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Citation: Méndez-Romero, R.A.;
Carter, J.; Carrerá-Martínez, S.;
Suavita-Ramírez, M.A.; Higgins, V.
Rethinking the Teaching of
University Statistics: Challenges and
Opportunities Learned from the
Colombia–UK Dialogue. Mathematics
2023,11, 52. https://doi.org/10.3390/
math11010052
Academic Editors: David Pugalee,
Michelle Stephan and
Erdinç Çakıro˘glu
Received: 10 October 2022
Revised: 25 November 2022
Accepted: 29 November 2022
Published: 23 December 2022
Copyright: © 2022 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).
mathematics
Article
Rethinking the Teaching of University Statistics: Challenges
and Opportunities Learned from the Colombia–UK Dialogue
Rafael Alberto Méndez-Romero 1, * , Jackie Carter 2, Sofía Carrerá-Martínez 1, María Angélica Suavita-Ramírez 3
and Vanessa Higgins 2
1Escuela de Ingeniería, Ciencia y Tecnología, Universidad del Rosario, Bogotá111711, Colombia
2
Department of Social Statistics, School of Social Sciences, University of Manchester, Manchester M13 9PL, UK
3
Grupo de Investigación Cambio Educativo Para la Justicia Social (GICE), Universidad Autónoma de Madrid,
28049 Madrid, Spain
*Correspondence: rafael.mendez@urosario.edu.co; Tel.: +57-601-2970200
Abstract:
The aim of this paper is first to examine, through a qualitative analysis of statistics syllabi,
the current state of statistical education in a sample of universities in Colombia. The focus is on
statistics teaching in degrees for economics and business administration students. The results from
the qualitative analysis reflect a preponderance of traditional and didactic teaching methods centered
on the teacher, not on the student. The second aim is to present findings from a case study that
has developed an innovative pedagogical intervention, called a data fellows program, from the
University of Manchester, United Kingdom, which evidences opportunities for how statistics can be
taught effectively to non-STEM majors. Further, the data fellows model has also been explored in the
context of developing statistical and data skills capacities in Latin America. We reflect on how the
lessons from the UK case study could open up opportunities for rethinking the teaching of statistics
in Colombia through developing data projects and experiential learning to practice statistics in the
real world.
Keywords:
statistics education; higher education; learning by doing; pedagogical innovation; data fellows
MSC: 00A35; 62P25; 97K70; 97C70; 97D40
1. Introduction
The teaching of statistics does not only happen in STEM subjects. In this paper, we
explore how statistics is taught in university curricula where the students are not studying
a STEM (science, technology, engineering and math) major. As such, we focus on statistics,
as a subject in its own right, rather than as a sub-branch of mathematics (the M in STEM),
and we consider statistics teaching where it is embedded in non-STEM subjects. We are
particularly interested in the application of statistical skills, which are also referred to in
this paper more broadly as quantitative skills and are highly relevant to the broader context
of STEM education. We contend that statistics education as a scholarly field can benefit
from understanding how the social, administrative and economic sciences teach statistics
to their undergraduate students. The paper contributes to the knowledge of how statistical
skills are, and can be, acquired for non-STEM majors. In a world where data increasingly
drive decisions, in the public and private spheres, statistical knowledge is in high demand.
As such, the examination of how and where in the curriculum statistics is taught, and
especially how students acquire statistical knowledge and skills for the twenty-first century
workplace, is important. By examining how non-STEM majors learn how to do statistics,
we can contribute to increasing the statistical capacity in society and bring our findings to a
wider audience that goes beyond STEM subjects.
This paper examines the current state of the statistical education in Colombia and
considers how it could be improved. We frame the research through the introduction of
Mathematics 2023,11, 52. https://doi.org/10.3390/math11010052 https://www.mdpi.com/journal/mathematics
Mathematics 2023,11, 52 2 of 17
statistics education generally, then focus on the situation in Colombia specifically. The
inclusion of a UK case study, which has also been considered for its applicability to statistical
capacity building in Latin America, contributes to our research. Our research questions are:
1.
What is the current state of statistical education in Colombia higher education non-
STEM majors as reflected in statistics curricula?
2.
What can be learned from other statistical education initiatives outside of Colombia
(considering a UK case study)?
3.
How might Colombia improve its statistical education by building on the UK
case study?
Using a sample of statistics syllabi from eight Colombian universities (two public,
six private), we seek to understand how statistics is taught to economics and business
administration students. A grounded theory approach is taken to qualitatively analyze
the content extracted from the syllabi, with attention paid to the mix of teacher-centered
versus student-centered pedagogical approaches. An exploration of whether the syllabi
included any innovative elements or enabled active learning is also undertaken. The latter
is especially of interest, as three of the authors have previously worked collaboratively
on a project (EmpoderaData) that proposed the use of innovative techniques for learning
statistics in real world contexts. In order to explore these approaches in the context of
teaching statistics in Colombia to non-STEM majors, we include here a UK-based case study,
which presents a strong case for students to be given the opportunity to learn statistics in
real-world settings through undertaking data-driven projects conducted in the workplace.
This program places ‘data fellows’ into organizations to practice statistics.
The results from the qualitative analysis of the statistics syllabi and the UK case
study, together with the lessons learned from testing the viability of the UK experiential
learning approach in Latin America through the EmpoderaData project, are followed with
a discussion of the challenges and opportunities. Finally, a conclusion that proposes a
major change to statistics education in Colombia is presented.
Understanding how quantitative skills are currently taught through statistics educa-
tion in non-STEM majors opens up opportunities to create a stronger statistically literate
population. This research, thus, contributes to STEM education more broadly.
2. Statistics Education and Why It Matters
2.1. Statistics Education: Where and How Statistics Is Taught across the Curriculum
Statistics is a discipline that involves ways of thinking to deal with uncertainty and
to understand the nature of inferential results drawing on sampling theory [
1
]. Thus, the
study of statistics is closely related to the development of random or stochastic thinking
that “helps to make decisions in situations of uncertainty, chance, risk or ambiguity due
to lack of reliable information, in which it is not possible to predict for sure what is
going to happen” [
2
] (p. 64). It follows that learning statistics will provide students with
powerful tools to enable them to critically interpret data and information, and that the
knowledge and skills acquired will equip them to better understand real-world problems.
Having an appreciation of statistics will help students discuss, discern and make better-
informed decisions, taking into account the uncertainty in the data and the limitations of the
analysis based on it. Disinformation poses a real threat to democracy, for example, and the
development of competent, statistically literate citizens is necessary for their participation
in decision making and in civic life [3].
