Learning to Read the Numbers

Integrating Critical Literacy and Critical Numeracy in K-8 Classrooms. A Co-Publication of The National Council of Teachers of English and Routledge

David J. Whitin, Phyllis E. Whitin

• Publisher: Routledge
• Year: 2010
• Print ISBN: 9780415874304
• eBook ISBN: 9781136907333
• Topic: Pedagogía
• Subtopic: Educación general

Being a critical reader of numerical information is an integral part of being literate in today's data-drenched world. Uniquely addressing both mathematics and language issues, this text shows how critical readers dig beneath the surface of data to better evaluate their usefulness and to understand how numbers are constructed by authors to portray a certain version of reality. Engaging, concise, and rich with examples and clear connections to classroom practice, it provides a framework of critical questions that children and teachers can pose to crack open authors' intentions, expose their decisions, and make clear who are the winners and losers – questions that are essential for building democratic classrooms.

Explaining and illustrating how K-8 teachers can engage students in developing the ability to be both critical composers and critical readers of texts, Learning to Read the Numbers is designed for teacher education courses across the areas of language arts, mathematics, and curriculum studies, and for elementary teachers, administrators, and literacy and mathematics coaches.

Learning to Read the Numbers is a co-publication of The National Council of Teachers of English (www.ncte.org) and Routledge.

1
Learning to Read the Numbers

It’s Everybody’s Business

An innumerate citizen today is as vulnerable as the illiterate peasant of Gutenberg’s time.

Lynn Steen (Steen, 1997a, p. xxvii)

Let us start with a few short stories about data. A teacher recently told us an anecdote about her daughter. Her 9-year-old really wanted a cell phone for Christmas but her mother refused to consider the request. In order to bolster her argument her daughter decided to poll friends and family members to see what their opinions were about this issue of cell phone ownership. After reviewing her results she decided not to count the votes of anyone over 30 because “they are really too old to understand what a 9-year-old needs.” She then added, “And besides, they are messing up my questionnaire!”

Here’s a story from a different context: an undergraduate class in statistics in which our son was a student. The professor talked about his work as a consultant for businesses. He related, “The first question that I ask a company is, ‘What is it that you want me to show?’ I tell them that I can use whatever data they have to tell the story they want their customers, stockholders, or employees to hear.”

Now take a minute and consider what these two stories have in common. What parallels do you see between this 9-year-old and a college professor? We’re struck by the fact that both of these individuals see data as a potential for power. They know that data can be used to persuade. They both also realize that data can be manipulated to support their own personal agendas. Similarly, they understand that a given set of data does not tell the whole story. They both recognized their power to decide what data to reveal and what to conceal.

If we look beneath the surface of these stories, we can infer several assumptions about what it means to be fully literate in today’s information age:

• Data-related texts, like all communication, are not value-free (Gee, 1992, 1996; Huff, 1954; Janks, 2010; Luke & Freebody, 1999).

• Especially due to mass media and the internet, people encounter data-related texts with increasing frequency and in wider contexts (Best, 2001; Steen, 2001a, 2001b).

• Data-related texts are multimodal; they incorporate language, as well as visual and numerical information (Jewitt & Kress, 2003; Steen, 2007a; Tufte, 1983).

• Interpreting data-related texts involves exposing the choices that were made in the creation of these texts (Best, 2008; Spirer, Spirer & Jaffe, 1998; Whitin, P. & Whitin, D. J., 2008).

These insights about twenty-first century literacies cut across all subject fields. A critical orientation toward statistics supports learners to exercise their essential democratic responsibilities as they participate in a range of personal, social, and civic contexts (Cope & Kalantzis, 2000). This critical stance is a call to examine how people use these tools of mathematics, language, and visual representation in the fields of science and the social sciences. From this perspective the development of a critic’s perspective is everybody’s business (Steen, 1999, 2007b).

This book primarily involves the fields of mathematics and language but also shows how children use these tools in a variety of contexts, including social studies and science. In the remaining sections of this chapter we will look at what scholars in both fields have been saying about being a critical reader. We will then describe a conceptual model and heuristic we have developed to integrate these perspectives. Finally, we share some classroom examples to illustrate how the questions in the heuristic may be used as an instructional guide.

