Northwest Journal of Teacher Education

Volume 5 Issue 1 Northwest Passage: Journal of Article 7 Educational Practices

January 2007 Public Perception: New Math and Reform Mathematics

Daniel L. Canada Eastern Washington University

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Recommended Citation Canada, Daniel L. (2007) "Public Perception: New Math and Reform Mathematics," Northwest Journal of Teacher Education: Vol. 5 : Iss. 1 , Article 7. DOI: https://doi.org/10.15760/nwjte.2007.5.1.7

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Public Perception: New Math and Reform Mathematics

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Daniel L. Canada Eastern Washington University ABSTRACT

Since connections are made in the public mind between current reform ef­ ~ forts in mathematics education and the changes of the past which were collectively 11 called "new math,", the purpose of this paper is to examine these two movements more closely. First, the beginning of both movements is examined, including not L only a look at the supporters of each movement, but also an examination of their 1: initial motivations. Next, the implementation of each movement is described, both by pro.filing the main features and by looking at how they were actually put into L practice. Lastly, the impact of these movements is detailed, by characterizing some b of the reactions they generated. Since a well-informed public is crucial to issues t I ~ I of educational reform, clarifying the features of the respective movements is one way to help smooth the journey towards improved mathematics education. . t Introduction tocollis, 2000, p.l). Newsweek portrayed I California's back-to-basics approach as a I' When the Portland Public School reaction against "this generation's version District voted in 1999 to adopt a different of 'new math'" (Kantrowitz & Murr, 1997), t mathematics curriculum, a list of Frequent­ and even the phrase "New-New Math" is ly Asked Questions (and answers) was frequently applied to contemporary trends, made available for public information. The which the U.S. World and News Report de­ second question addressed the concern: "Is scribed as producing the "dumbing-down this 'New Math' or some other kind of ex­ of math education" (Leo, 1997). Also, Ma­ perimental program?" (Clark, 1999). This clean's magazine gave the label "new new question reveals the link in the public mind math" to the National Council of Teacher of between the current changes in math educa­ Mathematics' "wave of curricular reforms" tion and the changes of the past which were I (Sheppard, 1998), and Time said this label I collectively called "new math" by many. recalls "the ill-fated New Math fad of the I Why would the public make such a con­ 1960s and '70s" (Ratnesar, 1997). It is easy I nection? For one thing, the media feeds this to see how people today get the sense that I perception: A New York Times article, for New Math has a strong bearing on current ! example, described reform efforts in math­ efforts to reform mathematics education; i ematics education as being "a cousin of the these latter efforts will be collectively re­ 'new math' popular in the 1960's" (Har- ferred to in this paper as Reform Mathe- I I I Published by PDXScholar, 2007 1 ~ : SPRING 2007 51 I,. ' "" ... .;., ...... --

Northwest Journal of Teacher Education, Vol. 5, Iss. 1 [2007], Art. 7

matics, to use a term employed by both ad­ each movement will be described, as well vocates and opponents (Clopton, 2001; Van as their respective implementation and im­ de Walle, 1999). As the Wall Street Jour­ pact. Some implications for the future of nal stated succinctly: "Not surprisingly, the math education as well as connections to New New Math has a lot in common with larger issues in educational reform are of­ the Old New Math" ("Math Wars," 2000). fered in conclusion.

Table 1. Comparison ofInception

/&. '-/ New Math Reform Mathematics w ~" .,. '"' • Origins in the 50s & ending in 70s • Origins in 80s & ongoing I I When • Prominent catalyst: Sputnik launch • Prominent catalyst: Publications like Agenda for Action (1980) and Nation at Risk (1983) I (1957) •. ] • New developments in mathematics • New research in how people learn math :i Increased federal money • Increasing technological developments ' Why . ) " . Dissatisfaction with traditional math • Dissatisfaction with traditional math • Primarily mathematicians • Primarily math educators .~ Who • Interested in creating more mathematicians • Interested in mathematics for all I .• ~ Garnering public support for educational Inception ' reform efforts cuts across all subjects, and the topic of mathematics provides an ex­ Looking first at the origins for New cellent example of why the need for such Math and then for Reform Mathematics, support is so acute: Rhetoric, often fueled the goal is to shed light not only on when by the media or vocal parental critics, often the movement began taking shape, but also drowns out and distorts the message of edu­ on why it occurred and who were some of cators. After all, as some of the earlier quo­ the main people and organizations behind tations show, comparisons of New Math to its development. Table 1 presents a brief Reform Mathematics are not meant as flat­ comparative overview, which is then sup­ tery. Indeed, because "the public memory ported by further details within this sec­ of the 'new math' period in mathematics tion. education is, to this day, an image of mis­ takes and failures" (Fey & Graeber, 2003, New Math p. 498), it is appropriate to not only exam­ .... ine this comparison more closely, but to When ...: It is difficult to put a firm " advocate for changes in public perception I. date on the beginning of New Math, be­ so that essential tenets of Reform Math­ cause of the variation in time spans which ematics might be more clearly articulated. are offered in reference to this movement. Therefore, the purpose of this paper is to The National Advisory Committee on explore the two movements of New Math Mathematical Education recommended and Reform Mathematics, illuminating tliat the term "new math" should be used as some commonalities among and differ­ a historical label for a variety of math edu­ ences between them, and to emphasize the cation developments which took place "be­ importance of changing public perception tween 1955 and 1975," but by also describ­ as it relates to mathematics education. To ing New Math as a "vague phenomenon", accomplish this purpose, the inception of it seems that even these years are open to

