Paper ID #27047

Active, Topic-centered Learning

Ing. Guisela Alejandra Illescas Ms, Universidad Galileo

Guisela Illescas is the Administrative Coordinator and Assistant Professor of the Applied Math Deparmentin Universidad Galileo. She holds a B.S. in Computer Science and a Master in Reingeneering.

Dr. Alberth E. Alvarado, Universidad Galileo

Alberth Alvarado received (with honors) the B.S. degree in Electronics and Computer Science Engineer-ing from Universidad Francisco Marroquı́n in 2004; the M.S. degree in Applied Mathematics and a Ph.D.in Industrial Engineering from the University of Illinois at Urbana-Champaign in 2010 and 2014, respec-tively. Currently, Dr. Alvarado is the Head of the Department of Applied Mathematics at UniversidadGalileo in Guatemala, Guatemala.

Ing. Jose Roberto Portillo, Universidad Galileo

Roberto Portillo is a mathematics instructor and sub-director of the Teaching Assistants Department ofUniversidad Galileo in Guatemala. He holds a Bs. in Electronics and Computer Science and a Ms. inOperations Research. In several years he was awarded with the ”Excellence in Teaching” award. Hiscurrent research interests are focused in Engineering Education.

c©American Society for Engineering Education, 2019

Active Topic Centered Learning

1. Introduction It is well known that Active Learning methodologies involve the students in their own learning and there is no doubt about their effectiveness in sharing knowledge with today’s students. Actually, undergraduate students taking traditional lecturing-based courses are 1.5 times more likely to fail than those enrolled in courses where active learning methodologies are implemented [1]. Thus, our university has centered its attention on investigating, applying, improving and designing new active learning methodologies. Examples of such methodologies are: The Math Operatory Skills Laboratory (MOSL), introduced in [2], as a remedial mathematics course for freshmen engineering students; and, the Guided-Lecture Team Based Learning (GL-TBL) targeted to teach mathematics for non-traditional students, see [3] for more details. Due to the outstanding results obtained from the implementation of the aforementioned schemes and many others presented in the related literature e.g. [4], in this paper, we introduce a new active methodology for teaching mathematics, which we call Active Topic Centered Learning (ATCL). The ATCL methodology aims to overcome the main drawbacks of lecture-based courses by minimizing the time spent on traditional lectures and by creating a suitable environment for the students to take the “leading role” in their own learning process. In pursuance of the latter objective, ATCL is based on the fact that the value of traditional activities, such as worksheets and laboratories, is increased when they are performed inside the classroom. Even more, according to [5], such in classroom activities produce an engagement in the student’s learning process. As a result, the proposed methodology prioritizes the students’ work inside the classroom by incrementing the time spent on problem-solving sessions. On the other hand, in traditional lecturing, multiple topics are covered in a single session, this can be overwhelming for most of the students [6]. As a result, the core of ATCL relies on teaching a single topic at a time by means of a short lecture. This frees up time for in-classroom problem-solving and it lets the students concentrate on one matter at a time. This is crucial if we really want the students to do most of the work by themselves and avoid frustration. In order to test the ATCL methodology, it was implemented in a second calculus course offered for engineering students. To quantify its performance, the midterms and final exams’ grades and their pass rates were compared with those obtained in the previous year (2017) course, taught using traditional lectures. A detailed analysis of each of the topics evaluated in the exams is also presented in this work. In general, the results of the ATCL implementation are significantly better than those obtained from the 2017 lecture-based course. The rest of this paper is organized as follows. In Section 2, the ATCL methodology is introduced along with all the details regarding the structure of each course session. Section 3 presents our case of study, that is, the implementation of ATCL in a calculus course. The results of such an implementation are discussed and analyzed in Section 4. Finally, we draw some conclusions in Section 5.

