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While researchers have examined how disciplinary and departmental cultures inuence
instructional practices in higher education, there has yet to be an examination of this re-
lationship at the embodied level of culture. In this article we utilize cultural models theory
to examine the theories of student learning and teaching practice espoused and enacted
by undergraduate math and science faculty. To examine these cultural models of teaching
and learning we use thematic analysis, clustering, scaling, and graphing techniques to
analyze interview transcripts and classroom observation data among 41 undergraduate
math and science instructors across three universities in the United States. We then focus
on three individual cases of instructors to examine how their cultural models interact with
other cultural models, existing forms of teaching practice, and features of instructional
environments to shape their teaching practices. The article concludes by setting forth an
agenda for future research and arguing that the “cultures of teaching” in these disciplines
should not only be perceived as barriers but also opportunities for meaningful pedagogi-
cal innovation.
Keywords: cultural models, undergraduate education, STEM, culture, cognition, peda-
gogy
As we go about our day-to-day lives we encounter incredible complex-
ity in our relations with others and our surroundings. Yet, more often
than not, we move from one situation to the next without feeling the
full burden of this complexity because we have constructed models—or
Cultural Models of Teaching and
Learning in Math and Science: Exploring
the Intersections of Culture, Cognition,
and Pedagogical Situations
Joseph J. Ferrare is Assistant Professor in the Department of Educational Policy Studies
& Evaluation at the University of Kentucky; joseph.ferrare@uky.edu. Matthew T. Hora,
Ph.D., is Assistant Scientist at the Wisconsin Center for Education Research at Univer-
sity of Wisconsin-Madison.
Joseph J. Ferrare
Matthew T. Hora
The Journal of Higher Education, Vol. 85, No. 6 (November/December)
Copyright © 2014 by The Ohio State University
Cultural Models of Teaching and Learning 793
“theories”—of how people, events, and objects t together. Social sci-
entists often refer to these as cultural models because they consist of
shared information and are internalized through patterns of socialization
within and between groups. Consider, for example, that on the rst day
of a new semester thousands of students lter into lecture halls, nd
seats, and wait for someone to assume responsibility at the front of the
room. This coordination of action occurs without explicit instructions
because each student has a cultural model for how people and practices
typically t together in this particular situation. These models perform
valuable social and cognitive work with tremendous efciency, which in
turn allows us to take on more complex practices. Of course, the world
does not always work so smoothly—sometimes our cultural models
conict with other models, objects, and events, reminding us that cul-
tural models are often deeply political (Gee, 2004a).
Social scientists from across the disciplinary spectrum have contrib-
uted to a rich body of literature focusing on the theoretical and applied
aspects of cultural models (for a general introduction see D’Andrade,
1995). In education, researchers have drawn upon cultural models
theory to describe and enhance literacy practices (Gee, 2004b), stu-
dent achievement (Ogbu & Simons, 1994), and cross-cultural relations
(Fryberg & Markus, 2007), among other topics. However, researchers
focusing on higher education contexts have yet to fully appreciate the
utility of cultural models theory. While culture theory has been used
to examine the nature of faculty work in general (e.g., Austin, 1996)
and teaching strategies in particular (Umbach, 2007), these applications
have tended to view culture as a homogenous set of beliefs and values
ascribed to a single social group (e.g., an academic department) that op-
erates to unilaterally inuence faculty behavior. However, this view of
culture overlooks areas of culture theory that emphasize how norms and
practices are internalized by individuals as they interact with a variety
of social groups and situations, which leads to a more differentiated,
contextualized, and, at times, contradictory view of culture and its rela-
tionship to action (DiMaggio, 1997; Trowler, 2008).
In this article we argue that cultural models theory is a useful tool
that researchers and policymakers can use to understand and transform
teaching and learning at the undergraduate level—particularly in math
and science disciplines. Our emphasis on math and science faculty oc-
curs during a time of tremendous energy and resource allocation aimed
at enhancing the recruitment and retention of undergraduates in science
and math majors. Researchers and educators have framed these efforts
as an important component of racial and gender equity within the edu-
cation system and occupational structure (e.g., Carter, 2006; Fox, Son-
794 The Journal of Higher Education
nert, & Nikiforova, 2011). In addition, many argue that undergraduate
science and math education is a critical factor in achieving economic
vitality (National Science Board, 2010), as projections estimate that the
fastest growing jobs requiring a college degree in the next ve years
will require extensive training in science and mathematics (Carnevale,
Smith, & Melton, 2011; Lacey & Wright, 2009).
One of the principal strategies employed to achieve these goals has
been to encourage science and math faculty to adopt pedagogical tech-
niques that are grounded in research on how people learn (e.g., Brans-
ford, Brown, & Cocking, 1999). Yet, preliminary evidence suggests
that the widespread adoption of these teaching practices has not yet
occurred (President’s Council of Advisors on Science and Technology,
2012), and one of the main reasons cited for this state of affairs is that
the disciplinary and organizational cultures of academia represent barri-
ers to change. Consequently, some are calling for a change in the “cul-
ture of teaching” among science and math faculty and departments at
large research universities (Anderson et al., 2011; Wieman, Perkins, &
Gilbert, 2010).
In the following we examine cultural models of teaching and learn-
ing in math and science as networks of cognitive schemata that are dis-
tributed between and among groups of faculty, and whose instantiation
in the classroom is mediated by perceived constraints and affordances
in instructional practices and environments. The construction of this ar-
gument is built around the exploration of three specic questions: (1)
What cultural models do math and science instructors have for how
students best learn the key concepts in their respective elds and for
the most effective ways to introduce students to those concepts? (2) To
what extent are these models enabled and/or restricted by instructors’
perceptions of constraints and/or affordances within their instructional
environments (e.g., class size, classroom technology, and student ex-
pectations)? (3) How might our understanding of these cultural models
inform the efforts to transform pedagogical practices in the math and
science disciplines?
To address these questions we drew upon interview and classroom
observation data collected from 41 instructors from math and science
disciplines across three research-intensive universities. We began by
using cluster analysis and multidimensional scaling to analyze thematic
codes derived from the interviews and to explore the principles underly-
ing these components of the cultural models. In the next phase, we drew
upon classroom observation data and interview transcripts to explore
the extent to which the models of three instructors guide their pedagogic
decisions and practices as they are activated in specic instructional sit-
Cultural Models of Teaching and Learning 795
uations. In addition, we used graphing techniques from social network
analysis to illustrate the different congurations of teaching methods,
cognitive engagements, and instructional technology use that constitute
each participant’s classroom practice. These data are brought into con-
versation with the interview transcripts to demonstrate how the instruc-
tors’ cultural models of teaching and learning are enabled, mediated,
and constrained at the intersections of cognition, social practice, and
instructional contexts.
The results from the analysis are suggestive for those interested in
undergraduate education, particularly the math and science disciplines.
These ndings offer researchers, instructional designers, and policy-
makers insights into how math and science faculty “theorize” student
learning and their own role in that process. While the theoretical under-
standing offered here portrays a complex account of cultural practice
that does not offer a single policy or leverage point to affect change, we
suggest that such a nuanced view of the processes underlying educa-
tional practice and change processes is nevertheless an advance over the
“silver bullet” perspective of educational transformation.
The Interface of Culture and Cognition: Cultural Models Theory
Attention to the role of culture in postsecondary institutions has a
long history. One of the dominant approaches to understanding culture
in academia has been to view culture as a unitary set of beliefs, values,
and practices that can be ascribed to entire disciplines or institutions.
This conceptualization of culture has led to the development of cultural
typologies (e.g., Bergquist, 1992) through which culture is used as an
independent variable in statistical analyses that predict faculty prac-
tice (e.g., Umbach, 2007). In recent years, however, researchers have
critiqued this perspective of culture theory for ignoring within-group
variability and faculty subcultures (Trowler, 2008), obscuring the inter-
pretive and evolutionary nature of cultural life (Tierney, 2008), and for
overlooking the subtle dynamics between individuals and the diverse
contexts of academic organizations (Ashwin, 2008; Trowler, 2008).
Cultural models theory—when combined with theoretical insights from
sociology and cognitive psychology—provides an insightful point of
departure for understanding these dynamics.
The development of cultural models theory has been guided by a de-
sire to understand how individuals internalize, organize, and enact cul-
tural knowledge. In particular, researchers have sought to understand
how cultural knowledge is organized into cognitive structures (often
referred to as “schemata”) held in long-term memory and activated in
796 The Journal of Higher Education
specic situations and environments. Cognitive anthropologists dene
cultural models as simplied theories about relations among people,
practices, and events that are developed through the repeated activation
of neural networks in relation to specic tasks and situations (Quinn &
Holland, 1987). These cognitive structures are distributed within and
between groups and linked to (prototypical) simulations in our minds
that help us assemble meanings and act upon them in social situations.
