Conference PaperPDF Available

Constructing “calculus readiness”: Struggling for legitimacy in a diversity-promoting undergraduate engineering program

Paper ID #16688
Working in the Weeds: How do Instructors Sort Engineering Students from
Non-Engineering Students in a First-Year Pre-Calculus Course?
Kevin O’Connor, University of Colorado, Boulder
Kevin O’Connor is assistant professor of Educational Psychology and Learning Sciences at the University
of Colorado Boulder. His scholarship focuses on human action, communication, and learning as socio-
culturally organized phenomena. A major strand of his research explores the varied trajectories taken by
students as they attempt to enter professional disciplines such as engineering, and focuses on the dilem-
mas encountered by students as they move through these institutionalized trajectories. He is co-editor of
a 2010 National Society for the Study of Education Yearbook, Learning Research as a Human Science.
Other work has appeared in Linguistics and Education; Mind, Culture, and Activity; Anthropology &
Education Quarterly, the Encyclopedia of Cognitive Science; the Journal of Engineering Education; and
the Cambridge Handbook of Engineering Education Research. His teaching interests include develop-
mental psychology; sociocultural theories of communication, learning, and identity; qualitative methods;
and discourse analysis.
Dr. Frederick A. Peck, University of Montana
Frederick Peck is Assistant Professor of Mathematics Education in the Department of Mathematical Sci-
ences at the University of Montana.
Julie Cafarella, University of Colorado, Boulder
Julie Cafarella is a PhD student in Educational Psychology & Learning Sciences at the University of
Colorado, Boulder. Before moving to Colorado, she worked as a public school teacher in New England.
Her current research focuses on issues of access and equity in STEM education.
Dr. Jacob (Jenna) McWilliams, University of Colorado, Boulder
Jacob (Jenna) McWilliams is a postdoctoral researcher in the Learning Sciences program at the University
of Colorado Boulder. Jacob’s research focuses on issues of gender and sexual diversity in education, and
recent work involves developing queer pedagogies for supporting new media literacies practices in the
elementary classroom and, most recently, drawing on queer and transgender theory for understanding the
dominant discourses of engineering education and how those discourses marginalize and exclude people
from traditionally vulnerable gender, sexual, and ethnic groups.
American Society for Engineering Education, 2016
Working in the Weeds: How do Instructors Sort Engineering Students from
Non-Engineering Students in a First Year Pre-Calculus Course?
1. Introduction
The calculus sequence is widely recognized by engineering students and faculty and by
engineering education researchers as one of the course sequences that “weed out”
students who are unlikely to survive the rigors of the engineering curriculum [1, 2, 3].
While this “weeding out” process is often critiqued, it nevertheless has remained
prominent in engineering education despite persistent efforts to mitigate its effects. How
does “weeding out” remain so central? This research paper reports on a discourse
analytic study that aims to address an important aspect of this question through a detailed
examination of a meeting of instructors from multiple sections of a pre-calculus course
for first year engineering and pre-engineering students.
We argue that “weeding out” is best viewed, not as a simply mechanical or technical
process through which students are linked with grades that do or do not allow them to
proceed in the curriculum. Instead, we show that it is a highly active process through
which instructors are engaged in producing identities for themselves, for other
instructors, and for students in response to practical dilemmas that they encounter in the
meeting. These dilemmas, and the identities that are produced in response, are aligned
with central ideological commitments of their department and discipline. Thus, grading,
and “weeding out,” is itself an ideological process of identity formation.
The specific institutional and disciplinary commitments that we identify are as follows:
1) demonstrated ability at calculus is a legitimate criterion for entry into the profession of
engineering; 2) calculus courses, as structured within the mathematics department, are
appropriate venues for students to develop their calculus ability; 3) calculus exams, as
structured within the calculus courses, are appropriate measures of students’ calculus
ability; 4) instructors are fair, neutral, and objective arbiters of who should “pass” and
who should not.
The identity work being performed in line with these ideological commitments are as
follows: 1) in working to set the final grades for the course, the instructors are
constructing themselves and one another as fair and objective; they hold one another
accountable to adhering to the particular framework outlined above; 2) when they engage
in representing students, instructors construct a model of ideal students (sometimes
explicitly, sometimes implicitly), and holding students accountable to that model.
It is important to note that the circumstances of grading are likely specific to the
instructional team at this university; for this reason we would not necessarily expect that
our findings be directly generalizable to the ways in which “weeding” happens at other
institutions. Nevertheless, we believe that the analytic strategy that we adopt—
examining practical dilemmas and their resolution—are likely to be generative and
powerful in looking at a range of practices through which institutional representatives
position self and others, including the ways in which these positioning processes result in
success and failure for students.
2. Theoretical framework
In this paper, we adopt a “cultural production of persons” perspective [4, 5, 6, 7, 8] in order to
examine aspects of the “weeding out” process. This perspective is part of a broader
project in the social sciences over the past several decades, a project that explores how
both persons and forms of social organization are constituted through social practice.