The research on statistics education has increased in recent decades, although to a
lesser extent in the countries of the global south. The role of statistical education in training
citizens who are required to make societal change, and be capable of good decision-making
in the face of crises, is highlighted as an important need [
4
]. Our approach in this paper
focuses on the statistics curriculum in higher education. However, statistical education
at all levels of education is expected to “respond to the need of empowering all citizens
and professionals in statistical literacy “ [
5
,
6
] (p. 1). Within schools, for instance, there is a
demand for more attention to be devoted to statistics and new calls for statistics to be a
Mathematics 2023,11, 52 3 of 17
crosscutting subject taught in areas of the curriculum, including outside of STEM subjects,
in which the use of data is required. Critical statistics teaching that pursues the training of
students or citizens for conscious and informed decision making with a positive impact on
society has been introduced as an important concept [
7
–
9
]. A statistically literate population
is desirable, as “an enlightened citizenry that is empowered to study evidence-based facts
and that has the capacity to manage, analyze and think critically about data is the best
medicine for a world that is guided by fake news or oblivious towards facts” [7] (p. 45).
Teacher training and the study of the processes involved in understanding statistical
concepts, as well as the skills and abilities involved in their use, are essential parts of
developing a statistically literate population [
10
,
11
]. Good teaching will help students to
learn statistics well, wherever statistics appears in the curriculum, and whatever educa-
tional level this is taught at. Factors affecting the effectiveness of statistics education have
been categorized as: (i) the processes or results of statistical education in formal education;
(ii) teacher
studies on teaching practice; (iii) innovative teaching methods; (iv) the study of
a specific topic of great relevance for learning or teaching from the perspective of another
discipline, such as mathematics education or psychology, among others [
12
]. Moving on to
examine developments around statistics education in higher education, research outputs
in this area are relatively scarce. This is the case despite the fact that statistics occupies an
important role in university curricula, both in mathematics departments, some of which
have separate statistics departments, as well as in other subjects. Recent publications on
teaching statistics [
13
–
16
] at the university level can provide some helpful insights on the
problems and challenges encountered at this level of education. One of these problems
is the difficulty that learning statistics can present for non-STEM majors students who
“do not have a solid mathematical foundation and frequently avoid activities that involve
numbers” [
17
] (p. 70), and this often ends in students feeling frustrated and lacking interest
in or motivation for learning statistics. The anxiety that learning statistics generates in
university students is reflected in several recent articles [13,14,18].
Given the scant literature on statistics education in higher education and in courses
that are in non-STEM degree subjects, statistics education in the university context provides
an opportunity for further research. An important contribution that will help the statistics
education community better understand what is taught in statistics courses is to study
what is included in the curriculum, and especially the extent to which this reflects real-
world problems. By studying the contents of statistics curricula, and the contexts in which
statistics is taught, we can start to reveal what and how university statistics courses are
being delivered. Moreover, since “in many university classrooms there are still traditional
models of education that focus excessively on the delivery of content
. . .
these models
have shown little effectiveness when they are evaluated (in terms of learning)” [
17
] (p. 78);
it is important to reflect on existing learning approaches and pedagogies if we want to
propose improvements.
The curriculum is an important starting point for understanding the current state
of statistics education (in Colombia), but as we state in the introduction, the findings
emerging from a UK program can also help progress our thinking in this area. Therefore,
we highlight here the role of statistical education in the social sciences, a subject area that
requires critical understanding of statistics to be able to make sense of the world that is
increasingly presented in the form of quantitative data.
2.2. Statistics Education: Lessons from a Social Sciences Perspective
We have commented that statistics education is not only delivered through the STEM
curriculum; thus, to add to the understanding of how non-STEM degree majors are taught
statistics, we turn to lessons learned from the social sciences. In this paper, our qualitative
analysis is based on statistics education through an examination of business administra-
tion and economics degrees in Colombia. To set the context for the research, this section
provides evidence from an initiative that has seen success in training undergraduate stu-
dents majoring in social science subjects on how to acquire and practice ‘quantitative
Mathematics 2023,11, 52 4 of 17
skills’ (for a fuller explanation of what we mean by ‘quantitative skills’, see below). The
Q-Step (Quantitative Step Change) program, which ran from 2013 to 2021, was a strategic
response to the UK seeking quantitative skills for careers in research and data-led profes-
sions. Seventeen universities participated and an external evaluation of the program was
published in 2022. The evaluation reported many positive outcomes, including that “par-
ticipation in Q-Step modules is associated with better employment prospects for students
compared to similar students on equivalent courses” [
19
] (p. 5) and that the centers have
“increased engagement with external stakeholders, particularly local employers, through
their networks of work placement providers” [
19
] (p. 38). The evaluation proceeds to
highlight the increased capacity across the participating universities to teach quantitative
skills, encouraging other higher education providers to follow their lead. It noted that
student satisfaction in these courses was high and significant value was placed especially
on the work placement activities the centers introduced. The recommendations arising
from this evaluation included sharing this good practice more widely across the scholarly
community and ensuring that the diversity of backgrounds in the programs of study and
work placements is broad. The report concludes with the recommendation that “Q-Step
should be presented as a showcase example that encourages other universities to invest
in the development of quantitative methods within social science programs and beyond.
The evidence from Q-Step suggests that investing in quantitative skills training increases
graduate employability, enriches the curricula, increases staff expertise and encourages the
recruitment of additional high-quality lecturers” [
19
] (p. 68). This strong evidence-based
recommendation from the Q-Step program evaluation report supports the inclusion of a
case study from this social-sciences-led initiative in this paper.
The focus on quantitative skills in the Q-Step program, as introduced above, requires
further elaboration in order to clarify its inclusion in, and contribution to, this article on
statistics education. In particular, this program was aimed not at STEM university students
but at social science undergraduates. Grundy [
20
], writing about the origins and aims of
the Q-Step program, highlights the quantitative skills that social science students are taught.
He places the Q-Step program’s emphasis on the acquisition of statistical and data skills,
with a clear focus on applying the learning to real-world problems. Grundy’s coverage of
quantitative skills includes understanding how to design surveys and experiments and how
to analyze and interpret the data they generate; understanding how to analyze and interpret
data from other sources such as social media, administrative data and longitudinal cohort
studies; and understanding how to evaluate the quality of data sources, what constitutes
good and bad evidence and how it can be used to make decisions. As such, the Q-Step
program addressed the need for students to acquire critical statistical and data skills and
to have the opportunity to practice them both in the classroom and importantly in the
workplace. These quantitative skills put STEM skills in general, and statistics and data
skills in particular, firmly in the spotlight for social science majors. Many of the Q-Step
centers established work placement programs through which undergraduate students
could take their statistical learning and data analysis a step further. Carter [
21
] presents
case studies and vignettes from the University of Manchester Q-Step program (and other
universities, including PhD students) evidencing how social science students put their
statistical skills into practice through undertaking ‘data fellowships’. The ‘data fellowships’
are based in multiple employment sectors, ranging from local government departments to
The World Bank, and show how social science students’ quantitative skills can be enhanced
in the workplace via experiential learning.