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interpretation (NACOME, 1975, p. 22). math" (Fey & Graeber, 2003, p.492). Fur­ Others agree that the New Math was not ther motivation for New Math was provided so much a distinct entity as a label for an by the federal government, which played a era when many changes were taking place pivotal role in the fifties by creating new (Stanic & Kilpatrick, 1992). While some organizations such as the National Science put the origins of New Math in the early Foundation (NSF) in 1950, and by passing fifties (Hirschi, 1977) and others point to legislation like the National Defense Edu­ the late fifties (Lindquist, 1980), Usiskin cation Act in 1958. The NSF contributed (1985) goes the farthest in terms of narrow­ subsequent financial support to new and ing down the date of inception by claiming experimental curriculum, and continued to "the new math was sparked by the launch increase its activities in mathematics edu­ of Sputnik in October 1957" (p. l). This cation in the late fifties (NCTM, 1970; Lap­ claim is contradicted by Davis (1967), who pan & Wanko, 2003). cites J. Goodlad in asserting that "it was not Sputnik that started it all" (p.3). Although Who - The proponents of New Math acknowledging the popular benchmark of included, as mentioned above, the NSF as the 1957 Sputnik launch, Rosskopf (1970) well as the CEEB, whose report was called wrote that "it is difficult to say where it all "one of the most influential policy leader­ began in the 1950s" (p. 23). ship documents of the 'new math' period" (Fey & Graeber, 2003, p. 495). Other advo­ Why - Examining some of the moti­ cates include the University of Illinois Com­ vating factors helps to see why New Math mittee on School Mathematics (UICSM), would emerge sometime in the fifties. Dis­ which was founded in 1951 to investigate satisfaction with the status quo was already problems with the secondary school cur­ present, and the traditional teaching of riculum (NCTM, 1970). Also, the School mathematics prior to the fifties was gen­ Mathematics Study Group (SMSG) came erally seen as unsuccessful (Kline, 1973; into being in 1958 and became the "largest Kraus, 1978). Mathematics education was and most prominent of the new math cur­ seen as a failure in part because the tradi­ riculum reform projects" (Kilpatrick, 1997, tional curriculum did not adequately reflect p.956). Although the SMSG was a result of contemporary mathematics - it reflected an­ a meeting of "eminent research mathema­ tiquated mathematics (Bidwell & Clason, ticians" who were interested in improving 1970; Kline, 1973). Emerging themes from school mathematics (Rosskopf, 1970, p. the field of math - themes such as struc­ 25), the advisory committees for the SMSG ture, proof, generalization, and abstraction actually reflected a wide variety of interests. - were underrepresented: "In other words, For example, among the 26 members of the the mathematics curriculum was extraordi­ first committee were people representing narily out of date" (NCTM, 1970, p.69). "all areas of mathematics education: col­ Prompted by the Educational Testing Ser­ lege, high school, experimental programs, vice (ETS), a Commission on Mathematics the NCTM, and the [CEEB's] Commission appointed by the College Entrance Exami­ on Mathematics" (NCTM, 1970, p. 75). nation Board (CEEB) made recommenda­ The main force behind New Math, how­ tions stressing the need for major reforms ever, really seems to be mathematicians in the school curriculum to bridge the gap (Stanic & Kilpatrick, 1992). As Hart (1985) between school and college math (Bidwell puts it, "pure mathematicians were the ma­ & Clason, 1970; Rosskopf, 1970; Kilpat­ jor proponents" of New Math (p.336), and rick, 1997). These changes were needed it is worth noting that the Cambridge Con­ "so that secondary school curricula would ference consisted mostly of pure mathema­ better reflect facets of pure and applied ticians (NCTM, 1970). This fits with the