Among the major aims of this work has been to challenge conceptions of culture as a
stable and relatively unproblematic body of knowledge that is transmitted from one
generation to the next. Instead, culture is seen as a dynamic process in which human
agents create meaning by drawing on cultural forms as they act in social and material
contexts; in so doing people produce themselves and others as certain kinds of culturally
located persons while at the same time reproducing and transforming the cultural
formations in which they act. In this sense, “cultural production” has a double meaning: it
is concerned with how persons are produced as cultural beings, and with how this
production of persons results in the (re)production of cultural formations.
Recent anthropological approaches to education have been concerned with this process as
it relates to learning and schooling. This work has focused on the interplay between
social structure and human agency in sites in which "educated persons" are produced. In
this view, becoming “educated,” as well as becoming “uneducated” or even
“uneducable,” however these might be locally understood, is an important way in which
persons become produced within certain cultural groups, and thereby contributes to the
production of the culture.[6]
In other work, we have examined aspects of the cultural production of educated persons
in the calculus sequence from the perspective of students, showing that “calculus
readiness” is much more than neutral diagnosis of a cognitive state. Rather, it is a human-
produced classification that is contingent on both history—including the struggles over
the place of math and science in engineering—and contemporary institutional practices
such as testing and grading. For students, this value-laden classifying process “twists and
torques” [9] their identities and trajectories.
It is also relevant to examine the practices of instructors and the role that they play in this
process. Horn et al. [10] have examined, at the K-12 level, how teachers through their
interactions socialize one another into sets of identities and perspectives associated with
emerging communities of practice. [11] These interactional processes are shaped but not
determined by the schools in which they take place, by curricular policies, and the like; in
responding to practical dilemmas[12] in student assessment, teachers position themselves
and students into identity categories that have implications for their instructional
practices and for the futures of their students.
Many scholars have recognized that language and discourse play a central role in the
processes through which identities are constructed and negotiated. De Fina, Schiffrin,
and Bamberg [13] have identified several trends in the study of discourse and identity that
frame the analyses presented here. One major trend is that discourse perspectives have
become closely aligned with a perspective that has been broadly identified as social
constructionism, of which the cultural production approach being adopted in this paper is
one variant. A second major trend is what De Fina, Schiffrin, and Bamberg term “anti-
essentialist visions of the self.” Whereas traditional approaches to self and identity have
tended to conceive of the self as a “core essence” of the person, discursive perspectives
maintain that self and identity are active processes, that they are accomplishments of
people acting together with one another and with the cultural materials, including
category and classification systems developed in institutions for identification of persons,
that are available to them. In this sense, any person both has more than a single identity,
and these various identities are shaped in response to specific actional and interactional
circumstances and dilemmas in which one finds oneself.
Thus, a major aspect of the interactional work being done by participants involves
“contextualizing” the interaction. Contextualization is understood in this tradition as “an
active process of negotiation in which participants reflexively examine the discourse as it
is emerging, embedding assessments of its structure and significance in the speech itself”
[14, p. 69]. Hanks [15] argues that contextualization is always evaluative and hence to some
degree ideological, involving judgments based on implicit or explicit criteria as to the
appropriateness of particular contributions to the discourse.
Understanding contextualization processes, and their ideological aspects, is a crucial part
of a social and relational approach to identity. When speaking, participants constitute the
interaction as being of a certain sort, while at the same time identifying themselves as
persons of a certain sort. The contextualization process, then, is the process by which
individuals position or identify one another with regard to the interaction and the broader
communities in which they take themselves to be participating. And, as Bucholtz and
Hall [16] argue, this is always an ideological process:
In identity formation, indexicality relies heavily on ideological structures, for
associations between language and identity are rooted in cultural beliefs and
values – that is, ideologies – about the sorts of speakers who (can or should)
produce particular sorts of language.
For example, instructors involved in grading students in a pre-Calculus course must
continually monitor their own and others’ contributions according to some understanding
of what Calculus is, what role it plays in students’ trajectories and in the institution, as
well as their role in the course, in the present interaction, and in the institution.
Such a perspective emphasizes the importance of careful and detailed attention to the
situated use of language in social practice. Contextualization processes centrally involve
participants’ awareness of the range of possibilities for action on particular occasions,
possibilities drawn from the multiple systems in which they participate or might
participate in the future. And, as Hanks [15, p. 165] points out, “it is the minute details of
linguistic structure that coordinate this awareness and make it known with a delicacy
unparalleled by any other mode of expression.” Given the centrality of language in the
organization of social relations, including those involved in identity, it is clear that “an
analysis of social relations that is deaf to linguistic practice will be blind to some of the
most revealing displays of its object” [15, p. 165] .
3. Research Questions
Following from this perspective, we aim to address the following questions:
How do representations of students by instructors function during a meeting in
which instructors are working to determine grades for the course? More
o How do the instructors position themselves and one another?
o How do the instructors position students within categories that have
consequences for success and lack of success?
o How do these positionings reflect an instantiate particular ideologies and
sets of values regarding calculus and its role in engineering?
4. Research Context, Data, and Methods
Our research focuses on a the Access Program, a diversity-promoting program in the
engineering school at State U., a flagship state university in the Western United States.
