will face even greaterchallenges?

Story Ideas and Questions to Ask About Algebra

Story Ideas about Math in the Workplace

By Sean Cavanagh

By John Mooney


Why Some Claims for High-Level Math Don’t ComputeCritics question whether all workers need to know Algebra II, as proponents contend.

By John MooneyDo people really need to know the high school staples ofalgebra, geometry and trigonometry after graduation?Policymakers and educators often argue that math edu-

cation is critical to the nation’s economic survival, butreporters who look closely at this widely accepted claimwill find a much more nuanced picture.

This push for more advanced math skills grows outof a decades-long effort by groups of business leaders, politi-cians and educators to counteract competition from coun-tries like China and India, which have made great stridesin upgrading the technical skills of their labor forceswhile keeping wages much lower than in the UnitedStates. Other worrying trends include the poor showingof U.S. students on international math and science com-parisons and alarm about a reported shortage of Americanstrained for high-tech jobs, especially engineering. At thesame time, many companies say that even entry-levelmanufacturing jobs now require a greater degree of mathcompetency. But is there merit to such claims?

One of the most prominent groups in this movementis Achieve, Inc., a nonprofit education reform organiza-tion that works with states to raise academic standards andgraduation requirements. Achieve has called for all highschool students to be proficient in at least Algebra II. Thegroup’s American Diploma Project, a set of graduation stan-dards that includes a requirement for Algebra II, hasbeen adopted by more than 30 states. Achieve pushes its

message by pointing out that precalculus and trigonom-etry are needed for many high-paying jobs in business,finance and health science. Even construction work clearly

requires geometry. “You see it inthe basic 3:4:5 triangle,” says KateBlosveren, a senior policy analystfor Achieve. “In math class, that’s thePythagorean theorem. In construc-tion, it’s the 3:4:5 triangle.”

Companies that need morehighly skilled workers have also beenat the forefront of the movement toimprove math education. One exam-ple is Verizon, with 220,000 employ-ees around the world who needstrong math skills no matter whattheir job, the company claims.Network engineers are at the heartof the business and need to under-stand the language of IP addressesand subnets, binary codes and octets.“Without networks, we’re not much

more than a marketing company,” says Alberto Canal, aspokesman for the corporation’s human resources division.

But its workers at lower levels also need to be adeptat calculation, Canal says. That’s true even in jobs where

the computation may not be apparent to the consumer.For example, the 40,000 customer service representa-tives must be able to compute and compare calling plansquickly. The computer will do the math, but the repre-sentatives must know which questions to ask. “Customerservice representatives need to continued on page 10

A Sample Question for Electrical ContractorsHere is a sample question from the apprentice test for

electrical contractors, who must take a year of algebra

for certification.

Consider the following formula: y=3(x+5)(x-2).

Which of the following formulas is equivalent?

a. y=3x2+9x-30 b. y=x2+3x-10

c. y=3x2+3x-10 d. y=3x2+3x-30

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be able to work out rate arrangements live, right then andthere,” Canal says. “It’s in the context of problem-solv-ing, which package works best for a customer. That’s avery real example of math skills.”

ACT, the organization that administers collegeentrance exams, also bolsters the argument for moreadvanced math in a series of case studies of companies likeSubaru, Dow Chemical and the Energizer battery com-pany. Applied mathematics is one of five skills consideredmost critical to Energizer’s hiring, right down to the bot-tom rung of employees. “Production machine operators– entry-level positions – must count incoming materials,determine the number of finished products, and count rawmaterials needed to run orders,” an ACT report says. “Thesetasks require mathematical reasoning, critical thinking, andproblem-solving techniques applied to work-related problems.”

Some of these assertions about the impor-tance of math are clearly true; no one disputesthat network engineers, for example, needsophisticated skills to do their jobs properly.But when reporters hear that Algebra II is nec-essary for what is basically counting – as inthe case of machine operators – it’s time topush back.

In fact, not everyone agrees that all grad-uates – regardless of career goals – need tohave specific math skills. Anthony Carnevale,director of the Georgetown University Centeron Education and the Workforce, has longmaintained that Algebra II is mostly usefulas a kind of marker for overall ability or edu-cational achievement. In other words, anemployee who has mastered Algebra II couldbe expected to master complex tasks on the job, even ifthey are not math-related. Carnevale has analyzed fed-eral labor data from interviews of workers in 1,000 occu-pations and found problem-solving and critical thinkingmore directly related to higher earnings. “It seems thatmath ability, that is Algebra II and beyond, is being usedas an initial screen, but most occupations really don’t requirea sound knowledge of trig functions or the quadraticequation,” he says.

Others say the gateway remains basic algebra (a jobrequirement in many trades), with Algebra II an impor-tant stepping stone to calculus and higher math skills butnot an end in itself. Joseph Rosenstein, a math professorat Rutgers University who has been critical of the Achievestandards, says that if a student isn’t going on to calcu-lus, such concepts as complex numbers, rational exponents

and cube roots have little value. “If you think about it, aclass in statistics would be more important than AlgebraII, in reading charts and determining probability,” he says.

Even in industries that are highly dependent on tech-nology, math is just one of a number of important skills.Peapod, Inc., the online grocery giant, uses a sophisticatednetwork of software systems and inventory controls.Behind its creation and management is an intricate webof equations and flow charts, requiring the expertise ofengineers, programmers and finance specialists. ButThomas Parkinson, a co-founder and now chief technologyofficer, says some of his best programmers are also oftenartists and musicians able to see the multiple dimensionsof a problem. “Frankly, spatial ability is more importantthan math,” says Parkinson.

And in Peapod’s on-the-ground operations, advancedconcepts are hardly necessary to determine how long itwill take to make a delivery or how to best position pack-ages in the delivery truck. The inventory staff who are thehigh-tech equivalent of stock boys and baggers just haveto follow the coding on the computers they wear on theirwrists. And the GPS in their trucks can provide the mostdirect routes. “To be honest, a lot of the math is done forthem,” says Nancy Kazarian, human resources directorat the Chicago distribution center. “It’s pretty mistake-proof. It tells them exactly what they need to do.”

John Mooney is a longtime education writer in New Jersey,previously on staff with the Bergen Record and Newark Star-Ledger. In addition to free-lancing for the New York Times andother newspapers, he is launching a state news and informa-tion service focusing on education.


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Can young children learn mathe-matics? What is the best way to teachthem? Herbert P. Ginsburg, a devel-opmental psychologist at TeachersCollege, Columbia University, hasbeen studying those questions formore than 25 years. The followingquestions and answers were mostly

adapted from his chapter on early mathematics educa-tion in Handbook of Child Development and Early Education(Guilford Press, 2009).

Why should journalists care about early mathematicseducation?

As early as preschool and first grade, children in EastAsian countries like Japan, South Korea and Singapore

do significantly better than American children. Althoughmiddle- and higher-income American children do very wellon average in international comparisons, low-incomechildren do not. That brings down the rating for the coun-try as a whole. Early math education could help those chil-dren succeed later on. Research also shows that early math– when done appropriately – can help all children do bet-ter once they get to school, and math can stimulate youngchildren’s naturally active minds so they enjoy schoolmore.

