Learner’s self-evaluation on performance rating in Linear Algebra at UPOU with asynchronous methods and synchronous meetings

doi:10.21203/rs.3.rs-1655969/v1

The purpose of the study showcases the Learner self-evaluation on performance rating as part of giving final grade by uncovering his personal experiences in his education about Linear Algebra at the UPOU. The study adopts and modify the theory of Rappe & Hayman (1996) on self-evaluation as the basis for rating performance, and used the conceptual framework introduced by Mahmood, Othman & Yusof (2012) in gathering data. Then, Grading Rubrics served as the basis for self-evaluation in giving final grade by proficiency indicated in the graphics presentation. In lieu to this study asked questions were hypothetically satisfied which revealed that the Learner compared his impressions about the subject prior and after he took the course; uncovered his difficulties and the causes in linear algebra; emphasized the real significance of the course by enumerating the techniques and skills he acquires which can be helpful on his future career; and described his participation in synchronous meetings with the asynchronous methods, reflected his understanding about the modules, homework, attendance to synchronous meetings, and relating the most helpful aspects about the course; provided self-evaluation on his performance rating from 0 to 100, with 100 being excellent and 60 being average, and justify his self-evaluation performance rating. Thus, based on the Grading rubrics his homework proficiency has accumulated with a total score of 329 over 400 with the equivalent percentage of 82.25% in Homework 1–6 which means within the range from 75–90% this result contemplated that Learner’s proficiency describes that his homework provides a complete, correct, rigorous proof or solution but is not that written well. Comprises also were an outcomes that from monitoring assessment on learning and teaching improvement, it has been recognized by a character that the learner has almost 100% in attendance to the synchronize meetings and participated, communicated in some instance important matters via emails, portal messenger; with complete compliance and perfect submission of homework and obtained a recognizable score by proficiency having 1 item with 60–80%, 1 item with 90–99%, and 9 items with 100%, and finally met a maximum rating score of 100% for final (summative) homework. Systematically, based on results from this study, the Learner’s performance rating probably can be computed anytime in the following criterion: Proficiency in Homework + Characteristic in the Learning Process + Monitoring Assessment on learning and teaching improvement + Learner's Principles in Linear Algebra (rated by the professor) of which the ultimate results for the Learner’s final grade, should be coming from the professor’s personal records and evaluation. Thus, the teacher’s objective criterion on giving final grade is the ultimate verdict.

Self-evaluation on performance rating

Linear Algebra

Asynchronous methods and synchronous meetings

University of the Philippines Open University

As expected by the author that Linear Algebra is typically it is about the x, y-axis where demonstrated thru a plot that showcase the fundamental properties of addition and scalar multiplication, with its norms that emphasized the addition and subtraction of vectors. Wherein, students were instructed to comprehend every definition of all related terms, applied the theorems, and provide proofs that reflected the law of addition, associative law of addition, the existence of identity element for addition, the existence of inverse elements for addition, distributive laws of scalar multiplication over addition, associativity of scalar multiplication and identity for scalar multiplication. Then, a manual of examples and solution are available that contains full solutions for each exercise that guides the learners in their succeeding exercises (Andrilli & Hecker, n.d.).

Those scenarios are eventually executed by Dr. NEIL JEROME A. EGARGUIN, Faculty In-Charge in Math211.Linear Algebra this mid-year-term (MYT), School Year (SY) 2020-21 under Ph.D. Mathematics Education at the University of the Philippines Open University (UPOU), Los Baños, Laguna. Eventually, Dr. Egarguin employed asynchronous teachings that help everyone learned the usage of Microsoft Team Application whereby all are encouraged for the synchronous meetings within the scope of the whole MYT, SY 2020-21. Technology pedagogy on how to use Mathlab Mathworks and Simulink, Google drive, emails, and some helpful electronic communication methods are used in this course. This study adopts and modified the theory of Rappe & Hayman (1996) on self-evaluation as the basis for rating performance, and used the conceptual framework introduced by Mahmood, Othman & Yusof (2012), see Figure 1. Self-evaluation in performance rating on Linear Algebra.