The College of Engineering at State U is predominantly composed of white, male,
middle- and upper-class students. The Access Program seeks to broaden access to the
college by admitting a cohort of approximately thirty (30) “next-tier” students to the
college each year. Students in the Access cohorts were initially denied admission to the
College of Engineering, but were accepted via the Access program after a second round
of admission screening. The Access program has explicit diversity goals, and is
composed almost entirely of women, students of color, and first-generation college
students. Although these students are admitted directly to the College of Engineering,
they are enrolled in a “performance-enhancing year,” in which they take courses designed
to prepare them for courses in the regular engineering curriculum.
The Access program has to date enrolled seven cohorts of students. After two cohorts
had performed below expectations in Calculus I, the program arranged for the
Mathematics Department to offer a pre-calculus course for Access students as part of
their performance-enhancing year. This course, offered by a single instructor to a single
class, was viewed as successful overall in its first two years, and the College of
Engineering and the Math Department subsequently decided to expand the course beyond
the Access Program and to offer it to pre-Engineering students and to directly admitted
Engineering students who elected to take pre-Calculus rather than taking Calculus I. In
the semester that we are examining in this paper, the course was taught by five (5)
instructors to five (5) sections of about thirty-five (35) students each.
Data for the analysis presented here is a single meeting of the five pre-Calculus
instructors. The meeting took place at the end of the Autumn semester, after students had
taken the final exam for the course. The purpose of the meeting was to convert students’
raw numeric scores for exams, homework, and other academic tasks into letter grades.
Prior to the meeting, instructors had been responsible for entering students’ raw scores
into a spreadsheet on the course’s learning management system; a major part of the
meeting involved examining these scores in order to find any anomalies and to determine
where to set the dividing points between specific letter grades.
This meeting was recorded by one of the research team members, and was subsequently
fully transcribed according to modified conventions from interactional sociolinguistics
and linguistic anthropology.
The first analytic step was to identify every instance in which the instructors represented
a student or students. Major categories of instructor representations of students were: 1)
direct references to particular students (e.g., “my guy”; “one kid with a zillion or
something”); 2) references to students as a group (e.g., “that’s why you see things with
people that got 40s and then 90s”); and 3) enactments of students in conversation with the
instructors (e.g., an instructor quotes a students as saying, “When I look at my exam, my
quiz average in D2L hasn’t dropped my lowest”).
Once each representation of students had been identified, we conducted a discourse
analysis to determine the boundaries of the segment within which those representations
took place. These segments were then examined in order to interpret the function of
student representation within the segment. In virtually every instance, student
representation was occasioned by the instructors’ response to some dilemma that had
arisen in that segment of discourse. The analysis reported here focuses on several of
these segments in order to show how such practical dilemmas provides an occasion for
position of self and other into particular identities, and how these identities reflect and
construct ideologies.
5. Analyses
We present three excerpts in which instructors position self, other, and students within
available cultural identities.
Segment 1: The bookkeeping dilemma
The first segment that we present can be characterized as a “bookkeeping” episode: led
by Adele, the instructors aim to account for gaps in their spreadsheet of final exam
scores. Until they know how to interpret those gaps—for example, are they temporary
holes because exam scores have not yet been graded, or do they represent students who
missed the final exam?—they cannot calculate final grades.
Although Adele represents this dilemma as a concern about performing grade
calculations, Randall takes it up as an opening to account for why missing scores exist:
That is, to express his interpretation of the students who missed the final exam. Adele
(lines 400-402; 404; 406; 410-11) seems to indicate that her purpose is to determine what
value to place in the incomplete lines; Randall, however, reorients the conversation
(beginning at line 407) around his confusion over students’ failure to attend the final
400 ADELE: Yeah, now the one thing with yours, Randall, is some
of the exam scores were missing. What was the
situation there?
RANDALL: Exam scores?
ADELE: Yeah, I think there was some [blank=
405 RANDALL: [From the final?
ADELE: =exam scores [Because I thought I saw
RANDALL: [Well, I know I had one kid with a
zillion or something that just gave up, so I know he
just didn’t go, [I think.
410 ADELE: [I would putput zeros in just so
it’s clear.
RANDALL: And then there’s- there’s this one kid though, this
is weird. He was very, very good. He transferred in
late, this {Name}. Doing very well, quiz scores are
415 all very well. There’s no final exam. ((A says, “uh-
huh” after each clause))
YEVA: Well, there has to be at least a few people who
missed your final exam because I had ten leftover
420 RANDALL: Well I know this- [yeah, uh-
ADELE: [Oh, right.
YEVA: And so it was your class and my class, right? And I
counted like, maybe five could’ve been from mine. So,
and I don't know if any of yours were in the special
425 testing room, [but you had to have at least
RANDALL: [No, no not one.
YEVA: So there has to be at least [some (missing)
RANDALL: [That’s what I’m saying,
but this one kid was a good student. He was one of
430 the best. I don't know what
ADELE: You think he missed it also?
RANDALL: I haven’t got an email from him. I don't know.
