Considerations about Flip Education in the Teaching of Advanced Mathematics
Round 1
Reviewer 1 Report
The article presents an experience of flipped classroom with a good statistical analysis of the applied methodology.
Conclusions are expected in an educational context: “Both the difficulty of the subject and the usefulness of the exercises are more perceived when reverse teaching is used rather than the traditional method, since it involves a continuous work that allows students to be more aware of both aspects.” It is known, but it is always interesting having data to confirm it.
On the other hand, the paper states the difficulty of implementing this methodology in groups with a big number of students.
It is said in the text there are references to studies comparing the marks obtained by the students in both metodologies: traditional and flipped, but I miss a similar comparison in this study. Moreover, It would be interesting comparing not only the marks but competences acquisition.
There are some expressions in Spanish in lines 360-361; 369; 371 that should be translated into English.
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Author Response
We would like to thank this reviewer for the constructive criticism of the paper. We have corrected all your suggestions.
Reviewer 2 Report
The paper discusses the 'flip education' method for teaching advanced mathematics.
The topic is motivated by the new behaviour of students and is is gact an important issue to consider. The reviewer consider that the paper is of interest, but needs some revision before publishing.
Some aspects to consider:
a) The writing style needs some careful attention. For example, at abstract "The changes in our society in recent years and the consequent change in the idiosyncrasy of our young people demand a change in teaching methodology" has 3 repetitions of "changes". Also I am not sure if write as "our" (students) is the best option.
b) In several places, namely in the Tables, we have numbers with comma instead of dot. For example, in Table 1, the 1st value 8,22 is probably 8.22. However, in thext sometimes it is and sometimes it is not. For example in line 190 "4,5 hours per week" is "4.5 hours per week", but in line 195 we have "methodology 4, 5 hours per week" where the space makes some confusion.
c) In the tables 1 and 2 we have numerical numerical values resulting from the questionnaires. Are they averages? And, in that case, what is the sandard deviation and what is the total number of responses?
d) We have some unclear concepts in the text. For example, "flip education", "reverse education", and "traditional classes". The reviewer recommends some precise definition of concepts.
Author Response
We would like to thank this reviewer for the constructive criticism of the paper. We have corrected all your suggestions.
Reviewer 3 Report
Good description of the 1st and 4th year students who were enrolled in the two mathematics courses designed with "flipped" classrooms.
Suggestions:
Add a description of the mathematics taught in each of the courses. Might there be something about the syllabus that contributes to the results you see?
Present the analysis and results from the MAD students before the analysis and results from the GMA students (1st year, then 4th year students)
Consider other differences between the MAD and GMA students when presenting the discussion and conclusions. The MAD students are at the beginning of their university experience and the GMA students are at the end of their university experience. How might this fact impact the results?
In terms of writing mechanics, the English grammar and vocabulary need a thorough review and editing. In addition, the formatting of the lists of objectives (line 111), and especially the nested list beginning on line 125, is very difficult to follow. Similarly, the lists of teacher and student activities are difficult to follow. Perhaps this information would be better organized in a table or other type of exhibit?
Author Response
We would like to thank this reviewer for the constructive criticism of the paper. We have corrected all your suggestions:
Suggestions:
Add a description of the mathematics taught in each of the courses. Might there be something about the syllabus that contributes to the results you see?
We have added it:
“The content of the subjects MAD and GMA correspond to the field of Discrete Mathematics. More specifically, in the subject MAD is studied, in the classroom classes, Logic of statements and predicates, principle of induction, set theory , binary relations, divisibility and congruences, Boolean algebras and combinatoria. These contents are complemented in laboratory classrooms with the principles of graph theory, focused on modeling. For its part, the content of the subject GMA is centered, as its name indicates, in the extension of graph theory studied in MAD. Specifically, the concepts seen in the first course ( shortest path problem, non-directed graph orientation problem , graphic successions and minimum spanning tree problem) are revised and expanded, different problems to be solved by using of network and flow theory, matching problem in non-directed, weighted and unweighted graphs, the search for Eulerian cycles and the Chinese postman problem , the search for Hamiltonian cycles and the low-cost salesman problem, and the colouring problem are studied. Special emphasis is placed on problem modelization, posing and solving numerous real context problems.”
Present the analysis and results from the MAD students before the analysis and results from the GMA students (1st year, then 4th year students.
We have changed it:
“We have applied the flip methodology only to groups in which Discrete Mathematics was taught, so we do not have the opportunity to comment on the suitability of this methodology for other subjects. We have added a paragraph about the reasons for which we believe that reverse education is an adequate way to teach Discrete Mathematics.”
Consider other differences between the MAD and GMA students when presenting the discussion and conclusions. The MAD students are at the beginning of their university experience and the GMA students are at the end of their university experience. How might this fact impact the results?
We have added a clarification on the differences of opinion between the students of fourth of GMA and those of first of MAD:”
Another factor influencing the success or not of the application of reverse education is the course to which the addressed students belong. Thus, we see that the results are better in fourth than in first grade, a possible consequence of a more mature student intellectually and with a greater interest in learning than in "passing" the course. Older students share our opinion about the advantages of this methodology in terms of deeper learning, which does not prevent them from also expressing that it implies a greater effort, which leads some of them to opt for a more traditional methodology. On the other hand, students' interest in learning also depends on the content of the subject. In our case, MAD is a compulsory first year mathematics subject, in a career in which the objective is to graduate in Computer Science. Although mathematics is totally necessary, in many cases first-year students do not perceive it that way, so in most cases they face it with little interest. The fourth year course, also of mathematical content, is optional, so we do not find this impediment.“
In terms of writing mechanics, the English grammar and vocabulary need a thorough review and editing. In addition, the formatting of the lists of objectives (line 111), and especially the nested list beginning on line 125, is very difficult to follow. Similarly, the lists of teacher and student activities are difficult to follow. Perhaps this information would be better organized in a table or other type of exhibit?
We have rewritten this part in an easier way to follow.
We want to thank again this reviewer because with your comments we feel we have really improved the paper.
Round 2
Reviewer 3 Report
Thank you for your thoughtful replies. I think the authors have well addressed my comments, just need some minor revisions.