Theoretical Perspectives from Mathematics

We live in an age that is inundated with data. Look around and see where you encounter data in your daily rounds. Perhaps you’ll find data in the pharmacy where you notice on a tube of antibacterial cream that it is recommended as the #1 cream by dermatologists. Or perhaps you will see data at the grocery store where “mom preferred” is advertised on the front of a child’s cereal box. When you look on the internet you might see a new diet formula which claims that 93% of women who were on this diet lost on average five pounds per week. Or perhaps when you turn on the television you hear a politician claiming that the economy is in good shape because the number of available jobs is increasing. In each case, data (or the implied use of data) are used to persuade. Marketers, politicians, and anyone else with an agenda to promote know that their chances of convincing the public about a certain product or issue are greatly enhanced if they can attach a number to their argument. They know that most people don’t question numbers. Most people don’t think about the way that issues of motives, power, and ideology come into play when numbers are used for social purposes (Borasi, 1989; Gee, 1992). There are colloquial expressions which people often use that convey this widespread belief in the inherent truth in numbers: Numbers don’t lie; the facts speak for themselves; the facts tell us … The verbs of “lie,” “speak,” and “tell” anthropomorphize the term “data” by bestowing on it human qualities. In this way the term “data” takes on an agency unto itself. The anthropomorphic language not only hides the identity of the authors of this numerical information but also makes the data seem more detached, abstract and therefore unlikely to be challenged.

So while the general public is often intimidated by numbers, the world continues to be awash with increasing amounts of numerical information. As Orrill (1997) notes, computers generate data “every time a purchase is made, a poll is taken, a disease is diagnosed, or a satellite passes over a section of terrain” (p. xvi). There is both a boon and a bane to this seemingly unlimited access to numerical information. The advantage is that now not only specialists, but everyone, can read the data about the latest nutritional studies, the risks of taking certain medications, and so forth. “Potentially, if put to good use, this unprecedented access to numerical information promises to place more power in the hands of individuals and serve as a stimulus to democratic discourse and civic decision making” (Orrill, 1997, p. xvi). However, there are also dangers in such a data-driven society. If individuals are not able to think critically about these data, then they cannot participate in meaningful discussions about what these numbers mean. In light of such dangers Lynn Steen has issued this dire warning: “In short, an innumerate citizen today is as vulnerable as the illiterate peasant of Gutenberg’s time” (Steen, 1997a, p. xxvii). This state of affairs has profound implications for educators.

Robert Moses, in his compelling account of the Algebra Project in Radical equations (Moses & Cobb, 2001), points out that this issue of mathematical illiteracy is particularly pronounced for underserved populations. He calls mathematical literacy the new “civil right,” and its development is as urgent an issue “as the lack of registered Black voters in Mississippi was in 1961” (p. 5). He extends this parallel further by arguing that mathematical literacy is particularly pervasive with Blacks and other minorities, “making them the designated serfs of the information age” (p. 11). Thus, the struggle for mathematical (and science) literacy is a struggle for citizenship, equality, and freedom (p. 14). Moses recognizes the demands of the data-drenched age in which we live and calls for citizens who are competent in evaluating and interpreting those numbers.

