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Team-Based Inquiry Learning
Drew Lewis, Steven Clontz, Julie Estis
1
Abstract: Team-Based Learning (TBL) is a cooperative learning strategy
blending elements of flipped learning, inquiry-based learning, and problem-
based learning. While used quite frequently in other disciplines, use of this
strategy in mathematics has been limited. In this article, we describe how
TBL can be implemented in math courses with adherence to essential elements
of TBL and introduce modifications specific to mathematics instruction. In
particular, we introduce a particular style of TBL, which we term Team-
Based Inquiry Learning, that satisfies the two defining pillars of inquiry-based
learning. 1
Keywords: Team-Based Learning
1 Introduction
Decades of literature supports the need to transition mathematics in-
struction to more active forms of teaching and learning [8]. However,
the (context-dependent) question of how to do so optimally is still very
much unanswered. In this article, we propose Team-Based Learning
(TBL) as an active, collaborative instructional method for mathematics,
and describe the success we have experienced in our current instructional
context.
Evolving from earlier forms of collaborative and active learning, Team-
Based Learning is a distinctive, highly structured approach to small-
group instruction that supports application of course content, requires
team problem solving, and leads to significant learning [15,16,17]. Stu-
dents acquire conceptual and procedural knowledge as they complete in-
dependent preparation work and then spend the majority of class time
solving problems in strategically organized, permanent teams. While
TBL is increasingly used in other disciplines, particularly the health
sciences, implementation in math courses is limited.
TBL has been shown to improve student achievement by encourag-
ing more scientific thinking, developing a deeper understanding of course
content, and increasing student reasoning, problem-solving and critical
thinking skills [4,10,11,14,27,28,29]. A meta-analysis of TBL ef-
fectiveness [9] showed several trends across studies. Teams consistently
performed better than individuals, communication was improved, and
class participation was improved with TBL. Though student enjoyment
was reportedly lower for TBL, student perceptions of self-efficacy and
interest were higher. Two studies showed successful transfer of interper-
sonal skills gained in TBL to job performance. One key finding across
multiple studies was that students tended to benefit from TBL regardless
of achievement or demographic profiles; however, students at the lower
1A revised version of this preprint has been published in PRIMUS:
https://doi.org/10.1080/10511970.2019.1666440
2
end of class achievement showed the greatest benefit. A more recent
meta-analysis [13] showed that TBL improves student learning gains by
an average of 0.5 standard deviations compared to the other methods
explored across studies.
TBL has been shown to be an effective pedagogy in several STEM
disciplines in particular. For example, Carmichael [2] reported that TBL
increases exam scores in an introductory biology course. Kreie, Headrick
and Steiner [12] showed that TBL increased retention in an introductory
information systems course, while Dinan and Frydrychowski [3] found
increased final exam scores in a chemistry implementation.
However, the literature on TBL in mathematics is quite limited. We
found only one article discussing student learning gains: Nanes [20] de-
scribes using a modified TBL methodology in linear algebra. He found
this approach to improve final exam scores and course grades versus a
historical control. A more faithful TBL implementation in upper level
courses such as combinatorics is discussed in [21,22].
In this paper, we provide an introduction to TBL, including its re-
lation to other forms of active learning. In our view, TBL (as applied
to math education) is a structure that facilitates instructors introducing
collaborative inquiry into their classrooms; in Section 3, we describe our
particular implementation, which we term Team-Based Inquiry Learn-
ing, and describe how it satisfies the twin pillars defining inquiry-based
learning. In section 4, we describe the changes we saw take place as a
result of implementing TBL.
2 Team-Based Learning
In this section, we briefly describe TBL; we refer the reader to [18,24]
for further details.
