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Abstract
This article reports on a literature review of 49 articles that cited a single monograph written in 1981 about early learning in mathematics to make claims of similarity or difference across lines of race and class in early mathematics. The review found that while about two-thirds of the articles cited the monograph to make claims of no significant differences across race and class in early mathematics performances (which is the perspective taken by the monograph’s authors in their conclusion and summary), almost one-third of the articles cited the monograph to establish significant social class differences in early mathematics, despite the claims of the monograph’s authors to the contrary. Similarly, a major US government report on early childhood mathematics cited the monograph to establish both race and social class differences. The reasons for and implications of these findings are discussed, including the tendency in recent years to understand race and class in US education primarily in terms of achievement gaps.
Recently, US educational organizations aligned with both mathematics and early childhood education have demonstrated renewed interest in the mathematical learning of young children (National Council of Teachers of Mathematics, 2010; National Council of Teachers of Mathematics and National Association for the Education of Young Children, 2010; National Research Council, 2009). Many texts drawing attention to early mathematics have framed their calls to action with a particular kind of equity argument—one which suggests that, in the USA, poor children and children of color fall behind in mathematics at very young ages, receive little support for mathematical learning in their homes, and require significant early intervention on the part of schools.
For example, in the introduction to their report, the authors of Mathematics Learning in Early Childhood: Paths toward Excellence and Equity justify particular attention to low-income and minority students by reporting that “young children from disadvantaged backgrounds show lower levels of mathematics achievement than children from middle-class and higher status backgrounds” (National Research Council, 2009: 12). Later in the report, they summarize the research around socio-economic status as showing that “striking individual differences in number sense emerge early in life and are present by the time children enter preschool” (96), and write that “some findings show that young children from low-income families receive less support for mathematics in their home environment than do their middle-income peers” (98). Similarly, the report describes research around race as demonstrating differences in young children’s learning outcomes across demographic groups. The earlier National Research Council (2005: 173) report on elementary mathematics in the USA, written by another set of authors, makes similar claims in the section on children’s early learning, writing “that poor and minority children entering school do possess some informal mathematical abilities but that many of these abilities have developed at a slower rate than in middle-class children.”
The summaries of research on race and class differences in young children’s mathematical performances provided in wide-reaching national reports in the USA overwhelmingly tell this same story—that significant differences in mathematical thinking and skills across demographic groups appear at very young ages. However, empirical studies are far less monolithic. While some studies (e.g. Aslan, 2013; Saxe et al., 1987) have found significant differences in children’s mathematical performance based on class in particular, several (e.g. Seo and Ginsburg, 2004; Tudge and Doucet, 2004) have found no significant differences in either young children’s mathematical performances or their engagement with mathematics in their homes, and few have reported significant differences in children’s early learning as a function of race or ethnicity. In addition, many studies document similarities in addition to differences across class lines. For example, Jordan et al. (1994) reported no differences across class lines on non-verbal tasks, while children from middle-income families performed better on verbal tasks. Given the contradictory findings in recent empirical research on the topic, I was curious about the way this line of research has been summarized in recent influential government reports on early childhood mathematics. These reports, which overwhelmingly emphasize difference, give little attention to the work that has found similarities.
In my initial literature review, I found, surprisingly, that in addition to contradictory categorizations of the body of work on race and class in early mathematics, there were also contradictions in the ways that scholars were reporting the outcomes of single studies, with some claiming that a study provided evidence for significant differences and others claiming that the same study provided evidence of no significant differences. This phenomenon was of interest to me not only because of the light that it could shed on equity work in early mathematics, but also because of the possibility that an exploration of these differences in interpretation could provide insight into the work of research more broadly. At the heart of the research enterprise lies a faith that we, as scholars, understand the meaning of each other’s reports, whether we agree with them or not. If we cannot, as a field, come to a shared agreement on whether a particular empirical study demonstrates a premise or its opposite, then we have a significant problem to address in the way we communicate our findings. In order to make my question researchable, I decided to focus on the way one particularly influential and frequently cited monograph was drawn on by various scholars.
The monograph by Ginsburg and Russell (1981) investigated the relationship of class and race to young children’s mathematical understandings with two interview studies of preschool and kindergarten children. This monograph has been cited heavily in work around class and race in early mathematics, and continues to be drawn on as evidence in recently published work. I wanted to determine whether scholars citing the monograph used the study to make claims of similarity or difference, and to explore possible explanations for and patterns around differences in interpretation. Guiding my work was the question: How has the Ginsburg and Russell monograph been cited and what does this indicate about the way equity arguments in early mathematics are made?
