MATH EDUCATION: TEA CHING'FOR UNDERSTANDING

The Development and Publication ofElementary'Mathematics Textbooks:Let the Buyer Beware!Fiercely competing textbook publishers claim that their materials are research-based andwill produce student success. The authors offer sound advice to educators trying-to sort outthese claims as they select mathematics textbooks that,will truly fit thbir schools' objectives.

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BY BABARAJ. REYS AND ROBERT E. REYS

~ATHEMATICS textbooks are critical tools for student learning in

Amrerican classrooms. Teachers use them daily to plan and ddiverlessons, 'and students use them in class to explore and learn math-ematics. When students bring the textbooks home for further study,parents can examine the books for a glimpse of their child's mathe-mat.ics classroom. Given tex:tbooks' potential to SUlSport studentlearning, it is important to understand how they are developed.

,Who produces school mathematics textbooks? Who decides on their contenit and

BARBARA]J. REYS is Distinguished Professor of Mathematics Education in the College of EducAtionat the University of Missouri, Columbia, where ROBERT E. REYS is Curators' Professor of Mathemat-ics Education. The development of this article was supported by the Center for the Study of Ma the-ma tics Curriculum (NSF Award No. ES1-0333879). The views and conclusions expressed are those ofthe authors.

Illustration byjem Sullivan JANUARY 2006 377

how this content is organized? Are the elementarymathematics textbooks currently in use research-based - i.e., are decisions about content and in-struction based on the best available research and arethe materials field-tested in classrooms before publi-cation? What evidence is available regarding the im-pact of particular textbooks on student learning?

While pressure is growing on curriculum develop-ers and publishers to gather and share evidence of theeffectiveness of textbooks, several forces are workingagainst the production of high-quality, research-basedcurriculum materials. These forcesinclude a lack of con-sensus on what mathematics should be emphasized atparticular grade levels and a highly competitive, market-driven industry that produces textbooks under very tighttime lines and, in some states, under very strict guide-lines. Given these conditions, publishers perceive theirchances of success - i.e., selling many textbooks -to be greater if their products are similar in content andstyle to the current market leaders, thereby limiting thelikelihood of innovation. Another complication is thatthe market-driven publishing industry and the academ-ic research community differ as to what constitutes "re-search-based" textbooks.

What can and should school leaders do to select goodtextbook materials? This article examines the currentenvironment and offers some advice for those consid-ering new elementary'mathematics textbooks.

THE CHANGING LANDSCAPEOF TEXTBOOK PUBLISHING

Each year thousands of elementary schools acrossthe U.S. buy mathematics textbooks, generally one bookfor every student in the school. This represents a largeand important market for textbook publishers. Yet thenumber of textbook series from which schools can choosehas decreased significantly in the past 10 years. In fact,the textbook industry has shifted from many smallercompanies to afew large publishing conglomerates. Old-er textbook-publishing companies, such as Scott Fores-man and Addison-Wesley, which were competitors foryears, are now owned by the same parent company -Pearson Learning Company. Likewise, both Harcourtand Holt, Rinehart, &Winston - two former com-petitors - are now owned by Reed Elsevier, a Britishcompany. Today there are only four large publishing

conglomerates that produce elementary mathematicstextbooks for the U.S. market - Pearson, Reed ElsevierGroup, McGraw-Hill, and Houghton Mifflin.1These

four publishing groups may produce one or more ele-mentary mathematics textbook series (see Table 1 fora list of the most popular series and their publishers).

Most of the textbook series noted in Table 1 are "pub-lisher developed." That is, their development was ini-tiated and funded by the publisher with the help ofstaff editors and an invited set of authors. Two series- Everyday Mathematics and Math Investigations -were developed by curriculum development teams withfinancial support from the National Science Founda-tion and then published and distributed by a commer-cial publisher.

A growing trend in mathematics textbook adop-tions is for publishers that offer more than one typeof series to provide a package of materials to schoolsthat includes the publisher-developed textbook seriesas the base adoption, along with supplemental com-ponents (e.g., a few modules) from the NSF-fundedseries. While this approach may help close a sale, it iscertainly not how the authors of either textbook seriesintended the materials to be used. Given the lengthof today's textbooks - 600 to 700 pages - it is un-clear how adding more material, particularly materialdesigned by different author teams with different in-structional philosophies, results in a coherent curricu-lum that can be used effectively by teachers.

