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Advances in Social Sciences Research Journal – Vol. 10, No. 5
Publication Date: May 25, 2023
DOI:10.14738/assrj.105.14687.
Harris, J. D. (2023). Statistical Success: Three-Year Analysis of Student Performance and Student Insights from a First-Year College
Statistics Course. Advances in Social Sciences Research Journal, 10(5).103-121.
Services for Science and Education – United Kingdom
Statistical Success: Three-Year Analysis of Student Performance
and Student Insights from a First-Year College Statistics Course
Jennifer D. Harris
DeVry University 1400 Crystal Drive,
Suite 120, Arlington, VA 22202
ABSTRACT
This study included quantitative and qualitative analysis of three years of students
in an introductory college-level statistics course. The quantitative analysis focused
on what aspects might be relevant to student success. The instructor and the
modality appear to be significantly related to student success. Somewhat
surprisingly, fully onsite courses had a lower success rate than online or partially
online courses. The qualitative analysis focused on the student comments on end
of course surveys for the same three years. These comments were categorized
based on topic and then rated from -3 reflecting a strong negative feeling, through
to +3 indicating a strong positive feeling. These comments highlighted the
importance students placed on live online lessons with the instructor. Students also
appeared to take responsibility for their learning, noting the importance of their
engagement to their success. This study provided unique insights to student success
in an introductory college-level statistics course. Instructor and student
engagement is key, along with opportunities for live connections.
Keywords: statistics, student success, college, quantitative, qualitative.
INTRODUCTION
Basic undergraduate statistics courses generally cover distributions, probabilities, confidence
intervals, hypothesis testing, and regressions, with problems, quizzes, and labs. Given the
consistency of the structure of these courses, they continue to stymie students, posing
challenges for course instructional designers and course instructors. This study builds on the
work of previous researchers in striving to find key elements or characteristics that can predict
success in this course. With those predictors identified, more focused strategies can be used to
improve the presentation, content, or design of the courses.
LITERATURE REVIEW
The literature around these courses considers different aspects of the course, the students,
and/or the instructors. While the administrative issues of the course, such as credit hours and
time of offering might also impact student success, the focus here is on other elements.
Student Characteristics
Student characteristics is one place to consider the potential reasons for challenges in statistics.
A number of students are unprepared to study statistics [1]. There may be a variety of opinions
on what is the best preparation for an introductory statistics course. If students are not
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prepared or do not apply themselves, then the content and the teaching are superfluous. It has
been shown that students that have higher grades in their previous math courses are more
likely to have success in their college statistics course [2]. While the Dupuis study considered
high school mathematics with college statistics grades, some students take the preparatory
classes for statistics after entering college. When looking at mathematics courses taken at
college, there have been mixed results. Johnson and Kuennen [3], found that achievement of
basic mathematic skills was a significant predictor of students’ statistics grades, while
completing calculus was not. In contrast, Green, Stone, Zegeye, and Charles [4] found that
students who had taken advanced mathematics courses were more likely to do well in statistics
class.
Attitudes can impact statistical achievement as well. Students in statistics might experience
high anxiety about taking the course or about math in general [5] [6]. Studies have been
consistent in showing that increased statistical concerns negatively impacted achievements in
the classroom [7]. Looking at various aspects of student anxiety, it has been found that
cognitive issues were of highest concern, such as language processing and attention [8].
Consistent with this, faculty identified student-related issues as the most common concern in a
study of college statistics faculty [9]. In that study, the most common student-related issues
noted by faculty were academic readiness, fear of math and statistics, and general student
characteristics. With a somewhat different outcome, Hedges [10], found that in the online
delivery mode, female students were more likely to experience anxiety. The study did not find
a difference in anxiety overall among males and females, nor between programs of study.
Presentation of Material
Another potential area of concern in basic statistics courses is how the material is presented.
Delucchi [11] noted that students’ knowledge of statistics increased during the course,
indicating that students learned through the content and presentation, more than their own
characteristics or test-taking ability. Some benefit has been found in using more videos to
present the material [12]. Alternatively, songs and mnemonics have found to be somewhat
successful as well [13]. Alternatively, including more real-world and practical examples such
as through a semester-long project has been shown to help students [14] [15].