2. ATCL Structure ATCL is an active learning methodology designed to teach mathematics with a novel vision on how a course should be structured, developed, taught and evaluated. ATCL is presented as an alternative methodology that can be used to teach mathematics courses while overcoming the well-known difficulties that traditional lecture-based courses are generating in today’s students [7]. It is worth mentioning that, even though the proposed methodology was originally conceived to teach mathematics and was tested under this setting, it can be adapted to teach courses in different disciplines. In order to understand the ideas behind ATCL, it is important to recall those that support traditional lecturing. The general structure of a pure lecture-based course is divided into 2 parts: (i) a class session where all the information is communicated to the students in one direction, that is, the instructor introduces (with almost zero students interaction) a great list of mathematical concepts and theoretical aspects, which are assumed to be understood by the students; and (ii) a discussion session where (in general) the teaching assistant (TA) solves a list of problems and exercises to the students; one more time, the TA-student interaction is negligible. Finally, students are expected to go home and solve a list of problems assigned in a worksheet, covering all the material presented in class. In practice, many students in classes following this scheme get frustrated when they sit alone in front of a huge list of mathematics problems. Sometimes, this frustration comes from the students’ perception that those problems are difficult to solve or their lack of confidence about the work done. Such frustration translates into poor learning outcomes and as expected, a bad academic performance. The ATCL methodology aims to overcome the main drawbacks of lecture-based learning by: (i) diminishing the number of topics covered in a single lecture so that the student is not overwhelmed and can focus in learning one topic at a time, this idea follows the traditional topic-centered instructional strategy (see [8]); and, (ii) increasing the students’ work inside the classroom allows the instructor to detect their difficulties, as well as, help them to overcome those. Different from traditional topic-centered instructional strategies, ATCL involves a meticulous session to session segmentation of each of the topics covered in the course leading to shorter lectures but longer problem-solving sessions, while increasing the student-instructor interaction. Hence, ATCL, as an active learning methodology, transfers the leading role from the instructor to the students. ATCL is based on the following six principles: 2.1 Topic Segmentation The term topic-centered sometimes appears in the literature (see e.g. [8]) as a synonym of traditional lecturing, meaning that the course content is taught subject by subject following a hierarchy. In our context, the key difference in the use of the term topic-centered relies on what we mean by topic, and how such topics are taught. Typically, the course contents are divided into units, which can be subdivided into topics. As a result, we define a topic as the smallest component of a course unit. In other words, a topic is the minimal unit component that is indivisible in subtopics. It is clear that a topic can include different aspects that need to be addressed within the topic, however, those aspects are totally related to the topic itself. To clearly understand this concept, think about the atom. Such a particle is indivisible, but it is composed

of protons, neutrons, and electrons. In our context, a good example is “Techniques of Integration” that can be considered as a unit of an integral calculus course. This unit is composed of topics such as “Integration by Parts”, within this topic “cyclic integrals” and “integration of inverse functions” are elements that can be studied as part of this topic. ATCL relies on a careful topic segmentation of the course content, taking into consideration the definition of a topic that was introduced above. The main objective of the ATCL topic segmentation is to devote one lecture, one problem-solving session and one evaluation per each topic. Clearly, such segmentation is determined by the course characteristics and the available number of credit hours. An example of a topic segmentation for a calculus course is presented in the following section. 2.2 Single Topic Lectures (STL) In ATCL, one lecture is dedicated per topic included in the course segmentation discussed above. In these lectures, the instructor presents the theoretical aspects underlying the single topic in discussion. Different from traditional lecturing, in STL the instructor discusses the main definitions and theorems giving the students enough time to visualize, talk and share information with their peers to help them understand and think critically about the new concepts. Once the topic is understood, sample problems are presented to the students and they collaborate with the instructor to find their solutions. A detailed description of the teaching method to be used in STL can be found in [9], where Lecture-Based Tutoring is introduced as a recently developed active learning technique. 2.3 Problem Solving Sessions (PSS) These sessions are the core of the course and they are guided by the instructor and the teaching assistants. The PSS includes a topic-designed worksheet where the students apply the theory learned on the previous STL. It is important to mention that these worksheets contain meticulously selected theoretical questions, exercises and word problems related exclusively with the STL. Such worksheets are solved in teams with a maximum of 4 students, however, each team member is required to turn in his own work. Each team member is responsible not only to solve the proposed problems but also to help their teammates, thus creating an achievement atmosphere [10]. The teaching assistants and the instructor are always available during these sessions to detect mistakes in the students’ work or if a student requests their help. In these situations, the instructor or the TA discusses the problem with the students and give them some hints rather than solving the problem for them. The duration of these sessions is recommended to be between 90 and 100 minutes, but it may vary according to the topic in discussion. Based on our experience, we strongly suggested limiting the number of problems so that the students have enough time to finish the assignments in the classroom. We do not specify the number of problems to include in the worksheet since this fact depends entirely on the topic under study. It is important to mention that, when a vast majority of the students in the class are not able to finish the worksheet, it is assigned as homework; however, this should be avoided. Finally, after each session, a detailed (step by step) solution of the topic-designed worksheet is posted.