Section 4.2 presents a case study from one of the UK Q-Step centers, the University of
Manchester, to present some of the outcomes and findings of a social-science-led approach
to teaching statistics and data analyses. In particular, we examine how this model of
skilling-up undergraduates, who have been taught statistics in the classroom and are
then immersed in the workplace to develop these skills, is one that educators should
consider. Moreover, building on this work through an international project, EmpoderaData,
in Latin America, we evidence how it is possible to contribute to the development of data
Mathematics 2023,11, 52 5 of 17
skills capacity for the delivery of the UN’s 2030 Sustainable Development Goals. It is our
contention that the findings and approaches we present in this article will help statistics
educators develop a more statistically literate graduate population and could change how
statistics is taught in Colombia.
3. Methods
Based on the authors’ aspirations to find actions to strengthen and opportunities to
improve statistical education in Colombia, this research concentrates on reviewing the
current state of statistical education in higher education institutions in Colombia. This was
based on a sample of universities as described below.
Bearing in mind that grounded theory was used, we worked with a final sample
of 19 syllabi (primary documents) once theoretical saturation was reached, i.e., when
the information gathered in these documents did not contribute anything new to the
development of the properties and dimensions of the categories of analysis. The syllabi
corresponded to business and economics schools, taking into account the authors’ interest
in focusing on the teaching of statistics in academic units that did not necessarily have
mathematics-dominated curricula. The sample aimed to be as diverse as possible, including
public and private universities and universities located in Bogotá, the capital of Colombia,
as well as others in different cities.
It is worth noting that a syllabus, according to the instructions of the Colombian
Ministry of National Education, must contain at least the following sections: the name
of the subject, the number of credits, the hours of mediated study by the teacher and the
autonomous work, the central themes, the expected learning results, the justification of the
subject or a summary of it, an evaluation methods and a recommended bibliography. We
only included syllabi that met this definition.
For the analysis, we used a qualitative approach [
22
,
23
] based on grounded theory [
24
].
We began with the research question ‘What is the current state of statistical education in
Colombia higher education non-STEM majors as reflected in statistics curricula?’.
Figure 1
shows how we undertook the coding starting with our primary data and how we devel-
oped a conceptual understanding of our research question through our data. Our sample
of statistics curricula—as described above—enabled us to develop and code our dataset for
the inductive analysis using Atlas.Ti Software. Our primary data were from the collection
of the 19 syllabi from our sample as described above. We allowed the codes to emerge from
the data, purposefully avoiding using a predetermined coding scheme, and in this way a
descriptive coding system was obtained to initiate the analysis. We then advanced from
these descriptive codes to eliciting categories that reflected a deeper and more conceptual
understanding of the syllabi. This was achieved by noticing central concepts and relation-
ships between codes, and through a process of iteratively reflecting on and interpreting the
collection of codes. The resulting expansion or division of some of them into clearer ones
allowed us to advance to this level of conceptual coding. Once this conceptual level was
reached, the categories were compared with the primary data and we questioned whether
theoretical saturation had been reached, i.e., the level at which the categorical scheme
could be understood as an emerging theory with meaning and value. If it was decided
that saturation had not been reached, a new iteration was begun, including a new primary
document, and this cyclical process continued.
Given the interpretative nature of the research, after theoretical saturation had been
reached, a sample size of 19 syllabi from the eight universities in our sample was suf-
ficient and guaranteed the discovery of a model for statistical education in Colombia,
from an emerging taxonomy based on grounded theory. The characterization and dis-
tribution of these syllabi are shown in Table 1. The hope was to discover a conceptual
model that accounts for the state of statistical education in Colombia in business and
economics departments.
Mathematics 2023,11, 52 6 of 17
Mathematics 2023, 11, x FOR PEER REVIEW 6 of 18
Figure 1. Cyclical scheme of a typical process guided by grounded theory.
Given the interpretative nature of the research, after theoretical saturation had been
reached, a sample size of 19 syllabi from the eight universities in our sample was sufficient
and guaranteed the discovery of a model for statistical education in Colombia, from an
emerging taxonomy based on grounded theory. The characterization and distribution of
these syllabi are shown in Table 1. The hope was to discover a conceptual model that
accounts for the state of statistical education in Colombia in business and economics
departments.
Table 1. Distribution of the syllabi.
University Type Location Program Syllabi
U. de los Andes Private Bogotá Business Administration and Economics 3
Escuela Colombiana de Ingeniería Private Bogotá Business Administration 1
Konrad Lorenz Private Bogotá Business Administration 2
U. de la Sabana Private Bogotá Business Administration and Economics 2
U. del Rosario Private Bogotá Business Administration and Economics 3
U. del Valle Public Cali Business Administration and Economics 4
U. Autónoma de Occidente Private Cali Business Administration and Economics 2
U. de Antioquia Public Medellín Business Administration andEconomics 2
Specifically, the descriptive coding system [25] was initially made up of 65 codes (see
the “codes” column in Appendix A) showing an emerging taxonomy from a purely
descriptive perspective. After incorporating decisions towards a conceptual convergence,
11 groups of codes (see Figure 2 and also column the “group codes” in Appendix A) were
organized, which ended in a categorical scheme of three nodes (Figure 3). The evolution
of the coding system from the descriptive segment to the conceptual segment is organized
in Appendix A.
Figure 1. Cyclical scheme of a typical process guided by grounded theory.
Table 1. Distribution of the syllabi.
University Type Location Program Syllabi
U. de los Andes Private BogotáBusiness Administration and Economics 3
Escuela Colombiana de Ingeniería Private BogotáBusiness Administration 1
Konrad Lorenz Private BogotáBusiness Administration 2
U. de la Sabana Private BogotáBusiness Administration and Economics 2
U. del Rosario Private BogotáBusiness Administration and Economics 3
U. del Valle Public Cali Business Administration and Economics 4
U. Autónoma de Occidente Private Cali Business Administration and Economics 2
U. de Antioquia Public Medellín Business Administration andEconomics 2
Specifically, the descriptive coding system [
25
] was initially made up of 65 codes
(see the “codes” column in Appendix A) showing an emerging taxonomy from a purely
descriptive perspective. After incorporating decisions towards a conceptual convergence,
11 groups of codes (see Figure 2and also column the “group codes” in Appendix A) were
organized, which ended in a categorical scheme of three nodes (Figure 3). The evolution of
the coding system from the descriptive segment to the conceptual segment is organized in
Appendix A.