The monograph
The 69-page monograph by Ginsburg and Russell (1981) reports the results of two studies in which the authors interviewed children using a set of mathematical tasks. The first study compared the performance of 25 poor black children with 13 black and 25 white middle-class children, while the second study compared black and white children from lower- and middle-class families. The children in the study participated in approximately 20-minute interviews with a single university researcher and were asked to do tasks such as identifying sets of more and less; making rows of an identical number of checkers to a given row; adding unseen objects; rote counting; and counting provided objects. In the first study, Ginsburg and Russell found that the poor children performed significantly worse in three tasks than the middle-class children, while they found no significant differences in four tasks, including counting and identifying the number in a set. They found no significant differences at all related to race.
The second study, which used a 2 x 2 x 2 design with race, social class, and grade level, looked at children in both preschool and kindergarten. The children were interviewed with similar tasks to those used in the first study. The authors’ analysis showed no significant social class differences in 13 of the 17 skills assessed. In another skill (cardinality), there was a significant difference in preschool that disappeared by kindergarten. In the remaining three skills (conservation, equivalence, and identifying the greater number), the middle-class children performed better. In relation to race, there were no differences in 15 of the 17 tasks, and the differences measured in the other two tasks were small. Effects related to age were significant in all the skills but one (which was too easy for the preschoolers, so all of them did well) and were larger than any differences attributed to race or class.
In summarizing both studies, Ginsburg and Russell wrote:
In the vast majority of cases, we found no social class differences and at most insignificant trends favoring middle-class over lower-class children. In the vast majority of cases, children of both social classes demonstrated basic competence on the various tasks and similar strategies for solving them. (Ginsburg and Russell, 1981: 51)
About race, the authors wrote: “Study I revealed a lack of racial differences between middle-class blacks and whites. Study II confirms this finding and goes further: it shows fewer racial than social class differences” (Ginsburg and Russell, 1981: 52). Given that the authors’ summary emphatically minimizes differences related to race and class in mathematical learning (which is echoed in their abstract), I found that it was worth investigating the use of this monograph by the National Research Council (2009) report on early childhood mathematics as evidence for both race (99) and class (12) differences. In fact, the Ginsburg and Russell monograph is the only study cited in the National Research Council report on early childhood mathematics after the sentence: “over the past several decades, research has found differences in children’s mathematics learning outcomes as a function of their race/ethnicity” (National Research Council, 2009: 99). This apparent contradiction between the interpretation of the results of the monograph by the authors of the study and the interpretation of the monograph by the writers of a major governmental report on early mathematics points toward a need to dig deeper into the discourse in the empirical research of race and class in relation to early mathematics.
Theoretical framework
In the background of this analysis is a notion of discourse where research, in addition to all other texts, is seen as producing a will to truth (Bakhtin, 1981; Foucault, 1980, 1990). In other words, it is assumed that rather than uncovering objective truth, research works to create certain notions that function as truth in particular times and places. The stories we tell inscribe particular narratives and relations of power in “social institutions, in economic inequalities, in language, in the bodies themselves of each and every one of us” (Foucault, 1980: 90). This is particularly true of stories that are often repeated. The more frequently stories are told, the more likely we are to shape new experiences to conform with these already existing stories, which are dense in the discourse. In addition, discourses can be seen as differentially powerful. Authoritative discourse, or “the word of a father, of adults and of teachers” (Bakhtin, 1981: 342), is often taken as true and is not seen as open to argument or critique. Alternatively, internally persuasive discourse is taken as true by individuals, even though “it is denied all privilege, backed up by no authority at all” (Bakhtin, 1981: 342). From these perspectives, the equity story referred to above—that poor children and children of color struggle with mathematics at the earliest ages—has been produced and reproduced by our repeated retellings until it has become an authoritative discourse. These retellings create a dense discourse around the story that makes it difficult to produce counter-readings, even in the face of contradictory information, although individuals may resist this story as a result of their own internally persuasive discourses. Adopting this discourse-based research perspective creates an ethical demand to examine both the ways in which this story is being produced and the discursive consequences of telling such a story (Parks, 2009). This theoretical frame also invites us to imagine other possible stories, as well as the possible consequences of creating such alternatives in the discourse.