MIXED MESSAGES AND COMPETING PROCESSES

There is little doubt that authors and editors of text-books want to produce materials that will support stu-dent learning and, of course, that will sell. However,both the development and adoption of elementary math-ematics textbooks occur within a flawed system charac-terized by several factors that we believe impede progresstoward the goal of producing high-quality, research-based textbooks.

Mixed messages regarding the content of textbooks. TheU.S. mathematics curriculum has been characterizedbyTIMSS (Trends in Mathematics and Science Study)researchers as a "mile wide and an inch deep" - thatis, curriculum frameworks and textbooks cover manytopics, some superficially, and much content is repeat-ed from year to year.' In the past four years most stateshave developed new mathematics curriculum frame-works that define grade-level learning expectations,which are to be the focus of instruction and assess-

ment.' While there are many similarities across theseframeworks, there are also many differences, particu-larly in the assignment of topics to different grade lev-

378 PHI DELTA KAPPAN

els. In fact, the placement of specific learning goals,such as fluency with whole-number computation orwith fractions, differs across state standards by as muchas two to four grade levels.'

Differences in state-mandated learning goals for math-ematics represent a majoi challenge for textbook au-thors and publishers and may result in laige books thatcover more topics than any one state requires. The or-ganization of the content may also differ across text-books. For example, one textbook might devote oneunit or chapter to mathematical problem solving, whileanother miAht integrate problem-solving lessons intoeach of its chapters. One textbook might emphasize astrand such as geometry early in the book, while an-other might place it at the end. Given the significantlength of elementary mathematics textbooks, both thedepth of the coverage and the placement of topics with-in the book affect what students have an opportunityto learn in a given year.

Textbooks also differ in their pedagogical orienta-tion - how the mathematics is presented to students.For example, one textbook series might be organizedso that the teacher is expected to present and work ex-amples for students and generally direct the way stu-

dents are to solve problems. In this approach, studentslearn to solve problems by repeating procedures present-ed by their teachers. Another textbook series might ex-pect the teacher to present a mathematical problemand encourage students to use prior knowledge to de-

There is little doubt that authors andeditors of textbooks want to producematerials thatwill support student learningand that will sell. However, both the,development and adoption of elementarymathematics textbooks occur within aflawed system.

velop their own strategies to solve the problem. Giventhese differences in approach, the textbook serves as avery important influence on how teachers nurture and,develop student learning. While there nray not be anyone right way to teach, the choice of textbook will af-fect how mathematics is presented to students and whatthey learn.

JANUARY 2006 ' 379

TABLE 1.

Market-Leading Elementary Textbo6k Series in 2005

GradesXK-2

Parent Percentage ofTitle Publisher Company Sample

Everyday Mathematics* Wright Group McGraw-Hill 19.2Mathematics Harcourt Harcourt 12.3Mathematics Scott Foresman-Addison Wesley Pearson 11.0Mathematics Houghton Mifflin Houghton Mifflin 9.6Mathematics Silver Burdett Ginn Pearson 8.7Saxon Math Harcourt Achieve Harcourt 7.8Math Advantage Harcourt School Publishers Harcourt 7.3Math Investigations* Pearson Scott Foresman Pearson 6.8

Grades 3-5Parent Percentage of

Title Publisher Company Sample

Everyday Mathematics* Wright Group McGraw-Hill 15.5Mathematics Scott Foresman-Addison Wesley Pearson, 15.1Mathematics Harcourt Harcourt 11.0Mathematics Houghton Mifflin Houghton Mifflin 11.0Mathematics Silver Burdett Ginn Pearson 9.1Saxon Math Harcourt Achieve Harcourt 8.7Math Advantage Harcourt School Publishers Harcourt 6.8

Source: Education Market Research, 2005, www.ed-market.com.*Series developed with support from the National Science Foundation.

Lack of evidence ofeffectiveness of textbooks. Some text-book series are piloted over several years to test and re-fine the way the books present mathematics to students.In other cases, publishers rely on the experience andknowledge of the authors to develop the content oftextbooks and do not field-test the material with stu-dents. Another concern is that publishers generally donot systemaiically.gather data about student learningonce their textbooks are adopted. They consider them-selves development centers, not research and develop-ment centers.