In order to satisfy the objectives, and to figure out the learner’s rating performance in Math211.Linear Algebra, SY 2020-21 in Mid-year term. Such that to showcase his comparative impressions about the subject prior and after he took the course; uncover his difficulties in linear algebra and the causes; his findings of the real significance of the course by enumerating the techniques and skills he acquires which can be helpful in his future career; and describe his participation with the asynchronous methods, considering his understanding of the modules, homework, attendance to synchronous meetings, and relating the most helpful aspects about the course; provide self-evaluation on his performance rating from 0 to 100, with 100 being excellent and 60 being average; and justify his self-evaluation performance rating. Thus, this study needs to be realized and so, this intention is beneficial to the educators, students, and researchers for futuristic endeavors.

The study

This study is descriptive though it uses some numerical data to give concrete information as pieces of evidence to display the learner’s personal records based on homework scores results, the learner’s promptness in his submission of those assignments thru the submission bin, and his learning improvements were gathered as bases for the Learner’s performance rating self-evaluation (Vallacher, Nowak, Froehlich & Rockloff, 2016; Taylor, Neter & Wayment, 2016; Sedikides & Strube, 1997) but still, the teacher’s evaluation of his learners are given more importance in giving the Learner’s final grade, as it was stressed by Rodin & Rodin (1972) that “there were two ways to judge teaching through the medium of the students: first, the objective criterion of teacher effectiveness is based on what students have learned from the teacher; second, the subjective criterion is based on student evaluation of teacher effectiveness.”.

The Data

The corpora adopt and modified the theory of Rappe & Hayman (1996) on self-evaluation as the basis for rating performance, and used the conceptual framework introduced by Mahmood, Othman & Yusof (2012) in gathering data.

Data analysis

Schünemann, et.al. (2019) provides suggestions for presenting authors' conclusions, the methods were used for computing, presenting, and interpreting relative and absolute effects for dichotomous outcome data. However, in this study, we analyzed data from homework scores and applied the Grading Rubrics in Table 1 as the basis on self-evaluation in giving final grade by proficiency indicated in the graphics presentation.

Table1. Grading Rubrics

Description	% of max points received
Provided a complete, correct, rigorous and well written solution or poof	100
Provided a complete, rigorous and well-written solution though with minor mistakes	90-99
Provided a complete, correct, rigorous proof or solution but is not that written well	75-90
Provided an incomplete work that is on the right track or line of thought	60-80
Provided a complete attempt to the problem but has serious technical errors	40-60
Submitted a serious and valid attempt to the problem	10-40
No submission	0

Then, the author proceeds on the self-evaluation of the Learner’s proficiency by simply using simple mathematical analysis to interprets the logical percentage results of the acquired data from the proficiency in homework as part of the basses in computing the final grade of the learner. The findings, results and conclusion were presented thru graphical, tabular, and textual expressions.

Hereby based on findings results showcase the Learner’s performance in linear algebra into the following aspects: his comparative impressions about the subject prior and after he took the course; uncovered his difficulties in linear algebra and the causes; his findings of the real significance of the course by enumerating the techniques and skills he acquires which can be helpful in his future career; his participation with the asynchronous methods, his understanding of the modules, homework, attendance to synchronous meetings, and relating the most helpful aspects about the course; his self-evaluation on his performance rating from 0 to 100, with 100 being excellent and 60 being average, and his justification onward to his self-evaluation performance rating.

Learner’s impressions about the subject prior and after he took the course

Linear Algebra is one of the major subjects taught under the Ph.D. Mathematics Education which includes field and vector space; bases of vector spaces; linear transformations; matrix representation of linear transformations; and some important algorithms in linear algebra. However, learning has always been difficult since it is highly technical and analytical, but then, this scenario helps to enhance and acquire some new ideas and techniques in teachings especially that assigned professor are excellent in nature with his pedagogy using asynchronous methods with synchronous meetings. The objectives is in giving authentic discussion and assess the learners has been possible easily, his eccentric thought has been replaced with an optimistic thinking onward for the better results.