While cultural models generate meanings, explanations, and practices in
a similar fashion to any scientic theory, they are often implicitly held
and thus difcult to articulate at a theoretical level (Quinn & Holland,
1987). However, individuals can usually offer insights into the work-
ings of their cultural models through judgments, perceptions, and ex-
planations of specic situations (D’Andrade, 1992, p. 34). In this sense,
cultural models frequently operate as a form of practical reason (Bour-
dieu, 1990).
Cultural models are not xed rules for behavior that, upon activa-
tion, immediately translate into specic actions. Instead, cultural models
have a causal form that allows us to act in the world without having to
fully consider all possible actions at the same time. These models as-
semble situated meanings on the spot, which in turn enable us to make
sense of complicated processes without necessarily considering every
detail (Gee, 2005). This does not mean that cultural models always gen-
erate reliable meanings or that knowing an individual’s cultural models
makes his or her behavior predictable in every situation. To the contrary,
cultural models are often inconsistent, incomplete, and/or exist in con-
ict with other cultural models.
The dynamic nature of cultural models is partly due to the fact that
different models are closely linked to features of the environment, such
that certain cues (e.g., a large classroom) not only activate a related net-
work of schemata but also constitute a part of the schema itself. Re-
search in cognitive psychology shows that environmental features are
noticed and encoded based largely on our physical interactions with
the world, and these embodied conceptualizations of the environment
are then combined with preexisting knowledge to form memories of
our surroundings (Glenberg, 1997). Furthermore, different organisms
will respond to different features of their environment based on their
unique needs and properties, such that some objects will be perceived
as “affording” particular uses or actions (Gibson, 1986). In the same
way, people can perceive objects or other entities to pose constraints
to practice, or otherwise discourage a particular use or limit the range
of possible actions. Individuals and groups will develop attunements to
the constraints and affordances represented by objects, policies, norms,
Cultural Models of Teaching and Learning 797
and social regularities in a given environment, which over time can be-
come a core aspect of decision heuristics or rules for particular tasks
(Greeno, 1998). In this way, rather than perceiving culture as inhering
in either public information “out there” or solely cognitive structures in
the mind, a more compelling view focuses on the interactions among
each of these realms (DiMaggio, 1997, p. 274).
Cultural models tend to be distributed unevenly within and between
social congurations. That is, there are divisions of labor to cultural
knowledge that differentiate who needs to know what. For cognitive
anthropologists such as D’Andrade (1984), these social structures are
aspects of the organization of cultural meaning systems—“the achieve-
ment of systematicity across persons through meanings” (p. 110). Criti-
cal theorists are likely to add that these social structures are also the
means by which certain forms of cultural knowledge are maintained as
scarce commodities and legitimate symbolic domination (e.g., Bour-
dieu, 1984). Thus, just as we rely on our cultural models to perform
important cognitive work, we also rely on social structures to perform
the consequential social work of dividing the cognitive labor within and
among groups. There is, then, a duality between social structure and
culture in which the patterning of social interactions and afliations
happens alongside differentiated cultural meanings and strategies (Mohr
& Duquenne, 1997).
Thus, an examination of cultural models in any context involves
understanding cultural knowledge as distributed at the individual and
group levels, as well as existing at the intersections of environmen-
tal and situational contexts (e.g., classrooms), social practices (e.g.,
teaching strategies and interactions), and cognition (e.g., folk theories
of teaching). It is at these intersections that we can gain insight into
the ways that instructors’ cultural models are enabled, adapted, and
even constructed in relation to constraints and affordances in teaching
practices, interactions with students, and features of their instructional
settings.
Specifying Cultural Models of Teaching and Learning
Although some researchers have paid close attention to the rela-
tionship between teaching practices and culture in higher education
(Trowler, 2008; Umbach, 2007), the literature lacks a targeted analysis
that connects these practices to instructors’ cultural models of teach-
ing practice and student learning. In this article we examine instruc-
tors’ cultural models of teaching and learning through the assumptions
they make about the ways students best learn the key concepts of their
disciplines and the most effective ways to introduce students to those
798 The Journal of Higher Education
concepts. Until now, we have considered only the general form of cul-
tural models. In order to investigate cultural models of teaching and
learning among math and science instructors it will be helpful to iden-
tify the form and functional work that these models perform as distinct
from other types of models. For this task we use the conceptual typol-
ogy of cultural models developed by Shore (1996, pp. 46–66).
The types of cultural models investigated below are examples of
special-purpose models comprising a combination of expressive/
conceptual models and task models (Shore, 1996, pp. 61–66). Expressive/
conceptual models designate crucial yet often tacit information and ex-
periences within (and sometimes between) certain communities. Among
the different types of expressive/conceptual models, undergraduate in-
structors’ cultural models of teaching and learning can be dened more
specically under the category of theories. This type of expressive/
conceptual model helps to simplify complex processes and interactions.
The cultural models of teaching and learning discussed below consist,
in part, of theories that range from tacit folk theories to more elaborate
scientic theories, and sometimes combinations of both.
Other components of the cultural models of teaching and learning
discussed below can be conceptualized as task models. As the name
suggests, task models organize strategies for completing practical tasks.
“Scripts” are a type of general performance task model that are com-
monly drawn upon (often implicitly) in instructional situations. For
instance, many mathematics instructors have a script for introducing
students to a new theorem. One such script proceeds as follows: The
theorem is introduced and proved as an abstract form and then followed
up by working through a series of example problems. Students are then
assigned problem sets that require them to work through more example
problems germane to the theorem. The cultural models of teaching and
learning explored below each consist of a theory of student learning
and a script for facilitating that learning. In practice, the line between
expressive/conceptual and task models may not be so clear, but the ana-
lytical distinction is helpful in understanding the different kinds of work
actually done by these cultural models.
Methodology: Analyzing Cultural Models of Teaching and
Learning in Theory and Practice
Researchers interested in examining cultural models have used a
variety of methodological strategies. These strategies include scaling
of judged similarities and clustering of folk taxonomies (D’Andrade,
Cultural Models of Teaching and Learning 799
1995), consensus modeling (Weller, 2007), as well as a variety of dis-
course analysis techniques (Gee, 2005). In this article we draw upon
multiple tools from within and outside the cultural models literature
to construct the cultural models of teaching and learning among all in-
structors in the study sample, and to examine how three of the instruc-
tors enact and use these models in practice. Details concerning our mul-
tistep analytical strategy are described below.
Data Sources
To examine the cultural models of teaching and learning among math
and science instructors we draw upon data collected through semis-
tructured interviews and classroom observations among undergraduate
instructors (N = 41) in math, physics, chemistry, biology, and geology
departments across three large research universities. As noted above,
the primary concern among reformers and policymakers is transforming
undergraduate STEM instruction at large research universities (Wieman
et al., 2010). Thus, the three sites in this study were selected specically
because they share the following characteristics: (a) public research-
intensive institutions as dened by the Carnegie Foundation for the Ad-
vancement of Teaching; (b) institutions with undergraduate enrollments
of similar size; and (c) institutions with similar 4-year averages of NSF
Division of Undergraduate Education (DUE) funding, which is a mea-
sure of the level of pedagogical reform activities at a given institution.
Based on these criteria, we selected Institution A located on the West
Coast, Institution B located in the Mountain West, and Institution C lo-
cated in the Midwestern United States.
A variety of pedagogical reform initiatives were active during the
time of data collection. At Institution A both the physics and biology
departments had external support for faculty development and curricular
reforms, and a campus-wide teaching and learning center offered work-
shops for students and faculty. At Institution B a major cross-disciplin-
ary effort involving curricular reform and targeted technical assistance
was active, in addition to other campus-wide and departmental efforts.
At Institution C a cross-disciplinary initiative focused on doctoral edu-
cation provided workshops to students and faculty, along with other ef-
forts including a center focused on biology education. Finally, at each
institution cross-disciplinary initiatives had engaged faculty from math-
ematics, chemistry and geology.
The sampling frame for this study included all individuals listed in
the spring 2010 timetable as the instructor of record for undergraduate
courses in math, physics, chemistry, biology, and geology departments
across the three institutions. Our focus on these courses was driven by
800 The Journal of Higher Education
the desire to examine instructional practices across the whole range of
undergraduate education in these elds—including the so-called “gate-
way” courses, upper-level courses for majors, and lower-level courses
for non-STEM majors. Thus, our sample included courses such as: Gen-
eral Chemistry, Organic Chemistry, General Physics, Mechanics, Calcu-
lus, Differential Equations, General Biology, Developmental Biology,
Intro to Geology, among others. Given our focus on these undergraduate
courses it should come as little surprise that over half of our participat-
ing instructors were non-tenure track (NTT) faculty at the time of the
data collection (see Table 1). Indeed, national estimates show that over
half (56.2%) of instructors across all institutions of higher education are
NTT faculty, a trend that appears to be steadily increasing since 1975
(American Association of University Professors, 2009).