It has been postulated that statistics needs to be presented with a more real-world perspective
in a practical approach [16]. Flipping the classroom where most of the preparation work and
readings are done prior to class, has also been suggested with some success [17]. In that study,
the flipped classroom had a variety of differences with the traditional lecture or control group.
To some degree, this was necessary in order to have the flipped versus traditional setting. One
key difference in the study design was in the flipped classroom, teaching assistants used
additional time to focus on the current week’s material, while the traditional classroom focused
on the previous week’s’ content. This makes the study results a bit more difficult to interpret.
Another modality would be online teaching, which may or may not be a flipped classroom.
Online teaching was found to improve students’ attitudes toward learning statistics [18].
In these previous studies, the impact of the various presentation methods considered was
somewhat impactful, helping a subset of students among all those taking the elementary
statistics course.
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Harris, J. D. (2023). Statistical Success: Three-Year Analysis of Student Performance and Student Insights from a First-Year College Statistics Course.
Advances in Social Sciences Research Journal, 10(5).103-121.
URL: http://dx.doi.org/10.14738/assrj.105.14687
Instructor
Finally, who presents the material during class periods can be key to student success. This
introduces the idea that some individuals more successful in their presentation, making the
“who” more important than the “what” or “how”. A 1990 study considered a professor who
introduced the use of cartoons in statistics class as a potential method for reducing student
stress and, therefore, increasing performance in the course [19]. One of the comments on the
course evaluations was, “I found that the use of cartoons along with a relaxed teaching style
made the class more enjoyable” (emphasis added). Such comments point to the importance of
the specific instructor to the course.
The importance of the instructor in the course was highlighted as well in a 2008 study focused
on the importance of first day activities, actively incorporating students throughout the course,
establishing common language, and monitoring students’ emotions [20]. These all point to the
role of the instructor in the classroom to create a successful environment. Similarly, an article
pointed to the importance of the instructor in reducing anxiety and producing a realistic
framework for the course, as students with those instructors were more likely to be successful
[21].
The key here is whether the success is partially based on the specific instructor, or whether
skills and strategies can be shared successfully across instructors.
CONCEPT OF STUDY
This study considers student characteristics, presentation of material, and specific instructors
over several years of a statistics course taught at a large, private university. This analysis
focused on an 8-week, 200-level statistics course that had an algebra prerequisite. In most
cases, students could take the statistics course anytime in their program of study. Most
students were business or computer majors, and none were mathematics nor statistics majors.
• Literature points to success in previous classes and anxiety as two key characteristics.
In the data available here, the score in previous math class will be tested as a potential
indicator of success in statistics. While anxiety is not measured within the database of
grades, this study will consider the age of students and when in a student’s program
statistics were taken as two potential indicators of success in statistics. Older students
might have more perspective and be less anxious. Students who take statistics later in
their degree program often do so, to avoid the class for as long as possible. Therefore,
to consider student characteristics, the success in statistics class will be considered
based on characteristics such as age, point in program when statistics was taken, and
grade in previous math class.
• To consider the presentation of material, pass rates will be considered between onsite
and online courses. The 2020 pandemic impacts these results as onsite classes needed
to meet virtually as well. The key difference was the length of the live sessions. If the
class was fully online, then class presentations could be for 60 to 90 minutes per week.
If the class was scheduled to be onsite, then the class presentation needed to meet
virtually for 210 to 240 minutes each week. Numerous course sections included both
onsite and online students. In these cases, the course met for the full onsite time.
• To consider the importance of specific instructors, pass rates were compared across
classes based on whether they were full time instructors or adjunct instructors.
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• The student perspective is important here as well. Beyond the pass rates in each of the
above analyses, student comments were analyzed for what students considered the key
elements to the course. While the comments cannot be tied to pass rates due to privacy
issues, the comments can still indicate which elements of the course (their
characteristics, the presentation of material, or the instructor) was most critical based
on their perceptions of the course.