[And then-
ADELE: [I’d put a zero in there for now. it’s all we
435 can go on, right?
YEVA: [Yeah.
ADELE: [What else can you do?
YEVA: But anyways, it- a- from what I counted, it would
440 make sense that some of your students [took it in the
RANDALL: [Well, then I had this {Name} kid who just missed it,
that I gave yesterday, ((Y: Yeah)) so that’s two, or
that’s three. I don't know.
In this exchange, Randall is accomplishing a good deal more than simply accounting for
missing numbers: When requested to describe “the situation,” he offers his interpretation
of the calculus-readiness—the skill level—of the students who missed the final exam.
Randall identifies three students who missed his final exam. One of the three has
completed a makeup exam, which Randall has not yet graded (discussed in lines 442-
444). In this case, since the score is only temporarily missing, it receives no further
explanation. Randall characterizes the other two as students who could have passed the
final exam: One student had “a zillion or something” points; the other was “very, very
In these narratives, Randall reinforces two pathways for success, which could be
identified as “effort” and “ability”. The first student has accumulated a sufficient number
of points to be presumed to be calculus-ready. The second student, despite beginning at a
disadvantage (“he transferred in late”), is “very, very good.”
Here, Randall aligns himself with dominant cultural assumptions about legitimate
pathways to academic success. It is an alignment that privileges rationalist,
individualistic, and masculinist perspectives on learning and teaching [12]. These
dominant assumptions presume that personal experience and individual experience are
largely irrelevant variables. This, perhaps, accounts for Randall’s confusion over why
two apparently calculus-ready students would fail to attend the final exam. His
accounting for the missing scores continues to work in support of the two established
pathways. The first student “gave up,” and therefore failed to continue down the “effort”
path toward success. He expresses confusion over the absence of the second, “very, very
good” student. The ability pathway has been constructed, and continues to be constructed
by Randall, as a clear and straightforward trajectory to success. If one is innately “good”
at pre-Calculus, then motivation and effort are irrelevant and these cannot be drawn on to
account for a student’s failure to attend the final exam. Other factors, such as personal
experiences, emotional or mental health concerns, or identity-based tensions, are never
introduced by Randall or considered by the instructor group.
There is, of course, no way to know how these factors would have been received by the
instructors; the point is that they did not have an opportunity to receive them in the first
place. The work of these instructors socializing each other into this community of
practice is, in large part, about how students, instructors, pre-Calculus, and education are
constructed—and about what concerns come into play as these concepts are enacted. By
offering an accounting for Adele’s bookkeeping concern that focuses on the effort/ability
dynamic, Randall reinforces for the group a commitment to dominant epistemological
assumptions—a commitment that is left unchallenged by the instructors.
In juxtaposing an “effort” narrative with an “ability” narrative, Randall is accomplishing
a key agenda item: Establishing that test scores can serve as a stand-in for students’
calculus readiness. If attitude really did matter as much as Randall claims, then it might
never matter whether a student is “very, very good” at pre-calculus. It might also make
sense to extend compassion and the benefit of the doubt to students who are lacking
innate skill but work very hard. To do so would be to discount the inviolability of the
numbers, however; to do so would require a very different assessment system from the
one that Randall and his colleagues have embraced. It would also require a rejection of
the national calculus-readiness averages, since assessments that account for attitude
might very well lead to a situation in which all students emerge from pre-calculus as
“calculus ready.” By presenting the stories of these two students who missed the final
exam, Randall supports a different system, one in which numbers alone indicate calculus
Segment 2: The numbers dilemma
Another dilemma arose as the instructors discussed the effect of adding four percentage
points to each student’s grade, in order to make the class average 75%. Sara determined
that, using this scheme, 78% of students would pass. She described this as “a lot,” and “a
high percentage.” Notice the comparison implicit in the adjectives, “a lot” and “high.” A
number can only be “a lot” or “high” relative to some normative state. The normative
pass rate remains implicit for a few turns until Yeva asked, “what’s supposed to happen?”
1630 YEVA: What’s supposed to happen?
RANDALL: Nat- National averages for Calc I is about 35 to 40
percent fail. So that’s Calc I. ((Y: Okay)) So
1635 figure [I think it would actually be higher-
JOE: [I think this is supposed to happen ((Draws a
vertically-oriented distribution to the left of the
grade ranges on the board))
RANDALL: I think it would actually be higher=
1640 ADELE: [It gets pregnant? ((Referring to the similarity of
the shape of the curve to a pregnant woman’s belly))
JOE: [A normal distribution around C
RANDALL: =but it’s lower, right? So you failed 35 percent of
Calc I students, I’m thinking here it would be five-
1645 ten percent higher.
YEVA: I would think it would be higher, too=
RANDALL: I would think it would be higher
YEVA: =because you’re really [not supposed to move
ADELE: [For this population
1650 YEVA: Yeah
ADELE: Right, so
RANDALL: But, I mean, the numbers are what they are, I mean, I
don't know.
In response to Yeva’s question, Randall invokes national failure rates for Calculus I, and
there is broad agreement among the instructors that the failure rate for their course should
be higher. Empirically, however, the failure rate is lower. This occasions a dilemma: not
enough students are failing.