Methods
I began my investigation by using Google Scholar to identify all of the times the Ginsburg and Russell monograph had been cited. On the day of the search (7 June 2013), the search engine identified 194 texts that cited the monograph. Because I was interested in the way informed scholars were contributing to discourse in the research community, I excluded any texts that had not been published in peer-reviewed scholarly journals or monographs. Applying this criterion produced a set of 91 articles. Using a PDF search function, I identified the sections of text in each of the selected 91 articles where the Ginsburg and Russell monograph was cited, copying and pasting this text into a chart, where I also tracked each article’s author(s), topic, year of publication, and journal of publication.
From this set of 91 articles, I coded each article to identify the claims that the Ginsburg and Russell monograph was used as evidence to support. These included some claims that were attributed only to the Ginsburg and Russell monograph and some claims that cited other articles in addition to the Ginsburg and Russell piece. In this process, I identified 101 claims that the Ginsburg and Russell monograph was used to substantiate. (There were more claims than articles because some articles cited the monograph multiple times or made two different claims with a single citation.) Of the 101 claims, 31 were related narrowly to mathematics, often either describing the types of tasks that Ginsburg and Russell used or the kind of mathematical knowledge young children possess. I counted 10 claims as “other” because they referenced a variety of topics, including gender, family structure, and interviewing methods. I focused my analysis on 60 claims related to race or social class made in 49 articles. In analyzing these claims, I coded them based on whether they emphasized differences or similarities in relation to race and social class, and looked for patterns related to the date of publication, type of journal, and topic of the article.
Claims of similarity and difference
As might be expected given the authors’ summary of the monograph in its abstract and conclusion, a majority of the articles cited Ginsburg and Russell (1981) to substantiate the claim that there are few or no significant differences in the early mathematical learning of young children in relation to either race or class. Of the 49 articles identified, 34 made claims related to similarities across demographic lines, including 5 articles by one of the monograph’s authors, which characterized the monograph in much the same way as the authors did in the originally published work. In 1997, Ginsburg (1997: 22) cited the 1981 monograph to make the following claim: “Within the United States there are few racial or social class differences in the development of basic aspects of preschool children’s concrete addition and other key informal abilities.” Other authors emphasizing similarities also made claims that echo the original monograph. For example, Scott-Jones (1984: 272) wrote: “Ginsburg and Russell (1981) found few class or race differences in a study of black and white preschool and kindergarten children’s mathematical thinking.” In general, studies that themselves demonstrated similarities across racial and class lines tended to cite the Ginsburg and Russell monograph as evidence of similarity.
Although claims that emphasized similarity were in the majority, about one-third of the identified articles did use the Ginsburg and Russell monograph to argue that there are significant differences in early mathematical learning related to social class (see Figure 1).
None of the articles used the monograph to argue that there are differences related to race—a claim that the National Research Council (2009) report on early mathematics learning did use the Ginsburg and Russell monograph to make. The Ginsburg and Russell monograph was cited to make a variety of global claims about difference related to social class, such as:
Moreover, a socioeconomic-related gap in children’s numerical cognition has been found during the pre-kindergarten year. (Starkey et al., 2004: 100)
These [low-income] children possess less mathematical knowledge than higher-income children even before first grade. (Clements and Sarama, 2007: 137)
The stability of individual differences in mathematical knowledge makes it especially unfortunate that children from low-income families begin school with much less mathematical knowledge than their wealthier peers. (Siegler, 2009: 118)
Other claims that the Ginsburg and Russell monograph was cited to substantiate include that “economically disadvantaged children are poorly prepared for formal schooling” (Bekman et al., 2011: 412), “children from low-income families lag behind their peers in many conceptual development areas” (Aslan, 2013: 651), and the monograph and similar studies raise “the possibility that there exist systematic SES [socio-economic status] related differences in neuropsychological functioning” (Waber et al., 1984: 1878). In most, although not all, cases, the stance and findings of the article matched the way the Ginsburg and Russell monograph was cited.
As a set, the 16 articles that cited the Ginsburg and Russell monograph to support an argument of significant class difference were published more recently than the articles that used the monograph to make an argument for similarities. Twelve of the 16 articles were published after the year 2003. The reverse is also true. In the 10 years immediately following the publication of the monograph (1981–1991), 18 of the 19 articles published used the monograph to make claims about similarities between social class or racial groups (see Figure 2).
This focus in recent years on social class difference in early childhood is likely informed by the discourse of the broader educational community in the USA, as well as in other countries, which has focused on “achievement gaps” in mathematics measured in the elementary grades. Discourse around the achievement gap in the USA has proliferated since the 1980s, when the term first came into common usage (Gutiérrez, 2008). In fact, the phrase is nearly absent from educational literature in the years leading up to the publication of the Ginsburg and Russell monograph. In an ERIC (Education Resources Information Center) search of peer-reviewed publications, the first article to appear with the phrase “achievement gap” in its title was published in 1989, and there were nine total articles with the phrase in their title published up to the year 2000, when the number began to steadily increase. From 2001–2014, there were 186 articles in ERIC that used the phrase “achievement gap” in their title.