2.4 Topic Quizzes After each topic has been discussed in the STL and practiced in the PSS, a short-written test (with a duration between 10 to 15 minutes) is administered to the students. As expected, such quizzes include one or two questions related entirely with the topic worked on the previous worksheet. In order to give immediate feedback to the students, the quizzes are graded by the teaching assistant while the instructor solves the test pointing out the most common mistakes committed by the students. A different possibility to provide immediate feedback is the use of “clickers” for implementing such quizzes. The main objective of these quizzes is to continuously measure the students’ understanding of each of the topics. If the students are not performing as expected, further outside class activities (such as homework, video lectures or readings) are assigned to the students. 2.5 Mini-Application Projects (MAPS) These projects are designed with the objective of linking the mathematical theory developed in the course with real-life problems. Thus, the MAPS are guided applied problems oriented towards the use of technology, mobile applications, and mathematical modeling, among others [11]. It is not necessary to elaborate a mini-application project for each topic covered in the course. The MAPS problems are carefully selected among those mathematical topics that can be readily applied in real life situation (see the next section for some examples). These projects are suggested to be developed in teams so that collaborative learning is encouraged. 2.6 Study Guides Before each midterm and the final exam, a study guide is provided to the students so that they can prepare for the evaluations. These guides summarize the body of knowledge that the students need to know in order to be prepared for the exam by combining exercises and problems from all the topics to be evaluated. Therefore, the main purpose of the study guides is to integrate all of the topics that were studied separated, so that the student can visualize the course as a whole. To summarize the discussion above, the overall ATCL structure is depicted in Fig. 1. This scheme shows the interaction between each ATCL component and the role it plays in this methodology. In the next section, we present a case of study where the proposed methodology was tested.

Fig. 1. ATCL Structure.

3. Case of Study: ATCL in a Calculus Course In order to test the outcomes of the ATCL methodology, it was applied to teach a second calculus course offered for freshmen students from different specializations within engineering. Such a course was taught during the second semester of 2018. All the sections of this course had a total of 222 students, 157 of which are full-time and 65 are part-time students. This calculus course was taught in nine different sections, among them, six were intended for full-time students, and three for part-time students. The full-time students’ sections are taught in the morning, while the part-time students’ sections are held at night. With respect to the number of students per section, we had five sections (four full-time and one part-time) with an average of 32 students, and four sections (two full-time and two part-time) with 16 students on average. The details on how some of the ATCL principles were applied to this course are given below. 3.1 Topic Segmentation and STL The syllabus of our second course in calculus includes two main topics: (i) applications of derivatives, and (ii) integral calculus of single real-valued variable functions including applications. Those main subjects lead us to divide the course into three main units that, in turn, gave origin to the topics to be discussed in each STL. Fig. 2 summarizes each of the topics that

are covered in each STL. Notice that we have a total of 25 punctual topics. It is important to mention that this course is taught in 15 weeks of classes with four sessions per week with a duration of 100 minutes per session. Note that, a disadvantage of ATCL is that it requires a lot of in-classroom time because most of the work needs to be done there. This requirement translates into an increase in the number of academic credits for courses following the ATCL framework. 3.2 Problem Solving Sessions and Topic Quizzes Based on the ATCL structure illustrated in Fig. 2, it follows immediately that the course had a total of 25 problem-solving sessions and 25 topic quizzes. Such classroom activities were designed following the details given in the previous section. Note that, the students do a lot of work inside the classroom since the number of worksheets and quizzes is clearly above those typically assigned in a traditional lecturing course. For an example of a typical PSS worksheet, its solution, and a topic quiz, see the figure Fig. 3, Fig. 4 and Fig. 5 respectively.

Fig. 2. ATCL Structure comprised of 25 single-topic-lectures.