The sample for this research was all students that took this 200-level statistics course from
January 2019 through December 2021, three full years which included 18 sessions that the
course was offered. All students from all sections and all instructors were included for this
three-year analysis. In this time, there were some changes to the course material. In July 2020,
instructor-graded labs were removed and replaced with auto-graded homework and quiz
assignments. In March 2021, the textbook was changed from a traditional textbook to an
interactive, online textbook where activities within the text counted to some degree toward the
students’ grade.
Since the material covered and the workload for each week remained about the same
throughout these changes, the benefits of including three years of data outweighed the
concerns of these changes to the course design.
DATA ANALYSIS: QUANTITATIVE
This study used regression analysis for the student characteristics, ANOVA analysis for course
modalities, a two-sample t-test to compare full-time to adjunct instructors, and an ANOVA test
to compare differences in the years between other courses and the statistic course. Ad hoc post
tests are used when needed after the ANOVA tests. Finally, student comments were analyzed
based on categorizing the comments to determine the most common areas of praise or concern
for students.
For student characteristics, a regression analysis is used with the final student grade as the
dependent variable. The independent variables would be the student’s age, when during their
program they took statistics, and their grade in the previous math course. Each of the
independent variables is continuous. Modality of the course will be tested through an ANOVA
test to see if the average grades were different across the course modes of onsite, online, or a
combination. After testing for the assumption of equal variances of grades across modalities,
then the least squared difference (LSD) ad hoc post test will be used to determine which grade
averages are significantly different than the others.
To compare final scores between full-time and adjunct instructors, an independent two-sample
t-test is used. An F-test will be used first to determine if the variances can be assumed to be
equal or not. Following that test, the appropriate t-test will be used.
The qualitative analysis of the comments from students requires recording and organizing.
Dedoose was used to categorize each comment based on its topic as well as whether it was
positive or negative. One open-ended question asks students why they would recommend or
not recommend the course. The second asks students what suggestions they have to improve
the course.
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Harris, J. D. (2023). Statistical Success: Three-Year Analysis of Student Performance and Student Insights from a First-Year College Statistics Course.
Advances in Social Sciences Research Journal, 10(5).103-121.
URL: http://dx.doi.org/10.14738/assrj.105.14687
Preparing the Data
The original data file of grades over the years 2019 through 2021 included 11,817 records.
Overall, most of these records are for students who took the course only once. Of the total,
1,806 took the course more than once. Each record is noted whether the record represents the
last attempt for this student. It is not possible in this data set to connect which attempts were
from the same student. These records were all kept as success on any attempt of the course
was considered insightful to the analysis. As detailed below in Table 1, about 7.6% of these
records were removed for a variety of reasons.
It was determined to focus this analysis on students continuing within their program. This
means that students that were new to the university, readmitted or were resuming their
programs were removed from this analysis. This action was taken at the individual records
level, so all student attempts taken while the student was continuing in their program were
kept in the analysis. This resulted in 730 records being removed, or about 6% of the original
records.
Two other groups of records were removed from the original data set. Students listed as being
less than 18 years of age were removed from the dataset. The course was offered to some high
school students in specific situations, but these students are likely to be different than the
population of college students, so were removed. This was a total of 109 students, or about 1%
of the original data set. The other group removed was those whose algebra grade was from an
engineering algebra course. The engineering majors were not required to take the statistics
course. Therefore, these are most likely students who switched from engineering degree
program to a business or computer program. These students had a slightly different
preparation for the statistics course, so were removed. A total of 62 records or less than 1%,
fell into this category. Details of this process are shown in Table 1.
Table 1. Records Removed from Dataset
Types of Records Number Totals
Original number of records 11,817
New students 394
Readmitted students 147
Resuming students 189
Students less than 18 109
Those in engineering algebra 62
Total remove records 901
Total records in analysis 10,916
The final dataset for analysis included 10,916 records, or 92.45 percent of the original dataset.
Subsequent percentages in this paper are out of a total of 10,916 records, unless noted
otherwise.
Description of the Data
The key variables in the data set were grades in the statistics course, when the course was
taken, the type of instructor, the mode of instruction, whether this was the student’s latest
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attempt of the course, and how many times the course had been taken. Since observations in
this dataset are based on students in statistics class over 18 sessions, it is possible that students
took the course multiple times.