Increasingly, there are calls for evidence of the ef-fectiveness of curriculum materials. While it is difficultto sort out the specific effects of textbooks - whichare just one of the many variables that can influencestudent learning - on teachers' decisions and studentachievement, a growing number of researchers are in-vestigating the impact of textbooks.

There is also a growing call for research-based cur-riculum materials. It is not uncommon for textbooksto promote themselves as such. For example, the fol-lowing descriptions appear in two popular textbookseries:

[Textbook Series A] provides a research-based in-structional plan that ensures success for teachers and

students.6

[Publisher B's] mathematics programs are contin-ually researched to determine "what works." Ourprograms are regularly revised to keep the best of

what has worked in prior editions, and to improve

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"Hey, Mom, I'm running for class president. Howabout throwing together a little fund-raising dinner fortonight?"

them to meet changing market and curriculumneeds.7

However, simply saying that a textbook series is re-search-based 'doesn't make it so. A National ResearchCouncil panel released a report in 2004 that summa-rizes current research on the effectiveness of curricu-lum materials and suggests criteria for gauging the ef-fectiveness of curriculum programs.

The committee recommends that a curricular pro-gram be designated as scientifically established as ef-fective only when it includes a collection of scientif-ically valid evaluation studies.., that establish that

an implemented curricular program produces validimprovements in learning for students, and when itcan convincingly demonstrate that these improve-

ments are due to the curricular intervention. Thecollection of studies should use a combination ofmethodologies that meet these specified criteria: 1)content analyses by at least two qualified experts (aPh.D.-level mathematical scientist and a Ph.D.-levelmathematics educator) (required); 2) comparativestudies using experimental or quasi-experimental de-signs, identifying the comparative curriculum (re-quired); 3) one or more case studies to investigatethe relationships among the implementation of thecurricular program and the program components(highly desirable); and 4) a final report, to be madepublicly available, should link the analyses, specifywhat they convey about the effectiveness of the cur-riculum, and stipulate the extent to which the pro-gram's effectiveness can be generalized (required).

Although efforts to encourage more and better re-search into the effectiveness of curriculum materials arecommendable, designing and completing good studieswill require time and the cooperation of school systems.In the meantime, district personnel should be wary oftextbook publishers that claim their materials are re-search-based. At the very least, consumers should askfor reports of evidence and examine them carefully.

Textbook adoption processes. The selection of a text-book is an important decision for schools that affectsboth teachers and students. It is a major expenditure andwill influence the mathematics content that teachersteach and that students have the opportunity to learn.Once selected, textbooks are typically used in the schoolfor six to eight years, so the decision has long-term con-sequences.

The first step in the selection process is to collectand examine available textbooks. Sales representativesfrom publishing companies typically provide examina-

380 PHI DELTA KAPPAN

tion copies of their textbooks, including teacher guidesandancillaries, to prospective customers. Representa-tives will also make sales presentations that highlightthe strengths of their program and do their best to con-vince you that their textbook is the best fit for yourschool..

As the sales process continues, representatives mayuse various tactics to win the adoption. Dinners andfavors,for members of the textbook selection commit-tee are not uncommon..The number and cost of thesefavors are directly proportional to the dollars that wouldresult from an adoption. If two companies are com-peting for the adoption, discounts of the list price orthe provision of free inservice training for teachers canoften be negotiated. Another way to tip the balancefor an adoption' is for the publishing company to pro-vide at "no cost" a wide range of ancillaries -study

guides, practice books, enrichment supplements, tests,transparencies, CDs, videos, workshops for teachers.

Figure 1 shows one grade level's worth,of materialsto be used with the 2004 edition of a popular ele-mentary mathematics textbook. In addition to the stu-dent and teacher editions of the book itself, the set in-cludes over 20 separate booklets, totaling over 3,000pages of ancillary materials. There is little wonder thatsuch a large and impressive collection of resources maysway an adoption decision.

Don't be fooled by the bounty of materials offered

FIGURE 1.

Set of Materials for One Grade Level of aPopular Mathematics Textbook Series

Photo: Courtesy the author

by publishers. While these ancillaries are attractive,the focus when adopting new textbooks:should be onthe core materials - the student and teacher editionsof the book. The content and instructional approachof these texts should be paramount in any adoptiondecision. Quality should be the standard, not quantity.