Why are adults often reluctant to consider teach-ing mathematics to young children?

In the United States, there is widespread fear andloathing of mathematics, which is often based on

people’s memories of their own unhappy school experi-ences. Many early childhood educators also believe thatmath is bad for young children because they are not readyfor it and will become anxious if they cannot succeed.Developmentally inappropriate math classes would indeedhave that effect, but well-designed programs would not.

Can little children really learn mathematics?

The overwhelming body of research conducted overthe past 25 years suggests that contrary to popular

opinion, young children can learn both concrete and

abstract mathematics. And what’s more, they often enjoyit. From birth to age 5, young children develop informalmathematical ideas about numbers, shapes, space, patterns,and other mathematical topics. For example, they can seethat one plate has five cookies and another has three, andthey understand that five is more than three. They caneasily distinguish between a circle and a square, althoughthey may not know the words for these shapes. They canlocate objects in space.

How powerful is the math that young children learn?

Modern research has shown that children’s mindsare complex. From an early age, they seem to

understand some abstractions involving numbers (forexample, that the order of counting a group of objects doesnot matter, so long as you count each object only once)and are even concerned to know what is the “largestnumber,” clearly a very abstract mathematical issue. Theydo not simply remember the isolated “addition facts” butinstead can spontaneously develop, without adult help, var-ious general methods or strategies for figuring them out.At the same time, children display certain kinds of math-ematical ineptitude. For example, they have difficultyunderstanding that a set of seven objects spread out in along line is the same number as a set of seven objectsarranged in a shorter line. Children’s mathematics is a kindof hidden world that adults have to learn to see.

What is the best way to teach mathematics toyoung children?

The leading professional organizations in the fieldrecommend that early mathematics instruction

cover the “big ideas” of mathematics in such areas as num-ber and operations, geometry (shape and space), meas-urement, and “algebra” (particularly patterns). Theresearch-based expectation is that early math educationshould involve topics more challenging than those usu-ally taught. This is not the kind of mathematics early child-hood teachers usually teach. Nor is it the trivial mathematicsof the drill sheets. It is a more genuine mathematics thaneither of these, and children can benefit greatly from learn-ing about it under teachers’ guidance.

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Why Very Young Children Can – and Should – Learn MathEarly lessons help preschoolers succeed later on and stimulate rapidly developing minds.


continued on page 12

Does this imply a “push-down” curriculum?

Not at all. That would be a disaster – just as it oftenis for the children in the higher grades! The pro-

posal is not to give young children textbooks, worksheets,and all the deadly drills that too often characterize (unsuc-cessful) elementary mathematics education. The goal israther to engage children in “big ideas.”

What else does early mathematics involve?

Mathematics involves not only the content – the bigideas – but also ways of thinking. Children need to

mathematize – to conceive of problems in explicitly math-ematical terms. One of the functions of mathematicseducation is to help children advance beyond their infor-mal, intuitive mathematics.

How can we help children to learn big ideas andto think mathematically?

First, the preschool classroom or child-care centershould contain a rich variety of objects and mate-

rials – such as blocks, water tables and puzzles – that canset the stage for mathematics learning. Modern elec-tronic toys and computers can be useful, too. The sec-ond important component is play. Children have a goodtime when they play, and it stimulates cognitive development.We know that children do indeed learn a good deal of every-day mathematics on their own in the course of free play.Third, projects can help teachers capitalize on children’snatural curiosity and can help them learn that making senseof real-life problems can be stimulating and enjoyable. Thesethree components are most effective if they are part of awell-planned curriculum that covers big concepts – likenumbers, shapes and patterns – in the context of specificand exciting activities. To succeed, a curriculum needs tobe of high quality and needs to be implemented well.

What does good implementation of a curriculuminvolve?

It involves intentional teaching of a planned sequenceof activities. The early childhood educator needs to

teach the material in an intentional, organized manner,while at the same time being sensitive to individual chil-dren’s interests. The teacher needs to provide thought-ful but firm guidance. Good teaching is in many wayslike good parenting. And like good parenting it does notalways produce immediate (or long-term) success!

How can you possibly use a single curriculum witha diverse group of children?

Dealing with varying abilities is always a problem,no matter what the age of the students or the sub-

ject being taught. Early childhood mathematics educationis no different. It cannot meet the needs of all children,and it often must fail. Teachers must do their best and whatis best depends on the individual teachers and on the indi-vidual students they are trying to teach.

What should journalists be looking for in the class-room?

I’m not sure that a brief visit to a classroom will dothem much good. But they can try to determine if

kids look bored, are restricted to chairs, or seem to be harshlydisciplined. On the positive side, they can observe howthe teacher talks to the kids. Does she try to explain, usereasonably complex language, and try to engage the kidsin some kind of dialogue rather than just lecture to themor tell them what to do?

What stories should we be writing about earlymathematics?

The most relevant story, I think, is about whethera district or some other education authority is try-

ing to promote education – literacy, math, science – foryoung children. If so, what kind of approach are they tak-ing? Do they favor drill? Do they rely exclusively onplay? Do they try to promote some intentional teaching?Are they trying to use some of the new math and sciencecurricula? And are they trying to institute long-term,intensive professional development for their teachers?

What mistakes have you seen in coverage?

I haven’t seen many stories on the topic, at least asfar as preschool is concerned. But here are some things

to avoid: Don’t assume that any one curriculum or methodis a magic bullet. Everything can be done badly. Don’t assumethat early math education is simple or easy. It takes a lotof skill to do it well. Don’t forget that at the heart of edu-cation at all levels is the teacher, and that most preschoolteachers have not been trained well in doing math edu-cation. But they should be, and that requires commit-ment and resources from the appropriate educationalauthority.

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U.S. Math Education Has a ‘Ham Butt Problem’International comparisons reveal that some of our practices are holding students back.

By Justin Snider


Ever heard of the “ham butt problem”? Here’show Erin McKean, founder and CEO ofthe online dictionary Wordnik, recentlydescribed it: “Woman’s making a hamfor a big family dinner. She goes to cutthe butt off the ham and throw it away,and she looks at this piece of ham andshe’s like, ‘This is a perfectly good pieceof ham. Why am I throwing this away?’She thought, ‘Well, my mom always did this.’So she calls up Mom, and she says, ‘Mom, why’d youcut the butt off the ham when you’re making a ham?’ Shesays, ‘I don’t know, my mom always did it!’ So they callGrandma, and Grandma says, ‘My pan was too small!’” 1

The “problem” at the heart of McKean’s anecdote isthis: People too often fall into the trap of thinking thatthe way things are is the way they’ve always been – which,it follows, is the way they must always be. We don’t stopto ask ourselves why.Nowhere is this truerthan in education. Highschool English teach-ers make their studentsread certain novels forno other reason thanthat they read them inschool, as did their par-ents and grandparents.Think of Catcher in theRye, Old Man and theSea, Siddhartha or TheScarlet Letter. Master -pieces? Not really.Worthy of readingbecause previous gen-erations have readthem? Maybe.