2.1 General aspects of TBL
Team-Based Learning is designed to engage prepared teams of students
in working together to apply course content. Differing from other col-
laborative learning approaches, TBL is a comprehensive instructional
strategy with a specific sequence of learning activities rather than inde-
pendent group activities within a course. A TBL course is comprised
of modules for each content area. Each TBL instructional module be-
gins with individual preparation. Students prepare for a content mod-
ule by reading, viewing videos, practicing problems, and/or completing
other instructor assigned preparation activities. The Readiness Assur-
ance Process, which includes an individual test, a team test, appeals,
and corrective instruction, is conducted during the first class of a mod-
ule. Through preparation and the Readiness Assurance Process, students
3
become prepared to answer deeper questions and solve problems collab-
oratively during in-class Application Activities. These activities are rich
tasks in which students work in permanent teams, using knowledge and
skills from the preparation phase to solve problems, create explanations,
or make predictions that become increasingly difficult as they expand
their knowledge of the content.
TBL consists of four essential elements [19]. First, teams must be
properly formed and managed. Typically, this is accomplished through
the use of permanent, diverse teams so that student resources are dis-
tributed across teams. When permanent teams are formed based on cri-
teria, rather than self-selection, barriers to team cohesion are reduced,
and teams develop skills from working together over time. Second, stu-
dents need to be accountable for their individual preparation and for
contributing to their teams. Individual Readiness Assurance Tests pro-
vide accountability for preparation, and peer evaluation is used to asses
individual contributions to the team. Third, students must receive fre-
quent and immediate feedback. Through the team Readiness Assurance
Test, students receive immediate feedback on the accuracy of their re-
sponses. Team activities are also structured in a manner that provide
frequent and immediate feedback. Finally, teams spend the bulk of class
time working collaboratively on Application Activities, which are de-
signed in a specific manner summarized by the 4S’s: 1) activities involve
aSignificant problem that is meaningful and relevant to students, 2) all
teams work on the Same problem, 3) students solve the problem by mak-
ing a Specific choice, and 4) teams Simultaneously report their choices.
Creating application activities within this structure and completing the
activities in class promote active student engagement, eliminate a “di-
vide and conquer” approach, and promote team development. By com-
bining the essential elements of TBL in this structured sequence, the
instructor facilitates deep, enduring understanding of the course content
with application of content and higher order problem-solving.
2.2 Contrast with other forms of active learning
The preparation activities referenced in the previous section bring to
mind Flipped Learning, a pedagogy that is increasingly used in math
education. Talbert [26] gives the following definition of flipped learning:
Flipped Learning is a pedagogical approach in which first contact
with new concepts moves from the group learning space to the
individual learning space in the form of structured activity, and
the resulting group space is transformed into a dynamic, interac-
tive learning environment where the educator guides students as
they apply concepts and engage creatively in the subject matter.
4
For the unfamiliar reader, “group learning space” is used in this con-
text as a generalization of classroom time; in many face-to-face classes,
it may be synonymous with the classroom. The “individual learning
space” refers to time students spend working alone; traditionally, this is
out-of-class work. TBL clearly satisfies the second part of this definition;
indeed, TBL instructors’ primary role is to facilitate students through
interactive team activities.
However, TBL does not inherently satisfy the first criteria. Quite
often, TBL instructors will structure the readiness assurance process to
initiate first contact with some new concepts in the individual space;
however, this is not required (and in fact, we argue below for a different
approach). Moreover, TBL does not require structured activity in the
individual space; in fact, we think many TBL instructors would do well
to improve their readiness assurance materials along these lines by, for
example, adding interactive quizzes to their static videos or readings.
TBL also has some similarities with Process Oriented Guided In-
quiry Learning (POGIL), a particular structure of collaborative inquiry
learning. POGIL is much more recent than TBL, originating in the last
twenty years in chemistry education [7] and is now being applied to math
courses [1]. In both TBL and POGIL classrooms, the instructor func-
tions as a facilitator, supporting and guiding as teams independently
work on activities. Unlike TBL, POGIL involves assigning specific roles
to team members and explicitly focuses on teaching process skills in
addition to content. Also, the 4-S structure of TBL application activi-
ties is not required in POGIL activities, limiting the ability to compare
student thinking across teams. Moreover, POGIL lacks a readiness as-
surance process, a TBL feature we find very helpful in ensuring students
are ready to solve challenging problems.