(a) (b)

Fig. 3. (a) Sample problems in a PSS worksheet, original version in Spanish (Problems taken or adapted from the course textbook [12], and [13]).

(b) Translation to English.

Fig. 4. Sample of a worksheet solution. This solution corresponds to Problem 2 in Figure 3.

(a) (b)

Fig. 5. (a) Sample problem in a Topic Quiz, original version in Spanish (problem taken from [13]).

(b) Translation to English.

3.3 MAPS In this particular course, three mini-projects were carefully designed so that the students can obtain a deep understanding of the calculus applications in the field of engineering. Fig. 6 summarizes the content of each MAP assigned to the students in this course. It is worth mentioning that, the MAPS topics selected in this particular course cover areas that can be found in different engineering fields. For more details regarding the MAPS, we refer the interested reader to [11].

Fig. 6. MAPS Topics.

3.4 Study Guides Our calculus course had a total of two midterms and one final exam; thus 3 study guides were provided to the students. Such guides included three parts. The first part is a summary of the most relevant results and theorems covered in the evaluation. The second part includes a list of exercises and problems integrating all the topics included in the test. Finally, the third part provides the answers to each of the problems in part two so that the students can check their work. 4. Results and Discussion In order to quantify the performance of the proposed methodology in the calculus course described in the previous section, we compared the ATCL outcomes with those obtained in the same course offered during 2017, however, the latter course followed traditional lecturing. From here on, we will refer to the 2018 calculus course as “ATCL-based course”, and the 2017 calculus course as “Lecture-based course”. It is worth mentioning that the Lectured-based course had a total of 239 students, 182 of which are full-time and 57 are part-time students. Such

a course was taught in 15 weeks of classes with four sessions per week with a duration of 100 minutes per session. Notice that the same amount of time was spent on both courses, however, in the Lecture-based course, three weekly sessions were dedicated for lectures and one weekly session for discussion. In the forthcoming analysis, we compared the following variables between the ATCL-based course and the Lecture-based course: (i) midterms and final exam topic by topic analysis, (ii) midterms and final exam grades, and (iii) midterms and final exam pass rates. It is important to remark that even though, the course exams administered in 2017 and 2018 were different, both followed the same structure and the level of difficulty of each question is similar. 4.1 Midterms and Final Exam Topic by Topic Analysis Fig. 7, Fig. 8, and Fig. 9 summarize the topic by topic comparison of the two midterms and the final exam between the ATCL-based course and the Lecture-based course. These bar charts show the average grade (in percent) obtained in all the questions from the midterms and final exam, respectively. To present a more detailed analysis, the exams’ questions were classified into three different categories:

• Conceptual Check (CC): questions related to theoretical aspects, e.g. conceptual check questions and simple proofs.

• Operatory Skills (OS): exercises centered around operative elements. • Word Problems (WP): application problems involving concepts evaluated in the exam.

Fig. 7. Average grades (in %) by topic evaluated in Midterm I.

The red line indicates the pass threshold (61%).

Fig. 8. Average grades (in %) by topic evaluated in Midterm II.

The red line indicates the pass threshold (61%).

Fig. 9. Average grades (in %) by topic evaluated in Final Exam.

The red line indicates the pass threshold (61%). To complete our analysis, we conducted several t-tests (with a level of significance of 0.05) to detect differences in the exams’ questions means between the ATCL-based course and the Lecture-based course. Tables 1, 2 and 3 summarize those results. Notice that, we found that the differences between the means (in most of the exams questions) are statistically significant.

*The t-test could not be applied (assumptions violated).

Table 1: Statistical Analysis of Midterm I by Topic.

*The t-test could not be applied (assumptions violated).

Table 2: Statistical Analysis of Midterm II by Topic.