Similar thinking prevails in American math classes.The familiar high school sequence – Algebra I, geometry,Algebra II, trigonometry – is so widespread and deeplyingrained that it’s easy to forget that it’s not the only wayfor students to master mathematics. And, in fact, it mightnot even be a particularly efficient or effective way to teachmath. If we look at countries that outperform the UnitedStates on international math assessments like the Trendsin International Mathematics and Science Study (TIMSS),

some of what we do starts to look very odd. Mathcurricula in other parts of the world are often

structured quite differently than those inthe United States.

But it’s not just curricula: Mathclasses elsewhere generally have a verydifferent look and feel. For instance,

math teachers in America devote muchmore class time to reviewing concepts than

to introducing or practicing new content. Incontrast, teachers in countries that outperform the UnitedStates tend to spend significantly less time on review (seeFigure 1). Reporters who cover mathematics in U.S.classrooms should be aware of such differences so theycan better understand and question what they observe.

William Schmidt, an expert on math education atMichigan State University, says American math curriculasuffer from the mile-wide, inch-deep phenomenon: far too

many topics, all of which are cov-ered superficially. At formerSecretary of Education RodPaige’s Mathematics Summit inFebruary 2003, Schmidt spoke ofthe arbitrary way in which text-books and state standards pres-ent math topics. “Teachers areexpected to introduce relativelyadvanced mathematics in theearliest grades,” he says, “beforestudents have had an opportunityto master basic concepts andcomputational skills.” 2

At the same time, most U.S.math curricula continue to focuson basic computational skillsthrough eighth grade. The result?Many American students master

neither basic computation nor advanced mathematical con-cepts. By the end of eighth grade, Schmidt estimates, U.S.students have fallen two or more years behind their peersin high-achieving nations.

In Japan, a typical lesson might consist of three indi-vidually presented problems, which take about 15 min-utes each. Discussions are “organized so as to makeconnections and relationships explicit,” according to an

continued on page 14

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FIGURE 1

Average percentage of eighth-grade mathematics lesson time devoted to various purposes, by country: 1999


analysis of the TIMSS 1999 Video Study that appearedin ON-Math, a journal published by the National Councilof Teachers of Mathematics.3 In Hong Kong, three-quar-ters of class time is on work in which the whole class par-ticipates and the teacher does almost all of the talking.4

The picture that emerges from international com-parisons of math instruction is that there is no one bestway to teach math. In many Asian countries, lectures aremore common than in the United States. In Switzerland,working in pairs or groups is the norm, whereas in theNetherlands, students often work alone and only seek helpfrom peers or the teacher when they’re stuck.5

So if the key to high math achievement isn’t a par-ticular pedagogical approach, then what is the answer?Schmidt and fellow researchers say it comes down tothree essential things: the coherence and depth of the cur-riculum, the quality of assessments and the content knowl-edge of teachers. A close look at international data suggeststhey’re right. Reporters should zero in on these threeingredients when covering math instruction.

CURRICULUM

The vast majority of American eighth-graders have littleor no familiarity with geometry, which shouldn’t be a sur-prise: They are busy with pre-algebra. Most do notencounter geometry until 10th grade. Contrast this withmath instruction in many Asian and Eastern European coun-tries: eighth-graders in these regions, according to Schmidt,have moved on to the study of algebra, geometry and basictrigonometry. Consequently, the problem6 below in Figure2 – taken from the 2007 TIMSS – isn’t hard for them:

At least 75 percent of eighth-graders in Taiwan,South Korea, Singapore, Japan, Hong Kong, Slovenia,Lithuania and Russia answered this question correctly in2007. The worldwide average among participating coun-tries was 57 percent. In the United States, however, only45 percent of eighth-graders got this question right.Why? The concept of an “isosceles triangle” – one withtwo sides of equal length – doesn’t appear on mostAmerican students’ radar until 10th grade.

ASSESSMENTS

The quality of assessments – whether at the local, stateor national level – matters because teachers learn over timewhat is commonly tested and, in response, often recali-brate what and how they teach. This is the “what gets taughtis what gets tested” trend that Linda Perlstein writesabout in Tested: One American School Struggles to Make theGrade (Henry Holt, 2007). American math assessmentsare heavy on multiple-choice questions, no doubt in partbecause they are easy and inexpensive to grade.

But multiple-choice questions often mask more thanthey reveal; two students might correctly bubble-in answer“C” on a given question, and yet there’s no way of dis-tinguishing the student who guessed and got lucky fromthe student who worked out the problem and knows with100 percent confidence that she’s right. Multiple-choicetests are particularly poor at telling a teacher where a stu-dent’s thinking went wrong. Did the error result from asloppy miscalculation or a fundamental misunderstand-ing? There’s no way to know.

Reporters should not shy away from asking teachers,schools, districts and states why they so often rely on mul-tiple-choice assessments. Teachers should be able to artic-ulate why they have opted to use a given assessmentmethod (multiple choice, matching, fill-in-the-blank,open-ended or “constructed” response, essay and soforth). Justifying the use of a multiple-choice test by say-ing “It’s just the way we’ve always done it” is insufficient– another instance of the “ham butt problem.”

How do high-performing countries assess their students’ math skills? A 2009 study by the AmericanInstitutes for Research that analyzed math assessments givento third-graders in Massachusetts and Hong Kong founda “greater depth of mathematical understanding requiredto solve many items on the Hong Kong assessment, compared with Massachusetts items.”7 Massachusetts waschosen because it is the highest-scoring state in the nationon the National Assessment of Educational Progress(NAEP) and it ranked fourth internationally on the 2007TIMSS. Hong Kong topped the list.


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Two points M and N are shown in the figure above. John is looking for a point P such that MNP is an isosceles triangle. Which of these points could be point P?

a. (3,5)b. (3,2)c. (1,5)d. (5,1)

1 2 3 4 5 6

FIGURE 2


The study’s authors found that 71 percent of thequestions on the Massachusetts exam were multiple choice,while in Hong Kong only 14 percent were (see Table 1).An even greater discrepancy was found in “computa-tional difficulty”: 97 percent of the Massachusetts ques-tions were of low computational difficulty, compared to61 percent of the Hong Kong questions. More chal-lenging assessments typically lead to higher expectationsand more thorough instruction, which in turn lead to higherstudent achievement. America has a lot to learn from othercountries when it comes to meaningful assessment.