Many readers will also be familiar with Inquiry Based Learning (IBL).
While not entirely well-defined, IBL is commonly described as having
“twin pillars” [5,6]: deep engagement in rich mathematics, and oppor-
tunities to collaborate. It is clear that TBL inherently provides (indeed,
mandates) opportunities to collaborate. TBL provides ample opportu-
nity for engaging students in rich mathematics through well-designed
application activities, but does not require doing so. In the next section,
we describe an approach that combines TBL and IBL as a means of
introducing inquiry learning into a structured collaborative classroom..
3 Team-Based Inquiry Learning (TBIL)
One of the difficulties many instructors encounter in implementing Inquiry-
Based Learning is a lack of structure. Often IBL is implemented by pre-
senting a problem set to students, and students are given broad latitude
to determine the direction of the class period by picking and choosing
5
which problems to work on. While this has the advantage of allowing
students the flexibility to solve difficult problems and ask interesting
questions perhaps not anticipated by the instructor, this risks the pos-
sibility of not covering all the standards intended by the instructor.
In many cases, particularly advanced mathematics courses, it’s “more
about the journey than the destination”: the problem-solving techniques
themselves are more important than the specific content, and thus failing
to cover a particular standard does not cause harm. But for prerequisite
courses that must train students to utilize a particular skillset to enable
success in future coursework, the implementation of IBL can become
more cumbersome for the instructor, in addition to becoming more diffi-
cult to sell to stakeholders who seek a more concrete outline of standards
of learning and a more rigid timeline for content coverage.
Another common difficulty instructors have in implementing Inquiry-
Based Learning is obtaining student collaboration and buy-in [6]. While
ideally students in a IBL course will share ideas and work together to
learn the material, many IBL implementations lack a mechanism to guar-
antee this. In addition, class time in many IBL classrooms is largely
individual-driven, often with a single student at the blackboard lectur-
ing on their solution to a particular problem. In such an environment,
advanced students may not have a strong incentive to support the in-
struction of their peers, while weaker students may become frustrated
by the lack of direct instruction.
Additionally, uneven preparation among students can pose a chal-
lenge for instructors using IBL approaches. While to some extent tasks
can be modified to be approachable by students of varying preparation
levels, quite often specific pre-requisite skills and knowledge are required
to progress to a particular new idea. Thus, some additional structure is
required to ensure students come to class prepared to engage with the
rich IBL activities.
To address these concerns, we developed what we coined Team-Based
Inquiry Learning, or TBIL, with the goal of marrying the structure and
ensured collaboration found in TBL with the opportunities for math-
ematical inquiry found in IBL. While the structure of TBIL is nearly
identical to the canonical structure of TBL, we consider TBIL to be a
distinct extension of TBL that utilizes several components of TBL to
foster inquiry by our students.
In [20], Nanes discusses aspects of TBL that he feels require mod-
ification for math courses: most significantly, the readiness assurance
process, and certain aspects of the 4-S structure of application activi-
ties. In the subsequent sections, we describe how these components of
TBL fit into the TBIL framework.
6
3.1 Readiness Assurance Process
Nanes asserts that the cumulative nature of mathematics courses re-
quires more frequent readiness assurance processes, and describes his use
of daily RAPs. Indeed, his interpretation of TBL tracks more closely
with flipped learning, in which more frequent readiness checks can be
effective (see [25], for example).