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motivations and timeline suggested earlier: Why - Among the motivating fac­ If World War II brought an "unprecedented tors in the Reform Mathematics, a key sim­ growth in mathematics" (NCTM, 1970, ilarity to New Math is the reaction against p.70), and many new applications and the­ the status quo - the sense of dissatisfaction ories of math were being expounded, the with what mathematics was taught and most natural source of enthusiasm for these how it was being taught. The "documented developments would be from within the failure of traditional methods of teaching field of math. mathematics" (Battista, 1999, p. 426) is a clear echo of sentiments in the fifties. The Reform Mathematics Back-to-Basics movement of the seven­ ties was seen by some as a terrible failure When - Looking next at Reform (Offner, 1978; O'Brien, 1999), and alarm Mathematics, a similar difficulty occurs in was expressed at the poor performance of locating the origins chronologically. There students on international math tests (Shep­ is support for putting the origins of Re­ pard, 1998). The 1989 NCTM Standards form Mathematics in the eighties, since the were seen as a response to "the consistently NCTM'sAgenda for Action was released in poor math scores of U.S. Children" (Ratne­ 1980, and this document pointed out needed sar, 1997). Data used to show low achieve­ direction in math education (NCTM,1980). ment included those gained from the Na­ Also, the year 1983 saw the publication of tional Assessment of Educational Progress A Nation at Risk, which lamented broad (NAEP) and the Second International practices in overall education, not just in Mathematics Study (SIMS). Other moti­ mathematics. Kilpatrick (1997) mentions vations for change came not so much from how the latest reforms had been building up developments within mathematics as from for over a decade, and he cites A Nation at developments in mathematics education, Risk as helping to set the tone of reform. and this is attributable to the increased ac­ Certainly, just like Sputnik helped link tivity of the mathematics education research 1957 to New Math, the NCTM publication community (Lester & Lambdin, 2003). Re­ of its Curriculum and Evaluation Standards search into the ways in which people learn helped link 1989 to Reform Mathemat­ mathematics has strongly influenced both ics, but in actuality there were contribut­ the content and the pedagogy which char­ ing forces at work prior to those years. M. acterizes Reform Mathematics (O'Brien, Battista (1999) claims "the movement to 1999; Hartocollis, 2000). Also, increasing reform mathematics education began in the technological developments, with a look mid-1980s" (p. 426), but he also goes on to towards the meeting the needs of the fu­ cite the 1989 release of the Standards as the ture, helped motivate Reform Mathematics "most conspicuous component of reform." (NCTM, 1989; NCTM, 1980). Finally, al­ Certainly Newsweek portrayed Reform though by the early seventies "distrust of Mathematics as being based on the 1989 federally funded materials was increasing" Standards (Kantrowitz & Murr, 1997), and (Lappan & Wanko, 2003, p. 918), again the Time concurred that "it all started in 1989" availability of federal funds has and contin­ (Ratnesar, 1997). It does seem likely that ues to help drive Reform Mathematics. the ideas behind Reform Mathematics were percolating even earlier than the eighties, Who - Included among the many however, and Hill (1983) noted that "the proponents of Reform Mathematics is the mathematics education community seemed NSF, which again provided support for new to be groping for a clearer focus and sense curriculum (Battista, 1999). Naturally, the ,·.• of direction" (p. 1) even in the seventies. NCTM is seen as the main figurehead in ,.