TEACHERS

It’s no secret that American elementary and middle schoolteachers often have weak math skills.8 And obviously it’sdifficult to learn math from someone who doesn’t under-stand the subject. Some policymakers are now seeking tofix this “ham butt problem” in a concrete way. In early2009, Massachusetts became the first state to begin requir-ing elementary teachers to pass a mathematics subtest beforeearning certification. Just 27 percent of those taking thetest at its first administration achieved passing scores.9 Andyet the bar isn’t particularly high; the concepts tested requireonly a modest grasp of algebra, geometry and probabil-ity. Massachusetts Education Commissioner Mitchell D.Chester wasn’t surprised by the low results, which con-firmed in his mind why such a test is necessary in the firstplace.10 The new Massachusetts regulation declares thata passing acquaintance with math is no longer acceptableamong elementary teachers: “Candidates shall demonstratethat they possess both fundamental computation skills andcomprehensive, in-depth understanding of K–8mathematics. They must demonstrate not only that theyknow how to do elementary mathematics, but that theyunderstand and can explain to students, in multiple ways,why it makes sense.”11

This is a start. But while Massachusetts is far aheadof most states in this regard, it remains woefully behindmany other countries. Liping Ma, a former senior scholarat the Carnegie Foundation for the Advancement ofTeaching, has shown how and why Chinese teachers tendto be more successful than their American counterpartsin teaching math to elementary students.12 The Chineseteachers she interviewed – none of whom had college degrees– were much more likely than American teachers to dis-play a “profound understanding of fundamental mathe-matics,” a term she coined that is now in wide use amongmath experts.

In Singapore, where students typically top the TIMSSrankings, future teachers graduate in the top third oftheir high school class and receive a free, four-year edu-cation courtesy of the government. Stanford professor LindaDarling-Hammond, an expert on teacher quality, reportsthat beginning teachers in Singapore earn more thanbeginning doctors.13

This, of course, is worlds apart from what we do inthe United States. But that is hardly reason not to ques-tion why we do things the way we do. Journalists can adda rich international angle to their reporting by lookingat how other countries tackle fundamental issues likecurricular coherence, student assessment and teacherquality. In the process, journalists just might discoverthat some countries have never had a “ham butt problem”because they’ve always used properly sized pans.

1 At the 2007 TED (Technology, Entertainment, Design) conference. A video of hertalk can be accessed at http://www.ted.com/talks/erin_mckean_redefines_the_dictionary.html.

2 A transcript of Schmidt’s talk is available online athttp://www.ed.gov/rschstat/research/progs/mathscience/schmidt.html.

3 Givvin, K., Jacobs, J. & Hollingsworth, H. (2006). “What Does Teaching Look LikeAround the World?” In ON-Math, 4(1). National Council of Teachers of Mathematics.

4 Ibid.

5 Ibid.

6 This question comes from the 2007 Trends in Mathematics and Science Study(TIMSS-4), available online at http://nces.ed.gov/pubs2009/2009001.pdf.

7 Leinwand, S. & Ginsburg, A. (2009, April). “Measuring Up: How the HighestPerforming State (Massachusetts) Compares to the Highest Performing Country(Hong Kong) in Grade 3 Mathematics.” American Institutes for Research. Page 4.Available online at http://tinyurl.com/ne9k38.

8 See, for instance, Ball, D.L., Hill, H.C. & Bass, H. (2005, Fall). “KnowingMathematics for Teaching.” American Educator. Available online athttp://tinyurl.com/kqxocr.

9 See Commissioner Mitchell D. Chester’s memorandum to the Massachusetts Boardof Education (dated May 13, 2009), available online athttp://www.doe.mass.edu/boe/docs/0509/item3a.html.

10 Ibid.

11 Massachusetts Department of Education. (2007, July). “Guidelines for theMathematical Preparation of Elementary Teachers.” Page 15. Emphasis in the original. Available online at http://www.doe.mass.edu/mtel/mathguidance.pdf.

12 Ma, L. (1999). Knowing and Teaching Elementary Mathematics: Teachers’Understanding of Fundamental Mathematics in China and the United States.Mahwah, NJ: Lawrence Erlbaum Associates.

13 Darling-Hammond, L. (2008, February 14). “How They Do It Abroad.” Timemagazine.

COMPARISON OF 3RD GRADE MATH ASSESSMENTS

IN MASSACHUSETTS AND HONG KONG

MASSACHUSETTSMCAS Spring 2007

(35 questions)

HONG KONG2007 Territory-Wide Spring Assessment

(36 questions)

Number of questions by“strand,” or area of math

Number: 17 (49% of test)

Measurement: 4 (11%)

Geometry: 4 (11%)

Data: 6 (17%)

Algebra: 4 (11%)

Number: 15 (42% of test)

Measurement: 12 (33%)

Geometry: 7 (19%)

Data: 2 (6%)

Algebra: 0 (0%)

Multiple-choicequestions

25 (71%) 5 (14%)

Computationaldifficulty ofquestions

Low: 34 (97%)

Medium: 1 (3%)

Low: 22 (61%)

Medium: 14 (39%)

TABLE 1

Source: American Institutes for Research

Math Teachers: Shortage Eases, but Issues RemainResearchers target high turnover, inadequate preparation as challenges needing attention.

By Sarah Neufeld


In recent years, school district administrators have searchedfar and wide to find qualified math teachers. They’ve trav-eled abroad to recruit, reimbursed for tuition costs, andoffered stipends and signing bonuses. The Obama admin-istration says recruiting and retaining quality math teach-ers, particularly for the neediest schools, must be a nationalpriority.

So what’s behind this shortage? Are colleges of edu-cation failing to turn out enough qualified candidates? Islack of support for new math teachers driving them away?

Richard M. Ingersoll, a University of Pennsylvaniaeducation and sociology professor, has generated substantialdiscussion with his research concluding that there actu-ally isn’t a lack of teachers in math and the other tradi-tionally hard-to-staffsubject, science. Theproblem, Ingersoll says,is poor working con-ditions – particularlyat schools servingimpoverished popula-tions – that cause teach-ers to leave long beforeretirement age. In1999–2000, the mostrecent year for whichIngersoll had data,8,021 math teachersentered the field, twiceas many as the numberwho retired. But 13,750 math teachers quit that year.

“We actually produce enough folks,” Ingersoll says.“It’s just that the turnover is such that we have these staffingproblems in particular types of schools.”

Secondary schools in high-poverty areas, both urbanand rural, have the most trouble finding and keepingmath teachers. “Almost every urban area has massivechallenges and problems,” says Henry Kepner, presidentof the National Council of Teachers of Mathematics(NCTM). “The rural areas, it’s almost a disaster formath.” Kepner also says that schools in the Southwest havehad trouble with math vacancies because of rapid growthin that part of the country.

But this year, some districts that have long struggledto find math teachers suddenly seem to have enough, theresult of the economic downturn. States such as California

are confronting the prospect of widespread teacher lay-offs. In New York City, a hiring freeze left 39 newlyminted math teachers – all of whom spent the past yearearning master’s degrees funded by the nonprofit groupMath for America – scrambling without placements.

“We don’t need any more math teachers in BaltimoreCity, first year ever,” says Linda Eberhart, the math coordi-nator in the Baltimore school district, where last year 90 per-cent of new high school math teachers and half of newmiddle school math teachers were recruited from thePhilippines.

Meanwhile, alternative certification programs formath teachers are seeing applications on the rise. LaylaAvila, a vice president of the New Teacher Project, a national

nonprofit that trainscareer-changers to workin urban and rural dis-tricts, says the challengeis making sure appli-cants are committed toa long-term change.“We don’t want peoplewho think, ‘I can do thisfor a couple of years andthen go back to my oldjob,’ ” she says.