Mathematics 2023, 11, x FOR PEER REVIEW 7 of 18
Figure 2. Relationship between the three dimensions of the analysis and the 11 code groups. The
red nodes represent the three dimensions (emergent categories) and all other nodes represent
groups of codes. This scheme comes from a first coding system of 65 codes, which is shown in
Appendix A.
4. Results and Findings from the UK Case Study
4.1. Results from the Qualitative Analysis of Statistics Syllabi in Colombia
The final results from the qualitative analysis show that in Colombia, statistical
education in higher education non-STEM majors can be conceptually reduced in three
dimensions—the curricular, the pedagogical and the applicability (application of
statistics) dimensions. We found that each is intrinsically connected to the other; what
these courses teach, how they teach and their learning goals are captured in these three
dimensions within the syllabi. We found that the applicability of statistics education,
although evident—and our stated focus in this study—is still emerging. The learning
strategies where students have some freedom to undertake their own research and
become novice users of statistics in their professional lives are most often controlled by
their professors and students are seldom allowed to leave the sandbox examples they are
given.
This categorization emerged after carefully examining the nineteen syllabi. We
created a coding system of 65 codes. In Section 4.1.1, we describe how we arrived at the
final three-dimensional model of statistical education based on our data (i.e., the
curricular, the pedagogical and the applicability dimensions) by outlining the most
relevant codes that emerged from the analysis and how they interact with each other.
4.1.1. The Dots: Main Characteristics of Colombian Statistical Education
We chose the most relevant codes—with the higher absolute frequencies—to describe
the results with the information closest to the syllabi. The codes were (1) applied focus,
(2) disciplinary focus, (3) technological focus, (4) theoretical focus, (5) traditional learning
approach, (6) project, (7) learning strategies and (8) theoretical evaluation. These eight
codes convey how statistics courses are taught, how they fit into the focus, the learning
Figure 2.
Relationship between the three dimensions of the analysis and the 11 code groups. The red
nodes represent the three dimensions (emergent categories) and all other nodes represent groups of
codes. This scheme comes from a first coding system of 65 codes, which is shown in Appendix A.
Mathematics 2023,11, 52 7 of 17
Mathematics 2023, 11, x FOR PEER REVIEW 9 of 18
Figure 3. Co-occurrence matrix. Cell ij of this matrix shows the co-occurrence of code i and code j,
i.e., the number of times these two codes are linked to the same citation.
The closest relations within the codes are between the theoretical evaluation and
traditional learning approach, with 79 co-occurrences. All of the syllabi describe
evaluations as written exams in which students have to solve problems, such as the ones
studied in class; some are during the class, while others are assigned as homework (these
were also classified with learning strategies, with 11 co-occurrences). Also related to the
traditional learning approach (with 46 co-occurrences), the learning strategies are those
exercises and class assignments – usually extracted from the textbooks – that professors
use to show a controlled and safe application of statistical theory. In some of these, the
students are expected to use statistical software programs to solve the problems, often
regarding topics close to their majors, showing the relations to the technological focus (the
technological focus and learning strategies have 21 co-occurrences. Additionally, the
disciplinary focus and the technological focus are closely related, with 22 co-occurrences).
Regarding the relations among the focuses, the syllabi show that often the applied
(the applied focus shares 9 co-occurrences with project, 22 with disciplinary focus and 11
with technological focus), technological (the technological focus has 8 co-occurrences with
project, 11 with applied focus and 3 co-occurrences with disciplinary focus) and
disciplinary (the disciplinary focus shares co-occurrences with project, 22 with applied
focus and 3 with disciplinary focus) focuses are joined together by a project—a student-
centered learning strategy that encourages the students to choose a problem related to
their major (disciplinary) to use the mathematical formulas learned in class (applied)
using statistics software (technological), as shown on Figure 2. Leaving aside the
innovative potential these projects have, in some universities students are expected to
choose a problem from a curated list created by the professor and to stay within the
bounds of what was taught during the term. This makes some projects also part of the
traditional learning approach, with 3 co-occurrences between project and traditional
learning approach.
The applied focus appears in two ways: mixed with a theoretical focus (36 co-
occurrences) or with a disciplinary focus (22 co-occurrences, see Figure 3). In the
theoretical focus, the applicability of statistics is limited to the use of formulas to solve
problems that are usually decided and controlled by the professors. This is also related to
the disciplinary focus (which is also tightly connected to the theoretical focus, with 18 co-
occurrences, as shown in Figure 3), as some of these problems are related to economics or
business administration. In this way, the applied focus joins how they teach statistics,
what they teach and what the goals of the course are.
Figure 3.
Co-occurrence matrix. Cell ij of this matrix shows the co-occurrence of code i and code j,
i.e., the number of times these two codes are linked to the same citation.
4. Results and Findings from the UK Case Study
4.1. Results from the Qualitative Analysis of Statistics Syllabi in Colombia
The final results from the qualitative analysis show that in Colombia, statistical
education in higher education non-STEM majors can be conceptually reduced in three
dimensions—the curricular, the pedagogical and the applicability (application of statistics)
dimensions. We found that each is intrinsically connected to the other; what these courses
teach, how they teach and their learning goals are captured in these three dimensions within
the syllabi. We found that the applicability of statistics education, although evident—and
our stated focus in this study—is still emerging. The learning strategies where students
have some freedom to undertake their own research and become novice users of statistics
in their professional lives are most often controlled by their professors and students are
seldom allowed to leave the sandbox examples they are given.
This categorization emerged after carefully examining the nineteen syllabi. We created
a coding system of 65 codes. In Section 4.1.1, we describe how we arrived at the final
three-dimensional model of statistical education based on our data (i.e., the curricular, the
pedagogical and the applicability dimensions) by outlining the most relevant codes that
emerged from the analysis and how they interact with each other.
4.1.1. The Dots: Main Characteristics of Colombian Statistical Education
We chose the most relevant codes—with the higher absolute frequencies—to describe
the results with the information closest to the syllabi. The codes were (1) applied focus,
(2) disciplinary focus, (3) technological focus, (4) theoretical focus, (5) traditional learning
approach, (6) project, (7) learning strategies and (8) theoretical evaluation. These eight
codes convey how statistics courses are taught, how they fit into the focus, the learning
approach and the student-centered learning groups from the pedagogical dimension of the
course (Figure 2). The first four categorize how the syllabi approach the topics and how
they frame the learning goals of the course; the fifth includes all references to lecture-like
classes, in which students are assumed to have a passive role; the final three show how
students are assessed via a research project, class assignments and exams.