A team of three researchers conducted all data collection activities
during the Spring semester of 2010. For the interviews, a semistructured
protocol ensured that all researchers asked the same general questions,
but interviewers were encouraged to explore certain themes if presented
an opportunity in the moment. One researcher observed two class peri-
ods of each participant, with interviews typically taking place immedi-
TABLE 1
Sample Characteristics
n / %
Sex
Female 19 / 46.3
Male 22 / 53.7
Discipline
Math 15 / 36.5
Physics 6 / 14.6
Chemistry 4 / 9.8
Biology 8 / 19.5
Geology 8 / 19.5
Position/Rank
Lecturer/Instructor 25 / 61.0
Assistant Professor 2 / 4.9
Associate Professor 3 / 7.3
Professor 11 / 26.8
Cultural Models of Teaching and Learning 801
ately prior to or after an observed class. During the data collection we
were sensitive to the possibility that the interview and our classroom
presence may inuence instructors’ teaching practices. In order to mini-
mize this inuence we maintained a low prole in the classroom and
made the effort to clarify that our research objectives were purely basic
and exploratory rather than evaluative. While our interviews certainly
prompted greater reection about instructional practices than many of
the participants typically engage in, given the candid and critical re-
sponses we recorded during the interviews we did not get the impres-
sion that our presence was considered threatening or judgmental toward
their instructional practices. Finally, given the variety of pedagogical re-
form initiatives underway at the three sites, many of the instructors were
already accustomed to having the presence of researchers or evaluators
in their departments and classrooms.
For this specic analysis we focused primarily on the participants’
responses to the following two questions: (1) What is your view about
how students best learn the key concepts in your eld? (2) What are the
most effective ways to introduce students to these key concepts? These
questions were part of a longer interview with each instructor ranging
between 30–60 minutes. While we focused primarily on participants’
responses to the two questions above, we also used a number of utter-
ances from across the entire interview. The interviews were conducted
in the privacy of participants’ ofces and the audio recordings were
later transcribed.
In addition to the interviews, each participant was observed for two
full class periods using the Teaching Dimensions Observation Protocol
(Hora & Ferrare, 2013), which was used to code the instructors’ use
of teaching methods (e.g., lecture, small group work, demonstration),
student/instructor interactions (e.g., forms of Q&A), cognitive engage-
ments (e.g., memorization, problem solving, creating), and instructional
technologies (e.g., clickers, chalkboard, slides) at 5-minute intervals
throughout the duration of each observed class period. Prior to the ob-
servations, the three researchers participated in a 3-day training process.
In order to test inter-rater reliability, the analysts coded three videotaped
undergraduate classes (two in chemistry and one in mathematics). The
following Kappa statistics were observed for each pair of raters: Ana-
lyst 1/Analyst 2 (.699), Analyst 1/Analyst 3 (.741), Analyst 2/Analyst 3
(.713).
Constructing Cultural Models of Teaching and Learning
The rst phase of the analysis involved two distinct steps: (1) a the-
matic analysis of the interview transcripts, and (2) clustering/scaling
802 The Journal of Higher Education
of the derived themes. All interviews were transcribed and entered into
NVivo® qualitative analysis software. Two analysts developed an initial
coding scheme in order to segment the data into thematically coherent
units. In developing the initial code list, the two analysts conducted an
inductive analysis of the data that entailed comparing each successive
instance of the code to previous instances in order to conrm or alter
the code and its denition (i.e., the constant comparative method) (Gla-
ser & Strauss, 1967). The two codes created during this process that are
salient to this article include “views of student learning” and “introduc-
ing new topics.” Prior to coding the entire sample, the analysts applied
the coding scheme to ve transcripts and inter-rater reliability was as-
sessed by calculating the percentage of agreement between the analysts
in applying the codes. The percentage of instances in which both ana-
lysts coded the same code relative to all coded instances was 89%.
Next, an in-depth analysis was conducted of all text fragments coded
as “views of student learning” and “introducing new topics” in order
to identify recurrent themes and patterns (Ryan & Bernard, 2003). This
entailed an open coding and constant comparative process as detailed
above. In analyzing the “introducing new topics” themes we discov-
ered that, while many participants had the same themes, the sequence in
which the themes were reported varied substantially. We therefore took
a second step in our thematic analysis in order to derive the temporal
sequence through which the themes were connected.
The second step involved creating a participant-by-thematic code
matrix in which each cell indicates whether participant i expressed the-
matic code j (1) or not (0). We then used cluster analysis and multi-
dimensional scaling to explore the dimensions underlying the relation-
ships within and between the two sets of themes (i.e., views of learning
and new topics sequences). Cluster analysis is a nonstatistical procedure
for partitioning objects (i.e., themes) into groups based on (dis)similar-
ity as measured through a distance matrix (in this case binary squared
Euclidean distance). The particular clustering algorithm used in this
analysis is referred to as Ward’s Method, which begins with each theme
(or theme sequence) as its own cluster and ends with a single cluster
that contains all the themes. In between the beginning and end are the
stages of clustering that are based on the merging of clusters that result
in the smallest increase in the value of the sum of squares index by the
clustering (Romesburg, 1984). The primary output in cluster analysis
is the dendrogram—a diagram that illustrates the clusters and decision-
steps the algorithm made to attain them.
As a complement to the cluster analysis we used multidimensional
scaling (MDS). Rather than partitioning the themes into mutually ex-
Cultural Models of Teaching and Learning 803
clusive clusters, MDS is a technique for graphically representing the
proximities (i.e. [dis]similarities) between objects (e.g., interview
themes) as distances in a low dimensional space. Two advantages of
using MDS as a complement to cluster analysis include the ability to
assess the t of the solution (discussed below) and to interpret the la-
tent dimensionality of the distances. The latter advantage provides op-
portunities for the analyst to interpret the underlying (and unobserved)
principles that explain the relative positions and distances between
objects in the data space. This interpretive step is very similar to the
interpretation of components in principal component analysis (Borg &
Groenen, 2005).
In the present application of MDS distance is conceptualized as Eu-
clidean distance, which is simply the geodesic between two points. In a
two-dimensional solution (X) the Euclidean distance (d) between points
i and j can be expressed as:
( ) ( )
22
11 2 2ij i j i j
d xx xx= − +−
(1)
Euclidean distance can be re-written more generally to apply to
m-dimensions:
( )
1/2
2
1
m
ij ia ja
a
d xx
−
=
=
∑
(2)
An optimal MDS solution is one in which the distances closely ap-
proximate the proximities. Borg and Groenen (2005) refer to this as a
representation function (f):
f : δ
ij
→ d
ij
(3)
in which f indicates the type of MDS model. There are numerous types
of MDS models, but by far the most common in social science research
is ordinal (or nonmetric) MDS. In ordinal MDS the proximities are
treated as a rank ordering rather than an actual distance. Therefore, the
distances (d
ij
) are regressed on the proximities (δ
ij
) by way of a mono-
tonic function. The resulting differences between the monotonic regres-
sion line and the nonmonotonic line are referred to as the disparities
(
ˆ
ij
d
), which represent a smoothed version of the distances (d
ij
).
In order to assess the t between the disparities and the distances ana-
lysts typically evaluate the “stress” value, which is a nonstatistical mea-
804 The Journal of Higher Education
sure of badness-of-t. Kruskal’s Stress is most appropriate for ordinal
MDS (Borg & Groenen, 2005; Kruskal & Wish, 1978):
(4)
( )
2
2
ˆ
[]
ij ij
i ji
ij
i ji
fd d
Stress
d
≠
≠
−
=
∑∑
∑∑
where f in this case refers to the monotonic function. While Kruskal and
Wish (1978) construct an arbitrary range for acceptable stress between
0.00 (perfect) and 0.2 (poor), Borg and Groenen (2005) suggest that in
practice researchers should factor in the ratio of dimensions (m) to ob-
jects (n) and the point at which increasing dimensionality no longer sub-
stantially improves t.