If the shortage ofteachers might be easing,for now at least, thedebate over what type of

preparation is required for a successful math teacher con-tinues to intensify – as schools and teachers face ever-increas-ing pressure to raise student test scores in math.

A college major in math education might be ideal, butKepner points out that colleges have never produced alot of math majors of any type, much less majors in matheducation.

The NCTM maintains that secondary math teach-ers should have the equivalent of a major in mathemat-ics, but often they do not. Some enter classrooms afteronly a few weeks of review in the subject from an alter-native certification program and then begin work onmaster’s degrees while they are teaching.

Kepner says people switching from math-orientedcareers often have limited exposure to the entire subject– an engineer, for example, might have an extensive


calculus background but never have taken a class in statistics – and need well-rounded training. And know-ing math doesn’t automatically translate into being ableto teach it effectively. Math teachers have to know mathin a way that’s different from mathematicians; they needto be able to look at students’ incorrect solutions to aproblem and diagnose the conceptual or procedural errorthat led them to that result.

In elementary grades, where teachers are trained asgeneralists in colleges of education, many mathematiciansbelieve that math preparation is grossly inadequate. A recentreport by the National Council on Teacher Quality(NCTQ)1 says that “teaching elementary math requiresmuch greater competency than is generally presumed.”It recommends that states require elementary teachers todemonstrate proficiency at least through Algebra II as acondition for admission to educationschool. But such knowledge is not requiredto pass even the licensing exams thatteachers take at the end of degree programs.

“If we are serious about making surewe stay globally competitive, individualswho were themselves unable to master evenhigh school-level math or science coursesshould not teach these subjects to thenext generation, no matter what levelthey plan to teach: elementary, middle orhigh school,” the report says.

Last year, NCTQ evaluated the ele-mentary education programs at 77 collegesand universities and found that “almostanyone” can get through the math require-ments; even the people teaching math toelementary teacher candidates are “not pro-fessionally equipped to do so,” it said.

A growing number of schools arehiring math specialists to make up forteachers’ shortfalls, according to a report released last yearby the National Mathematics Advisory Panel.2 The panelconcluded that “the mathematics preparation of elemen-tary and middle school teachers must be strengthened”and recommended research on the use of full-time mathteachers in elementary schools.

While mathematically oriented people can often earnmore money for arguably less demanding work in otherfields, Ingersoll found in his research that money didn’tdrive math and science teachers from the profession morethan it did teachers of other subjects. The most commoncomplaints, he says, were students misbehaving and – anissue easier to resolve – administrators not allowing teach-ers to be a part of school decisions. Those problems are

most acute in the neediest schools, and teachers oftenleave after a few years for easier assignments in thesuburbs.

UTeach at the University of Texas at Austin hasgained national attention for its work preparing math teach-ers early. The program, which places undergraduate mathand science majors in education classes and gives themstudent-teaching experience from as early as freshman year,is being replicated at 13 other universities around the nation.It has graduated 500 students so far, and 80 percent arestill teaching after five years.

Math for America (no relation to Teach for America),founded by billionaire Jim Simons, is also growing, havingexpanded from New York to four other cities. It pays forfellows to spend a year earning master’s degrees in matheducation before teaching in high-need schools and

provides them a $100,000 stipend overfive years. Retention is a big emphasis,with a monthly social event and two orthree professional development sessionsa month. The retention rate after the f irst f ive years is more than 90 percent.

While new-teacher recruitmentefforts are often covered in the media,reporters covering the math teaching pro-fession should return to explore theirimpact. How many math teachers are stillthere after two years? Five years? Howmany quit mid-year? If your district hasrecruited math teachers abroad, howlong do they stay? What kind of supportdo they receive? How do average tenurescompare at the urban versus suburbanschools in your region? What mathpreparation is required of teachers by col-leges of education and alternative cer-

tification programs in your area? This year, there are also many story possibilities

involving the recession’s impact on math teacher recruit-ment and retention: How many math teachers is your schooldistrict hiring and how many are leaving in comparisonwith past years? Has the district made hiring commitmentsit isn’t keeping? What’s happening with applications?

Sara Neufeld, a Baltimore-based reporter, has written abouteducation for the past nine years. She covered schools for sixyears at the Baltimore Sun and three years at the San JoseMercury News.

1 http://www.nctq.org/p/docs/nctq_nmsi_stem_initiative.pdf

2 http://www.ed.gov/about/bdscomm/list/mathpanel/report/final-report.pdf

Math teachers have to

know math in a waythat’s different from

mathematicians;they need to be ableto look at students’incorrect solutionsto a problem and

diagnose theconceptual or

procedural errorthat led them to

that result.

“

”

How an Education Reporter Schooled Herself in Math Enrolled in an Algebra II class, a journalist conquers her fears and starts a discussion.

By Liz Willen


After two years on the education beat, Washington Post edu-cation reporter Michael Alison Chandler noticed she wasdoing more stories about math: new graduation standards,training issues for math teachers, pressure to develop amath-savvy workforce.

As Chandler thoroughly wrote and reported each newtrend and issue, a nagging fear followed her: Could a math-phobic reporter who dodged the subject whenever pos-sible do a thorough job of covering math?

“I started thinking about what I was missing. Howwould I see the world differently if I had more math skills?”Chandler says.

Her daring solution? Go back to high school, enrollin Algebra II, and blog about it for the Post in “X = Why?A year reliving highschool math.”

Attending anAlgebra II class at FairfaxHigh School in Virginiaand blogging about itgave Chandler a valu-able opportunity to re-examine the quality ofher own math educa-tion 15 years earlier at aprivate, all-girls highschool in Ohio. Beingback in a classroomoffered a close-up viewof teaching and learningthat few reporters expe-rience; it also promptedher to consider ques-tions she could notanswer while scramblingto cover the standardeducation beat menu ofbudget battles and testscore debates.

“There were moremath stories and stan-dards stories coming up,and the paradox is thatwhile I’ve always thoughtmath was important, itwas as small a part of

my career as I could make it,” Chandler says. “Both myparents taught writing. They never encouraged me to domath. I never had a real reason to focus on it.”

Chandler suddenly had a reason. With the help of aprep book, a tutor and about 12 hours of preliminary home-work, she took her seat in class last September “to revisithigh school algebra and find out what I might be miss-ing and what it might take to create a generation of stu-dents who aren’t afraid to call themselves math people.”

Chandler came to class every other day at 7:20 a.m.both to learn math and to report on its meaning and impactin her blog. At 32, she cut something of an odd figure ina classroom of 27 teenagers in Fairfax County, a high-per-forming district that is the 12th largest in the country, with

169,000 students. “Iwas older than theirteacher, but I wasn’t ateacher,” Chandlersays. “They knew Iwas a reporter, but Inever had a well-defined role. I thinkthey were a little sus-picious… but I wasan adult , so theyweren’t sure what todo about me.”