The applied focus (code 1) drives the courses towards problem-solving strategies.
Through the learning strategies, evaluations and approach to certain topics, students
are taught how to use statistics in real-life situations, albeit frequently controlled by the
professors. This can open students’ curiosity to explore new ways in which they can use
statistics in their professional lives further on.
The disciplinary focus (code 2) involves topics, methods and approximations to the stu-
dents’ major. In some syllabi, unsurprisingly the main motivation of the course converges
Mathematics 2023,11, 52 8 of 17
on how statistics can be used in business administration and economics, such as business
risk and performance indicators, stock market fluctuations and project management. This
allows students to get closer to their major, with clear explanations of the use of statistics.
The technological focus (code 3) is, in essence, the use of statistical software. In these
courses, they mostly use R, Stata and SPSS. This provides a more hands-on model of
education, in which students are encouraged to transfer their theoretical knowledge to
statistical software, which ultimately they will most likely use in their career.
The theoretical focus (code 4) delves into the study of statistics on an abstract level,
covering how mathematical formulas work and how to use them. The core of these syllabi
is the mathematical component rather than real-life examples and data. This approach,
while important, on its own drifts students further away from their potential interest in
mathematics and might deepen their frustration towards learning statistics.
The traditional learning approach (code 5) arises from the courses that follow the
conventional professor–student roles. Basically, the professor teaches the topics from
a textbook chapter, which is previously read by the students, who usually solve some
exercises in class or are left some homework. This approach encapsulates students into
boxes, whereby their only job is to learn, have questions and be able to solve textbook
problems. This also limits the students’ creativity and curiosity and the possibility to
learn-by-doing.
The project (code 6), learning strategies (code 7) and theoretical evaluations (
code 8
)
are how the professors evaluate the students. Although most of these revolve around
problem-solving strategies, the problems are in controlled environments in which the
statistics and data are perfectly clear and the concepts can be easily applied—far from what
students will have to deal with in their professional lives. The connections among these
eight codes let us draw conclusions on how statistics is taught in Colombia.
4.1.2. Connecting the Dots: How Different Course Focuses and Learning Approaches
Interact with Each Other
Grounded in the conceptual coding system and aligned with the most frequent codes,
using Atlas.Ti, we built a co-occurrence matrix (Figure 3) that shows how the eight most
relevant codes are interrelated. A co-occurrence matrix (or adjacency matrix) shows how
many times two nodes (codes in this case) occur in the same part of a syllabus.
The closest relations within the codes are between the theoretical evaluation and
traditional learning approach, with 79 co-occurrences. All of the syllabi describe evaluations
as written exams in which students have to solve problems, such as the ones studied in
class; some are during the class, while others are assigned as homework (these were also
classified with learning strategies, with 11 co-occurrences). Also related to the traditional
learning approach (with 46 co-occurrences), the learning strategies are those exercises and
class assignments – usually extracted from the textbooks – that professors use to show
a controlled and safe application of statistical theory. In some of these, the students are
expected to use statistical software programs to solve the problems, often regarding topics
close to their majors, showing the relations to the technological focus (the technological
focus and learning strategies have 21 co-occurrences. Additionally, the disciplinary focus
and the technological focus are closely related, with 22 co-occurrences).
Regarding the relations among the focuses, the syllabi show that often the applied
(the applied focus shares 9 co-occurrences with project, 22 with disciplinary focus and
11 with technological focus), technological (the technological focus has 8 co-occurrences
with project, 11 with applied focus and 3 co-occurrences with disciplinary focus) and
disciplinary (the disciplinary focus shares co-occurrences with project, 22 with applied
focus and 3 with disciplinary focus) focuses are joined together by a project—a student-
centered learning strategy that encourages the students to choose a problem related to
their major (disciplinary) to use the mathematical formulas learned in class (applied) using
statistics software (technological), as shown on Figure 2. Leaving aside the innovative
potential these projects have, in some universities students are expected to choose a problem
Mathematics 2023,11, 52 9 of 17
from a curated list created by the professor and to stay within the bounds of what was
taught during the term. This makes some projects also part of the traditional learning
approach, with 3 co-occurrences between project and traditional learning approach.
The applied focus appears in two ways: mixed with a theoretical focus (
36 co-occurrences
)
or with a disciplinary focus (22 co-occurrences, see Figure 3). In the theoretical focus, the
applicability of statistics is limited to the use of formulas to solve problems that are usually
decided and controlled by the professors. This is also related to the disciplinary focus
(which is also tightly connected to the theoretical focus, with 18 co-occurrences, as shown
in Figure 3), as some of these problems are related to economics or business administration.
In this way, the applied focus joins how they teach statistics, what they teach and what the
goals of the course are.
4.1.3. Three-Dimensional Model of Statistical Education
As stated in Section 4.1, the final results from the data we collected and analyzed
show three dimensions of how statistics is taught in Colombia (as shown in Figure 3
and mentioned in the methodology): (A) the curricular dimension of the courses, (C) the
pedagogical dimension of the courses and (B) the applicability, which is the bridge that
joins both (A) and (C).
The curricular dimension (Figure 4A) includes the topics and bibliographies stud-
ied in the courses. Although we do not elaborate here on what is taught in statistical
courses, we categorize the topics and bibliographies for the syllabi. The topics cover both
probability and statistics, from random variables to the design of statistical models. The
bibliographies focus mostly on statistical theory; they are used as guides for the course and
exercise workbooks.
Mathematics 2023, 11, x FOR PEER REVIEW 10 of 18
4.1.3. Three-Dimensional Model of Statistical Education
As stated in Section 4.1, the final results from the data we collected and analyzed
show three dimensions of how statistics is taught in Colombia (as shown in Figure 3 and
mentioned in the methodology): (A) the curricular dimension of the courses, (C) the
pedagogical dimension of the courses and (B) the applicability, which is the bridge that
joins both (A) and (C).
The curricular dimension (Figure 4(A)) includes the topics and bibliographies
studied in the courses. Although we do not elaborate here on what is taught in statistical
courses, we categorize the topics and bibliographies for the syllabi. The topics cover both
probability and statistics, from random variables to the design of statistical models. The
bibliographies focus mostly on statistical theory; they are used as guides for the course
and exercise workbooks.
Figure 4. Main categories of statistic education in Colombia.
