El aprendizaje de las Matemáticas en la Educación Básica en Excale

In recent decades, composition research on error has come to emphasize the social context of rhetorical situation. Most studies also focus on pedagogy, in whole or in part, so the literal reader examined in those studies is often the writing teacher. In the late twentieth century, Mina Shaughnessy’s Errors and Expectations marked a turn in theories of error, prompting composition instructors to look for illuminating patterns in the errors of their least fluent writers. She eloquently describes error as "unprofitable intrusions upon the

consciousness of the reader" that "demand energy without giving any return in meaning" (12). Three years later, in 1980, David Bartholomae’s “The Study of Error” was an extension of and response to her approach, based on close reading and interpretation of student error. Some of the research that has focused on the perception of error as residing in the reader reaches beyond the teacher-student dyad, such as Maxine Hairston’s “Not All Errors Are Created Equal,” which collected data about nonacademic professionals’ reactions regarding the severity of various errors, and Attitudes, Language, and Change by Anne Ruggles Gere and Eugene Smith, expressing a hope for change not only in teachers’ responses to perceived error but in the general public’s attitude, in a broad-based cultural shift to be led by teachers (a movement that has met with only partial success). Joseph William’s “Phenomenology of Error” delves thoroughly (and slyly) into the notion of error as located in the reader’s perception, in his landmark essay that embeds one hundred errors in its text.

The twenty-first century opened with Chris Anson’s 2000 call for research into error, “Response and the Social Construction of Error,” specifically focusing on teacher response to error. As he describes it, “many teachers continue to feel torn between denying attention to error in their response because of its incompatibility with newer theoretical perspectives and experiencing the unavoidable effects of error as they read their students' writing” (4). Anson defines error as “recognized deviations from specific language conventions imposed on texts by readers with varying knowledge that they call into play depending on the context, purpose, level of formality, and other elements of their reading” (17), and his probing into this

multifaceted nature of error illuminates why errors are hard to ignore, annoying even those theoretically committed to finding them insignificant, an annoyance through which errors undermine pathos as well as the aforementioned logos and ethos that error can tarnish.

Tracy Santa’s 2008 Dead Letters offers a thorough history of both the theory and

pedagogy of error, in which he confirms the social nature of error and locates its existence, like Williams, in the reader, who performs Foucault’s “clinical gaze” (Santa 131). Santa notes Bartholomae’s comment, nearly twenty years after writing “The Study of Error,” that he

[Bartholomae] had been “committed to … determin[ing] a grammar of error” which had turned out to be a “vain hope”; instead, Bartholomae came to see error as “a social rather than a

linguistic phenomenon” (71). While the plane upon which writing errors occur is linguistic, what defines a given usage as error is, finally, social.

Relevant to any study on error is Andrea Lunsford’s work with Robert Connors and, later, Karen Lunsford, respectively: “Frequency of Formal Errors in Current College Writing” (in 1988) and "Mistakes are a Fact of Life: A National Comparative Study" (in 2008). The focus

of both studies is to establish the number and types of errors appearing in a wide sampling of student papers, and they compare the findings of each study with earlier research. In the latter paper, the authors make numerous, specific, but incidental comments on the observed effects of spelling and grammar checkers, which are having measurable impacts on the nature of errors appearing in student papers (796). While grammar checkers are not the focus of either study, Lunsford and Lunsford’s 2008 findings bear directly on my argument and evidence regarding the impact of the technology. They note that spelling and grammar checkers are changing the nature of errors that are common in word-processed writing (799) – a change which inevitably alters expectations about what kinds of error readers then deem acceptable or severe.

Another “major shift” that the 2008 study noted as a change from 1988 is also pertinent to my research: a change in “type of paper” from “personal narrative” to “argument and research” (793), a shift in what they aptly label as “genre” (801). This change has created new challenges with error types, three of which appear on the new list of their top twenty errors, all three regarding integration of quotations, attribution of sources, and the punctuation of both according to a disciplinary style guide (796-97). Such a change in genres creates new social exigencies.

Directly or indirectly, the effects of the grammar checker figure into almost every notable finding in Lunsford and Lunsford’s research, as they reflect on the changing nature of errors now in the student papers. One is the large drop in the number of spelling errors, which had comprised the top number of errors by far in papers of the 1988 study but ranked only fifth in 2008. The authors deduce that “the spell-check function took care of many spelling

mistakes that spell-checkers understandably do not flag” (796). (Word 2013 checks both these item types, as Chapter 2 will discuss.) Another major change in error type is the new front- runner, “wrong word,” now “by far the most frequent formal error” (796). Ironically, the shift turns out to be a trade-off, as the researchers notice that “many of the wrong word errors appear to be the result of spell-checker suggestions,” often combined with a “simple failure to proofread” (796).

Invoking Williams’s focus on the reader in “The Phenomenology of Error,” Lunsford and Lunsford note that what they quantify in their study as “error” is more aptly understood as “attention to error” (801), the idea that forms the basis of the definition and theory of error in my study.