Of all the students in this data set, 24% earned a grade of A, 28% earned a B, 19% earned a C,
with the remaining students earning a D, F, or withdrawing from the course. In the 18 sessions,
the most students in any one session were 855 students, while the least was 469 students.
There did not appear to be any pattern to when more or fewer students took the course.
Of the 10,916 students in the data set, 36 percent were taught by full-time faculty, while the
remaining were taught by adjunct instructors. Of all the students, 5.6 percent took the course
as a fully onsite course, 52.5 percent took the course as a full online experience, and 41.9
percent took the course as a combination of onsite and online experience. As noted above, these
18 sessions include all of 2020 and 2021 when courses were impacted by the pandemic. During
that time, onsite courses did not meet on campus, but did hold virtual classes for the equivalent
onsite time, much longer than fully online courses would meet.
Finally, for nearly all these students’ records (92 percent), this information reflects their most
recent attempt on the course. Nearly all students (84 percent) took the course only one time
within these 18 sessions. Fourteen percent took the course twice, and less than 2 percent took
the course three or four times, during this time. Again, the records are based on each student,
each attempt. Therefore, about 16 percent of the records represent a multiple of the same
student.
Regression on Student Characteristics
A regression analysis was completed using the statistics course grades as the dependent
variable, and the independent variables were the age, when the course was taken, and the
student’s grade in the previous math course. Both grade variables were recoded from letter
grades to a 0 to 4 scale with A being 4, and both F and W being 0. The session variable was a
six-digit numeric code with the four-digit year and the session from 01 to 06.
While the overall regression was significant with an F statistic of 447.74 and a p-value of
<0.0001, only two of the independent variables were significantly different than 0, as shown in
Table 2. Both the coefficient of the age of the student (t=11.73, p-value<0.0001) and the
coefficient of the previous math course grade (t=33.93, p-value <0.0001) were statistically
different than 0. The session when the statistics course was taken was not found to be
significantly different than 0.
Table 2. Regression Results with Age, Session, and Previous Course Grade
Variables Parameter Estimate t Value p value
Intercept 12.20679 0.34 0.7311
Age 0.02005 11.73 <0.0001
Session -0.00007 -0.40 0.6882
Previous Course Grade 0.98648 33.93 <0.0001
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In the ANOVA analysis, the F statistic was 2.47 with a p-value of 0.0849, significant at the 0.10
level. This indicates that at least one modality has a different average grade in statistics from
the others.
Based on this outcome of the ANOVA test, a least squared difference (LSD) ad hoc post test was
run to determine which combinations of modalities were different. Interestingly, the average
grade of those in the fully onsite and fully online modalities were not different from each other
(p-value=0.5278). Further, the average grade of those in the fully onsite modality was not
statistically different than the combination modality (p-value=0.6915). However, the average
grade of those in the fully online modality were significantly different than the combination
modality, with a p-value of 0.0269.
The average grade in the fully online modality was 2.237 compared with an average grade in
the combination modality of 2.300. This indicates that the combination modality provides good
support for students. Further, it could be inferred that the combination modality provides more
support for the online students than a fully online modality. In the combination modality, the
classes meet with the instructor longer each week onsite and/or virtually. That additional time
appears to provide online students some needed support to improve their grades.
Full-time versus Adjunct Faculty
To determine if there was a difference in the grades of students taught by full time versus
adjunct faculty, a two-sample t-test was completed. First, an F-test was used to determine if the
variances were equal. In this case, the F value of 1.04 had a p-value of 0.1640, which is
insignificant, so the variances can be assumed to be equal.
Based on this outcome, the pooled version of the t-test was used to determine if there was a
difference in the average grade between full-time and adjunct faculty. In the pooled version,
the t-value was 1.89 with a p-value of 0.059. This is significant at an alpha of 0.10.
This indicates that there is a difference in the average grades in the statistics course between
these two groups of faculties. The average score among full-time faculty was 2.30 compared
with an average of 2.25 among adjunct faculty.