The pedagogical dimension (Figure 4(C)) encompasses the methodology and central
axis of the class. The methodology is the main line of work in the syllabi, dictating how
the topics are taught and afterwards how they are evaluated. The central axis of the class
reflects who the main character of the course is: whether the lectures revolve around the
professor, or whether they embrace the students as the true protagonists. As we discussed
above, this is the center of attention of this research.
The bridge that connects both the curricular and pedagogical dimensions is the
possibility to apply the knowledge acquired in class. This is the applicability (Figure 4(B)).
We found that certain topics, such as statistical models, are usually taught using examples
applied to real life problems, some of them regarding the disciplines (majors). These,
however, are often controlled and delimited by the professors, not letting the students
learn statistics in a real-world environment but in a textbook-safe way.
4.2. UK Case Study: Developing Statistical and Data Skills in Higher Education
Our second research question is ‘what can be learned from other statistical education
initiatives outside of Colombia (considering a UK case study)?’
The focus of this section is to consider recent developments in teaching statistics to
non-STEM majors to help educators reflect on how statistics teaching could be improved
wherever it is delivered in the curriculum. This is important, as in order for statistical
educators to be able to tackle some of the challenges that have been elicited in the previous
section, we need to consider alternative approaches and ways of developing statistically
literate citizens [26]. In the UK, the acronym given by the British Academy to those who
Figure 4. Main categories of statistic education in Colombia.
The pedagogical dimension (Figure 4C) encompasses the methodology and central
axis of the class. The methodology is the main line of work in the syllabi, dictating how
the topics are taught and afterwards how they are evaluated. The central axis of the class
reflects who the main character of the course is: whether the lectures revolve around the
professor, or whether they embrace the students as the true protagonists. As we discussed
above, this is the center of attention of this research.
The bridge that connects both the curricular and pedagogical dimensions is the possi-
bility to apply the knowledge acquired in class. This is the applicability (Figure 4B). We
found that certain topics, such as statistical models, are usually taught using examples
applied to real life problems, some of them regarding the disciplines (majors). These,
however, are often controlled and delimited by the professors, not letting the students learn
statistics in a real-world environment but in a textbook-safe way.
Mathematics 2023,11, 52 10 of 17
4.2. UK Case Study: Developing Statistical and Data Skills in Higher Education
Our second research question is ‘what can be learned from other statistical education
initiatives outside of Colombia (considering a UK case study)?’
The focus of this section is to consider recent developments in teaching statistics to
non-STEM majors to help educators reflect on how statistics teaching could be improved
wherever it is delivered in the curriculum. This is important, as in order for statistical
educators to be able to tackle some of the challenges that have been elicited in the previous
section, we need to consider alternative approaches and ways of developing statistically
literate citizens [
26
]. In the UK, the acronym given by the British Academy to those who
graduate from social science, arts or humanities degrees is SHAPE (social science, humani-
ties and arts for people and the economy), with ‘the Right Skills’ report [
27
] highlighting
the importance of quantitative skills developed by SHAPE graduates for the labor market.
International bodies concerned with developing and evaluating statistical education have
increasingly been paying attention to the development of data skills. Watson and Smith [
4
],
who are particularly concerned about the increasing need to educate students to evaluate
data and information critically since the COVID-19 pandemic, note that “the Practice of
Statistics’ should be
. . .
recommended
. . .
wherever data-based questions are relevant in
context and informal inferences can be made.” [
4
] (p. 177). In a recent focus on research
outputs examining the teaching of statistics and data analyses in the social sciences, scholars
have taken different approaches, including drawing attention to the importance of making
students part of the dataset [
28
], reflecting on the embedding of the real world context of
teaching statistics to social science students [
29
] and using a project-based approach with
datasets of interest to the students [
30
]. International bodies concerned with the develop-
ment of statistical literacy, including the International Association for Statistical Education
(IASE), need to take note of these approaches to developing statistical reasoning and data
skills, including applied learning, beyond STEM-only subjects. It is the combination of the
context of the research and subject expertise that social science students excel at, as well as
their understanding of the complexity of modelling social systems and behaviors.
Adopting the precept that students’ curiosity will drive them to learn to use tools
and methods, including statistical techniques and software, to investigate interesting
social research questions was the premise for the development of the Q-Step Center at the
University of Manchester and the Data Fellows program. A data fellow is the term given to
a University of Manchester undergraduate student who has satisfied eligibility criteria (at
the degree program level and having taken the required prerequisite statistics courses), has
applied through a competitive process to undertake an 8-week-long data-driven research
project with an external organization and subsequently has been successfully embedded in
the host’s workplace to conduct the project. To date, 330 data fellows have been placed in
around 60 host organizations. Some of these data fellows now work in social research and
statistical careers. Posters produced by each year ’s cohort, dating back to 2014, can be found
online (https://www.humanities.manchester.ac.uk/q-step/student-stories/; accessed on
14 September 2022) [31].
The interaction between teaching statistics and data analysis and the resulting analyti-
cal and research skills that can be applied in the workplace provides compelling evidence
for the success of this data fellows program [
21
,
32
]. Some data fellows have their heads
turned. Some return to university to undertake a quantitative research dissertation in their
final year. Examples of former students who have done so, and gone on to win research
dissertation prizes, include those who wrote theses involving sophisticated statistical anal-
yses and data-driven research. The following dissertation titles reflect three former data
fellows who graduated with sociology or politics degrees: ‘The Pattern of Relative Material
Deprivation in the United Kingdom in 2011 using an Updated Version of the Carstairs and
Morris Deprivation Index’; ‘Why Can’t iSleep? A Sociological Perspective on the Impact
of Screen Time on Adolescents’ Sleep Duration’; and ‘Who are the ‘Left Behind’? The
Status Stratification of UKIP Support’. Another former data fellow, a criminology graduate,
analyzed the Scottish Crime and Justice Survey data to explore victim reporting of partner
Mathematics 2023,11, 52 11 of 17
abuse to the police using bivariate and logistic regression analyses of the factors involved.
For this dissertation, she scooped up a prestigious national prize [
31
]. Three of these former
data fellows are now working in careers in regional or national government, two as lead
data analysts, one as a government statistician and the fourth is studying for a PhD. We
include these as examples here not to claim that they are representative, but to show how
social science degrees, coupled with experiential learning opportunities, can produce highly
trained graduates who can and do enter professions and advanced study that require a
high level of statistical training. As these examples show, graduates who move into data
or statistical professions do not need to have studied a STEM degree. Indeed, non-STEM
majors from the social sciences can and do learn statistics to a level that can help them find
roles in data and statistical careers.