In line 1653-54, Randall offers a tentative resolution to the dilemma, which is to trust the
veracity of the empirical numbers over what is “supposed” to happen. However, by
sprinkling the resolution the particle “I mean” and ending with a face protecting, “I don’t
know,” he signals that this resolution should be understood as tentative.
Why is Randall tentative here? From a technocratic perspective, Randall’s solution is
perfectly acceptable. From this perspective, actually, there is no dilemma. The numbers
literally “are what they are.” The dilemma only occurs because the technocratic solution
conflicts with the particular historical location of the instructors—that is, a location in
which, historically, a particular failure rate is realized. This history matters to the
instructors, otherwise Sara’s claims about the pass rate being “high” and Yeva’s question
about what is “supposed” to happen would not be sensible. Each would have had to
account for discursive moves that invoke history. Neither did, and thus we can surmise
that the historical precedent matters to the instructors.
If we couple this understanding of the historical location of the instructors with a
perspective that the instructors are concerned with “making sense,” then Randall’s
hedging is sensible. His purely technocratic solution still leaves a question of why these
numbers are behaving badly—viz. ahistorically. In the next turn, Joe introduces a means
of interpreting the behavior of the numbers, by constructing students in a particular way.
1655 JOE: There’s a lot of people who, um, I mean most
everybody in this class is, basically reviewing
everything, right?
SARA: Yeah.
Although students have been invoked in this meeting, this particular characteristic of the
students—that most of them are “reviewing”—has not been invoked yet. It was always
there, of course (see the immediate agreement and from Sara and Adele, with no
questions or contradictions from the others), but its salience has changed due to the
emergence of the “not enough failing” dilemma. In constructing students with this
characteristic highlighted, Joe offers a way to make sense of the numbers, which Randall
takes up:
1660 RANDALL: [Well, that’s why you see things with people that got
40s and then 90s, you know=
YEVA: [Yeah.
ADELE: [Yeah.
RANDALL: =Cuz they just decided to care [for that exam.
1665 YEVA: [um-hmm, exactly
ADELE: It took ‘em two exams to figure that out.
RANDALL: Yeah, and that’s why we can’t say things, “well this
person could go on, ((Y: yeah)) or this person
deserves” because it’s not about aptitude. It’s
1670 about their attitude.
YEVA: Yeah, [exactly. Exactly.
SARA: [Right.
ADELE: [Oh yes.
RANDALL: We have to justwhatever the number are, we just
1675 gotta roll with them.
ADELE: Yeah, I think so. !
In a sequence of turns, with overlapping agreement turns interwoven, Randall produces
an account for the behavior of the numbers. Essentially, because students are all
reviewing, the numbers represent a student’s attitude, rather than their aptitude. And
students’ attitudes vary from exam to exam. Producing a high score on an exam is “just”
a function of “decid[ing] to care” about “that exam” (italics added). Because of this
variability, the instructors shouldn’t expect the numbers to be consistent across time. The
sequence ends with Randall offering the same resolution that he had offered earlier, only
this time the resolution is stated as an imperative. They “have to” go with the numbers.
Adele’s uptake, in turn 26, signals that no further accounting is necessary. She agrees
with the account, and then uses the marker “so” to indicate that the remainder of the turn
is contingent on the acceptance of Randall’s resolution. Subsequent turns build on
Adele’s turn and thus tacitly accept Randall’s resolution.
In this segment, students got constructed in a particular way to resolve a practical
dilemma. In doing so, the instructors accomplish the ideology that numbers are fair and
accurate representations of students. In the beginning of the segment, this ideology was
under threat, because based on the numbers, not enough students were failing. By
constructing students as “reviewers” whose “attitudes” vary wildly from exam to exam,
Randall and Joe were able to sensibly account for the threat, thus resolving the dilemma
while maintaining the ideology. In addition, Randall constructs an identity for the
instructors as objective, neutral, and fair arbiters, people who “roll with” the numbers
without questioning them.
Segment 3: Dilemmas of cheating, time, and objectivity
In this final segment, we examine a stretch of discourse that is different in several ways
from those analyzed above. First, this segment takes place after the grading tasks have
been completed; at this point in the meeting, Yeva has left for her office, and Adele, Joe,
Sara, and Randall remain in the room. Second, this segment involves an enactment of
students, rather than simply reference to students; that is, the instructors are playing out
an (imagined) scenario in which they are interacting with students as part of a “game
Just prior to the start of this segment, the instructors have engaged in a lengthy
conversation about “cheating,” an activity that they take to clearly threaten the fairness of
the grading process. Adele, beginning in line 2591, expresses a wish that the instructors
could eliminate cheating on exams by administering individual oral exams:
2591 ADELE: Hmm. [I wish we had time=
JOE: [They (inaudible)
ADELE: =to do oral exams for the finals, but we don’t have
time, ((R: go ahead)) even next semester. We ha- If
2595 we have 60 students, the three of us, there wouldn’t
be time.
SARA: That might be too subjective.