Years between Courses
One school of thought is that students should take their math courses as closely as possible to
each other. In other words, a college-level algebra course should be taken the session before
statistics to maintain the mathematics thinking, knowledge, and momentum. Data were
collected on when a college-level algebra course was taken along with when statistics was
taken. Of the original 10,916 records, 2,647 did not have the algebra course session, so 8,269
records are used in this analysis.
To complete this analysis, the difference in the sessions was converted into years. A value of 1
for the difference variable means that the statistics course was taken within 1 year of the
algebra course. A value of 2 for the difference variables means that the statistics course was
taken more than 1, but within 2 years of the algebra course, and so forth. Few students had
taken the course 10 or more years after the algebra course, so those were all coded to 10.
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Harris, J. D. (2023). Statistical Success: Three-Year Analysis of Student Performance and Student Insights from a First-Year College Statistics Course.
Advances in Social Sciences Research Journal, 10(5).103-121.
URL: http://dx.doi.org/10.14738/assrj.105.14687
The analysis indicates that those students taking statistics 9 or more years after algebra had
the highest average grade. However, the number of students taking statistics more than 5 years
after algebra was much smaller than the other groups as shown in Table 4.
Table 4. Mean and Standard Deviation of Statistics Grade by Years Since Previous Math
Course
Years Since Last
Math Class
Number of
Observations
Mean Statistics
Grade
Standard Deviation of
Statistics Grade
1 3765 2.25 1.43
2 2821 2.17 1.45
3 705 2.16 1.42
4 435 2.17 1.39
5 192 2.10 1.39
6 74 2.24 1.29
7 81 2.32 1.34
8 41 2.15 1.33
9 44 2.48 1.42
10 111 2.67 1.22
One theory might be that those students with a large break between the courses are older, and
likely returning students that may be more motivated to complete college. In looking at the
average age in each year group, along with the minimum value and maximum value, those in
the later years are a bit older on average. The oldest students, however, are in the groups with
the smallest difference in years between the two courses. This is a bit different than earlier
analysis that showed that younger students tended to perform better in their statistics course.
The wide ranges shown in Table 5 between the minimum and maximum ages may account for
this seemingly different outcome.
Table 5. Average, Minimum, and Maximum Ages by Years Since Previous Math Course
Years Since Last
Math Class
Number of
Observations Mean Age
Minimum
Age
Maximum
Age
1 3765 32.15 18 67
2 2821 32.11 18 68
3 705 32.93 18 67
4 435 32.34 18 61
5 192 32.90 20 58
6 74 33.08 19 63
7 81 34.14 21 65
8 41 34.27 22 60
9 44 32.23 24 50
10 111 37.55 23 62
Given the smaller group size, those taking the course 5 or more years after algebra were
combined for additional analysis. This resulted in groups of more similar sizes with 435 with
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4 years between their math and statistics courses and 543 students with 5 or more years
between their last math class and the statistics class. Using the 8,269 with the difference
variable, an ANOVA test was run to see if there is a difference between the scores and the years
between the algebra and statistics course. Based on this analysis, no such difference exists. The
F value of 1.91 has a p-value of 0.1051, an insignificant difference between the groups. This
would say that the time between the two courses does not significantly impact the grade in the
statistic course.
However, the graph of these average statistics grades by the years since the algebra course was
taken indicates a possible quadratic relationship. Figure 2 shows the years between the last
math class and statistics along the horizontal axis and their average grade from statistics class.
The dots appear to decline and then increase when there are 4 or more years in the horizontal
variable.
Figure 2. Years Between Last Math Class and Statistics Course
A quadratic regression with the years between variable indicates a significant regression
output and both the coefficients for both the linear and quadratic versions of the difference
variable are significantly different than 0. However, the coefficient of determination is 0.0022.
This outcome appears consistent with the ANOVA analysis above. This result indicates that
there is a quadratic relationship, but it is not related to the statistics grade outcomes.