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Reform Mathematics, based on the numer­ Principles and Standards for School Mathe­ ous references to their 1989 Standards as matics (PSSM) for release in the year 2000, being the genesis of the movement. Kilpat­ the NCTM asked major math organizations rick (1997) assigns much of the leadership like the American Mathematical Society in Reform Mathematics to the NCTM, but (AMS) to work with its own Commission in looking at the people who make up that in shaping the document (Wu, 1997). Thus, organization and who makes contributions the PSSM was "written with significant to its publications, it is clear that there is input from mathematicians" (Addington, a broad spectrum represented: Educators, Clemens, Howe, and Saul, 2000, p. 1073). math educators, school teachers, math­ A final key group which transcends the ematicians, and more (Apple, 1992). The NCTM and has a vested interest in Reform 1989 Standards were actyally developed Mathematics is the mathematics education by groups comprised mainly of teachers research community mentioned earlier: (Romberg, 1992a). In minimizing the role This group vastly sharpened its profession­ of parents in these documents, however, al identity during the seventies (Lester & the NCTM effectively marginalizes these Lambdin, 2003). critical stakeholders: As Peressini (1998) notes, "parents receive minimal attention in Implementation the analysis and prescriptions that are ad­ vanced by the organization" (p. 568). Cer­ Having looked at some of the de­ tainly parents are not currently said to be fining issues of when, why, and who, the ardent advocates of Reform Mathematics at next step is to examine what were some of this time. Neither could it be said that the the key features of the content and intended mathematicians are the major proponents pedagogy for each movement and the ex­ of Reform Mathematics, and this is a big tent to which they were or have been imple­ distinction from New Math. Instead, many mented. Table 2 presents a brief compara­ critics of Reform Mathematics are math­ tive overview, again supported by further ematicians such as James Milgram, who, details within this section. in written testimony to the U.S. Congress, claimed that "the level of mathematical un­ Table 2. Comparison of Implementation derstanding on the part of the mathematics educators on this panel was unimpressive" (Milgram, 2000, p.l). In developing its New Math

Content - Among the content of Table 2. Comparison ofImplementation

"' ,,, ' '""~ ~ New Math Reform Mathematics w $ ''', ,,, '' , • Associated w/ characteristic themes: . Transcends easy characterization: o Heavy on set theory & logic o More attention on topics like data analysis Content o Precise language & symbolism o Less attention on topics like long division • New topics like probability & statistics . New focus on use of technology • Socratic, or Discovery learning . Constructivist interpretation Deductive approach . Active rather than passive approach to learning Pedagogy . • Understanding principles instead of • Priorities on conceptual understanding as well relying on rote memorization as problem solving and aoolications , . Perception is of widespread use • Perception is of widespread use . Reality is that few curricula actually . Reality is that few curricula actually reflects Extent reflected tenets ofNew Math, with tenets of Reform Mathematics, again with questionable implementation questionable implementation

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Northwest Journal of Teacher Education, Vol. 5, Iss. 1 [2007], Art. 7 11 New Math curricula, there was an empha­ some key features of New Math included sis on unifying concepts like sets, relations, the change of content to reflect a rigorous and functions, tied with a strong sense of development, and a set of unifying math­ structure (Kilpatrick, 1997). Set theory ematical principles. Also, students were to and axiomatics, were seen as essential in­ gain an understanding of these principles gredients to add to the school curriculum, instead of simply relying on rote memori­ and also served as a "framework around zation (Crabtree, 1997). which to reorganize that curriculum" (Stan­ ic & Kilpatrick, 1992, p. 412). New Math Extent - Of all the facets to the im­ was also structured to lend itself to precise plementation of New Math, the most strik­ language and heavy symbolism, and among ing is the extent of implementation. From specific new topics recommended were the many current references to New Math, logic, modern algebra, probability, and sta­ and copious literature on the movement, it tistics; actual materials included set theory, is easy to get the idea that New Math was different base systems, congruences, and widely used in an extremely high number symbolic logic (NACOME, 1975; Kline, of schools: New Math "swept the coun­ 1973; NCTM, 1970). Other adjustments to try" (Hart, 1985, p. 334), and "introduced the contents were the merging of plane ge­ millions of students to math arcana like set ometry with solid, and the placing of trigo­ theory and congruences" (Ratnesar, 1997). nometry within the second-year algebra Kline (1973) agrees that hundreds of texts course (Usiskin, 1970). The first course in were written and that millions of children UICSM's four-year curriculum contained were being taught New Math, with "tens of the distinction between number and numer­ thousands of teachers" having experience al, as well as properties of number systems with it (Mueller, 1966, p.621). A picture like the commutative property (Bidwell & of widespread use is painted: Even in the Clason, 1970). midst of the movement, the UICSM had the view that the nation's school were "ready to Pedagogy - Regarding pedagogy, move in large numbers" towards the curric­ the Socratic, or discovery, approach re­ ulum of the New Math (Hale, 1961, p.618). ceived much attention in New Math (Price, Therefore, given the references suggestive Kelley, & Kelley, 1977). As supported by of massive usage, it is all the more surpris­ psychologistJ. Bruner, discovery learning's ing to realize how many questions abounded essential tenet was that "the learner dis­ concerning the extent of implementation of .I covers things for himself' (Bruner, 1960). New Math. That is, in the individual class­ ' I Math teachers were urged to use discovery rooms, there was little research to show learning, which was naturally opposed to how New Math had been put into practice a passive acceptance of statements about (Price et. al., 1977; Hirschi, 1977). New math (Fey, 1979). The deductive approach Math actually seems never to have made it was incorporated so that students could into the majority of schools (Kline, 1973): start with axioms and prove conclusions Kilpatrick (1997) wrote that "in most class­ - Not only in geometry, but in arithmetic, rooms the reforms were never really tried" algebra, and trigonometry (Kline, 1973). (p.957), and Hirschi (1977) claimed that ·' While the SMSG did not explicitly experi­ New Math was not taught in any "signifi­ ment with pedagogical methods, the UIC­ cant percentage" of schools (p.244). The SM did encourage student discovery as an NACOME also questioned the extent to instructional procedure (Hale, 1961; Begle, which New Math was actually used, and 1973). In fact, "discovery teaching and others suggested that nationwide data was learning became the hallmark of the UIC­ needed to explore the question (Fey, 1979; SM program" (NCTM, 1970, p.254). Thus, Hirschi, 1977).