ATCL - Based Course 203 10.793 3.383Lecture - Based Course 218 9.633 3.451ATCL - Based Course 203Lecture - Based Course 218ATCL - Based Course 203 4.663 3.811Lecture - Based Course 218 5.661 3.820ATCL - Based Course 203 4.271 2.260Lecture - Based Course 218 3.674 2.286ATCL - Based Course 203 9.054 4.242Lecture - Based Course 218 6.798 4.665ATCL - Based Course 203 5.660 3.153Lecture - Based Course 218 4.372 3.696ATCL - Based Course 203 2.335 1.667Lecture - Based Course 218 1.312 1.774ATCL - Based Course 203 6.980 4.080Lecture - Based Course 218 4.798 4.724ATCL - Based Course 203 8.273 6.276Lecture - Based Course 218 6.037 6.176ATCL - Based Course 203 7.985 5.860Lecture - Based Course 218 3.321 5.333ATCL - Based Course 203 61.798 25.599Lecture - Based Course 218 47.156 26.429

- -

10

15

15

100

4

10

6

12

8

4

Topic

CC1

CC2*

OS1

OS2

OS3

0.0001

2.6E-09

Points per Topic nGroup Mean

Standard Deviation

Mean Difference p - value

16 0.0006

- -

0.0076

0.0074

3.5E-07

2.18

2.24

4.66

14.64 1.6E-08

2.3E-16

0.0003

6.4E-07

1.16

-1.00

0.60

2.26

1.29

1.02

OS4

OS5

WP1

WP2

WP3

MIDTERM I

ATCL - Based Course 172 5.786 1.874Lecture - Based Course 191 5.497 2.139ATCL - Based Course 172 - -Lecture - Based Course 191 - -ATCL - Based Course 172 5.916 2.511Lecture - Based Course 191 4.720 3.256ATCL - Based Course 172 4.505 2.134Lecture - Based Course 191 3.603 2.496ATCL - Based Course 172 8.721 2.164Lecture - Based Course 191 7.387 3.700ATCL - Based Course 172 8.378 2.988Lecture - Based Course 191 6.524 4.194ATCL - Based Course 172 8.337 3.363Lecture - Based Course 191 6.382 4.654ATCL - Based Course 172 8.186 3.399Lecture - Based Course 191 5.152 4.512ATCL - Based Course 172 7.198 4.242Lecture - Based Course 191 4.576 4.820ATCL - Based Course 172 6.988 3.836Lecture - Based Course 191 2.089 3.607ATCL - Based Course 172 8.453 3.292Lecture - Based Course 191 2.099 4.078ATCL - Based Course 172 77.039 22.599Lecture - Based Course 191 53.077 26.379

p-valueTopicPoints per

Topic

OS3

OS4

n

0.2887

-

1.1959

Standard Deviation

Mean Difference

OS5

OS6

8

6

10

10

CC1

CC2*

OS1

OS2 0.9021

1.3335

1.8543

1.9550

3.0342

2.6218

10

10

10

MeanGroup

10

10

100

OS7

OS8

OS9

MIDTERM II

8

8

4.2E-12

8.2E-08

3.4E-30

7.7E-45

2.1E-18

4.8994

6.3540

23.9615

-

0.1744

0.0001

0.0003

4.5E-05

2.3E-06

7.6E-06

Table 3: Statistical Analysis of the Final Exam by Topic.

From all the data collected, it can be inferred that the results from the ATCL-based course are better than those from the Lecture-based course in almost every topic. In particular, notice that the students taught with ATCL demonstrated an improvement in their ability to solve word problems and also in their operatory skills in comparison with the Lecture-based students. However, in the Concept Check Section, although there is a slight improvement for the ATCL students, it is not as evident as in the rest of the categories. Moreover, Fig. 8 shows that ATCL is by far more efficient than traditional lecturing when the integration techniques are taught. This result makes sense since the integration techniques are basically operatory skills that are learned by doing a lot of exercises, and this is enhanced in the ATCL methodology via the problem-solving sessions. It is important to mention that there is a significant improvement from the results obtained in the Midterm I to those in the Midterm II for the ATCL-based course. We believe that such a difference occurred because of two reasons: (i) the students needed some time to get used to the new ATCL methodology because their first calculus course was taught using traditional lecturing; and, (ii) the midterm II involved more operatory skills than Midterm I. 4.2 Midterms and Final Exam Grades and Pass Rates Analysis Let us turn our attention to the overall midterms and final exam grades and pass rates. Fig. 10, Fig. 11, and Fig. 12 presents the histograms of the grades from the midterms I, II and the Final Exam from our calculus course taught in 2017 and 2018, respectively. The pass and fail rates of such tests are also presented within the histograms.