CRITICAL QUESTIONS

If you are involved in a textbook adoption, we en-courage you to ask probing questions about any text-book series being considered. Obtaining clearand ac-curate answers to questions like those below will helpyou make a-wise'decision.

Who -wrote the textbook? You might assume thatwhen authors, names, and often their pictures, appearin a textbook, these are the people 'who wrote the book.In some cases,.this is true. In other cases, the listed au-thors served in an advisory capacity, meeting period-ically to discuss content organization and map out atable of contents for the series of textbooks. They alsomay have decided on special features - e.g., Extra forExperts, Check-Up, Connections - that will appearregularly throughout the textbook series. And they mayhave written a few sample lessons, which then servedas prototypes for the other 'lessons in the book thatwere written by consultants or development houseshired to produce them quickly.

These "writers for hire" are contracted by the text-book publisher to produce a certain number of les-sons for a fixed price. The lessons are to follow explicitspecifications and be geared toward particular objec-tives, typically including as many of the characteris-tics of the market leader for that textbook as possible.The development houses produce the required'lessonsand then go on to another job, sometimes writing les-sons for a different publisher. They generally have nolong-term commitment to the materials they produce.Yet their ability to create large amounts of materialquickly has led many publishers to abandon the royal-ty-based author system for the more cost- and time-efficient system of contracted writers.

What is the basis of thd mathematics content and theinstructional philosophy of the textbook series? Is the text-book series aligned With the National Council of Teach-ers of Mathematics' Principles and Standardsfor SchoolMathematics?9 Most publishers claim to be aligned withthese standards; however, textbook series mtist be ex-amined carefillly across grades to ensure that that sucha claim is actually true. Is the material presented in the

JANUARY 2006 381

textbook focused on student understanding? Are prob-lem solving and reasoning main themes? Are studentsencouraged to learn and use different representationsof mathematical ideas in order to understand mathe-matics and communicate that understanding?

As discussed earlier, alignment of textbook contentwith state-level curriculum frameworks is even moreproblematic because of the variation in states' grade-level expectations. Most publishers solve this conun-drum by including in each textbook series content thatis expected at particular grade levels by several, if notall, states. For example, the 2004 California mathe-matics framework calls for the development of fluencywith basic number combinations (basic facts for ad-dition) at grade 1. In Tennessee, fluency with basic ad-dition facts is expected at grade 2, and in Minnesota,at grade 3.11 Therefore, publishers that want to mar-ket their textbooks in each of these states will proba-bly include material on this topic at each of the gradelevels.

While some review of topics from grade to grade isreasonable, alignment of textbook content with mul-tiple states' curriculum frameworks is likely to producetextbooks that are large and unfocused - the "mile-wide and inch-deep" phenomenon. So finding a text-book that aligns with a particular school district's cur-riculum is tough. Instead, most districts choose text-books that include more content than they expect teach-ers to cover, requiring the district to convey to teach-ers how the textbook can and should be used to ad-dress their district's or state's learning expectations.

Is the series research-based? Research-based textbooksare those that 1) make use of research on student learn-ing to guide the books' sequence and instructional ac-tivities, 2) field-test early versions of lessons and unitsand revise materials based on the feedback, and 3) pro-vide data on the impact of the final version of the ma-terials on student learning.

Is this a newly developed mathematics textbook seriesor a revision of an existing_program? If it i's a revision,then investigate the changes that were made. How isthis version different from the previous edition, andwhat factors influenced the changes? What impact didthe earlier edition have on student achievement? Whatdistricts used this series, and how did their studentsperform on state or local assessments? Contact otherusers of the textbook series to learn their perceptionsof the strengths and weaknesses of the program, andcheck with teachers about their experience with theprogram. What did they like? Dislike? If they had it

to do over again, would they have chosen the samemathematics textbook series? Answers to these ques-tions from actual users can help inform your decision.

In selecting newly developed textbooks, district per-sonnel should ask questions such as: What researchguided the development of the textbook series? Wasthe series field-tested before finalizing the material?What data are available to describe the context of thefield test (e.g., location of study, number and type ofschools included, number and characteristics of teach-ers and students included, length of study)? And whatdata are offered on the impact of the materials on stu-dent learning? How did the field test influence thecurrent edition? Pilot studies should provide feedbackon lesson content and organization. Without appro-priate field-testing of the entire program, it is impos-sible to develop an accurate pacing guide for a math-ematics textbook or to gauge the various componentsof a lesson.