RANDALL: [Umm, maybe
ADELE: [Yeah, unless we did it together, the three of us.
2600 SARA: Ohhh, yeah.
Adele’s suggested solution to the dilemma posed by student cheating, however, presents
a different dilemma—that is, the instructors don’t have sufficient time to individually
examine the number of students that they will be responsible for grading. Sara, in line
2597, adds a further dilemma, one in line with the ideology of objectivity, when she
suggests that such a procedure “might be too subjective,” indicating perhaps that
individual instructors might grade their students differently, as opposed to the present
grading procedures, in which each of the instructors is responsible for scoring certain
questions from all students across sections. Adele counters this “subjectivity” claim in
line 2599 with a suggestion that all three instructors could be involved in the oral
Randall goes on to take this conversation in a different direction, suggesting that such a
format, with a “panel of judges” could be made into a reality show:
RANDALL: A panel? [A panel of judges=
ADELE: [15 minutes
RANDALL: =You could make it into a reality show.
2605 ADELE: I like it. On the spot.
From this point, all four instructors begin to play out a scenario in which they and the
students are part of a reality show or game show:
RANDALL: [You know what, the students would probably love-
JOE: [Oh oh, and like, “lock in your answers!” [No
that’s brilliant.
RANDALL: [It’ll be-
2610 JOE: [They’ll do their work=
SARA: [It’s like a game.
JOE: =They’ll do their work on like an iPad that will like
project it, so we can see the work on the page, and
we’ll just grade based off of what we see on the
2615 page. We’ll lock in our [answer=
ADELE: [We won’t even know!
JOE: [=And then, they’ll come in!
ADELE: It’ll be like [The Voice, ((R: Yeah, yeah)) right?
“Turn around!” ((Laughs))
2620 JOE: [Yeah yeah! ((laughs)) And then they’ll
be like, “So, I thought that was a good problem. I’m
from Michigan.”
RANDALL: Why not- Hey, whatever incentivizes, who cares?
2625 ADELE: Oh, no, whatever makes our job easier. ((Laughs))
RANDALL: Yeah, no, that’s really it, yeah.
JOE: And then we show ‘em their grade right then and
ADELE: Yeah, right.
2630 RANDALL: [“Your grade is-
JOE: [We reveal!
ADELE: [And then [there’s the tears=
JOE: [Reveal!
ADELE: =and then they go=
2635 JOE: Eight!
ADELE: =“But I’m so grateful for the experience.”=
JOE: Seven point five.
ADELE: =”I’ll go on to be a better person.”
JOE: [“Pass.”
2640 RANDALL: [“Go sit with the other failing students!” ((laughs))
JOE: Oh yeah, maybe it’ll just be a pass or fail.
ADELE: [The pit!
JOE: [We’ll walk in, pass or fail.
RANDALL: Yeah, there you go.
2645 JOE: We’ll uncover it
ADELE: Yeah, oh, crap! I gotta go! I got another meeting.
Throughout this segment, the instructors build up this scenario, drawing on practices that
are found in such shows as “Who Wants to Be a Millionaire,” as when Joe in line 2607
tells a student to “lock in your answers,” and “The Voice,” explicitly mentioned by Adele
in line 2618, and then drawn on in line 2619 when Adele says, “Turn around,”
referencing the practice of judges in The Voice first being unable to see contestants, and
then turning around to view them.
For our purposes, several aspects of this segment are noteworthy. First, likening exam
grading to game show judging normalizes the competitive and high stakes nature of
examinations in determining whether or not a student will pass the course or not. Adele
references this in lines 2602 and 2605 when she says, “15 minutes,” and “I like it. On the
spot.” Second, the game show format foregrounds a view that only some
students/contestants can be permitted to, or ought to, be judged as worthy to pass, or to
continue in the competition. Third, for one of only very few times in this meeting, there
is some indication of the humanity of students, as when Joe provides a fictional
background for a student contestant in lines 2621-22 (“I’m from Michigan”) and Adele in
line 2632 recognizes that there are strong emotions associated with losing the competition
(“And then there’s the tears”). Fourth, Randall’s instruction to a competition loser in line
2640 (“Go sit with the other failing students”) indicates that they are aware that there are
consequences for those who are judged as failing, that they become located with “other
failing students,” out of or at least in a different place (“the pit,” Adele calls it) in the
Overall, this segment involves the playful construction of a scenario in which students are
separated into winners and losers by neutral, fair, objective judges who are concerned
only with the performance of contestants, and who take steps to make sure that they are
not biased in their high stakes judgments by students’ backgrounds, emotions, or any
other criteria that ought not to influence their evaluations.