The EmpoderaData Project: Adapting the Data Fellows Model to Latin America
Our third research question was ‘How might Colombia improve its statistical edu-
cation by building on the UK case study?’ The success of the University of Manchester
data fellows program has already led to interest from other countries in developing the
model in international contexts. The EmpoderaData research project was a transnational
partnership between the University of Manchester (UK), Universidad del Rosario (Colom-
bia), Fundação Getulio Vargas (Brazil) and Data-Pop Alliance (US and France) to explore
the transferability of the data fellowship program to Colombia, Mexico and Brazil. The
project used a mixed-methods, three-stage approach to explore this issue with stakeholders
who were involved in data or statistical literacy advocacy (including university teachers) or
policy-making in the three countries. First, a workshop was held in São Paulo (
May 2019)
with 30 key stakeholders from the three countries. The workshop was followed by in-depth
semi-structured individual interviews, held remotely in June–July 2019, with 18 stake-
holders (some of whom were at the first workshop). The final stage involved a workshop
at the University of Manchester (October 2019) to present and discuss the preliminary
findings with potential partners or advisors who had emerged from the first two stages of
the project.
The results from the project illustrated a need for basic data skills training in the
three countries. In particular, in Colombia and Brazil, there was a very keen interest
in adopting the data fellows model to build the statistical and data literacy capacity to
help deliver the SDGs. Furthermore, a key recommendation from the research was the
notion of a hybrid model that would bring together data fellows with complementary
backgrounds (such as social scientists and STEM students) to work collaboratively on
SDG-related challenges [
33
,
34
]. This finding—that hybrid teams are required to conduct
rigorous statistical analyses informed by strong subject expertise—is at the heart of what we
propose in this paper. The notion of teams with mixed skills and backgrounds is not new,
but developing teams in civic and business society that can tackle complex data-driven
problems is evidenced by our work. Thinking about the talent pipelines leading into such
teams is an important area of investigation if we are to be able to deliver on the SDGs
country-by-country. As a result of phase 1 of the EmpoderaData project, two parallel
in-country projects emerged in Colombia (led by the Universidad del Rosario in Bogotá)
and Brazil (led by the FGV Business School in São Paolo). This second phase notes “the
results from the EmpoderaData project give a very clear narrative that a data fellowship
model can be flexibly adapted to different disciplines or subjects (traditional social science,
business studies and mathematics), within different country contexts and with different
curriculum designs” [34] (p. 1019).
5. Discussion: Challenges and Opportunities in Colombia
Much has been said about the project-based approach [
35
–
37
] and its importance for
science teaching and meaningful learning. The advantages of endowing concepts with
meaning through contextualized learning are that this also places the learning subjects
(the students) as the main actors in such a way that they remain active and motivated and
Mathematics 2023,11, 52 12 of 17
become builders of methodologies and solutions that allow them to learn. However, as
has been shown in our research, methodologies like these are not used in the educational
reality of Colombia, particularly in relation to project-based learning and learning by doing;
there is still much work to be done and much to transform.
The research exercise carried out by this group of researchers shows how, although
there is a declaration of applicability when teaching statistics, in reality most of the learning
continues to be centered on the teacher; learning based on experience does not have
important representation. Although an aspiration has emerged to focus the learning on the
student, applicability and autonomous work, this is summed up, in many cases, in the use
of already structured formulas and procedures; where critical and significant thinking does
not have much prominence.
It is essential to remember that statistics is the science of data and that data are not num-
bers, but rather numbers in context, where “contextual knowledge is indispensable” [
10
]
(p. 339). It is also important to remember that students’ experiences are important, i.e., that
they will be using statistics to interpret their nearby reality and solve their problems.
Moving towards a student-centered model in Colombia is a great challenge because
of the amount of transformation that would be needed around teaching existing practices.
For example, it is necessary: (i) to review the curricula in order to be able to guarantee the
time required for this model; (ii) to include this type of model in teacher training, since the
professor no longer reproduces but rather generates relevant questions for the development
of the students and produces dynamics that favor doubt, debate and the construction of
knowledge; (iii) to propose new didactics of statistics; and (iv) to rethink the dynamics in
which universities bring students closer to the situated use of their learning.
Now, we highlight the need for and relevance of field practices, as they are powerful
activities that allow the student to establish and stimulate a dialogue between the learning
that emerges within the class and the reality of its use in the context of a specific practice,
thereby developing important competencies and skills for their profession. Learning by
doing is a method with which students can discover and correct errors that emerge from
their practices in the reality of the situation they are dealing with [
38
,
39
]. In addition,
they strengthen an essential skill—to know in which scenario they should use a piece
of knowledge and what knowledge to use [
40
,
41
]. This “ability to apply mathematical
knowledge is often much more difficult than is supposed, because it requires not only
technical knowledge (such as preparing a graph or calculating an average), but also strategic
knowledge (knowing when to use a concept or given graph)” [42] (p. 9).
The results from the current teaching of statistics in Colombia and the data fellows
program used in the UK suggest that changing the way statistics is taught in Colombia
would be beneficial for non-STEM majors and for social science students in particular.
The UK Q-Step program arose from the call for social science professionals with strong
quantitative skills. In Colombia, the context is not that different. The research prior to
EmpoderaData enlightens how data-literate professionals are needed for jobs in private
industry, public policy making and the government.
As this shift in teaching statistics for social sciences would respond to these positions
in the job market, graduates would be perfectly suitable for these vacancies. Furthermore,
students would learn to learn and learn by doing, both of which would expand their
curiosity and encourage them to challenge how they approach their dissertations and other
research projects. By building on the students’ curiosity, linked to a strong basis of statistical
skills, the UK model has been successful in driving students to do their dissertations on
social sciences using quantitative data-driven research. We find no evidence that this would
be any different with Colombian business or economics students.
6. Conclusions
Statistics education is key for social science students in a data-driven world. Scholars
highlight the bridge that statistics provides to join different disciplines together, to train
students to draw conclusions from data in order to make informed decisions and to
Mathematics 2023,11, 52 13 of 17
encourage students to upskill their critical thinking and statistical skills. We explored how
selected universities in Colombia and the UK teach statistics. We focused on students in
non-STEM degrees, recognizing that studying statistics might cause students some concern.
Our contributions apply to two different scenarios: a traditional approach to teaching from
Colombia and a hands-on approach from the UK.
Our first research question was to explore ‘What is the current state of statistical edu-
cation in Colombia higher education non-STEM majors as reflected in statistics curricula?’