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the name is derived "from the view that Reform Mathematics learning is primarily a process of concept construction and active interpretation" Content - Although the NCTM (Schifter & Fosnot, 1993, p.8). In Reform Standads do not encompass all aspects of Mathematics, students are to personally this movement, they have functioned as an develop their own math ideas and make umbrella which covers a broad spectrum . their conclusions, and these ideas "must be of common elements (Apple, 1992). Thus, personally constructed by students as they the content advocated across the spectrum try to make sense of situations" (Battista, of documents from the 1989 to the 2000 1999, p.429). Romberg (1992b) wrote that Standards give a reasonable representation Reform Mathematics posits learning not as of the general tenets commonly held for the the absorption of others' knowledge, but Reform Mathematics movement. Where­ as something which much be actively con­ as New Math had some defining content structed by the learner. The sense of math themes (such as set theory and properties learning as an active, rather than passive, of number systems), the themes for Reform process - whereby relevant problem situ­ Mathematics transcend easy characteriza­ ations are used to help students "actively tion. In the 1989 Standards, for example, construct knowledge" (Kilpatrick, 1997, p. there were degrees to which certain content 959) - is no doubt among the defining char­ should receive increased or decreased at­ acteristics of Reform Mathematics. tention. Probability and statistics were to be emphasized more, while computational Extent - Even though there are ma­ skills like long division were to be empha­ terials and training which model Reform sized less. Modeling and data analysis are Mathematics tenets, however, there is two other examples of content to receive again Gust as in New Math) a question as more attention, and another broad theme to how widespread is the actual use of Re­ of Reform Mathematics' content is an em­ form Mathematics curriculum, or how well phasis on the uses of technology (NCTM, the materials are being used. Like in New 2000). Many of these changes were guided Math, the perception may be that Reform by parallel changes in society: For example, Mathematics is a dominant movement in as we increasingly become a data-driven America, just as it is supposed to be "flow­ culture, bound up in technology complete­ ing like hot lava" in Canada (Sheppard, ly unavailable a generation ago, the math­ 1998). Time magazine expected nearly half ematical needs have likewise changed. of elementary students to be under the in­ fluence of Reform Mathematics in 1997; Pedagogy - While the content of it mentions how the NSF spends $10 mil­ Reform Mathematics may differ in empha­ lion a year on curricular materials, which sis from that of traditional curriculum, it is can be used by the 40 states that had in­ in the method of teaching that this move­ stituted Reform Mathematics programs in ment draws the most distinction. Advo­ their schools (Ratnesar, 1997). Yet there cating real-life applications and problem is no real evidence that constructivism has solving, Reform Mathematics curriculum allowed Reform Mathematics to become a encourages students to reason and com­ full-scale revolution in math education (Kil­ municate mathematically (NCTM, 2000): patrick, 1997). O'Brien (1999) contends In this movement, "students must learn that Back-to-Basics has not only always mathematics with understanding, building been the dominant approach in schools, new knowledge from experience and pri­ but that it continues to be dominant. As he or knowledge" (p. 20). Labels are easy to notes, activity-based math is "unknown come by, and constructivism fits the bill: in the majority of American classrooms"