6. Discussion
We have presented several segments of discourse in which an instructional team
constructs identity positions for students in the course of a meeting intended to translate
raw numeric scores into course grades, thus determining who is “calculus ready” and who
is not. We have shown that this is not simply a straightforward technical process, but
rather involves the construction of identities for both instructors and students. A major
focus of our analysis has been on the recognition and resolution of practical dilemmas in
the work of the instructors. These dilemmas often involve two different ways of viewing
students. On one hand, it is necessary given the institutional demands of their work that
they engage in an objective, fair, and neutral process for assigning grades to students,
thus assuring that only those students who “deserve” to pass are in fact the ones who pass
the course. On the other hand, there are indications that students are not just numbers on
a spreadsheet, but people with their own backgrounds, characteristics, interests,
problems, and futures. These differing ways of viewing students are, in the course of the
meeting, often constructed as incompatible, thus requiring instructors to choose between
them. In resolving this dilemma, the instructors construct themselves as fair, objective,
and neutral arbiters of who deserves to pass, and in so doing, they often construct the
students as having important personal, even moral, failings. Unsuccessful students are
not simply given low grades, but they are also held personally responsible for these
Our analysis suggests that, while there are multiple possible ways of viewing students,
they are viewed here primarily in terms of what Cech[17] has called an “ideology of
meritocracy,” that is, a belief “that inequalities are the result of a properly-functioning
social system that rewards the most talented and hard-working.” This ideology, Cech
argues, “legitimates social injustices and undermines the motivation to rectify such
inequalities.” [17, p. 67]
We want to acknowledge a limitation of our analysis. We recognize that such group
grade-setting meetings are very likely not the norm for courses in the calculus sequence,
in other courses that serve as pre-requisites for engineering, or in engineering courses. In
this sense, we would not expect our findings to generalize to the specific ways in which
students are “weeded out” at other institutions. At the same time, we believe that our
strategy of analyzing practical dilemmas of grading and sorting, whether this work is
carried out individually or in groups, is a potentially productive one in understanding
ideological aspects of success and failure.
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... Being more strategic about scheduling students into different lecture sections based on their concurrent math class is one potential means to address the two distinct tiers of students enrolled in Y2 and potentially in Y3 (Pre-Calc vs. Calc 1A). However, continuing to sort students based on math placement levels may have the undesirable effect of reinforcing math as a marker of status and progress through undergraduate engineering [15]. ...
... Not all students know that prerequisites are not strictly enforced at their particular department or institution, which puts the disadvantage of the prerequisite structure on students with low knowledge of how college works. (O'Connor 2015). ...
... Prior publications stemming from the overarching research project have explored the impact of math placement tests on student success through the mathematics curriculum [16], the initial success of the Pre-Calculus for Engineers course for GS students [17], and the negotiated and contested process through which students are assigned the milestone status of being "ready for calculus" as a result of this course [18]. This paper adds to the overall body of knowledge by examining the transition process and scaling-up of the Pre-Calculus for Engineers course, explaining via both qualitative and quantitative data what is lost and gained when a high-touch model for engineering education becomes incorporated into the larger structural production mechanisms of a public state research-active university. ...
... In other work O'Connor, Peck, Cafarella, Sullivan, Ennis, Myers, Kotys-Schwartz, & Louie, 2015) we have examined aspects of the cultural production of educated persons in the calculus sequence, focusing on consequences of collective action for students. This work demonstrated that "calculus readiness" is not simply a neutral, more-or-less accurate diagnosis of an individual state of knowledge. ...
Background Many engineering students fail to proceed through required prerequisite mathematics courses. Since these courses strongly influence engineering student attrition, we should examine to what degree these courses truly serve as prerequisites for following engineering coursework. Purpose/Hypothesis We examined two research questions: Which concepts and skills learned in calculus are applied in engineering statics and circuits homework assignments? How are calculus skills applied in engineering statics and circuits homework assignments? Design/Method This study analyzes the homework problems of two engineering courses—statics and circuits for nonmajors—using the mathematics‐in‐use method. These courses were chosen since they often require calculus as a direct prerequisite and are taken by most engineering majors. The mathematical content of each homework problem is carefully analyzed, with attention to alternative solution paths that may not match the instructor solution. Results Only 8% of statics problems and 20% of circuits for nonmajors problems applied calculus. Furthermore, these problems applied only the simplest calculus skills (e.g., integration of polynomials). Conclusions Circuits and statics apply relatively little calculus; most problems consist primarily of algebra. We may be able to modify prerequisite structures to ease or speed student progress.
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Facing increased pressure to improve retention and graduation rates, engineering departments are increasingly scrutinizing whether they are getting their desired outcomes from core mathematics coursework. Since mathematics courses are a significant source of attrition and many engineering faculty are unhappy with students’ mathematical abilities, more engineering departments are increasingly looking at drastic options of taking students out of mathematics courses and teaching students mathematics themselves. To mitigate this trend, it may be valuable to better understand what engineering faculty hope students learn from their mathematics coursework. When engineering faculty explain why they require these high-failure prerequisites, many claim that “mathematical maturity”, not calculus skill, is the desired outcome of completing the core math sequence of courses. To better understand what engineering faculty mean by “mathematical maturity”, we conducted a qualitative thematic analysis of how 27 engineering faculty members define “mathematical maturity”. We found that these engineering faculty believed that the mathematically mature student would have strong mathematical modeling skills supported by the ability to extract meaning from symbols and the ability to use computational tools as needed. Faculty frequently lamented that students had underdeveloped epistemic beliefs that undermined their modeling skills, thinking that mathematics is unrelated to the real world and has little practical value. They attributed these dysfunctional epistemic beliefs to their perception that mathematics is too often taught without genuine physical context and realistic examples. We suggest potential avenues for reform that will allow mathematics departments to better serve their client departments in engineering and thus retain control of their courses.