ATCL - Based Course 161 8.491 3.117Lecture - Based Course 145 6.814 3.963ATCL - Based Course 161 6.248 4.191Lecture - Based Course 145 7.428 4.079ATCL - Based Course 161 10.702 8.188Lecture - Based Course 145 9.007 8.535ATCL - Based Course 161 13.006 7.844Lecture - Based Course 145 11.593 7.365ATCL - Based Course 161 8.814 8.821Lecture - Based Course 145 4.655 6.202ATCL - Based Course 161 9.075 7.906Lecture - Based Course 145 5.048 6.319ATCL - Based Course 161 56.335 26.819Lecture - Based Course 145 44.662 25.051

0.00005

0.0001

0.0000

0.0000

0.1064

0.0774

0.0133

20

100

1.677

-1.179

1.695

1.413

4.158

4.026

11.673

WP4

FINAL

n

10

10

20

20

20

CC1

OS1

WP1

WP2

WP3

p-valueTopicPoints per

Topic Group MeanStandard Deviation

Mean Difference

Fig. 10. Histogram of Midterm I Grades (2017 - 2018). Pass and fail rates included.

Fig. 11. Histogram of Midterm II Grades (2017 - 2018). Pass and fail rates included.

Fig. 12. Histogram of Final Exam Grades (2017 - 2018). Pass and fail rates included.

Table 4: Statistical Analysis by Midterms I, II, and Final Exam.

Based on Fig. 10, the ATCL-based course shows a positive impact on our students’ achievements. The pass rate from Midterm I - 2017 (33%) compared with Midterm I - 2018

2017 2018 2017 2018 2017 2018Total of Students 218 203 191 172 145 161Mean 47.16 61.80 53.08 77.04 44.66 56.34Median 46 66 51 82 44 56Mode 6 78 64 93.4 45 100Standard Deviation 26.43 25.60 26.38 22.60 25.05 26.82Pass Rate 33.0% 58.6% 40.3% 80.2% 24.1% 41.0%Fail Rate 67.0% 41.4% 60.7% 19.8% 75.9% 59.0%Attrition Rate 8.8% 8.6% 20.1% 22.5% 39.3% 27.5%

Midterm I Midterm II Final Exam

(59%) is slightly higher. However, the pass rates for Midterm II increased from 40%, for the 2017 test, up to 80%, for the 2018 test. In the case of the Final Exam, the pass rates increased from 24% to 41%. As a result, the pass rates using ATCL consistently beat the average pass rates from the Lecture-based course. More precisely, the number of students who passed Midterm I in 2018 increased by 65%, while for Midterm II it increased by 79% and for the Final Exam it increased by 89%. Finally, Fig. 10, Fig. 11, Fig. 12, and the descriptive statistics in Table 4 show that the students not only approve the exams but also, they improve their grades (on average). This observation in conjunction with the results from the topic by topic analysis presented above suggests that ATCL enhances the students’ understanding in each of the course topics. A variable that is worth analyzing is the attrition rate. From the descriptive statistics of Tables 1, 2 and 3 it can be seen that in the course under the ATCL methodology the attrition rate was reduced from 39% to 27% (16 students) compared to the previous year with the Lecture-based course. This can be a direct consequence of the good results obtained by the students in their Midterms, as well as the commitment that the active learning methodologies induce in the students. As a side note, the final grades of the lecture-based and the ATCL-based courses are not reported in this paper because, as expected, the results obtained are consistent with those in the midterms and the final exam. To conclude the discussion, it is important to enumerate some of the drawbacks that we found during the implementation of ATCL to the calculus course described above; these are:

a) ATCL requires more in-classroom time than traditional lecturing. Thus, the proposed methodology may need an increase in the number of periods dedicated to the course. In general, calculus courses are taught in approximately four hours per week, under the ATCL methodology the weekly hours must be duplicated.

b) Even though, the proposed methodology was tested in sections of different sizes (ranging from 11 to 36 students) with similar outcomes, we recommend its implementation in small groups due to the “active” nature of the STL and the PSS. In our first implementation, we had one instructor and one TA per section. In the case of larger groups, more teaching assistants may be needed for taking care of the problem-solving sessions.

c) Since most of the work is done by the students, ATCL requires the students’ commitment

to do all the assignments.

d) For students used to courses following the lecture-based methodology, it may take some time to adapt to ATCL courses.