Learner’s findings of the real significance of the course by enumerating the techniques and skills he acquires which can be helpful in his future career

Eventually, the Learner learned some significant technology pedagogy on how to use Microsoft Teams Application, MathLab MathWorks and Simulink, and verified that a given set is a field; checked whether a set, together with two operations is a vector space over a given field; proved some statements involving fields; checked whether a subset of a vector space is linearly independent; checked whether a subset space is a basis for the vector space; identify or construct a basis for some specific vector spaces; proved some statements involving linear independence, bases, and the dimension of vector spaces; check whether a given map between two vector spaces is a linear transformation; finds the kernel and range of a linear transformation, illustrate the Rank-nullity Theorem; proved some statements involving linear transformations; find the matrix representation of linear transformation and vice versa; use the matrix representation of a linear transformation of a linear transformation by using its matrix representation; use Matlab to find the rank and nullity of a linear transformation; determined whether a matrix is invertible; calculate various norms of vectors and matrices; proved statements regarding invertible matrices and vector and matrix norms; employ the classical and modified Gram-Schmidt orthogonalization process; finds a QR factorization for a matrix and use this to solve linear system; comment on the conditioning of a matrix; solve linear system the pseudo-inverse of the matrix, and proved statements regarding the aforesaid linear algorithms.

Learner’s difficulties in linear algebra and the causes

His health condition is due to arthritis, the gap of knowledge, unfamiliar to some extent problems, and other intervening factors e.g. prerequisite from other courses enrolled, work-related workloads, family needs, which resulted to time constraints that made the Learner to do his assignments in 24/7 during days and nights just to cope up the deadlines and complied the tasks these factors has caused his difficulties, which sometimes frustrates him to pursue the challenges in this course. But with all the virtues, and God’s blessings he made things possible and succeeded.

Table2. Learner’s participation with the asynchronous methods

Modules No.	Description	No. synchronous meetings	No. of Attendance	No. of Homework Problems	No of Submission
1	Fields and Vector Spaces	3 meetings in a week	With perfect attendance	7	7
2	Bases of Vector Space	3 meetings in a week	With perfect attendance	8	8
3	Linear Transformations	3 meetings in a week	With perfect attendance	6	6
4	Matrix Representation of Linear Transformations	3 meetings in a week	With perfect attendance	7	7
5	Inverse and Norms	3 meetings in a week	Missed 1 meeting	5	5
6	Some Important Algorithms in Linear Algebra	3 meetings in a week	With perfect attendance	3	3

The modules provided were highly focused on the technicality and the analytical process which presumed to be that learners are also highly technical hence, it was on the Ph.D. level of studies However, the assigned Faculty is savant genius tried to understand that not all had gone through the process such that learners’ intelligence probably matter on his environment and previous experiences, this exactly the same with the theory of Mackintosh, (1988).

On the teacher’s way to go forward on synchronous meetings he developed the participative approach by having first the survey to find out the plurality of same chosen schedules of meetings, by then, he introduced the asynchronous electronic communication software which is the Microsoft Teams, with his pedagogy the synchronous meetings, was so very interesting and profoundly beneficial to everyone and he even workout on how to guides the learners to be more oriented on using the Microsoft Teams Application. His expertise in doing lectures, would really contemplate to satisfy the learners hence, the topics would probably be highly technical and critical it seems difficult for the learner to go forward to what is being explained. However, the learners had been motivated, to attend the scheduled meetings and participated this can be attested because meetings were recorded, although how much the learner wishes to participate more but since topics were still under arguments so he only limits his participation but more focus on understanding the lectures provided by his savant professor and so submitted all the prerequisites thereby within his limitations.

Learner’s self-evaluation on his performance rating from 0 to 100, with 100 being excellent and 60 being average, and justify his self-evaluation performance rating.

Ph.D. Mathematics Educations students who enrolled in Math211.Linear Algebra in midyear term, SY 2020-21 has been instructed provided in the course syllabus and modules. Then, in the syllabus, the number of homework problems were enumerated and the deadlines are set, then every after the submission of that homework in the submission bin right away it was given with feedback and scores. This how fast and furious on giving feedbacking the assigned faculty but with accuracy and complete discussion as to the correction.

Herewith are the scores earned by the learner and the total number of scores assigned by the teacher were displayed below thru a graphical presentation in sequence from modules 1 to 6, and the score were indicated in detail per homework problem, see below.