Nurturing a critical perspective in mathematics is supported by two important instructional emphases: (1) teaching for understanding; and (2) connecting mathematics across the disciplines. Being a critic of statistical texts requires an understanding of the mathematics as well as an understanding of how people create and use numerical information in various contexts. Since the publication of its Principles and standards for school mathematics (2000), the National Council of Teachers of Mathematics has taken a leading role in promoting teaching for understanding. Some of its standards include communication, representation, connections, and reasoning and proof. It is a call for a curriculum that encourages questioning, argumentation, and problem posing, as well as multiple forms of representation, such as writing, drawing, graphical displays, and models. These efforts by NCTM are intended to combat a transmission model of teaching and learning that has dominated mathematics teaching in the past, and is still a persistent voice in the “math wars” discussions of today. Jo Boaler succinctly described this transmission model as: Learning without thought, Learning without talking, Learning without reality (2008). Alan Bishop has labeled such teaching as “a technique-oriented curric-ulum” that emphasizes mathematics as a way of doing rather than as a way of knowing (1991, p. 3). This kind of curriculum “cannot help understanding, cannot develop meaning, cannot enable the learner to develop a critical stance either inside or outside mathematics” (p. 8). It shuts off any personal interpretation, invention and opinion (p. 9). Bishop argues that what is needed is a recognition that education—and by extension, mathematics education—is a social process. And yet, “the social, the human, the essentially interpersonal nature of education is so often ignored in the rush for the acquisition of mathematical techniques and in the desire for so-called efficiency in mathematics education” (pp. 13–14).

Recognition of mathematics as a social process reinforces the belief that it is a human-construct, and may therefore be examined and critiqued. Thus, connecting mathematics to other subject fields means viewing it in its sociopolitical contexts. This aspect of mathematical learning has been largely side-stepped by NCTM (Apple, 1992; Williams & Joseph, 1993). However, if students are to be the kinds of critics who are essential to the civic discourse of a democracy, they must come to understand how people use numbers to wield power, promote arguments, and influence public policy. Bishop states, “At the societal level mathematics is mediated by various institutions in society and is subject to the political and ideological forces in that society” (p. 14). Mathematics and science are not ethically and morally neutral enterprises but have an increased social responsibility to explore its uses in their social and political contexts (Ernest, 1989). Unless these contexts become a regular part of the learning of mathematics the social significance of mathematics is lost, and mathematics becomes a field of abstract calculations rather than meaningful interpretations. Ernest (1989, p. 202) issues this sharp warning to the mathematics field:

Can we hide behind the argument that we only provide the metaphor and concepts for the dehumanization of social issues and that therefore our hands are clean? If providing such tools leaves the tool-maker free from responsibility, is not the same true for weapon manufacturers?

When the National Council of Teachers of Mathematics published its first Curriculum and evaluation standards for school mathematics in 1989 Michael Apple rebuked them for not addressing this socio-political dimension. He claims that one of the major responsibilities of educators is to support our students “to critically assess the nature of truth claims, and the uses and abuses of knowledge they are being asked to learn” (Apple 1992, p. 423). He continues his argument by asserting that the high status granted to mathematical knowledge in the various reform efforts has nothing to do with its elegant formulas, internal beauty, or its conceptual ways of knowing the world, “but because of its socioeconomic utility for those who already possess economic capital” (p. 423). Even though the Standards were revised in 2000 we believe that Apple’s criticisms are still appropriate and justified. Thus, a critical perspective in mathematics cannot be developed unless students have regular opportunities to use it for real purposes. In this way they can recognize the role of context in their work, and examine the choices and decisions they make as a set of a much larger pool of possibilities. A critical perspective also entails a close examination of mathematical concepts. Such concepts as time, ratio, area, and average may be known as generalizations in the narrow confines of a textbook. But out in the real world they become tools that authors use to frame an issue or build an argument. It is this critical interrogation of concepts in use that the mathematics field has largely ignored.

Perspectives from Literacy Theory

The attention that English language arts educators pay to the critical dimensions of literacy can offer perspectives and strategies for developing a similar orientation toward statistics. Although this discipline has its own history of struggles against a transmission model of teaching, the field has historically taken a persistent stand about the relationship between literacy and civic responsibility. Participants at the 2005 Conference on English Education Leadership and Policy Summit articulate this stance: “English education, more than any other academic discipline, because of its focus on language and representation, contributes vitally to the processes ...

Table of contents

• Contents
• Preface
• Acknowledgments
• 1 Learning to Read the Numbers
• 2 Getting What You Ask For
• 3 Definitions and Categories
• 4 Creating the Visual
• 5 What We Don’t Know
• 6 Learning to be Critics
• Appendix A Investigating Commercials on Children’s Television Shows
• Appendix B
• Appendix C
• References
• Index