However, we take a slightly different approach. Instead of assign-
ing readings and videos on new material and giving a test to ensure
students have read and/or watched these materials, we take the tau-
tological view that the purpose of the readiness assurance process is
to ensure that our students are ready for the application activities we
have planned. In TBIL, we devote class time to students discovering
new material by themselves through guided mathematical inquiry. This
frees us to use the readiness assurance process to alleviate a different
problem: in our instructional context, we have found that many of our
students are under-prepared, in that they do not retain material from
pre-requisite courses such as calculus, pre-calculus, and even high school
algebra. Thus, we focus the readiness assurance process on ensuring
students recall this necessary pre-requisite material. For example, in a
module containing a discussion of determinants, one of the outcomes of
the readiness assurance process will be for students to be able to find
the area of a parallelogram, something students have (in our experience)
previously learned but almost always forgotten.
As discussed in [25], it is essential that the readiness assurance ma-
terials are well structured. We provide students with a list of “readiness
assurance outcomes”, which explicitly state what students will need to
be able to do in order to be ready for the application activities of that
module. We then provide resources (often videos) to refresh students
on that pre-requisite material. We note that several free and commer-
cial products even allow instructors to embed practice problems in these
videos, an approach we find highly effective.
Before beginning this module, students should be able to
•Add Euclidean vectors and multiply Euclidean vectors by scalars.
•Add complex numbers and multiply complex numbers by scalars.
•Add polynomials and multiply polynomials by scalars.
•Perform basic manipulations of augmented matrices and linear
systems.
Figure 1. Readiness Assurance Outcomes
7
Figure 1provides a list of appropriate readiness assurance outcomes
from a module introducing vector spaces, span, and linar independence.
Students are responsible for (re)mastering these prerequisite skills so
that they are ready to engage with the scaffolded inquiry that leads to
the discovery of the new mathematical ideas to be mastered in the course.
Students are provided this list in advance, along with resources (in this
case, videos) to remind them how to do these tasks. Note that while
the first three items are all concepts covered in prerequisite mathematics
courses, the final outcome listed here is based upon the material covered
in the previous module on systems of linear equations. This earlier
module includes three learning standards all of which will be necessary
for success in this module, so they are explicitly specified for review by
students.
As with other interpretations of TBL, students are held account-
able for this out-of-class preparation by means of individual and team
Readiness Assurance Tests (iRAT/tRAT). These tests are a two-stage
assessment covering ten questions. For example, we often have a ques-
tion intended to assess mastery of the readiness assurance outcome re-
lated to polynomials. This also serves to expose students to the notion
of a linear combination of abstract vectors, which will be defined and
investigated during the module. After completing this assessment indi-
vidually, students repeat the exact same assessment, working as a team,
and immediately receiving feedback on the correctness of their answers.
This approach to the Readiness Assurance Process also increases the
interleaving of crucial pre-requisite material through the course. Stu-
dents will be reminded of the material before the module begins, and
then use it throughout the module. Moreover, when a readiness assur-
ance outcome is a learning objective from earlier in the course, this serves
to interleave that learning objective further throughout the course. This
interleaving serves to create more durable learning [23].
Some critics of the RAP have suggested that there is little value
in the team portion, as students will simply vote on the most popular
answer. To test this, we compared teams’ actual tRAT scores with
what they would have scored through a voting strategy. Teams’ actual
scores were 9.7% higher on average (a t-test showed this difference to be
significant, p < 0.0001), indicating that team discussions were actually
driving teams towards the correct answer instead of simply the most
popular answer. Additionally, our observations as instructors are that
the tRATs usually produce rich discussions within teams on the more
difficult questions.
8
3.2 4-S Activities
As described above, a typical TBL implementation will have teams
spending class time working on 4-S application activities: teams work on
the Same problem, which is a Significant problem; and they Simultaneously
report a Specific choice to the class.