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(p.435). When O'Brien asked colleagues in .of New Math," UICSM's Max Beberman various states what proportion of elemen­ was reported by Time to have been con­ tary school classrooms were actually con­ cerned that New Math was lessening stu­ structivist-minded, the figures were never dents' abilities to compute (Mueller, 1966). above 20%. For all the talk about Reform Furthermore, Beberman said that New Mathematics, it seems less likely there is Math failed to relate to the real world, that .,I widespread practice of its core features, it emphasized "esoteric branches of math­ ' and more likely "traditional mathematics ematics at the expense of fundamentals," teaching .. .is still the norm in our nation's and that he "feared that 'a major national schools" (Battista, 1999, p.426). scandal' may be in the making" (Kline, 1973, p.110). In fact, the era of New Math Impact is seen as a sort of black eye in the history of math education - if not scandalous, then Among the many components of at least a poor show (Fey & Graeber, 2003). education that can be impacted by large­ The movement was widely ridiculed, and scale reform efforts, such as inservice and Offner (1978) affirms the popular concep­ preservice teacher training, federal or state tion of New Math having had "disastrous funding, the components most relevant to results" (p. 211). Back-to-Basics became this paper are the public and academic re­ the refrain in the seventies, and "New Math actions, with a special concern for public overwhelmingly was rejected" (Crabtree, perception to changes in educational policy 1997). and practice. Once again, Table 3 presents a brief comparative overview for New Math Academic Reactions - It is likely, and Reform Mathematics, supported by however, that most schools never seriously further details within this section. embraced New Math and thus had noth­ ing to reject: Aside from the experimental New Mathematics curriculum of SMSG and UICSM, com­ mercial publishers were only producing Public Reactions -In looking at the texts with superficial changes (Hirschi, impact New Math had, it is easy to agree 1977). New Math increased the attention with Kilpatrick (1997) that "reaction was given to test scores, and this concern was swift" (p.956), but it is important to remem­ reflected throughout the seventies (NCTM, ber that the beginnings of New Math were 1980; Carpenter, Coburn, Reys, and Wil­ difficult to define with precision. The tone son, 1975). Residual effects of New Math of a 1956 Time magazine article expressed are also seen in some of the symbolism and optimism at the New Math movement, terminology of today's curricula, and even and concerning public opinion, F. Mueller courses such as precalculus are a testament (1966) reports that 1956-65 were the "hap­ to New Math's impact (Kilpatrick, 1997). :I py years" for New Math (p. 620). There Another big impact was that New Math I were discussions about parental difficul­ helped further develop the math education ties in helping their children with the New community (Stanic & Kilpatrick, 1992). Math, and a result was the publication of Kline (1973), towards the end of his book books helping explain the math to the par­ describing the failure of New Math, called ents (Rosenthal, 1965). In 1962, a memo­ for leadership from people who are expe­ randum against New Math was signed by rienced in both math and education. With 75 mathematicians and published (Kline, a conciliatory spirit, New Math advocates 1973). By1965, more reservations about were encouraged to work with those of the New Math began to manifest themselves to Back-to-Basics approach for the common .. a broader audience: Under the title "Trials goal of improved math instruction (Kraus, ::; https://pdxscholar.library.pdx.edu/nwjte/vol5/iss1/7 DOI: 10.15760/nwjte.2007.5.1.758 NORTHWEST PASSAGE 8 Canada: Public Perception: New Math and Reform Mathematics

1978). Cossey, 1999). Public opinion remains a miasma of distorted perceptions. In particu­ Reform Mathematics lar, the role of parents has remained limited, and relegated to discussions in which they Public Reactions - Analysis of the . are "addressed as barriers to mathemat­ impact of Reform Mathematics must be ics education reform" (Peressini, 1998, p. prefaced by the comment that, unlike New 568) Math - which had some form of conclusion at least in the seventies (NACOME, 1975) Academic Reactions - One effect - this movement is still ongoing. Opposi­ thus far has been the continued develop­ tion to Reform Mathematics. has indeed ment of new curricula, and while there are been building, but Kilpatrick (1997) writes many reform-based materials available, it is that "this time around, the negative reaction still unclear how well Reform Mathematics to reform proposals and activities has been is actually being implemented in the class­ slow to come" (p. 958). Because of the ad­ room (O'Brien, 1999). Most commercial vent of the internet as a popular informa­ texts "consist of traditional curricula with tion medium, more and more criticism and enough superficial changes" so that pub­ reactions against Reform Mathematics are lishers can say their materials are consistent posted on the web (Sheppard, 1998; Kilpat­ with Reform Mathematics (Battista, 1999, rick, 1997). p.433). Curcio (1999) supports this claim, Even an anti-reform letter, signed maintaining that although new curricula by many mathematicians just as in the era "may claim to support the reform efforts, of New Math, can be found online (Mathe­ many are pseudo attempts at fulfilling the matically Correct, 2005). Critics ascribe la­ goals of reform" (p. 3). Another effect of bels such as "math lite," "fuzzy math," and the movement is to again assert the primacy "fuzzy crap" to the Reform Mathematics ef­ of test scores in the public eye. Low scores forts (Crabtree, 1997; Black, 2000). Given in the Third International Mathematics and the negative connotations of New Math, it Science Study, for example, cause critics can be seen why most references to Reform to blame Reform Mathematics and clamor Mathematics as "New New Math" are not for improvements in basic skills (Cossey, generally intended as endorsements (Ratne­ 1999; Crabtree, 1997). Reform Mathemat­ sar, 1997; Leo, 1997). Traditionalists, who ics also highlights the position of the math advocate a Back-to-Basics approach, are education community (Lester & Lambdin, gaining momentum in their revolt against 2003), and Battista (1999) calls for deci­ Reform Mathematics, and California re­ sions on curricula to be placed in the hands cently enacted state standards that reflect of professional math educators. Calls for this traditional approach (Crabtree, 1997; different groups to work together toward