Earlier equity analyses carried out in the USA during the 1960s and 1970s tended to focus on unequal distributions of resources, such as quality textbooks or the amount of school funding. However, over the last few decades, a large amount of equity scholarship has shifted its focus from educational inputs to educational outcomes, such as student achievement scores in tests or course-taking in high school and college (Parks, 2009). This shift from a focus on inputs to a focus on outputs has contributed to a dominant discourse where race and class in relation to mathematics education are primarily understood in terms of differences in performance among demographic groups. The predominance of this focus on gaps likely contributed to the relatively larger number of times the Ginsburg and Russell monograph was cited to bolster claims of difference from 2003–2013, relative to the first 10 years after its publication, because researchers have come to expect these disparities across demographic groups.
In addition, of the nine studies that made the strongest claims about class difference using the Ginsberg and Russell monograph, six of these were intervention studies, where the class difference claims were used to contribute to an argument for a new curriculum or program. (In contrast, only one study in the rest of the pool focused on interventions). Studies that used the monograph to support claims of difference sought to show that programs designed by the researchers had positive impacts on low-income children, and frequently began by painting a bleak picture of the early mathematical skills of low-income children. For example, such intervention studies have begun with claims that “this early achievement gap is evident on a wide range of foundational tasks” (Siegler, 2009: 118) or that “many of the economically disadvantaged children are poorly prepared for formal schooling” (Bekman et al., 2011: 412).
Making sense of the emphasis on difference in early mathematics
The question of why this analysis matters depends on the theoretical frame in which the study is located. If research is seen not just as an objective description of empirical reality, but instead as a will to truth—indeed, as a production of what is true—then the way we use citations to inscribe particular stories matters. This is especially true when the stories we tell seem directly to contradict the empirical evidence and when they have the potential to do harm to the populations being described. When National Research Council reports emphasize differences in early mathematics learning across demographic groups and downplay similarities, they not only mischaracterize the contradictory findings of research in this area, but also create a discursive environment where it is easy to feel that interventions in even the earliest grade levels are already too late. In addition, these characterizations may minimize the roles that schools play in producing differences.
The fact that one in three times the Ginsburg and Russell monograph (1981) was cited was to bolster a claim that the authors seemed to reject should not be read as an accident or as merely a product of the variations of interpretation that are inevitable in an enterprise as diverse and complex as educational scholarship. Instead, the substantial number of times the Ginsburg and Russell monograph has been cited to strengthen claims of significant class difference in early mathematics learning should be read as evidence that there is a dominant story which may be impacting our interpretations of new (and old) evidence. This story—as demonstrated from the quotes above—says that there are enduring individual differences in important mathematical understandings in the earliest years that are attributable to inadequacies in children or their families. The alternative story—substantiated by a number of studies, including the Ginsburg and Russell monograph—is that low-income children come to school prepared to learn significant mathematics, and that schooling practices can either build on what students know or fail to serve low-income and minority children adequately. This story, if told as often as the story of difference, would be likely to produce different kinds of educational practices.
The reasons for the dominant story of social class difference in early childhood mathematics are complex. Ginsburg and Golbeck (2004: 193) speculated that “we tend to remember, and to report, research showing significant differences,” despite the fact that many studies identify similarities. In addition, the emphasis on difference is likely related to the challenges of writing and publishing research reports. Small differences may be exaggerated in order to lend significance to studies, and studies that report on interventions directed at low-income children and families may emphasize difference as a way of arguing for the importance of the work. Walkerdine (1998: 62) has written about this phenomenon in relation to research on gender difference in mathematics, reporting on the ways that a study of hers on gender and play was taken up by another researcher, who took Walkerdine’s finding of slight differences in play preferences between boys and girls as evidence of significant differences between boys and girls, “making the data say exactly what they do not say.”