In an early blogposting, she laid outsome of her reasonsfor taking math andexploring math trends.“Algebra has beencreeping into middleschools and elemen-tary schools at analarming rate,”Chandler wrote. “Andadvanced algebra isrequired increasinglyfor all students, notjust the nerdy ones.A national testingobsession is causingeveryone to pay closerattention to pesky


math scores. And chief executives and politicians are try-ing to drum up workers for a changing technology-basedeconomy that they maintain is built upon an invisible moun-tain of equations.”

Beyond chronicling her struggles with a graphing calculator and unfamiliar equations, Chandler used the blogto introduce math topics ranging from quadratic equa-tions to teacher quality, all while attempting to create adialogue with readers. She tackled the topic, “AspiringElementary Teachers Fail New Math Test”; posed the ques-tions: “Is Math Fun? ShouldIt Be?”; and described effortsto encourage NativeAmerican girls in scienceand math.

Fairfax High SchoolPrincipal Scott Brabandwelcomed Chandler’s pres-ence in class and the blogbecause he felt it wouldshowcase the work of teach-ers, help connect math classwith “real world applica-tions,” and give parents aclose-up view of what theirchildren were learning.

Chandler made itthrough the first semesterwith an A – “barely,” as sheput it – and spent the sec-ond half of the year audit-ing the class instead ofparticipating as a student. Asshe scrambled to catch up,the class moved quicklythrough topics and reviewedthem repeatedly. Ultimately, she found “a hard-workingteacher who knew her math, a fast-paced, too-crammedcurriculum, and a group of teen agers who mostly tried theirbest.”

Chandler’s editor, Nick Anderson, considered theblog a worthwhile experiment, especially because itinspired readers to tell their own stories about the differentways math is taught from school to school and classroomto classroom.

As the blog evolved, Chandler found it easier to getsome items in the print edition, where space is at a pre-mium, while others remained online only. Some topics gen-erated a great deal of comment and debate, others less so.The paper learned lessons about blogging (timing and fre-quency are critical) along with insights from blog con-

tributors about math education.At times, the dual role of journalist and student cre-

ated some discomfort for Chandler, who became part ofthe classroom dynamic and even posted her quizzes andscores on the blog, although not those of her students. “Ifelt a little weird about exposing the students and theteacher,” she says. “I felt that I owed them a little more.In some ways, it was uncomfortable.”

It wasn’t always possible to remain a critical and neu-tral observer in class, as Chandler fought to keep up with

both math and the demands of the education beat. Thatconflict was the reason why she decided to audit the classduring the second semester.

Chandler finished her last blog entry in June 2009,concluding that lessons she’d learned had influenced bothher journalism as well as her math phobia. Her lack ofmath skills had left her feeling vulnerable in a batteredeconomy, especially with a troubling shakeout in thenewspaper industry beset by declining advertising revenues.

Chandler has since enrolled in a financial planningclass for women and acknowledged in her final blog entrythat she was “tackling the numbers in my credit report(ugh) and my bank statements right now,” and had plansto study more statistics and economics. And, she added,“Who knows, someday I might even take calculus.”

How Calculators Are Changing the Math ClassroomDevices help teachers cover more ground, but students still must understand the basics.

By Emily Sachar


Walk into almost any classroom in America – from elementary school on up – and you will prob-ably see students using calculatorsand other tools that performinstant computation. Thesmart story today is notthe 20-year-old debateabout whether this tech-nology belongs in schools.That fight is over. Instead,reporters should focus onhow these new tools havetransformed the way math istaught and learned. Whenshould calculators be introducedto young children? Are studentsbetter problem-solvers because theyhave these tools? Are they able to advancemore quickly and master higher-level con-cepts? And are all students – rich and poor– able to benefit?

These stories are critically important to par-ents, who often struggle to support their chil-dren’s mastery of mathematical concepts. Mostparents learned math without a lot of the tech-nology available today, so much of what goes onin their children’s classrooms is a mystery to them.They need to understand how calculators are usedin their district at various ages and what they can do tohelp their children succeed in math. Parents also want toknow whether their local schools are making the best useof the technology that’s available. Are the teachers well-trained? Has the district developed a consistent philoso-phy for calculator use?

The answers to such questions play out in differentways, depending on the grade level. The federal govern-ment supports effective use of technology in mathemat-ics instruction through research programs at the NationalScience Foundation and the U.S. Department of Education,but does not write calculator policies for schools. Instead,it is the responsibility of state education departments toweigh in on technology use in grade-by-grade math stan-dards that guide state testing programs and textbookselection. Individual districts then determine how they willincorporate calculators and other math technologies as wellas how teachers will be trained to use these tools.

Math standards in more than a dozen states men-tion using calculators as early as kindergarten or

first grade to teach kids number patterns.1

“For even young kids, calculators just makemath much more efficient,” says Susan

Garthwaite, elementary math resourceteacher for the 138 public elementaryschools in Fairfax County, Va.

Students still need to understandthe basics of addition, subtraction, mul-tiplication and division and be able toperform those and other simple oper-ations on their own – just as later on,they need to understand the basics

of algebra so that graphing func-tions makes sense and they’re

not just punching random keys.Without that basic knowl-edge, students can become socalculator-dependent thatthey can’t do division ormultiplication by hand.The 2008 NationalMathematics AdvisoryPanel report2 stressed

the absolute necessity ofmastering these skills without

the aid of technology. But once students have gained that fluency,

calculators can enable them to move forward quickly. Bythe third or fourth grade, students are learning to use basicfour-function calculators. Teachers can focus instruc-tional time on word problems and the logic of math.

Calculators can also be a great boon to students whoenjoy thinking about mathematical concepts but are terrified of numbers because they fear making computa-tional errors. “Nothing suggests that calculators are damaging students,” says Henry Kepner, president of theNational Council of Teachers of Mathematics (NCTM).“Make sure kids understand the work they’re doing, thenteach them how to work the calculator appropriate to thesubject they’re studying, then let them use it to take thedrudgery out of math.”

From middle school on, the math curriculum virtu-ally requires calculators for students to keep up, andmany teachers have made dramatic changes in the way they

teach. “I find myself asking higher-order questions andskills of my students,” says Natalie Jakucyn, who teachespre-calculus to sophomores at Glenbrook South HighSchool in Glenview, Ill. “They are thinking about math-ematical problem-solving from many more perspectivesthan when I was in school.” Her students use the $150TI-Nspire CAS (Computer Algebra System) from TexasInstruments.3

Many teachers believe the benefits extend far beyondschool. They say students need to feel comfortable withtechnology starting at an early age in order to be readyfor the working world. “It is my job to prepare studentsfor their future, not my past,” says Peg Cagle, an eighth-grade math teacher at the Lawrence Gifted MagnetSchool in Los Angeles. “We are digital immigrants andour kids are digital natives.”