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In this chapter, I consider some ways in which linguistic anthropology can contribute to understanding "the cultural production of the educated person" (Levinson & Holland, 1996), to use a phrase that nicely captures an important focus in recent anthropological approaches to education. Work on cultural production is part of a broader project in the social sciences over the past three decades, a project that explores how both persons and forms of social organization are constituted through social practice. Among the major aims of this work has been to challenge conceptions of culture as a stable and relatively un-problematic body of knowledge that is transmitted from one genera tion to the next. Instead, culture is seen as a dynamic process in which agents create meaning by drawing on cultural forms as they act in social and material contexts, and in so doing produce themselves as certain kinds of culturally located persons while at the same time reproducing and transforming the cultural formations in which they act.
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The article proposes a framework for the analysis of identity as produced in linguistic interaction, based on the following principles: (1) identity is the product rather than the source of linguistic and other semiotic practices and therefore is a social and cultural rather than primarily internal psychological phenomenon; (2) identities encompass macro-level demographic categories, temporary and interactionally specific stances and participant roles, and local, ethnographically emergent cultural positions; (3) identities may be linguistically indexed through labels, implicatures, stances, styles, or linguistic structures and systems; (4) identities are relationally constructed through several, often overlapping, aspects of the relationship between self and other, including similarity/difference, genuineness/artifice and authority/delegitimacy; and (5) identity may be in part intentional, in part habitual and less than fully conscious, in part an outcome of interactional negotiation, in part a construct of others’ perceptions and representations, and in part an outcome of larger ideological processes and structures. The principles are illustrated through examination of a variety of linguistic interactions.
Engineers will incorporate considerations of social justice issues into their work only to the extent that they see such issues as relevant to the practice of their profession. This chapter argues that two prominent ideologies within the culture of engineering—depoliticization and meritocracy—frame social justice issues in such a way that they seem irrelevant to engineering practice. Depoliticization is the belief that engineering is a “technical” space where “social” or “political” issues such as inequality are tangential to engineers’ work. The meritocratic ideology—the belief that inequalities are the result of a properly-functioning social system that rewards the most talented and hard-working—legitimates social injustices and undermines the motivation to rectify such inequalities. These ideologies are built into engineering culture and are deeply embedded in the professional socialization of engineering students. I argue that it is not enough for engineering educators to introduce social justice topics into the classroom; they must also directly confront ideologies of meritocracy and depoliticization. In other words, cultural space must be made before students, faculty and practitioners can begin to think deeply about the role of their profession in the promotion of social justice.
Slow faculty uptake of research-based, student-centered teaching and learning approaches limits the advancement of U.S. undergraduate mathematics education. A study of inquiry-based learning (IBL) as implemented in over 100 course sections at universities provides an example of such multicourse, multi-institution uptake. Despite variation in how IBL was implemented, student outcomes are improved in IBL courses relative to traditionally taught courses,as assessed by general measures that apply across course types. Particularly striking, the use of IBL eliminates a sizable gender gap that disfavors women students in lecture-based courses. The study suggests the real-world promise of broad uptake of student-centered teaching methods that improve learning outcomes, ultimately, student retention in college mathematics.
It has long been an interest of researchers in economics, sociology, organization studies, and economic geography to understand how firms innovate. Most recently, this interest has begun to examine the micro-processes of work and organization that sustain social creativity, emphasizing the learning and knowing through action when social actors and technologies come together in ‘communities of practice’; everyday interactions of common purpose and mutual obligation. These communities are said to spark both incremental and radical innovation. This book examines the concept of communities of practice and its applications in different spatial, organizational, and creative settings. Chapters examine the development of the concept, the link between situated practice and different types of creative outcome, the interface between spatial and relational proximity, and the organizational demands of learning and knowing through communities of practice. More widely, the chapters examine the compatibility between markets, knowledge capitalism, and community; seemingly in conflict with each other, but discursively not.
Major paradigmatic changes in mathematics education research are drawing attention to new perspectives on learning. Whereas deficit models were previously in the foreground of research designs, these have been replaced by a wide variety of theoretical directions for studying diverse approaches to learning mathematics. There is now an acceptance of the need for richness and variety in research practices so that approaches can be studied, compared and mutually applied and improved. Psychological and quantitative approaches and methods are now increasingly complemented, or even replaced, by new directions that rely on social and anthropological theories and methods. Rather than reviving ideas about deficit research in mathematics education, the aim of this chapter is to present some socio-cultural perspectives of mathematics learning, and to show how these perspectives go beyond the deficit model of learning. Framing the main traditional markers of discrimination in school mathematics—gender, social class and ethnicity—in a perspective of social justice, the chapter concludes with a reflection on equality in terms of the democratic principle of meritocracy in mathematics education.