This paper shows that from an analysis of the syllabi included in our sample, the way in
which Colombian universities teach statistics has two main dimensions—the curricular
and the pedagogical. Both are joined by applicability; some topics and teaching strate-
gies are driven by how statistics is used in real-life scenarios. These scenarios, however,
are frequently decided and controlled by the professors, which adds to the traditional
approach to statistics that these courses have. Although there are some innovative exam-
ples, most topics are covered in a traditional way; students must prepare for the lecture,
do some exercises in class, take theoretical exams and in some cases do a group project
for applicability. Our research was based on a small sample of statistics and probability
courses’ syllabi for economics and business administration students. Whilst we do not
claim this to be a representative sample, it nevertheless offers a new insight into Colombian
statistics education.
Our second research question was ‘What can be learned from other statistical education
initiatives outside of Colombia (considering a UK case study)?’ The inclusion of the UK
case study showed how the University of Manchester has addressed the quantitative data
skills deficit among social science students. This model involved students acquiring critical
data skills in the classroom and then putting those skills into practice via paid employment
(through data fellowships) during the course of the undergraduate degree. The Q-Step
program from which the data fellowship model arose has been highly commended because
of the impact on the future careers and studies of the students who participated, and has
demonstrated that social science degrees, coupled with experiential learning opportunities,
can produce graduates who are highly statistically literate. The transferability of the data
fellowship model to Colombia, Mexico and Brazil was explored via the EmpoderaData
project and the results produced a very clear narrative that the model can be flexibly
adapted to different disciplines or subjects (traditional social science, business studies and
mathematics) in different country contexts and with different curriculum designs. The
results also suggested that hybrid teams within civic and business society, with mixed
skills and backgrounds, are needed to tackle complex data-driven societal challenges,
illustrating the importance of real-world statistical literacy education for both STEM and
social science students.
Thirdly, we sought to address through our research the question of ‘How might Colom-
bia improve its statistical education by building on the UK case study?’ The Q-Step program
in the United Kingdom was designed to create a step-change in teaching quantitative skills
to university undergraduates in the social sciences. If statistical education in Colombia
is to be reformed in a similar way then universities could start by creating experiential
learning opportunities to extend the classroom learning into real-world contexts. This
could be achieved in two ways. First, more real-world examples are needed in statistical
curricula, and these could transform students’ engagement with statistics. This would be a
relatively low-cost solution but could radically reshape what is taught. Second, a program
like the data fellows initiative could be initiated and evaluated to test the extent to which
this improves the student experience (and career outcomes) in learning statistics using
real-world projects in the workplace. This immersion-in-the-workplace approach would be
more costly but the advantages of creating meaningful links with industry for participating
universities could be enormously beneficial. The framing of this work using the UN’s
Sustainable Development Goals would be a further aim to provide a global meaningful
approach to statistics education.
Mathematics 2023,11, 52 14 of 17
This paper has addressed a highly topical issue, namely that of the approach to
teaching statistics through university curricula. The inclusion of a UK case study, which
embraces learning by doing (through the embedding of students in the workplace to
practice their statistical and data analysis skills learned in the classroom), opens up the
opportunity for a radical rethink of how statistics could be taught in Colombia. This also
provides an opportunity for future research to be conducted in which students reflect
on their learning and instructors redesign curricula to embrace these hands-on learning
experiences. A systematic analysis of new methods of teaching and learning statistics in
Colombia would offer much for understanding how statistics curricula in Latin America
could be redesigned with a focus on twenty-first century skills for the workplace.
Author Contributions:
Conceptualization, R.A.M.-R., S.C.-M., M.A.S.-R., J.C. and V.H.; methodology,
R.A.M.-R. and S.C.-M.; software, R.A.M.-R. and S.C.-M.; validation, R.A.M.-R., S.C.-M., M.A.S.-R., J.C.
and V.H.; formal analysis, R.A.M.-R. and S.C.-M.; investigation, R.A.M.-R., S.C.-M., M.A.S.-R., J.C.
and V.H.; resources, R.A.M.-R., S.C.-M., M.A.S.-R., J.C. and V.H.; data curation, R.A.M.-R., S.C.-M.,
M.A.S.-R., J.C. and V.H.; writing—original draft preparation, R.A.M.-R., S.C.-M., M.A.S.-R., J.C.
and V.H.; writing—review and editing, R.A.M.-R., S.C.-M., M.A.S.-R., J.C. and V.H.; visualization,
R.A.M.-R. and S.C.-M.; supervision, R.A.M.-R.; project administration, R.A.M.-R. All authors have
read and agreed to the published version of the manuscript.
Funding: This research received no external funding.
Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.
Data Availability Statement: Not applicable.
Conflicts of Interest: The authors declare no conflict of interest.
Appendix A
Table A1 shows the descriptive coding system (composed of 65 codes) (see column
“Codes”); a next step in the understanding of the data is shown in the column “group
codes”, which represents the way in which, from the researchers’ interpretation, certain
codes could be grouped into more conceptual and dense associations. Finally, the column
“dimensions” shows the three final categories (pedagogical, curricular and applicability)
that will allow us to account for the state of statistical education in Colombia.
Table A1.
Relationship between dimensions, code groups and codes from the analysis conducted in
this research.
Dimensions Group Codes Codes
Pedagogical and Applicability dimensions Focus Applied focus
Pedagogical and Applicability dimensions Learning approach Innovative
Pedagogical dimension
Focus
Disciplinary focus
Technological focus
Theoretical focus
Learning approach
Prerequisites
Service
Traditional
Student-centered learning
Independent learning
Learning strategies
Project
Research
Teamwork
Theoretical evaluation
Unorthodox evaluation
Curricular and Applicability dimensions Bibliography Applied bibliography
Mathematics 2023,11, 52 15 of 17
Table A1. Cont.
Dimensions Group Codes Codes
Curricular dimension
Applied statistics Graphs
Indexes
Bibliography Tech bibliography
Descriptive analysis
Central tendency
Covariance
Descriptive analysis
Dispersion
Introduction—statistics
Mathematical concepts
Inferential statistics
Chi-square test
Confidence interval
Estimation
Experiment design
Goodness of fit test
Hypothesis testing
Inferential statistics
Regression and correlation
Statistical models
Types of errors
Probability Distributions
Bernoulli
Binomial
Central limit theorem
Cumulative
Exponential
Gamma
Geometric
Hypergeometric
Introduction—Probability
Logistic
Moment-generating function
Multivariate Distribution
Normal
Poisson
Probability Distribution
Random variable functions
Uniform
Probability methods
Bayes theorem
Counting
Rao-Blackwell theorem
Random variables
Bivariate models
Discrete and continuous variables
Multivariate models
Random variables
Univariate models
Sampling
Conditional probability
Probability laws
Sampling
Stochastic convergence
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