A Case-Analytic Approach to Analyzing Cultural Models in Action
The second phase of the analysis focused on three instructors in order
to examine individual instantiations of the cultural models of teaching
and learning identied in the analysis of themes. The three cases were
selected according to three criteria. First, we sought to select cases that
together would exemplify the full range of our ndings from the cluster
and scaling analysis of interview themes. Second, the three cases each
represent courses that serve a different role in the trajectory of STEM
majors. For example, our rst case below is of an instructor teaching an
introductory biology course for majors (i.e. a “gateway” course). The
second case is of an instructor teaching a midlevel mathematics course
that is required of many STEM majors. The third case includes an in-
structor teaching an upper-division course that serves as a capstone for
biology majors. Finally, each case represents an instructor that is differ-
entially positioned within their respective departmental and disciplinary
communities with respect to tenure status, research interests, and schol-
arly productivity. Thus, while it is not possible to statistically general-
ize from these three cases, the criteria used for selection are intended
to provide a more in-depth look at the variety of cultural models we
observed in relation to a range of positional contexts (i.e. tenure and
disciplinary status) and instructional situations.
In each case the instructor’s themes were unpacked in order to exam-
ine more specic meanings associated with his or her cultural model,
and to analyze the models in relation to their observed teaching prac-
tices. In addition to the narrative accounts of the observed classes, we
used graphing techniques from social network analysis to represent the
Cultural Models of Teaching and Learning 805
co-occurrences between the different coded dimensions of practice:
teaching methods, student/teacher interactions, cognitive engagements,
and instructional technologies. Social network analysis represents a
range of analytical and theoretical tools used to examine and interpret
relations between sets of actors and/or events (Wasserman & Faust,
1994), such as simple directed and undirected graphs to more formal
modeling approaches. Following Hora and Ferrare (2013), we use sim-
ple undirected graphs to explore the afliations between instructional
“events” across the different dimensions of practice.
The raw data for this analysis are in the form of two-mode (or af-
liation) matrices that consist of each instructor’s 5-minute intervals as
rows (mode 1) and observation codes as columns (mode 2). In each ma-
trix a “1” denotes that the particular code was present in the observed
interval, and a “0” denotes that the code was not present in that ob-
served interval. Each two-mode matrix was transformed into a one-
mode (code-by-code) valued co-occurrence matrix in which each cell
corresponds to the number of intervals that observation code i is afli-
ated with code j. Next, we used the program NetDraw (Borgatti, 2002)
to graph the co-occurrences between each pair of codes for each instruc-
tor. The lines connecting the codes denote a co-occurrence (i.e., codes
that were co-coded in the same interval), and the line thickness indicates
the relative strength of the co-occurrence. Thus, for each instructor a
network afliation graph provides a graphical snapshot of their instruc-
tional practices and serves as a basis for linking the cultural models of
teaching and learning to concrete classroom activities.
Cultural Models of Teaching and Learning Among Math and
Science Instructors
The presentation of results follows three steps. First, we present the
themes derived from the thematic analysis of the interview transcripts.
Next, we illustrate the results of the cluster analysis and MDS of the
themes, drawing primarily on the dendrogram and the MDS plot (shown
in Figures 1 & 2, respectively, below) to describe the principles of or-
ganization underlying the “views of learning” themes and “introducing
new topics” sequences constituting the cultural models. Finally, we con-
clude with the three case analyses.
Thematic Analysis
The thematic analysis yielded 15 distinct “views of learning” themes,
10 “new topics” themes, and 3 “new topics” sequences. Table 2 de-
scribes the “views of learning” themes in descending order of frequency.
806 The Journal of Higher Education
By far the most prevalent theme is “practice/perseverance,” which
was coded in half (53.7%, n = 22) of the interviews. This theme is pred-
icated on the belief that students learn best through a sustained struggle
to solve problems (both computational and conceptual) on their own.
As one math faculty member stated, students “will not learn until they
do it a thousand times.” Interestingly, several faculty described this
view in physical or even violent terms, such as “banging one’s head
against the table,” “mental weight lifting,” and “grinding away at it.”
One-third (34.1%, n = 14) of the participants expressed the view that
the classroom is not a good venue to learn the key concepts of their
respective disciplines (the “outside the classroom” theme). In other
words, faculty expressing this view felt that of all possible learning en-
vironments (e.g., laboratories, discussion sections, eld work) the class-
room format, particularly large “lecture” style classes, was the least
amenable to facilitating student learning. In disciplines such as geology
and biology, where research experiences in the eld are a core part of
advanced undergraduate and graduate training, faculty stated that stu-
dents only really understand how to “do science” when they are forced
TABLE 2
“Views of Learning” Themes Derived From the Thematic Analysis
Views of Learning n Description
Practice/Perseverance 22 Learning comes from prolonged effort in solving problems (often by oneself).
Application 14 Learning is best facilitated through active, hands-on engagement with the
material (e.g., labs, eld work).
Outside the classroom 14 The classroom is not the best venue for learning.
Articulating 13 Students learn best when vocally articulating their own thoughts, ideas, and
problem-solving processes to others.
Variability 12 Students learn differently (e.g., visual, auditory, hands-on, etc.).
Visualizations 11 Students learn effectively when material is put into visual or physical form.
Construction 10 Students must actively develop their own understandings of the material.
Experiential 9 Learning is best facilitated when course material is explicitly linked to students’
own experiences.
Scaffolding 7 Learning is best facilitated when course topics are presented in a sequential
fashion from least to most difcult.
Clear explanations 5 Learning is best facilitated through the clear explanation of topics.
Examples 4 Students learn from concrete examples and illustrations of course material.
Repetition 4 Students learn through repeated exposure to a topic or idea.
Osmosis 2 Students learn by being in the presence of an expert (i.e., an academic).
Individualized 2 Learning is facilitated through one-on-one interaction with an instructor.
Memorizing 1 Learning is accomplished through memorizing facts or computational rules.
Cultural Models of Teaching and Learning 807
to design studies or collect and analyze data in the eld (i.e. outside the
classroom).
Many instructors (34.1%, n = 14) expressed the view that learning the
key concepts is done through “application” involving hands-on engage-
ment with the material. For example, a physics faculty member stated
that students should take the principles of physics gleaned from their
classes or readings and “apply them to real things.” Other frequently
mentioned views of learning, described in more detail in Table 2, in-
clude “articulating” (31.7%, n = 13), “variability” (29.3%, n = 12), “vi-
sualizations” (26.8%, n = 11), “construction” (24.4%, n = 10), “expe-
riential” (22.0%, n = 9), and “scaffolding” (17.1%, n = 7). Less fre-
quently mentioned views include “clear explanations” (12.2%, n = 5),
“examples” (9.8%, n = 4), “repetition” (9.8%, n = 4), “osmosis” (4.9%,
n = 2), “individualized” (4.9%, n = 2), and “memorizing” (2.4%, n = 1).
Table 3 describes the “introducing new topics” themes and sequences
in descending order of frequency. Every participant (n = 41) mentioned
“covering,” which is simply the idea that the topic is dened in gen-
eral or abstract terms (e.g., a theorem is presented or “oscillation” is
dened). The next most frequently referenced views of how to best in-
troduce students to key concepts is “scaffolding” (51.2%, n = 21, e.g., “I
always try to use connections to things they already know.”) and “prac-
ticing/examples” (48.8%, n = 20). Other themes, described in Table 3,
include: “assessing” (26.8%, n = 11), “motivating” (26.8%, n = 11),
“illustrations” (17.1%, n = 7), “foreshadowing” (12.2%, n = 5), “out-
lining” (9.8%, n = 4), “announcing” (4.9%, n = 2), and “empathizing”
(2.4%, n = 1).
As noted, the “introducing new topics” themes are not indepen-
dent. Rather, they only make sense in relation to a specic sequence
(or script) in which participants reported their views of introduc-
ing students to the key concepts in their discipline. For instance, two
participants may have mentioned the same themes (say, covering,
scaffolding, and practicing) but in the opposite order (covering→
practicing→scaffolding vs. scaffolding→practicing→covering). Thus,
a secondary thematic analysis classied the theme sequences. The
three sets of sequences, shown in Table 3, include “specic→general”
(43.9%, n = 18), “general→specic” (41.5%, n = 17), and “multi-
sequential” (14.6%, n = 6). The key factor in determining the ow of
the sequences was the location of the theme “covering” within the se-
quences. In the specic→general sequences the participants reported
that “covering” was the nal step in the sequence. That is, the process
of introducing the topic consisted of a series of specic examples, fore-
shadowing, illustrations, and/or assessments that build up to a general
808 The Journal of Higher Education
denition of the concept or theorem (i.e., covering). In contrast, the
general→specic sequences were dened by beginning with the gen-
eral denition of a concept or theorem (i.e., covering) before moving on
to specic examples, assessments, illustrations, scaffolding, and so on.