The ability to apply technology appropriately hasbecome the hallmark of a good math and science education.The NCTM strongly endorses calculator use: “Calculatorsand other technological tools, such as computer algebrasystems, interactive geometry software, applets, spread-sheets, and interactive presentation devices, are vital com-ponents of a high-quality mathematics education,” theNCTM says in its March2008 position statement onthe use of technology inmath instruction. “Withguidance from effectivemathematics teachers, stu-dents at different levels canuse these tools to supportand extend mathematicalreasoning and sense-mak-ing, gain access to mathe-matical content andproblem-solving contexts,and enhance computationalfluency.”

Some issues for reporters to explore:� At what age should calculators be introduced and

what mathematical concepts do students need tounderstand before they can use these tools effec-tively? Is fluency with basic mental math a prerequi-site for success in more challenging mathematics?

� What is the research on the effectiveness of calcula-tors? According to data from the National Center forEducation Statistics, calculators don’t have much ofan impact on test scores in fourth grade, but do appearto make a big difference by eighth grade. ResearchersJeremy Roschelle and Lawrence Gallagher of SRI

International in Menlo Park, Calif., have found thatthe correlation between frequent calculator use andhigh scores holds true for eighth-graders from alleconomic backgrounds. Roschelle suspects that poorteacher training accounts for the weaker scores forfourth-graders.

� What tasks should not be performed on a calculator?Some educators think that certain “real world” tasks,like learning to make change, should be taught in ahands-on way using real money. What other kinds oflearning experiences are better without calculators?

� How are teachers in different grades trained to use cal-culators in class? Older teachers often are reluctantto use these tools, especially in the early grades. Howdo districts overcome this opposition?

� How does technology affect the way learning disabledstudents learn math? Do calculators help or hurtyoungsters who have trouble reading numbers andunderstanding numerical concepts?

� Are the benefits of technology shared equally by richand poor kids? Calculators used in advanced highschool math classes are generally under $200, buteven that amount can be daunting for some families.

What are schoolsdoing to bridge thatgap? Cagle, for in -stance, has one class setof calculators, so shedoes not give home-work that requires cal-culator use. But shedoes give tests thatrequire calculators.Teachers like Cagleoften juggle class setsamong all of their students or evenamong various teach-

ers. How does that affect students’ comfort level andexpertise with these tools?

Emily Sachar is a two-time winner of the Grand Prize for Dis-tinguished Education Reporting from the Education WritersAssociation. She has been an education reporter for Newsdayand New York Newsday as well as a math teacher in the NewYork City public school system.

1 See the Fordham Foundation’s January 2005 analysis of state math standards, available online at http://www.edexcellence.net/doc/mathstandards05FINAL.pdf.

2 http://www.ed.gov/about/bdscomm/list/mathpanel/report/final-report.pdf.

3 Texas Instruments provided support for this publication.



Journalists writing about math should look beyond the usualsuspects. A good example is actress Danica McKellar, best knownfor her roles on The Wonder Years and The West Wing.But as co-author of a theorem that bears her name (The Chayes-McKellar-Winn Theorem), she is also an internationallyrecognized mathematician and an advocate for math educa-tion. A summa cum laude graduate of UCLA with a degreein mathematics, McKellar has tried to encourage girls’ inter-est in math with two best-selling books, Math Doesn’t Suck:How to Survive Middle School Math Without LosingYour Mind or Breaking a Nail (2007) andKiss My Math (2008) about pre-algebra,both from Hudson Street Press. McKellaris currently working on a third book inthe series, due out next year. The followingis excerpted from Kiss My Math.

n high school, a teacher oncesuggested that I be a mathmajor in college. I thought,

“Me? You’ve got to be jok-ing!” I mean, in junior high,I used to come home andcry because I was so afraidof my math homework.Seriously, I was terrified ofmath.

Things had gottenbetter for me sincethen, but still – collegemath? That soundedreally hard; I didn’tthink I could hackit. Besides, whostudies math incollege otherthan peoplewho want tobe mathteachers, right?

Boy, was I wrong. Just ask my friend Nina.

In college, Nina wanted to be a doctor morethan anything in the world. She’d always wanted todeliver babies! She was smart, funny, and totally capa-

ble of doing whatever she set her mind to – until shefound out that calculus was a required course. Theidea of taking calculus scared her so much that shedropped out of the pre-med program and gave up herdream!

And Nina isn’t the only one. Believe it or not, lotsof people change their majors and abandon their dreamsjust to avoid a couple of math classes in college.

So, what does “kiss my math” mean?It means: “Um, excuse me, I’m going to do what-

ever I want with my life, and I’m sure as heck not goingto let a little math get in my way.”

Who knows what you’ll do? Armed withmath, you might become a cutting-

edge scientist and developyour own lineof all-naturalmakeup or

therapeutichigh heels. You

might discover acure for cancer or

travel into space.You might create

some cool engineer-ing trick that destroys

trash or creates super-clean energy and saves

the planet!Something else, per-

haps? Doctor, lawyer, cloth-ing designer, architect?

Maybe you’ll work for a big magazine or your favorite fash-

ion line, or maybe you’ll startyour own business. Believe it or

not, all of these fabulous careersuse – that’s right – math. Betcha

never knew math could give youpower and freedom in those areas.

And if anyone tells you it’s impos-sible to be fabulous and smart and

make a ton of money using math, well,they can just get in line behind you – and

kiss your math.

Actress Danica McKellar Extols the Wonders of Math to Girls

I

Experts on Mathematics


Alejandro Ádem Díaz de LeónUniversity of [email protected]

Expertise: algebra and topology

Elaine M. AllensworthConsortium of Chicago School ResearchUniversity of [email protected]

Expertise: factors that affect highschool graduation and dropout rates, statistical methodology

Deborah Loewenberg Ball*University of [email protected]

Expertise: teaching and teacher prepa-ration

Camilla Persson BenbowVanderbilt [email protected]

Expertise: gifted education and thedevelopment of mathematical talent

Sean CavanaghEducation [email protected]

Expertise: covering algebra and mathpolicy

Philip DaroStrategic Education Research [email protected]

Chair of the Mathematics Develop-ment Work Group of the CommonCore State Standards Initiative

Francis “Skip” Fennell*McDaniel [email protected]

Former NCTM presidentExpertise: teacher education andmath education

Herbert P. GinsburgTeachers College, Columbia [email protected]

Expertise: young children’s under-standing of math

Henry KepnerPresident, National Council of Teachers of [email protected]

Expertise: teacher education andmath education

Jeremy KilpatrickUniversity of [email protected]

Expertise: math education and curricula

Steve LeinwandAmerican Institutes for [email protected]

Expertise: international comparisons

Tom Loveless*Brookings [email protected]

Expertise: math standards and NAEP

R. James MilgramStanford [email protected]

Expertise: math standards and curricula

Richard SchaarTexas [email protected]

Expertise: calculator usage, educationpolicy

Wilfried Schmid*Harvard [email protected]

Expertise: math education

William SchmidtMichigan State [email protected]

Expertise: math curricula, international comparisons

Laura SloverAchieve, Inc.Washington, [email protected]

Expertise: state-level policy on mathematics; math standards, content alignment and benchmarking

Sandra Stotsky*University of [email protected]

Expertise: state standards and standards-based reform

Uri TreismanCharles A. Dana CenterThe University of Texas at [email protected]

Expertise: the teaching of math, mathachievement among minorities

Hung-Hsi Wu*University of California, [email protected]

Expertise: math education and curricula; professional developmentfor math teachers

*Member of the National Mathematics Advisory Panel

Resources on Math: Reports, Publications and Web Sites


Achieve, Inc. (2008, May). “The BuildingBlocks of Success: Higher-Level Math forAll Students.” Washington, DC: Author. Accessible online athttp://tinyurl.com/nyv9c7.