One of the benefits of TBL is the rich inter-team discussion that
takes place after simultaneous report. Indeed, the reasoning behind
requiring a specific choice is to force teams to make a specific claim, and
be prepared to argue for their answer. In the context of a math class,
this need not mean that students must answer a multiple choice question
(though as we describe below, this is often helpful). It may mean that
they have done a specific computation (e.g. computed a determinant)
and simultaneously report that result. Inter-team discussion is then
facilitated by asking teams to explain their reasoning; this is wonderfully
effective on tasks with many possible appropriate techniques. Moreover,
this puts student thinking at the (metaphorical) front and center of the
classroom.
One of the motivations for the Readiness Assurance Process in TBL is
to free up the group space (e.g. class time) for interactions between stu-
dents as they complete application activities to bring theoretical knowl-
edge into practice. However, in mathematics it is the theoretical knowl-
edge itself we are often concerned with, so our application activities must
be designed to develop this.
To this end, application activities in TBIL are designed around build-
ing upon the background knowledge refreshed during the Readiness As-
surance Process to (dis)cover new material. By carefully scaffolding
questions that get students moving through a particular line of inquiry,
students are enabled to conjecture or even prove new mathematical ideas
for themselves, rather than having these ideas dictated to them via a
lecture or reading. These activities can broadly be sorted into three
categories.
1. Scaffolded Exploration and Discovery. Students are guided
to a new concept through a sequence of carefully scaffolded activ-
ities. These activities include exploratory activities to motivate
an entire line of thinking; working a series of examples to have
students realize the need for a new definition; and working a care-
fully scaffolded problem to develop a general algorithm for solving
similar problems, for example.
2. Fluency Builders. Once a new mathematical concept has been
established, students need an opportunity to put it into practice
and build fluency in procedural tasks. These activities are often
similar or identical to exercises that would be asked on assessments,
9
but are solved within teams in order to provide students a model
for how to organize their thoughts and writing when demonstrating
mastery on quizzes or exams.
3. Flexible Extension. Once a concept is established and students
gain some fluency working with it, we ask students to apply this
new concept to slightly different contexts. This can take various
forms, such as checking if something satisfies a new definition; ex-
tending an idea from its “natural” setting to more generality; or a
true application to another field such as balancing chemical equa-
tions by solving systems of linear equations. In these activities, the
emphasis is on helping students develop a flexible mindset when
faced with new problems.
We note that the same task could be in different categories depending on
the context; for example, the first encounter with a particular question
might be an extension, but once a model for answering such a question is
established, asking a similar question again might be a fluency builder.
Activity 2.1 The vector
−1
−6
1
belongs to span
1
0
−3
,
−1
−3
2
ex-
actly when there exists a solution to the vector equation x1
1
0
−3
+
x2
−1
−3
2
=
−1
−6
1
.
Part 1: Reinterpret this vector equation as a system of linear equa-
tions.
Part 2: Find its solution set, using CoCalc.com to find RREF of its
corresponding augmented matrix.
Part 3: Does
−1
−6
1
belong to span
1
0
−3
,
−1
−3
2
?
Figure 2. Scaffolded Exploration Activity
In Figures 2and 3, we provide approximately one class day’s worth
of activities to exemplify the three categories of activities. Activity 2.1
in Figure 2gives an example of a scaffolded exploration activity; stu-
dents work through the steps to discover an algorithm to answer these
questions. After completing this activity, we present the algorithm for
10
Observation 2.2 A vector ~
bbelongs to span{~v1, . . . , ~vn}if and only
if the linear system corresponding to [~v1. . . ~vn|~
b] is consistent.
Put another way, ~
bbelongs to span{~v1, . . . , ~vn}exactly when
RREF[~v1. . . ~vn|~
b] doesn’t have a row [0 · · · 0|1] representing the con-
tradiction 0 = 1.
Activity 2.3 Determine if
3
−2
1
5
belongs to span
1
0
−3
2
,
−1
−3
2
2
by
row-reducing an appropriate matrix.
Activity 2.4 Determine if
−1
−9
0
belongs to span
1
0
−3
,
−1
−3
2
by
row-reducing an appropriate matrix.