Finally, those participants classied as “multisequential” reported using
both sequence forms depending on the topic and/or students involved.
Clustering and Scaling of Themes and Sequences
The next step of our analysis involved examining the patterning of
these rst-person accounts of student learning and teaching practice
across all instructors. We began with an exploratory cluster analysis of
the themes and sequences. The dendrogram in Figure 1 suggests two or
three meaningful clusters related to participants’ views of how students
best learn key concepts and the best ways to introduce students to these
concepts. In the two-cluster stage of the analysis the rst cluster com-
prises two subgroupings: 1A. specic→general sequences and scaffold-
TABLE 3
“Introducing New Topics” Themes and Sequences Derived From the Thematic Analysis
Introducing Topics n Description
Themes
Covering 41 Denes the topic in general terms (e.g., presents denition or theorem).
Scaffolding 21 Links new topic to previous course material.
Examples 20 Illustrates the concept by working out problems or computations.
Assessing 11 Poses questions to students to check for understanding.
Motivating 11 Makes the case for why the topic is important.
Illustrations 7 Demonstrates the topic through an experiment or real world example.
Foreshadowing 5 Assigns preparatory reading or task that precedes the in-class introduction.
Outlining 4 Highlights the main points of the new topic and/or learning goals.
Announcing 2 Announces that a new topic is coming in the near future.
Empathizing 1 Puts self in students’ shoes to anticipate misconceptions.
Theme Sequences
Specic→General 18 Begins with scaffolding and/or examples before describing the concept in
general (e.g., foreshadowing→scaffolding→covering).
General→Specic 17 Describes the new concept in general before demonstrating through
examples (e.g., covering→practicing).
Multi-sequential 6 Sequence of introduction is contingent upon the topic (i.e. uses multiple
sequences).
Cultural Models of Teaching and Learning 809
ing, examples, variability, visualizations, and experiential themes; 1B.
both sequencing scripts (“multisequential”) and osmosis, construction,
individualized, memorizing, repetition, clear explanations, and articulat-
ing themes. The second cluster comprises general→specic sequences
and the application, outside the classroom, and practice/perseverance
themes.
While the dendrogram suggests a patterning into two or three clus-
ters, it would be a mistake to interpret these clusters as neatly bound
types of cultural models of teaching and learning. This caveat becomes
clearer when we examine the results of the MDS analysis. Although the
horizontal distances between the themes and sequences in Figure 2 fol-
low an ordering consistent with the cluster analysis, the distances do not
suggest two or three discrete groupings. Instead, the horizontal dimen-
sion of the MDS space illustrates an opposition between the themes in
subgroup “A” (from cluster 1) and cluster 2, with the themes in sub-
group “B” being more similar (i.e., closer) to the former than the latter.
The principle underlying this opposition approximately follows a dis-
Figur e 1.
Dendrogram (Ward’s Method) of “views of learning” themes and
“new topics” sequences.
810 The Journal of Higher Education
tinction between learning as a result of teaching (e.g., scaffolding, os-
mosis, clear explanations, visualizations, etc.) versus learning that is the
result of doing (e.g., application, outside the classroom, and practice).
While this nding does not discredit a two-cluster model, it does sug-
gest a greater deal of variation in the way these instructors assemble the
themes within cluster 1.
While the horizontal distribution of themes in Figure 2 approxi-
mately replicates the pattern of clustering, the results are more nuanced
when we integrate the second dimension of the MDS space. With the
notable exception of the practice/perseverance theme, this vertical di-
mension contrasts teacher-constructed views of knowledge construc-
tion and learning to that of student-constructed views. The teacher-
constructed views include themes that emphasize techniques and strate-
gies that the instructor must do to construct knowledge, such as provid-
ing visualizations, scaffolding, and examples. In contrast, the student-
constructed views include themes suggesting that students must articu-
late, construct, and apply—particularly outside the classroom. Coincid-
ing with the initial clusters, then, is an additional principle pointing to
contrasting views related to who is responsible for the construction of
Figur e 2.
Ordinal MDS of “views of learning” themes and “new topics” sequences
(Stress = 0.104).
Cultural Models of Teaching and Learning 811
knowledge in the pedagogic relationship. Thus, the MDS results add
a dimension to the cultural models of teaching and learning presented
thus far.
Practically speaking, rather than thinking of these cultural models
as discrete types, it is more accurate to conceptualize them as spatially
proximal combinations of learning views and new topic sequences that
are organized across multiple principles of differentiation. That is, in
practice, the boundaries between these cultural models appear to be sep-
arated less by rigid “either/or” categories and more by “to what degree”
distances. This premise will prove even more convincing once we move
from examining cultural models on paper (i.e., as theoretical constructs
in Euclidean space) to an analysis of cultural models in practice.
Case Analyses
While the case analyses below reinforce the theoretical boundaries of
the cultural models identied heretofore, they also portray a degree of
uidity with which each instructor constructs meanings and practices
in relation to their cultural model of teaching and learning in specic
instructional situations.
“Dr. Spicoli.” Dr. Spicoli is a professor of biology who teaches a large
(~350 students) introductory-level course in genetics that is required
of all biology majors. The two class periods we observed covered gene
identication, gene sequencing techniques, embryonic testing, and tech-
nologies for measuring DNA. Dr. Spicoli’s cultural model of teaching
and learning falls primarily in cluster 2, or the “learning by doing” re-
gion of the MDS space. This can be seen in his theory that the way
students best learn the key principles of genetics is through practice
that happens outside the classroom, and his general→specic sequence
script (covering→motivating→scaffolding) as the best way to introduce
students to these concepts.
Dr. Spicoli does not hesitate when asked about what he thinks is the
best way for undergraduate students to learn the key concepts of genet-
ics: “Problem solving,” he replies assuredly. “[T]o get them procient
in solving genetic problems and understanding concepts,” he continues,
“is just to do problem solving.” It is not surprising, then, that Dr. Spicoli
holds that learning primarily occurs outside the classroom where stu-
dents can engage in problem solving specic to genetics. To this end,
Dr. Spicoli assigns weekly problem sets and makes graduate students
and procient undergraduates available for 1 hour per week so that stu-
dents can ask questions and get feedback on their work.
While Dr. Spicoli’s model locates student learning in problem-
solving contexts outside of the classroom, he nonetheless is tasked with
812 The Journal of Higher Education
introducing students to the principles of genetics inside the classroom.
When introducing students to new material Dr. Spicoli believes it best
to begin by dening the key terms and providing an overall denition of
the concept(s). This initial step of covering and outlining is followed by
motivating and scaffolding the new material so that, in his words, “it’s
not just me lling 50 minutes with some technical stuff that they may
or may not be interested in, but try to tell them how it’s relevant and
how it’s connected to other parts of the course.” Yet Dr. Spicoli’s ratio-
nale also links back to his model of student learning based on practice
through problem solving. As he notes, “[I] try and give them the ow
of how a geneticist goes through trying to gure out when they have a
new mutation or a new phenotype.” Thus, Dr. Spicoli’s theory of how
students best learn key concepts in genetics operates in association with
a script for introducing students to those concepts.
By observing Dr. Spicoli’s instructional practices we can begin to
understand how his cultural model of teaching and learning is enabled
and adapted to the specic context of his instructional environment.
The network-afliation graph in Figure 3 illustrates that Dr. Spicoli’s
primary pedagogical repertoire consists of a didactic style that requires
students to frequently receive, follow, and memorize information pre-
sented through lecturing with the use of a pointer and PowerPoint
slides. In some ways Dr. Spicoli’s practice appears to contradict his
cultural model. However, he does frequently supplement his didactic
style by asking students to solve conceptual genetics problems through
the medium of clicker response systems (i.e., real-time polling). These
questions are often situated within a specic genetics case study (e.g.,
homologous genes and gene sequencing).
Although Dr. Spicoli’s cultural model of teaching and learning is
clearly at work in his instructional practice, the application of the model
is not purely deterministic. Rather, his cultural model is recontextual-
ized by the constraints and affordances of his instructional environ-
ment. Most notably, the high enrollment numbers and varying levels of
student ability shape the extent to which he can incorporate problem
solving into the classroom. This is particularly evident with the use of
clickers. As he notes, “With the size of the class and very different skill
levels among the entering students here in biology, I don’t do a lot more
sophisticated clicker stuff that some of my colleagues do.” Even though
Dr. Spicoli’s cultural model of teaching and learning represents a rela-
tively coherent theory that he uses to make sense of his instructional
environment, this same environment pushes back in a way that requires
him to adapt his cultural model (or at least make concessions) to the
constraints he perceives in the situation. Even in the face of those con-
Cultural Models of Teaching and Learning 813
straints, however, instructional technologies such as clickers afford Dr.