Conclusion to Quantitative Analysis
The analyses above are based on the characteristics of the course and of the students, indicates
that the instructor and the modality may have some influence on student success in an
introductory college-level statistics course. Courses taught by full-time faculty had average
grades of 2.30 compared with 2.25 in sections taught by adjunct faculty. Sections that combined
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For a simpler analysis, the data were also coded to group all negative responses and all positive
responses in each category. The distribution for each category of responses is shown in Table
7. This allows for more direct comparisons across the responses in these six categories.
Table 7. Percentage of Responses at General Rating Level by Category of Comment
Ratings
Live, Online
Lessons Content Book
Faculty
Engagement
Faculty
Responsiveness
Faculty
Grading
Negative 11.1% 40.2% 41.8% 7.9% 26.9% 57.9%
0 1.6% 5.1% 5.0% 0.2% 1.0% 0.0%
Positive 87.3% 54.7% 53.2% 91.8% 72.1% 42.1%
Total 1,155 707 541 429 201 38
Three of these categories specifically address faculty characteristics: engagement,
responsiveness, and grading. The live lessons could also be considered a reflection of a faculty
characteristics. Given the distinction above in between full-time and adjunct faculty, these
responses were split between those two groups. Grading was not included due to the small
number of students that noted any opinion on that aspect.
The largest differences were seen in faculty responsiveness, where 34.7 percent of comments
for adjuncts were negative in this area, compared with 14.3 percent of comments for full-time
instructors. Certainly, adjunct instructors likely have other responsibilities beyond teaching
the assigned course which might inhibit their ability to be as responsive as full-time instructors.
However, being unresponsive to the point that students are more than twice as likely to have a
negative impression of faculty responsiveness points to the importance of this to students.
Table 8 shows the differences in the comments by ratings in these faculty categories between
full-time faculty and adjunct faculty.
Table 8. Percentage of Responses at Each Rating Level by Category of Comment
Ratings Live, Online Lessons Faculty Engagement Faculty Responsiveness
Full-time Adjunct Full-time Adjunct Full-time Adjunct
Negative 6.4% 14.7% 7.0% 8.7% 14.3% 34.7%
0 1.6% 1.7% 0% 0.4% 0% 1.6%
Positive 92.0% 83.6% 93.0% 90.9% 85.7% 63.7%
Total 502 653 187 242 77 124
Positive Comments
The most common comments were focused on the live, online lessons provided by faculty with
1,155 total comments and 87.3% of those being positive. These comments were similar to, “No
other teacher explains very complex real-life problems like this prof. Very helpful videos and
assistance was provided for us slower students. I loved this course and how simple [the
instructor] was able to make this difficult course.” Given the prevalence and positivity of these
comments, the live, online lessons are valued by students.
Comments on faculty engagement were also overwhelmingly positive with 91.8% of the 429
comments in this area being positive. Faculty responsiveness was perceived positively as well
with 72.1% of the 201 comments being positive.
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Table 11. Number and Distribution of Suggestions to Strengthen the Course
Category Number of Comments Percent of All Comments
This instructor 126 5.5%
Content 488 21.2%
Simplify course 196 8.5%
Student suggestion 561 24.4%
Book 35 1.5%
Not instructor 64 2.8%
Course fine 59 2.6%
None 769 33.5%
Total comments 2,298 100%
It is encouraging that the most common responses were in the “none” category, or in “student
suggestions”. This implies that students saw a key to course success lays within the hands of
the students taking the course. Here are some representative sample quotes from those that
had suggestions for students.
“Starting the reading on Mondays so you can ensure that you do the discussion posts on time.
The reading helps you understand how to do the discussion posts.”
“Future students do the work and read, educate yourself and ask questions and you’ll be in great
shape to pass the class.”
“Attending the live [online] lessons is extremely helpful in a class like this. The textbook can
only take you so far.”
The next most noted area for potential improvement was the content. There was a variety of
responses that fell into this category. These comments were further classified into different
areas. Table 12 shows the different areas of suggestions for changes to the content of the
course. Other areas of comments had less than 15 comments so were not included in the table.
Table 12. Detailed Comments Regarding Suggestions to Strengthen Course Through
Content
Area of Comment Number of Comments
More examples 86
More online meetings 80
Teaching 52
Resources 52
Technical 52
More videos 37
Each of the areas above is worth more analysis to determine what students were suggesting in
those areas. Many of the comments related to “more examples” specifically said just “more
examples”. Those that gave more details included a wish for additional real-world examples
and step-by-step examples. Some students wanted instructors to provide more examples