Activity 2.5 Does the third-degree polynomial 3y3−2y2+y+ 5 in
P3belong to span{y3−3y+ 2,−y3−3y2+ 2y+ 2}?
Part 1: Reinterpret this question as an equivalent exercise involving
Euclidean vectors in R4. (Hint: What four numbers must you know to
write a P3polynomial?)
Part 2: Solve this equivalent exercise, and use its solution to answer
the original question.
Figure 3. A sequence of activities on span
reference in Observation 2.2 (Figure 3); students then work two proce-
dural activities (2.3 and 2.4) for practice and to build fluency. Then, an
extension activity (2.5) asks them to apply their knowledge of how to
answer questions about span for Euclidean vectors to an abstract vector
space (in this case, polynomials).
While teams are working on an activity, the instructor circulates
the room to ensure each team is progressing towards a solution. Some-
times this involves a short conversation with a team; sometimes a single
question posed to a struggling team will suffice; and sometimes an im-
promptu mini-lecture might be needed. As teams finish the activity, the
instructor should make a mental note of each team’s solution.
After each team is given a chance to complete the activity, the in-
structor facilitates a class-wide discussion by asking a team to explain
their reasoning. Even when all teams report the same ‘answer’, they of-
ten take different approaches, and the instructor can ask another team
to explain their reasoning.
11
Statement Responses Agreement
“The use of Team-Based Learning
during class time was a valuable
learning experience.”
48 77%
“The use of Team-Based Learning in
this course helped me to learn more
than in a traditional course.”
55 71%
“This course helped me improve my
problem solving skills.”
55 87%
Table 1. Quantitative survey responses
4 Impact on Student Learning
We administered surveys to students in six sections of TBIL Linear Al-
gebra taught by the first two authors at a large, public university; the
third author also conducted two focus groups (9 total students). These
sections ranged from 9-30 students each and included a mixture of math
majors and other STEM (primarily engineering) majors. In the sur-
vey, we asked students to rate their agreement on a six-point Likert
scale to several statements, and then explain their responses in an open-
ended format. Table 4shows they generally agreed that TBL was valu-
able, helped them learn more, and improved their problem solving skills.
When asked an open-ended question “What aspect of this course did you
enjoy the most?”, 40% of students mentioned the team activities.
Several themes emerged from the focus groups and survey responses.
First, students recognized the value provided from peer instruction in
their teams. This was mentioned by 38% of students explaining their
response on the survey question on the value of TBL. Students spoke at
length about this in the focus groups as well; as one student said “It has
really given me confidence because I might not be able to get all the way
to the right answer, but ... you can sort of work together to get further
on the problem.” Survey responses indicated that students found value
in hearing both alternate techniques and alternate explanations (e.g. in
novice language rather than expert language) for the same concept from
their teammates.
Several students indicated that they understood the material better
and that TBL increased their learning. They indicated that the learning
was occurring in class primarily during application activities. “The best
experience I had was doing it and seeing what needs to be done for each
topic and concept.” One student also noted that “I learned a bit more
by having to explain the concepts to my team members.”
Students also noticed that class time is focused on what matters
12
most, because they came to class prepared. Individual preparation and
review outside of class led to increased class time for new topics and chal-
lenging problems during class. Students recognized that their knowledge
and skills developed over the course of the module with distributed prac-
tice: “I think it helped that you are not trying to learn it all in one day,
but you are trying to build off what you think you know.”
When describing the TBIL class environment, students discussed ac-
tively working together to solve problems and reported increased en-
gagement. One student said, “Zoning out is easier in lectures.” They
frequently stated that they “worked it out together.” Other comments
were “I feel I spend more time actively engaged with learning in class,
and less time distracted or bored” and “When you are able to work
together and discuss problems, you get a better understanding of the so-
lution.” They recognized that when solving problems together with the
support of teammates and the instructor they persisted with challenging
problems.