Table 3. Comparison ofImpact

' ' New Math Reform Mathematics . Many parents & mathematicians concerned . Many parents & mathematicians concerned Public . Media gives voice to concerns . Media and Internet gives voice to concerns Reaction . Overwhelming sense ofrejection . Intense ongoing debate involving stakeholders . Mainstream curricula has limited carryover . Mainstream curricula has limited carryover Academic . Promoted development of math education • Highlights position and continued development Reaction research community of math education research community • Increased attention to test scores • Increased attention to test scores

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the common goal of better math education ongoing attempts at educational reform that have been frequently heard (Wu, 1997; Bat­ "has continued unabated in this [20th] cen­ tista, 1999). tury" (p. 3 ). He notes familiar and persis­ tent debates over teacher-centered versus Connections & Conclusion student-centered instruction, and mentions the many metaphors for students such as Like in New Math, there is a strong the "blank slate" or the "rich clay" or the interacion between public opinion and "flourishing garden." What is particularly the Reform Mathematics movement. The interesting is his attention to historical cy­ Agenda for Action acknowledged this im­ cles, and how in the mid-1800s educational portance, mentioning that such public opin­ reformers reacted against "teacher-centered

ion needs to be well-informed (NCTM, instruction with its emphasis on a textbook" ,I' 1980). Others affirm the need for educating (p. 4). As he invokes images of cyclical re­ the public in the ways of Reform Mathe­ form, and the picture of the swinging pen­ matics (Jacob & Akers, 2000), and Battista dulum, it is easy to place the Math Wars in (1999) cites the public lack of knowledge a sort of historical context amongst those about Reform Mathematics as one of the many general educational reforms attempts main impediments of the movement. Isolat­ that have preceded the current era and those ed examples of alleged failings of Reform that will follow. Cuban specifically men­ Mathematics are cited in the push to return tions the need for public support, noting to traditional teaching, and this reaction that "without credibility, there is no chance is spearheaded by well-organized groups of the schools being viewed as successful" of extremely vocal critics (O'Brien, 1999; (1990, p. 11). In focusing squarely on the Battista, 1999). In fact, writes Van de Walle issue of public confidence in education, (1999), "Ten years after NCTM's release Loveless (1990) describes the fervency of of the Curriculum and Evaluation Stan­ educational reform critics and defenders, dards for School Mathematics, this country citing cliches that transcend disciplines, is having a wrenching debate about what such as how "education now stresses 'high­ should be taught in mathematics and how er level thinking and problem solving, not it should be taught. Debate has degenerated rote learning"' (p. 128). He stresses that to 'math wars"' (p. 1). It is this effect, the "despite the endless rhetorical wars waged public perception quagmire of the Math by critics and defenders of public schools, Wars, which remains a contentious source [... ] research on public attitudes toward ed­ I of consternation to the Reform Mathemat­ ucation in confined to a handful of texts and I i ics community, for whom the current chal­ articles" (p. 128). This lack of research on lenge is to "convince the general public public attitudes suggests that what we see of the credibility of their work" (Lester & playing out in the media is truly a war of Lambdin, 2003, p. 73). This challenge per­ rhetoric without !1 winning strategy. t , I vades the field of mathematics education, I ' and is valid for many other disciplines be­ In conclusion, Addington (2000) sides mathematics. may be right in saying that reforming math education is "like turning the Titanic around In fact, when looked at in the larger with a canoe paddle" (p. 1072), but caution context of educational reform, we see the is in order when comparing Reform Mathe­ same dynamic of misrepresentation, in­ matics to New Math. The Titanic, like New flamed rhetoric, and public criticism con­ Math, sunk: Reform Mathematics remains nected to a range of specific topics and di­ afloat. Though sharing some commonalties, rected at public education in general. Writing Reform Mathematics should not be seen as a over a decade ago, Cuban (1990) describes mere revisitation of New Math. In fact, Re-