Results are shown in graphical form that the learner has got a minimal score from problems 1 and 2, and also with a perfect score in problems 4 and 7 in Module 1.

In actual setting, the teachers give 7 problems but only four should be answered and some of those are flow rated with zero scores. However total submissions of homework problems mainly done for assurance that he received the answers’ key hence a prerequisite thereby was to submit all the problems prior to the release of the answers’ key.

But exactly learners were only permitted to do homework at least four (4) out of the seven (7) choices. Below is Figure A. Professor’s Adjusted Homework Problem. So, problems 3, 5, and 6 are excluded from the point system.

Results are shown in graphical form that the learner’s scores in proficiency are very minimal ranging only from 0.5 to 0.8 in all of the homework in Module 2. Though this results in rubrics earned an equivalent point ranging from 10-40% based on the description.

Results are shown in graphical form that the learner has earned only a minimal score in proficiency out of the six (6) homework in Module 3. Relative only 4 out of the six (6) choices of homework is inclusive for points system because the learners were advised to choose at least 4 problems out of 6.

Results are shown in graphical form that the learner had met the maximum in proficiency in five (5) homework out of the seven (7) homework in Module 4.

Results shown in a graphical form that the learner had met a maximum score in proficiency in five (4) homework out of the five (5) homework in Module 5.

Results are shown in graphical form that the learner scores in proficiency have got zero in his first problem of the homework then has minimal scores on the second problem and also for the third homework problem ranging only from 1 to 1.25 in all of the homework in Module 6. However, when we focus not on score, progressively the results are optimistic hence, linearly his performance rating was increasing though slowly from zero, next to 0.5 and got 1.25 on the third item.

Homework 7. Final (Summative) Homework

This article will serve as Homework 7, wherein Dr. NEIL JEROME A. EGARGUIN, Faculty In-Charge in Math211.Linear Algebra_MYT_2020-21 in Ph.D. Mathematics Education at UPOU, Los Baños, Laguna gave a final grade based on his objective criterion (see in Figure 1-A).

The Learner's Principles in Linear Algebra based on the objective criterion of the teacher has met the highest proficiency with a rating of 100%.

The authors revealed that the learners had completely complied and submitted all the homework from 1-6 on time on the Submission bin, but for practical reasons only two among the submitted output can be shown thru screenshot the Homework 1 and Homework 6 to save the number of article’s pages (see Figure 2.1 and Figure 2.2 ).

Submission of an output has been submitted 3 days, 11 hours early as expected.

This screenshot declared that submission was late 23 hours and 36 minutes. However, it was proclaimed by the Faculty-In-charge that submission will be extended until August 9, 2011 in the 11:59 midnight, instead of August 8 (see Figure.3 screenshot on extended deadlines of Homework6 submission).

Based on records, the learner’s performance rating as to the following aspects, are tabulated on details (see tables 3).

Table 3. Proficiency in Homework (as to the grading rubrics)

Module/Homework	Answered Homework Problem for scoring	Assigned Points Score per Homework Problem	Earned Score per Quiz	% Score per homework problem	% Points earned as to Grading Rubrics
1	1	10	1	10	10-40 %
	2	10	1	10	10-40 %
	4	5	5	100	100 %
	7	5	5	100	100 %
2	1	5	0.5	10	10-40 %
	3	5	0.8	16	10-40 %
	5	5	0.8	16	10-40 %
	6	5	0.8	16	10-40 %
3	1	5	.05	10	10-40 %
	2	5	.05	10	10-40 %
	3	5	1.5	30	10-40 %
	5	5	0.5	10	10-40 %
4	1	5	1	10	10-40 %
	2	5	1	10	10-40 %
	3	5	4.8	96	90-99 %
	4	5	5	100	100 %
	5	5	5	100	100 %
	Extra 1	3	3	100	100 %
	Extra 2	3	3	100	100 %
5	1	5	5	100	100 %
	2	5	5	100	100 %
	3	5	Submission = 0	10	10-40 %
	4	5	5	100	100 %
	5	3	2	66.67	60-80 %
6	1	7	Submission = 0	10	10-40 %
	2	5	1	20	10-40 %
	3	5	1.25	25	10-40 %