What kind ofprofessional development should be pro-vided for teachers to use the textbook series effectively?Some orientation to the materials making up the text-book series (student text, teacher guide, assessment pack-age, and other ancillaries) is usually provided to teach-ers and principals prior to its actual implementation.However, some elementary mathematics textbooks re-quire additional content knowledge and include newteaching strategies. If this is the case, then the needfor additional professional development must be wellunderstood by teachers and administrators prior tothe selection of a program. A willingness to engage inthe necessary professional development will improvethe chances that the adopted mathematics programwill be implemented in a manner consistent with thephilosophy on which the textbooks are based.

CONCLUSION

Careful study of available textbook series is neces-sary to understand the philosophies underlying the pro-grams, the scope of the content of different series, andthe organization of lessons and units of instruction. Dis-tricts must also be aware of the nature and extent ofthe professional development required to effectively im-plement the programs. There are useful resource ma-terials available for districts to use when evaluating math-ematics textbooks for adoption."

Answering the questions noted above will help youmake an informed decision about which textbook serieswill best meet your district's needs. As a'potential text-

382 PHI DELTA KAPPAN

book buyer, you need to adopt thephilosophy of "let the buyer be-ware." Demand clear and compre-hensive information from textbookpublishers, and examine their an-swers carefully to make sure youhave the information you need to"make the best choice.

1. Gilbert T. Sewall, "Textbook Publishing,"Phi DeltaKappan, March 2005, pp. 498-502.2.For a more thorough discussion of these andother points, see Harriet.Tyson-Bernstein, A Con-spiracy of Good Intentions: America's Textbook Fi-asco (Washington, D.C.: Council for Basic Ed-ucation, 1988); Chester E. Finn, Jr., Diane Ray-itch, and Institute Staff, The Mad, Mad Worldof Textbook Adoption (Washington, D.C.: ThomasB. Fordham Institute, 2004), www.edexcellence.net/institute/publication/publication.cfm?id=335; and Sewall, op. cit.3. William H. Schmidt, Curtis C. McKnight,and Senca A. Raizen, A Splintered 1ision: An In-vestigation of U.S. Science and"Mathematics Ed-:ucation (Dordrecht, Neth.: Kluwer, 1997).4. Barbara Reys et.al., Development of State-LevelMathematics Curriculum Documents: Report ofaSurvey (Washington, D.C.: Center for the Studyof Mathematics Curriculum, National Science,Foundation, March 2005), http://mathcurricu-lumcenter.org/news.htrml.5. Barbara Reys et al., The De Facto U.S. Na-tional Mathematics Curriculum: An Analysis ofState-Level Mathematics Curriculum Standards(in preparation).6. Evan M. Maletsky et al., Harcourt Math,Teacher Edition, Grade 3, vol. 1 (Orlando, Fla.:Harcourt, Inc., 2003), p. T10.7. Randall I. Charles et at., Prentice-HallMath-ematics Course I (Needham, Mass.: Prentice-Hall, 2004), p. T43.8. Jere Confrey and Vic&li Stohl, eds., On Eval-uating Curricular Effects: Judging the Quality ofK-12 Mathematics Evaluations, Executive Summary(Washington, D.C.: Commiftee for a Review ofthe Evaluation Data on the Effectiveness of NSF-Supported and Commercially Generated Mathe-matics Curricular Materials, National AcademyPress, 2004), p. 5.9. Princles and Standards for School Mathemat-ics (Reston, Va.: National Council of Teachers ofMathematics, 2000).10. Reys et al., The DeFacto U.S. National Math-ematics Curriculum.11. Glendon W. Blume and Robert E Nicely,Jr., eds., A Guide for Reviewing School Math-ematics Programs (Reston, Va.: National Coun-cil of Teachers of Mathematics, 1991); andLynn T. Goldsmith, June Mark, and IleneKantrov, Choosing a Standards-Based Mathe-matics Curriculum (Portsmouth, N.H.: Heine-mann, 1998). K

JANUARY .2006 383

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TITLE: The Development and Publication of ElementaryMathematics Textbooks: Let the Buyer Beware!

SOURCE: Phi Delta Kappan 87 no5 Ja 2006WN: 0600101226011

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