Spicoli a medium through which to act upon certain features of his cul-
tural model.
“Dr. Denny.” Dr. Denny is a senior instructor in the mathematics de-
partment. At the time of the interview and observation, Dr. Denny was
teaching a linear algebra course (~40 students). The week we visited Dr.
Denny’s class he was covering basic principles in matrix algebra and
more complex concepts related to vector spaces. Dr. Denny espouses a
cultural model of teaching and learning that is primarily comprised of
themes from subgroup A of cluster 1 (i.e., “learning through teaching”)
and the teacher constructed region of the MDS space. For instance, in
addition to “practice,” his theory of how students best learn key mathe-
matical concepts is characterized by variability, working through exam-
ples, and integrating concepts through scaffolding. Dr. Denny also has
a specic→general script for introducing students to key mathematical
Figur e 3.
Dr. Spicoli’s graph of instructional practice.
Note. The black boxes refer to teaching methods and interactions, white boxes refer to
cognitive engagements, and gray boxes refer to instructional technologies.
814 The Journal of Higher Education
concepts that begins with numerous examples and gradually builds to a
general principle or theorem.
When prompted to think about his views of how students best learn
the key concepts in linear algebra, Dr. Denny notes that linear algebra
marks a transition from strictly doing computations to more abstract
forms of mathematical reasoning. In this context he perceives students
to learn at different speeds and through varying styles and thus stresses
variability. Regardless of speed or style, though, Dr. Denny contends
that in order for students to learn key mathematical concepts they
must “grind away” through numerous specic examples and gradually
work up to the general principle or theorem. He also holds that stu-
dents must have a strong foundation (i.e., scaffolding) in the fundamen-
tals of mathematics before they can grasp more advanced and abstract
concepts.
Associated with Dr. Denny’s theory of how students best learn key
concepts in linear algebra is a script for introducing students to those
concepts. This script runs counter to what he describes as the “common
model” (i.e., general→specic) in mathematics:
I know a lot of people who come in and will state the theorem . . . and prove
it and then nally do some examples, and I never do that. I do an example,
and then I’ll do another example, and as I do them I’ll point out some feature
and I’ll say, “Well, we call this thing . . . Gauss-Jordan elimination. . . .” I do
a bunch of examples and then try to lead into the abstract denition.
When asked to say more about the common model (i.e., proving the
theorem and then providing examples), Dr. Denny says that most math-
ematicians teach that way because “[t]hat’s the way they’re comfortable
thinking.” He continues:
But it doesn’t seem like the most natural way to learn to me personally. I
think you understand it abstractly. [W]hen you learn algebra, that’s very ab-
stract. You learn arithmetic—even numbers are abstract, right? . . . But even-
tually you learn that numbers are something and then in algebra you have to
say let X be a number. So you have this variable, which is an abstraction of a
number, and a number is an abstraction of something else . . . but you don’t
learn algebra until you’ve really learned arithmetic . . . Because then you
have a bunch of examples of computations that you can imagine you would
want to write in this language—and it keeps going like that. [Y]ou always
work from the particular to the general.
The latter quote captures the essence of Dr. Denny’s cultural model
of teaching and learning, as it illustrates his views that students must
Cultural Models of Teaching and Learning 815
work through specic examples and build scaffolds as they proceed to
higher levels of abstraction. Thus, the way Dr. Denny believes new top-
ics should be introduced is a microcosm of his broader model of pro-
gression in mathematics.
In the classroom it was easy to see Dr. Denny’s cultural model of
teaching and learning in action. During each class period he meticu-
lously worked through examples, beginning with easy applications and
gradually working up to more difcult problems that prompted student
questions. This core pedagogical style is evident in Figure 4, which
shows that Dr. Denny frequently lectures while working through prob-
lems at the chalkboard. The graph also demonstrates that Dr. Denny
supplements his primary strategy of working through problems by oc-
casionally posing algorithmic and conceptual questions to the students,
and he frequently checks for student understanding. What the graph
does not illustrate, however, is that as Dr. Denny progressed through
each problem he would periodically stop and point out certain features
of the problems that eventually could be assembled into an abstract
principle.
For Dr. Denny, the use of the chalkboard provides a medium through
which he is able to act upon his cultural model of teaching and learn-
ing. Since he prefers to provide students with many examples, Dr. Den-
ny’s modus operandi is to stand at the board and work out problems.
Although the component of Dr. Denny’s cultural model related to in-
troducing key mathematical concepts runs counter to what he claims
is “the more common model,” he is certainly not alone in relying on
the chalkboard as an instructional tool. When asked to clarify his use
of instructional technology, Dr. Denny notes that while he does believe
the students should be using the computer program MATLAB—a pro-
gramming environment for algorithm development, data analysis, vi-
sualization, and computation—he is conicted about the use of such
technology:
And there is a move to [use MATLAB], but mathematicians are kind of con-
servative. I’m kind of conservative. We sort of like our discipline to be sort of
pure in some sense and so what we really want [students] to see is the beauty
of these ideas, and of course . . . kicking and screaming we admit that these
things are actually useful for something, and . . . we’ll teach you how to do it.
. . . But really we want you to be stunned by the loveliness of it.
This sentiment illustrates the conicting components of Dr. Denny’s
cultural model. On the one hand, his model guides him to sequence the
material in contrasting style to the more common model in mathematics.
816 The Journal of Higher Education
On the other hand, he is intent on accommodating the conicting posi-
tions within his model by using the chalkboard to work through exam-
ples as opposed to a technological medium that he admits the students
“should learn.”
“Dr. Bishop.” As a senior instructor in biology, Dr. Bishop is primarily
responsible for teaching undergraduate courses covering a variety of bi-
ological concepts. In addition to her teaching commitments, Dr. Bishop
is involved in undergraduate science education research projects that
have provided her with data to inform her teaching. In this sense her
cultural model of teaching and learning extends beyond a folk theory
and includes features of a scientic theory. The particular course that
was observed in the present case was Developmental Biology, which
is an upper division course for biology majors in the department (~100
students). Dr. Bishop’s cultural model of teaching and learning cannot
easily be characterized. It is considerably more nuanced than the previ-
Figur e 4.
Dr. Denny’s graph of instructional practice.
Note. The black boxes refer to teaching methods and interactions, white boxes refer to
cognitive engagements, and gray boxes refer to instructional technologies.
Cultural Models of Teaching and Learning 817
ous two cases, and it contains themes from across the entire spectrum of
cultural models analyzed thus far. In total, Dr. Bishop expressed seven
distinct thematic views of student learning—variability, construction,
articulating, outside the classroom, osmosis, individualized, and appli-
cation—and espouses multiple scripts for introducing students to the
course material.
The complexity of Dr. Bishop’s model is captured in her initial re-
sponse to being queried about the best way students learn key concepts
in developmental biology. “I guess there [are] two answers to that ques-
tion,” she replies. The rst answer, according to her, is that “differ-
ent people learn the key concepts differently” and that “students have
a clear preference for [certain] learning styles.” Some students, she
claims, are most comfortable coming to class, taking notes, and then
going on their own to piece together the key bits of information rather
than actively pursuing that knowledge in the classroom. For Dr. Bishop,
independent study, reection, and application outside of the classroom
are “critical components” to learning the key concepts.
Despite her belief in variability and acknowledging that some stu-
dents are not comfortable in an active learning environment, Dr. Bish-
op’s second answer is more denitive in the other direction. “So I guess
. . . there’s a student perspective” she says, “but from my own perspec-
tive I think that students learn by being active.” Dr. Bishop continues:
I think that a lot more is gained from—and there’s data to support this too—
but there’s a lot more to be gained from an active pursuit of the topic in
the classroom. Where the things that are confusing you, [you can] actually
hash it out when you’ve got the professor there to talk with you about it and
you’ve got your neighbor to go, “Well, I don’t think that’s the way it works.”
Being active, according to Dr. Bishop, thus involves a combination
of construction (“active pursuit of the topic in the classroom”), articula-
tion (“hash it out”), and individualized interaction between the instruc-
tor and each student. In the process of explaining her cultural model, Dr.
Bishop notes that “there is data to support” her model. Here we can see
that Dr. Bishop’s cultural model of teaching and learning is more explic-
itly theoretical than what is typical among many of the scientists and
mathematicians we interviewed.