Framing studies in this way may be related not only to the desire to frame the researchers’ interventions in compelling ways, but also to expectations related to funding. Government and philanthropic agencies often require—formally or informally—that researchers document severe need on the part of populations that will be impacted by the study in order to justify funding. This creates a temptation on the part of those who seek funding to highlight differences and problems, and to minimize similarities and resources. Beyond expectations to highlight deficiencies, standards of scholarly writing—particularly for empirical studies—may make it challenging to summarize studies that find both similarity and difference, or to acknowledge these studies in ways that still work to support the author’s own claims. Expectations about the length of articles, as well as about the necessity of clean, logical arguments, make it challenging to discuss conflicting or complex results from previous research, although a few studies I reviewed (e.g. Jordan et al., 1994; Siegler and Ramani, 2009) did make space in their literature reviews to make more nuanced claims—such as that low-income children performed worse on cardinality tasks than middle-income children, but showed no differences in relation to verbal counting. This demonstrates that it is possible to conform to writing conventions and word counts and to make an argument for one’s own scholarship without oversimplifying the research base.
In their conclusion, Ginsburg and Russell wrote:
This monograph shows that predictable academic failure cannot be explained by deficient intellectual skills possessed by young children on entrance to school. Future research needs to examine other possibilities: subsequent cognitive difficulties, motivational problems, expectation of failure related to caste status, and inadequacies of the educational system. (Ginsburg and Russell, 1981: 56)
This point is important. Ginsburg and Russell are not denying that students from low-income homes experience differential outcomes in school, or that the sources of such difference are potentially related to the experiences of growing up poor or minoritized. Such a stance would be harmful to an equity-oriented agenda (Lubienski, 2003). Instead, Ginsburg and Russell are pointing researchers in particular directions—ones that are at odds with summaries of research that simply label children from particular groups as coming to school without the capabilities to learn important mathematics. Instead, they suggest that schools themselves may play a role in producing learning difficulties in mathematics, whether through race- or class-based discrimination or inadequate instructional strategies. This hypothesis is difficult to consider seriously when the story of significant pre-existing differences is reiterated in the research so frequently, and the roles schools, instructional strategies, and classroom cultures play in producing achievement differences are often overlooked in interpretations of the available data. For example, the National Research Council (2009: 100) report on early childhood mathematics says that “few data exist on early childhood mathematics teaching and learning in relation to race/ethnicity, but one can extrapolate from K–12 studies.” The assumption that claims about young children can be extrapolated from data collected in K–12 schools discounts the possibility that schooling itself may negatively impact the performance of poor and minority children, and minimizes the perceived need for empirical studies that investigate such relationships.
In addition, the articulating of claims of difference—particularly with little empirical backing—in research reports produced by the government is troubling. Because of their status, these sorts of reports generate authoritative discourse, which “demands that we acknowledge it, that we make it our own; it binds us, quite independent of any power it might have to persuade us internally; we encounter it with its authority already fused to it” (Bakhtin, 1981: 342). Researchers wishing to make brief statements about the role of race and class in early childhood mathematics in the USA might pull a quote from the National Research Council report without considering how that claim came to be produced and, because of the source, other researchers are likely to read the quote as true. This is particularly problematic when one considers that the claim of significant racial difference in the National Research Council report relies on the Ginsburg and Russell monograph as key evidence, even though the monograph itself rejects significant racial differences and none of the studies I examined in peer-reviewed journals cited the monograph to make such a claim. The fact that the claim of significant racial difference in early mathematics appeared in the National Research Council report at all is evidence of how powerful these stories that are continually reiterated in discourse become. They stand on their own, even without empirical research to substantiate them.
Because schools do produce less positive outcomes for poor and minority students, researchers have an ethical obligation to be precise in their claims about what empirical work about marginalized populations does and does not demonstrate. Reporting the nuances of studies not only serves an ethical requirement to respect marginalized communities, but also serves the enterprise of research. By reporting complex findings, we support other scholars’ engagement with educational problems in complex ways, making it more likely that future studies will take into account the rich knowledge base already available, rather than relying only on commonly circulated narratives.
The complicated story of the Ginsburg and Russell monograph demonstrates that the production of truth claims in research is strongly influenced by the stories that we already take to be true. This suggests a need for researchers to take greater care in thinking about the truth claims they make in order to both capture the complexity of the variety of stories told in research and to push the field toward conceptions of what children know and can do which are likely to lead researchers and educators toward productive engagements with poor and minority children.
Declaration of conflicting interests
The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.
Funding
The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The writing of this article was supported in part by a grant from the National Science Foundation (844445). The opinions expressed in this article do not necessarily reflect the position, policy, or endorsement of the National Science Foundation.
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Author biography
Amy Noelle Parks is an Associate Professor in the Department of Teacher Education at Michigan State University. She works in the fields of early childhood and mathematics education, and her research is concerned with equity issues related to young children’s experiences of schooling, mathematical play, and representations of children and families in research.