https://pdxscholar.library.pdx.edu/nwjte/vol5/iss1/7 DOI: 10.15760/nwjte.2007.5.1.760 NORTHWEST PASSAGE 10 ----C'll Canada: Public Perception: New Math and Reform Mathematics

form Mathematics is not New Math. Even SMSG. Mathematics Teacher, 66, 207- a group critical of Reform Mathematics, 214. California's Mathematically Correct, notes in its website that New Math "has nothing Bidwell, J., & Clason, R. (1970). Readings to do with the changes to math education in the History of Mathematics Education. today" (2005, p.1), but the common public. Washington, DC: National Council of association remains. To gain a public will­ Teachers of Mathematics. ing to advocate for Reform Mathematics, it makes sense to listen to their concerns and Black, L. (2000, April 12). Math teach­ to be able to articulate the perspectives of ers debate traditional vs. New-New Math. the ongoing movement to improve mathe­ Chicago Tribune. Retrieved December 4, matics teaching and learning. It is important 2000, from http://www.chicago.tribune. for the future of math education to continue com defining and clarifying Reform Mathemat­ ics efforts, and to draw distinctions be­ Bruner, J. (1960). On learning mathemat­ tween contemporary programs and those ics. Mathematics Teacher, 53, 610- 619. of the past. Romberg envisioned decades to Carpenter, T., Coburn, T., Reys, R., & fully enact the goals of the 1989 Standards, Wilson, J. (1975). Results and implications which he helped author (Ratnesar, 1997). of the NAEP mathematics assessment: Over fifteen years later, it is clear that Re­ Secondary school. Mathematics Teacher, form Mathematics has a long way to go; the 68, 453-471. path will be smoother and the burden made lighter if the baggage of the New Math stig­ Clark, A. (1999). Frequently asked ques­ ma is shed. Since a well-informed public tions about the math adoption. Retrieved is crucial to issues of reform, clarifying the November 10, 2000, from http://www.pps. features of the respective movements is one kl 2. or. us/ district/ depts/itss/ppsmath/april/ way to help further the journey towards im­ faq.html proved mathematics education for all. Clopton, P. (2001). Reform Mathematics References Education: How to "Succeed" Without Re­ ally Trying Retrieved December 10, 2001, Addington, S., Clemens, H., Howe, R., & from http://mathematicallycorrect.com/re­ Saul, M. (2000). Four reactions to Princi­ form.htm pals and Standards for School Mathemat­ ics. Notices of the American Mathematics Cossey, R. (1999). Are California's math Society, 47, 1072-1079. standards up to the challenge? Phi Delta Kappan, 80, 441-443. Apple, M. (1992). Do the standards go far enough? Power, policy, and practice Crabtree, S. (1997). Warm and fuzzy math in mathematics education. Journal for meets cold resistance. Insight on the News, Research in Mathematics Education, 23, 13, 12-13. 412-431. Cuban, L. (1990). Reforming Again, Battista, M. (1999). The mathematical Again, and Again. Educational Research­ miseducation of America's youth. Phi er, 19, 3-13. Delta Kappan, 80, 425-433. Curcio, F. (1999). On my mind: Dispelling Begle, E. (1973). Some lessons learned by myths about reform in school mathemat­ ics. Mathematics Teaching in the Middle

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School, 4, 282-285. Hirschi, L. (1977). The "new math." Math­ ematics Teacher, 24, 241-245. Davis, R. (1967). The Changing Curricu­ lum: Mathematics. Washington, DC: As­ Jacob, B., & Akers, J. (2000). "Research sociation for Supervision and Curriculum Based" Mathematics Education Policy: Development, NEA. The Case of California 1995-1998. Inter­ national Journal for Mathematics Teach­ Dean, B. (2006, June 27). Math test fails ing & Learning. Retrieved October 1, state. Spokesman-Review, p. B4. 2002, from http://www.intermep.org

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