5. Conclusions Based on the results presented in this paper, it can be concluded that the students taught using the ATCL methodology performed better than those following the traditional lecturing methodology. By a better performance, it is meant a significant improvement in terms of exams’ grades and pass rates. Even more, the midterms topic by topic analysis suggests that the ATCL methodology is a suitable choice for teaching calculus. More precisely, when the aim is to develop mathematical operatory and word problems resolution skills, ATCL seems to be a convenient option. In spite of the good results obtained in this first ATCL implementation, the main limitation that we have noticed so far is that it requires a significant increase in the number of weekly hours dedicated to teaching a calculus course. This opens the discussion of reevaluating the number of credits needed for mathematics courses. In our future work, we will continue gathering more data from ATCL implementations and a more detailed study will be reported somewhere else. We are also interested in the implementation of ATCL in courses from different disciplines and study their outcomes. 6. Acknowledgements We would like to thank Universidad Galileo, in particular, Jean Paul Suger (vice-president of Universidad Galileo) for the support provided in this research. Last but not least, the authors are grateful to reviewers for offering many constructive comments that have improved the presentation and content of this paper. 7. References

[1] S. Freeman, S. L. Eddy, M. McDonough, M. K. Smith, N. Okoroafor, H. Jordt, M. P. Wenderroth, “Active learning increases student performance in science, engineering, and mathematics,” in Proc. of the Nat. Academy of Sciences, vol. 111, no. 23, pp. 8410-8415, 2014.

[2] J. R. Portillo, A. E. Alvarado, J. A. Samayoa, “MOSL: An innovative approach to a supplementary course of mathematics in engineering,” 2017 ASEE Annual Conference and Exposition, American Society for Engineering Education, Columbus, Ohio, June 2017.

[3] J. R. Portillo, A. E. Alvarado, J. A. Samayoa, “Guided-Lecture Team Based Learning at Work: Teaching Differential Calculus to Part-time Engineering Students in Latin America,” 2018 ASEE Annual Conference and Exposition, Salt Lake City, Utah, June 2018.

[4] F. S. Tsai et al., “From Boxes to Bees: Active learning in freshmen calculus,” 2013 IEEE Global Engineering Education Conference (EDUCON), Berlin, pp. 59-68.

[5] M. Prince, “Does Active Learning Work? A Review of the Research,” Journal of Engineering Education, vol. 93, pp 223-231, 2004.

[6] J. K. Knight, W. B. Wood, “Teaching More by Lecturing Less,” Cell Biology Education, vol. 4, pp. 298–310.

[7] J. Zhu, L. Zheng and Z. X. Hu, “The Teaching Methods of Calculus,” 2011 International Conference on Control, Automation and Systems Engineering (CASE), Singapore, 2011, pp. 1-4.

[8] R. B. Rosenberg-Kima, “Effects of Task-Centered vs. Topic-Centered Instructional Strategy Approaches on Problem Solving: Learning to Program in Flash,” Ph.D. dissertation, Dept. Educational Psychology and Learning Systems, Florida State University, Tallahassee, FL, USA, 2012.

[9] T. Easton, “Implementing Based Tutoring to Improve Student Learning,” 2016 ASEE Midwest Section Conference, Manhattan, Kansas, September 2016.

[10] R. Hernández, “Collaborative Learning: Increasing Students' Engagement Outside the Classroom,” US-China Education Review, vol.2, n. 9, pp. 804-812, 2012.

[11] J. R. Portillo, A. E. Alvarado and J. A. Samayoa, “Calculus and Engineering: Boosting their link with Transparent Assignments,” manuscript in preparation.

[12] J. Stewart, “Aplicaciones de la Derivada,” in Cálculo de una Variable Trascendentes Tempranas, 8th ed., México: Cengage Learning, 2018, ch. 4, sec. 4.7, pp. 330-343.

[13] R. Larson, B. Edwards, “Aplicaciones de la Derivada” in Cálculo de una Variable, 9th ed., México: McGraw-Hill, 2010, ch. 3, sec. 3.7, pp. 218-228.