The complexity of Dr. Bishop’s cultural model is also captured
by her views of how to introduce undergraduate students to the key
concepts in biology. Dr. Bishop espouses both a general→specic
(covering→examples) and specic→general (assessing→covering)
script for introducing material. When asked if there is a pattern to her
818 The Journal of Higher Education
use of the former or latter sequence, she has to think about it for a few
seconds:
I’m trying to think about whether there is a method to my approach. . . . I
guess, all right just being honest, I think I would prefer . . . to start every
class period or every topic with an exploration on their part, culminating
with some wrap-up by me. But in practice there are some number of topics
that I don’t start that way, and it’s just because I haven’t developed the right
sequence of things that I think will trigger them to really learn it that way.
Similar to her views of student learning, Dr. Bishop’s views of how
to introduce key concepts must be understood in relation to her inter-
actions with students. That is, she clearly prefers active over inactive
learning and specic→general over general→specic sequences. Yet,
rather than expunging these elements from her cultural model, Dr.
Bishop has instead adapted them to t (albeit in conict) alongside what
she believes is the best way to teach and learn.
Figur e 5.
Dr. Bishop’s graph of instructional practice.
Note. The black boxes refer to teaching methods and interactions, white boxes refer to
cognitive engagements, and gray boxes refer to instructional technologies.
Cultural Models of Teaching and Learning 819
Given the complexity of Dr. Bishop’s cultural model of teach-
ing and learning, it should come as no surprise that her pedagogical
style is highly varied. Indeed, the total number of unique nodes (i.e.,
observation codes) in Dr. Bishop’s graph (n = 21) is nearly double
that of Drs. Spicoli (n = 11) and Denny (n = 12). In addition, a core/
periphery relation of techniques is not as distinct as in the previous
graphs; Dr. Bishop’s graph is more diffuse. It is in this graph that we
can see a multifaceted conguration of educational action that is ap-
proximately homologous to her multifaceted cultural model of teaching
and learning. For instance, note that lecturing from a laptop and slides
is still a key feature of the graph. During these times both sequences of
introducing material were at work. Often when lecturing, for example,
Dr. Bishop was introducing a principle or process (e.g., axonal move-
ment) followed by a series of examples. At other times she would in-
stead share very specic pieces of data and ask the students, “What is
happening here?”
While lecturing with a laptop and slides is an important feature of
the graph, the prevalence of active instructional practices and technolo-
gies illustrates the varied aspects of Dr. Bishop’s cultural model in ac-
tion. For example, Dr. Bishop makes regular use of conceptual clicker
questions, brainstorm sessions, small group discussions, individual
deskwork, and a variety of question styles. In the process she creates
the conditions for a number of active cognitive engagements such as
creating, connections, problem solving, and integration. Finally, all of
this is accomplished through a mixture of instructional technology that
includes an overhead projector, laptop and slides, digital tablet, and
clicker-response system.
Discussion and Conclusions: What Can We Learn From Cultural
Models of Teaching and Learning?
At the outset of this article we claimed that cultural models are an
important theoretical tool that can help us to better understand postsec-
ondary instructional practices and attempts to reform them. Our primary
theoretical argument was that cultural models of teaching and learning
should be explored at the intersections of instructor cognition, teach-
ing practices, and instructional environments. We began this process by
examining the rst dimension (i.e. cognition) in relation to instructors’
expressive/conceptual models of how students best learn foundational
concepts and their scripts for introducing students to this material. The
clustering and MDS analyses point to two (or possibly three) broad
820 The Journal of Higher Education
forms of cultural models for these practices that are primarily organized
by two underlying principles. These principles differentiate the partici-
pating math and science instructors’ views of who constructs knowledge
in the pedagogic relationship and how such knowledge is learned or ac-
quired. Thus, while very few of the participating instructors formally
study pedagogy, it is notable that their expressive/conceptual models
and scripts are organized into relatively coherent theoretical constructs.
In fact, it was Dr. Bishop—the most sophisticated, articulate, and the-
oretically astute pedagogue among our participants—who had the most
theoretically diverse and contradictory cultural model. We conjecture
here that instructors who intentionally seek to transform their models of
teaching and learning do not fully expunge their initial model. Instead,
they add new meanings and strategies and adapt them to t alongside
components of their preexisting models—even when the new meanings
exist in conict with the preexisting. In the case of Dr. Bishop, these
conicts exist out in the open and represent a source of tension in her
practice. Thus, an important question for future research is: What are
the consequences of conicting models for the ways instructors teach
and, subsequently, how these practices impact students’ learning expe-
riences in classroom settings? At rst thought it may seem that having
multiple, conicting models can have contradictory consequences in the
classroom. On the other hand, having multiple models allows for greater
reection and critique (Gee, 2005) and may assist instructors in adapt-
ing to a greater range of instructional situations.
The results above also suggest that cultural models of teaching and
learning among math and science faculty are differentially distributed
within and between groups. While we did not formally explore the pre-
cise social contexts of this distribution, some anecdotal references from
the transcripts indicate that disciplinary and status positions may be a
productive starting point for future examination. For example, both Dr.
Denny and Dr. Bishop—as non-tenure track senior instructors—refer-
enced their positions within the academic hierarchy as affording them
opportunities to reect on student learning and pedagogical strategies.
Dr. Spicoli—as a tenured professor—also recognized that the disciplin-
ary and institutional reward system unevenly motivates teaching inno-
vation. In addition, Dr. Denny’s statement about the “common model”
of introducing a theorem in mathematics points to discipline-specic
components to the cultural models. These statements lead us to posit
that instructors perceive constraints and affordances in their disciplin-
ary and organizational status positions (cf. Martin, 2011). Future work
should look deeper into these sociological facets of cultural models and
Cultural Models of Teaching and Learning 821
further develop the theoretical links between social and cognitive struc-
tures in these settings.
While our three cases illustrate the generative properties of instruc-
tors’ cultural models of teaching and learning with respect to their class-
room practices, they also point to the danger in viewing these models
as directly corresponding to those practices. Indeed, as we saw above,
it is at the intersections of instructors’ practices and the constraints and
affordances that they perceive within their instructional settings where
we come to understand how these cultural models are enabled and con-
strained. This may partially explain why, at times, the instructors used
teaching practices that embodied components from cultural models
other than those they espoused. Thus, while there can be little doubt that
instructors’ cultural models of teaching and learning motivate practice,
we must also recognize the powerful ways in which instructional situ-
ations and environments (e.g., class size, access to instructional tech-
nology) interact with these models to ultimately shape practices. This
relational view suggests that the transformation of cultural models of
teaching and learning necessarily involves a transformation of the envi-
ronment and the ways in which those environments are perceived as af-
fording or constraining certain actions. Indeed, it is hard to imagine the
evolution of these cultural models occurring without the coevolution of
the environments in which they are constructed and enacted.
It is not only the instructional environment that shapes how instruc-
tors translate their cultural models into instructional practice. Another
important intersection is in relation to actually existing instructional
practices. That is, the extent to which instructors are able to translate
their models into practice is dependent upon the availability of an exist-
ing form of practice that embodies the principle underlying its use. For
example, recall that one of Dr. Bishop’s scripts for introducing students
to new topics is constrained by the lack of an existing practice to match
her model. As she notes, “But in practice there are some number of top-
ics that I don’t start that way [specic→general sequence], and it’s just
because I haven’t developed the right sequence of things that I think
will trigger them to really learn it that way.” A similar process was ob-
served with Dr. Spicoli, who had yet to nd a way to implement some
of the more sophisticated problem solving techniques using clickers in
his large lecture hall setting. In this instance we see his cultural model
constrained by multiple intersections—the instructional setting and the
lack of available (or known) practices to match his model.
Our analysis of math and science instructors’ cultural models of
teaching and learning also point to a number of implications for those
involved in the ongoing efforts to transform undergraduate STEM
822 The Journal of Higher Education
education. A commonly referenced step toward transforming the edu-
cational experiences of undergraduates in these elds is to change the
culture of instruction (Kezar & Eckel, 2002; Trowler, 2008; Wieman et
al., 2010). Although the denition of culture can vary widely across re-
searchers and reformers (if it is dened at all), proponents of this view
generally argue that it is necessary to change instructors’ preexisting
understanding(s) of how students best learn and the strategies that create
the conditions for this learning to ourish. In other words, proponents of
this view are making an argument for changing the cultural models of
teaching and learning within math and science disciplines.