Results overviewed that in Module 1 homework, the learners had only gotten a score of 1 on his first and second attempts which adjectively this submission is equivalent to a serious and valid attempt to the problem. But then, the good thing is his homework 4 and 7 has provided a complete, correct, rigorous, and well-written solution or poof in homework. Then in modules 2 and 3 he only got a score on percentage ranging from 10-40% per rubrics scoring system. In module 4 he has a score ranging from 10-40% good for problems 1 and 2, followed by a score ranging from 90-99% for problem 3, and then 100% for problems 4, 5, extra 1 and 2, as well as to Module 5 in problems 1 and 2, yet he missed and got zero in score points but this is good for 10-40% into the assigned rubrics scoring system. Then, got a score of 100% for problem 4, while got only a percentage score ranging from 60-80%. While, for Module 6. In some Important Algorithms in Linear Algebra he only obtains a score ranging from 1-40%.

Moreover, as to the Learner's Principles in Linear Algebra, he met a maximum score of 100% in the Final (Summative) Homework based on the teacher’s objective criterion.

Characteristic in the Learning Process

It was being recognized by a character that the learner is attentive in his homework submission, almost 100% attendance to the synchronize meetings and participated, communicated in some instance important matters via emails, portal messenger; with complete compliance and perfect submission of homework and obtained a recognizable score by proficiency having 1 item with 60-80%, 1 item with 90-99% and 9 items with 100%. Besides, gained 100% on his final (summative) homework.

Monitoring Assessment on learning and teaching improvement

It was observed that the more exercise and lectures have been provided by the professor the learner got a higher score this is a fact the teaching has been consummated progressively and allows the learner to learned more and acquire new ideas and techniques in solving. Thus, Ph.D. Mathematics Education in UPOU established teaching-learning with experts who could be able to draw conclusive desirable outcomes wherein learners should do things possible in all possible means. However, this strategy in teaching is quite difficult e.g. of those with health problems, and unstable internet connections, these aspects have brought forward the significance of the school management, administrators, or head of offices to be responsive with this call of duty.

Eventually, the teacher’s politeness takeover to make this course admirable and motivating the learner to more courageous in doing the homework and keeps following his advice.

Learner's Principles in Linear Algebra

The Learner’s principles in Linear Algebra could be observed in this article, the value practically differ from one’s understanding, and this is agreeable that linear algebra has been studied for future careers.

The study has contemplated and satisfied all the hypothetical questions such that the Learner compared his impressions about the subject prior and after he took the course; uncovered his difficulties and the causes in linear algebra; determined of the real significance of the course by enumerating the techniques and skills he acquires which can be helpful in his future career; and described his participation during the asynchronous meetings, reflected his understanding about the modules, homework, attendance to synchronous meetings, and relating the most helpful aspects about the course; provided his self-evaluation on performance rating from 0 to 100, with 100 being excellent and 60 being average; and justified his self-evaluation performance rating.

The author’s self-evaluation has been revealed, the revelation was narrated in the following stanzas, below:

Characteristic in the Learning Process

Out of the six modules of Linear Algebra that represents a field and vector space; bases of vector spaces; linear transformations; matrix representation of linear transformations; and some important algorithms in linear algebra. The professor has also intended to provide homework with a given set of deadlines, and that by the end of the semester students must be confirmed that he submitted all their homework in the submission bin, and thereby the teacher should grade him a final grade. In this study, the authors within his self-evaluation have partially obtained a passing grade based on the criterion set by the teacher indicated in the Syllabus. Indeed, from the overview of the author, the lectures and discussions have ended fun and progressive. The course is significant for the learner’s professional development and would help anyone’s future career of those who are in the field of Mathematics.

Proficiency in Homework

It also revealed from the Author’s self-evaluation in his performance rating in Math211.Linear Algebra that from among the given homework problems he got 16 items with a score ranging from 10-40%, 1 item ranging from 60-80%, 1 item ranging from 90-99%, and 9 items with 100% score and percentage. If all the ranges of scores will be flow rated with equal distribution with a numerator score of 100, and favorably the 16 items have got a score ratio of 40:100, then 80:100; 99:100 and 100:100. Therefore, considering the flow the homework has computed with a total score of 329 over 400 based on the rubrics scoring system and has an equivalent percentage of 82.25 which is within the range of 75-90% which describes that Learner’s homework provides a complete, correct, rigorous proof or solution but is not that written well.