Ball, D.L., Hill, H.C. & Bass, H. (2005, Fall).“Knowing Mathematics for Teaching.”American Educator. Accessible online athttp://tinyurl.com/kqxocr.

Ginsburg, A., Leinwand, S., Anstrom, T. & Pollock, E. (2005, January 28). “What the United States Can Learn FromSingapore’s World-Class Mathematics System (and what Singapore can learnfrom the United States): An ExploratoryStudy.” Washington, DC: American Insti-tutes for Research. Accessible online athttp://tinyurl.com/5mass.

Ginsburg, H.P. (1989). Children’s Arith-metic: How They Learn It and How YouTeach It. (2nd ed.) Austin, Texas: Pro-Ed.

Ginsburg, H.P. (2009). “Early MathematicsEducation and How to Do It.” In O. Barbarin& B.H. Wasik (Eds.), Handbook of Child De-velop ment and Early Education: Researchto Practice. New York: The Guildford Press.

Givvin, K., Jacobs, J. & Hollingsworth, H.(2006). “What Does Teaching Look LikeAround the World?” In ON-Math, 4(1).National Council of Teachers of Mathematics.

Kilpatrick, J., Swafford, J., & Findell, B. (Eds.)(2001). Adding It Up: Helping ChildrenLearn Mathematics. Washington, DC: National Academy Press.

Lampert, M. (2001). Teaching Problemsand the Problems of Teaching. New Haven& London: Yale University Press.

Leinwand, S. & Ginsburg, A. (2009, April). “Measuring Up: How the Highest Perform-ing State (Massachusetts) Compares tothe Highest Performing Country (HongKong) in Grade 3 Mathematics.” Washing-ton, DC: American Institutes for Research.Accessible online athttp://tinyurl.com/ne9k38.

Ma, L. (1999). Knowing and Teaching Elementary Mathematics: Teachers’ Understanding of Fundamental Mathe- matics in China and the United States.Mahwah, NJ: Lawrence Erlbaum Associates.

National Association for the Education ofYoung Children. (2002). Early ChildhoodMathematics: Promoting Good Begin-nings. Statement of the National Associationfor the Education of Young Children(NAEYC) and the National Council of Teach-ers of Mathematics (NCTM). Washington,DC: Author.

National Commission on Mathematicsand Science Teaching for the 21st Century.(2000). Before It’s Too Late: A Report tothe Nation from the National Commissionon Mathematics and Science Teaching forthe 21st Century. Accessible online athttp://tinyurl.com/mlv3pn.

National Council of Teachers of Mathe matics.(2000). Principals and Standards forSchool Mathematics. Reston, VA: Author.Accessible online athttp://standards.nctm.org.

United States Department of Education.(2008). “Foundations for Success: TheFinal Report of the National MathematicsAdvisory Panel.” Accessible online athttp://tinyurl.com/yopzor.

Wu, H. (1999, Fall). “Basic Skills VersusConceptual Understanding: A Bogus Dichotomy.” American Educator (AmericanFederation of Teachers). Accessible onlineat http://tinyurl.com/n4nvbn.

Achieve, Inc.http://www.achieve.org/

Achieve is an independent, bipartisan, non-profit education reform organization thathelps states raise academic standards andgraduation require ments, improve assess-ments and strengthen accountability.Achieve’s Math Works advocacy kit(http://www.achieve.org/MathWorks) provides resources that make the case forwhy all high school students should en-gage in rigorous math course-taking.

Charles A. Dana Center, The University of Texas at Austinhttp://www.utdanacenter.org/

The Dana Center provides Texas educationleaders with new knowledge about teach-ing and learning, and supports K-12 teach-ers and leaders working to implement highacademic standards for all students.

Conference Board of the Mathematical Scienceshttp://www.cbmsweb.org/

The Conference Board of the MathematicalSciences (CBMS) is an umbrella organiza-tion consisting of seventeen professionalsocieties, all of which seek to increase ordiffuse knowledge in the mathematical sci-ences. Its purpose is to foster understand-ing and cooperation among these nationalorganizations to promote research, im-prove education and expand the uses ofmathematics.

National Council of Teachers of Mathematics (NCTM)http://www.nctm.org/

NCTM is a public voice for mathematics ed-ucation, providing vision, leadership andprofessional development to support teach-ers in ensuring equitable and high-qualitymathematics learning for all students.

The Mathematical Association of America (MAA)http://www.maa.org/

The MAA is the largest professional societythat focuses on mathematics accessible atthe undergraduate level. Its mission is toadvance the mathematical sciences, espe-cially at the collegiate level.

Reports and Publications

Web Sites

Math Matters: A Hechinger Institute Primer for Journalists

The Ewing Marion Kauffman Foundation

was established in the mid-1960s by the late entre-preneur and philanthropist Ewing MarionKauffman. Based in Kansas City, Mo., the KauffmanFoundation seeks to foster a society of economi-cally independent individuals who are engagedcitizens, contributing to the improvement of theircommunities. In service of this vision, and inkeeping with its founder’s wishes, the foundationfocuses its grant-making and operations on two areas:advancing entrepreneurship and improving theeducation of children and youth.

The Hechinger Institute on Education andthe Media at Teachers College, ColumbiaUniversity, is dedicated to promoting fair, accu-rate and insightful coverage of education, from pre-kindergarten through graduate school, in all formsof media. The Institute holds seminars for nationalaudiences of journalists, publishes guides andprimers such as this as resources for journalists, andoffers online courses and Webinars. The publica-tions are available on our Web site, along with otherresources, commentaries and analyses of educationcoverage. Journalists from news organizations suchas National Public Radio, the Los Angeles Times,

Washington Post, Boston Globe, ChicagoTribune,ChristianScienceMonitor,

Philadelphia Inquirer, Miami Herald, USA Todayand others are regular participants. The Instituteis named in memory of the late Fred M. Hechinger,a former Teachers College trustee and educationeditor of the New York Times. Support for theInstitute and its work comes from a variety ofnational foundations including The BroadFoundation, Bill & Melinda Gates Foundation, JoyceFoundation, Kauffman Foundation, LuminaFoundation for Education, the Spencer Foundation,and The Wallace Foundation.

Recent Hechinger Publications:

Covering the Pre-K Landscape:New Investments in Our Littlest LearnersJuly 2009

Understanding and Reporting on Academic RigorJune 2009

Making Sense of the Dollars:Reporting on Higher Education Budget CutsNovember 2008

The Hechinger Institute Guide toEducation Research for JournalistsJuly 2008

Leadership and LearningJuly 2008

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