However, the momentum of evidence points to a Sisyphus scenario
in which reformers have invested impressive efforts and resources with-
out widespread change (President’s Council of Advisors on Science and
Technology, 2012). Our ndings suggest that the downfall of this strat-
egy is in the failure to recognize and appeal to the practical logic of
instructors’ preexisting cultural models. Preexisting cultural understand-
ings are persuasive by denition (Gramsci, 1971; Quinn & Holland,
1987), and this is no less true for math and science instructors’ cultural
models of teaching and learning. Rather than perceiving instructors’
preexisting understandings as the sole objects of change, therefore, it
may be more productive to recognize those understandings as also con-
taining elements of “good sense” (to use Gramsci’s phrase) upon which
to build (cf. Spillane, Reiser, & Reimer, 2002). That is, just as some in-
structors perceive affordances in instructional tools to overcome practi-
cal constraints, practitioners and policymakers can perceive affordances
in instructors’ cultural models to motivate pedagogical innovation. In
this sense the “culture of instruction” represents an opportunity to ini-
tiate meaningful transformation in the educational experiences of stu-
dents and educators (see also Trowler, 2008).
At the same time, our theoretical perspective focusing on the inter-
sections of cultural models, teaching practices, and instructional en-
vironments indicates that transforming instructors’ cultural models
of teaching and learning is an incomplete goal. As we saw above, in-
structors often perceive a variety of constraints (e.g., class sizes, stu-
dents’ own cultural models of teaching and learning, and technological
resources) that are associated with pedagogical strategies and actions
that, in effect, constitute concessions and adaptations to their model that
they would not otherwise make. This suggests that the burden of re-
sponsibility for meaningful transformation is not solely that of instruc-
tors, but is distributed throughout the actors, events, and environments
that constitute educational activities. An instructor-centric approach to
pedagogical transformation evades the complexity and relational nature
Cultural Models of Teaching and Learning 823
of education. A more complete approach must account for the features
of instructional environments and situations, social structural positions
(e.g., tenure systems), and students’ own cultural models of teaching
and learning. These additional intersections may point to educational
opportunities that have yet to be pursued.
Notes
This research was supported by the National Science Foundation—Grant # DRL-
0814724. In addition, we would like to thank Sarah Bell, Ross Collin, Amanda Ole-
son, and the anonymous reviewers for their thoughtful critiques and feedback on this
manuscript.
References
American Association of University Professors. (2009). Trends in instructional staff
employment status, 1975–2009 [Figure]. Retrieved from http://www.aaup.org/NR/
rdonlyres/7C3039DD-EF79–4E75-A20D-6F75BA01BE84/0/Trends.pdf
Anderson, W. A., Banerjee, U., Drennan, C. L., Elgin, S. C. R., Epstein, I. R., Handels-
man, J., . . . Warner, I. M. (2011). Changing the culture of science education at research
universities. Science, 331(6014), 152–153.
Ashwin, P. (2008). Accounting for structure and agency in ‘close-up’ research on teach-
ing, learning and assessment in higher education. International Journal of Educational
Research, 47(3), 151–158.
Bergquist, W. H. (1992). The four cultures of the academy. San Francisco: Jossey-Bass Inc.
Borg, I., & Groenen, P. J. F. (2005). Modern multidimensional scaling: Theory and ap-
plications. New York: Springer.
Borgatti, S. P. (2002). NetDraw software for network visualization. Lexington, KY: Ana-
lytic Technologies.
Bourdieu, P. (1984). Distinction: A social critique of the judgment of taste (R. Nice,
Trans.). Cambridge, MA: Routledge & Kegan Paul Ltd.
Bourdieu, P. (1990). The logic of practice. Stanford: Stanford University Press.
Bransford, J. D., Brown, A. L., & Cocking, R. R. (1999). How people learn: Brain, mind,
and school. Washington, DC: National Research Council.
Carnevale, A. P., Smith, N., & Melton, M. (2011). STEM: Science, technology, engineer-
ing, mathematics. Washington, DC: Center on Education and the Workforce, George-
town University. Retrieved from http://www9.georgetown.edu/grad/gppi/hpi/cew/pdfs/
stem-complete.pdf
Carter, D. F. (2006). Key issues in the persistence of underrepresented minority students.
New Directions for Institutional Research, 130, 33–46.
D’Andrade, R. G. (1984). Cultural meaning systems. In R. A. Shweder & R. A. LeVine
(Eds.), Culture theory: Essays on mind, self, and emotion (pp. 88–119). New York:
Cambridge University Press.
824 The Journal of Higher Education
D’Andrade, R. G. (1992). Schemas and motivation. In R. G. D’Andrade & C. Strauss
(Eds.), Human motives and cultural models (pp. 23–44). New York: Cambridge Uni-
versity Press.
D’Andrade, R. G. (1995). The development of cognitive anthropology. New York: Cam-
bridge University Press.
DiMaggio, P. (1997). Culture and cognition. Annual Review of Sociology, 23, 263–287.
Fox, M., Sonnert, G., & Nikiforova, I. (2011). Programs for undergraduate women in
science and engineering: Issues, problems, and solutions. Gender and Society, 25(5),
589–615.
Fryberg, S. A., & Markus, H. R. (2007). Cultural models of education in American Indian,
Asian American and European American contexts. Social Psychology of Education,
10(2), 213–246.
Gee, J. P. (2004a). Discourse analysis: What makes it critical? In R. Rogers (Ed.), An
introduction to critical discourse analysis in education (pp. 19–50). Mahwah, NJ: L.
Erlbaum Associates.
Gee, J. P. (2004b). Situated language and learning: A critique of traditional schooling.
New York: Routledge.
Gee, J. P. (2005). An introduction to discourse analysis: Theory and method (2nd ed.).
New York: Routledge.
Gibson, J. J. (1986). The ecological approach to visual perception. New York: Psychology
Press.
Glenberg, A. M. (1997). What is memory for? Behavioral and Brain Sciences, 20(1), 1–55.
Gramsci, A. (1971). Selections from the prison notebooks (Q. Hoare, Trans.). New York:
International Publishers.
Greeno, J. G. (1998). The situativity of knowing, learning, and research. American Psy-
chologist, 53(1), 5–26.
Hora, M. T., & Ferrare, J. J. (2013). Instructional systems of practice: A multidimensional
analysis of math and science undergraduate course planning and classroom teaching.
Journal of the Learning Sciences, 22(2), 212–257.
Kezar, A., & Eckel, P. D. (2002). The effect of institutional culture on change strategies in
higher education: Universal principles or culturally responsive concepts? The Journal
of Higher Education, 73(4), 435–460.
Kruskal, J. B., & Wish, M. (1978). Multidimensional scaling (Vol. 11). London, UK: Sage.
Lacey, T. A., & Wright, B. (2009). Occupational employment projections to 2018. Monthly
Labor Review, 132(11), 82–123.
Martin, J. L. (2011). The explanation of social action. Oxford, UK: Oxford University
Press.
Mohr, J. W., & Duquenne, V. (1997). The duality of culture and practice: Poverty relief in
New York City, 1888–1917. Theory and Society, 26, 305–356.
National Science Board. (2010). Preparing the next generation of STEM innovators: Iden-
tifying and developing our nation’s human capital. Arlington, VA: Author.
Ogbu, J. U., & Simons, H. D. (1994). Cultural models of school achievement: A quantita-
tive test of Ogbu’s theory. Berkeley: Graduate School of Education, National Center for
the Study of Writing, University of California, Berkeley.
Cultural Models of Teaching and Learning 825
Quinn, N., & Holland, D. (1987). Culture and cognition. In D. Holland & N. Quinn (Eds.),
Cultural models in language and thought (pp. 3–42). New York: Cambridge University
Press.
Romesburg, H. C. (1984). Cluster analysis for researchers. Belmont, CA: Lifetime Learn-
ing Publications.
Ryan, G. W., & Bernard, H. R. (2003). Techniques to identify themes. Field Methods,
15(1), 85–109.
Spillane, J. P., Reiser, B. J., & Reimer, T. (2002). Policy implementation and cognition:
Reframing and refocusing implementation research. Review of Educational Research,
72(3), 387–431.
Tierney, W. G. (2008). The impact of culture on organizational decision-making: Theory
and practice in higher education. Sterling, VA: Stylus.
Trowler, P. (2008). Culture and change in higher education: Theories and practice. Lon-
don, UK: Palgrave Macmillan.
Umbach, P. D. (2007). Faculty cultures and college teaching. In R. P. Perry & J. C. Smart
(Eds.), The scholarship of teaching and learning in higher education: An evidenced-
based perspective (pp. 263–317). Dordrecht, NL: Springer.
Wasserman, S., & Faust, K. (1994). Social network analysis: Methods and applications.
New York: Cambridge University Press.
Weller, S. C. (2007). Cultural consensus theory: Applications and frequently asked ques-
tions. Field Methods, 19(4), 339–368.
Wieman, C., Perkins, K., & Gilbert, S. (2010). Transforming science education at large
research universities: A case study in progress. Change: The Magazine of Higher Learn-
ing, 42(2), 7–14.