In addition, the Learner met a maximum rate of 100% on his final (summative) homework based on the teacher’s objective criterion.

Monitoring Assessment on learning and teaching improvement

It has been recognized by the character that the learner is attentive in his homework submission, almost 100% attendance to the synchronize meetings and participated, communicated in some instance important matters via emails, portal messenger; with complete compliance and perfect submission of homework and obtained a recognizable score by proficiency having 1 item with 60-80%, 1 item with 90-99%, and 9 items with 100% and 100% for the Final (Summative) Homework.

Systematically, based on results in this study the Learner’s performance rating probably can be computed in the following criterion: Proficiency in Homework + Characteristic in the Learning Process + Monitoring Assessment on learning and teaching improvement + Learner's Principles in Linear Algebra (rated by the professor) of which the ultimate results for the Learner’s final grade, of course, should be coming from the professor’s personal records and evaluation.

Although, the study displayed the fact that the Learner has obtained proficient results in homework, has been courageous in doing and submitting his homework on time, and religiously comprehended the modules, attended the synchronous meetings, have learned the technology pedagogy extended through teacher’s effectiveness but still the teacher’s objective criterion on giving the final grade is the ultimate verdict.

Ethical statement

Not applicable

Consent statement

This article does not involve human intervention and animal interference, rather this is beyond’ author perspective and personal assessment on his experiences, wherein he wishes to brought out for global information.

Disclosure of potential conflicts of interest This article has no conflict of interest.

Andrilli, S., & Hecker, D (n.d.). Elementary Linear Algebra. Retrieved August 10, 2021, from https://books.google.com/books/about/Elementary_Linear_Algebra.html?id=Hg65zoqiUgoC;

Rappe, M. & Hayman, K (1996). The effects of video feedback on the self-evaluation of performance in socially anxious subjects. Behaviour Research and Therapy, 34(4), 315–322. https://doi.org/10.1016/0005-7967(96)00003-4;

Mahmood, A., Othman, M. F., & Yusof, Y. M. (2012). A Conceptual Framework for Mathematical Ability Analysis through the Lens of Cultural Neuroscience. Procedia - Social and Behavioral Sciences, 56, 175–182. https://doi.org/10.1016/j.sbspro.2012.09.644;

Taylor, S. E., Neter, E., & Wayment, H. A. (2016). Self-Evaluation Processes: Personality and Social Psychology Bulletin. https://doi.org/10.1177/01461672952112005;

Sedikides, C., & Strube, M. J. (1997). Self-evaluation: To thine own self be good, to thine own self be sure, to thine own self be true, and to thine own self be better. In M. P. Zanna (Ed.), Advances in experimental social psychology, Vol. 29, pp. 209–269). Academic Press. https://doi.org/10.1016/S0065-2601(08)60018-0;

Vallacher, R. R., Nowak, A., Froehlich, M., & Rockloff, M. (2016). The Dynamics of Self-Evaluation: Personality and Social Psychology Review. https://doi.org/10.1207/S15327957PSPR0604_11;

Rodin, M., & Rodin, B. (1972). Student evaluations of teachers. Science, 177(4055), 1164-1166;

Schünemann, H. J., Vist, G. E., Higgins, J. P., Santesso, N., Deeks, J. J., Glasziou, P., ... & Cochrane GRADEing Methods Group. (2019). Interpreting results and drawing conclusions. Cochrane handbook for systematic reviews of interventions, 403-431;

Mackintosh, N. J. (1988). Approaches to the study of animal intelligence. British Journal of Psychology, 79(4), 509-525.

Learner’s self-evaluation on performance rating in Linear Algebra at UPOU with asynchronous methods and synchronous meetings

Status:

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Abstract

Figures

Introduction

Methodology

Findings

Results And Discussion

Conclusion

Declarations

References

Status:

Version 1