Students in the focus group recognized that the TBIL structure pro-
vides a safe environment for productive struggle. As one said, “If every-
thing is easy you are not retaining it”. Another noted that “to really
genuinely learn you have to struggle.” While sometimes they did not
know how to solve problem initially, “[TBL] gets you brainstorming and
actually struggling to learn.”
Instructors and students both observed reduced anxiety in students.
One student said, “With me, it’s been 15 years since I’ve taken a math
class so I was really nervous about coming into a math class, but it’s
been really relaxed. We are working in teams it’s been great, so I didn’t
think I needed to be nervous.”
4.1 Instructor reflections
In a TBIL environment, the role of the instructor shifts from that of a
lecturer to that of a facilitator. Since students are working in teams the
vast majority of class time, the instructor is able to spend most of their
time observing student thinking. Eavesdropping on team discussions
can provide a much richer picture of how students are making sense of
the material than one is able to discern in a lecture. In our first few
TBIL class sessions, we had concerns that students were not picking up
concepts as quickly as they might seem to do in lecture. However, as
the course progressed, it became clear that this confusion also would
have existed in a comparable lecture, but in TBIL it was exposed during
team interactions. More importantly, TBIL allowed us to identify and
remedy such issues during class.
Students in our TBIL classes seem to develop more flexible problem
solving skills than when we have taught via lectures. While we hope to
13
quantify this in future work, we will provide an anecdote here: when
computing determinants, our students in lectures would most often re-
sort to using Laplace expansion, likely because it is an algorithm they
can follow. However, in our TBIL classes, students are more likely to
perform a clever row operation or two to simplify the resulting calcula-
tion, rather than blindly following an algorithm. We hypothesize that
the team reporting phase of class is the crucial feature supporting this
behavior; the instructor can highlight distinct approaches by different
teams, all resulting in the same correct answer, but some approaches
involve less computation than others.
We have also noticed that students tend to ask more questions in
TBIL classes. In a lecture, a question by a student draws the attention
of the entire class, and many shy or introverted students are hesitant to
ask. However, while the instructor is circulating the room during team
activities, these same students seem to be more willing to ask a question.
Moreover, we observe students are much more willing to pose questions
to their classmates; as one student put it in a survey response, “I feel
that the team based learning curriculum helps students that are afraid
to ask a question, get their question answered by a classmate.”
Finally, we note that we found the TBIL structure to be quite helpful
as we were developing the application activities for the course. Our
initial reaction (matched by many other mathematicians we’ve presented
TBIL to) was that the 4-S structure of application activities was too
rigid for mathematical tasks, but in practice we found this to not be
the case. Indeed, in our first attempt at writing an activity, we often
disregarded one of the 4-S components, such as specific choice. However,
after using the activity in class, we would often realize that the class
discussion was improved by modifying the activity to be more closely
aligned with the 4-S structure. In particular, not requesting a specific
choice in an activity would often leave students sitting silently as they
pondered how to proceed. But by defining the specific choice to be
made (even sometimes going as far as to make the activity multiple-
choice), the increased scaffolding helped students be more willing to
take risks with the problem and engage with their team. Regardless
of how many individual teams might come to the correct conclusion,
the following class-wide discussion clarifying the correct conclusion was
typically deeper and more productive.
5 Conclusion
Our experience with this initial exploration of implementing TBL in the
undergraduate mathematics curriculum leaves us optimistic that TBIL
is a promising format for introducing inquiry learning into a heteroge-
neous sophomore mathematics classroom serving both mathematics and
14
other STEM majors. The strong structure of TBIL seems to lessen the
culture shock and potential loss of buy-in risked by other active learn-
ing formats, making it an appealing option for instructors looking to
increase collaboration and inquiry in their classrooms. Future work is
planned to collect more concrete evidence of the anecdotal claims of
this paper, including comparing concrete measures of student learning
between TBIL and other classes.
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