Rubrics as an Alternative for the Teaching of Geometry at the Engineering Faculty at the Catholic University of Santiago De Guayaquil

International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395 -0056
Volume: 04 Issue: 06 | June -2017 www.irjet.net p-ISSN: 2395-0072
© 2017, IRJET | Impact Factor value: 5.181 | ISO 9001:2008 Certified Journal | Page 5624
RUBRICS AS AN ALTERNATIVE FOR THE TEACHING OF GEOMETRY AT
THE ENGINEERING FACULTY AT THE CATHOLIC UNIVERSITY OF
SANTIAGO DE GUAYAQUIL
Nancy Varela Terreros1
1Professor of the Faculty of Engineering of the Catholic University of Santiago de Guayaquil
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Abstract - As part of the proposal of thedesignofthecourse
of Geometry for the career of Civil Engineering the author
proposes the use of the system of rubrics within the evaluation
process. The rubrics are instruments that allow evaluation by
defining different criteria, and estimating the student
performance according to each one of them. The rubrics are
represented by tables that define the levels of qualificationfor
each criterion, and can be global, if they cover
comprehensively the subject to be evaluated, or analytical, if
they break it down according todifferent measurementpoints.
Well used, they have the advantage that they arenotonly used
to evaluate the student 's performance but also to know how
to improve the interactions between the criteria, aswellasthe
performance of the teacher and the teaching - learning
process. The main disadvantage is that they require
preparation time, and teacher training for their design and
use.
Key Words: Rubric, learning, Geometry, assessment,model.
1. INTRODUCTION
This document is madeaspartofaresearchprojectaimed
at finding a support system for the teaching of Geometry for
students of Civil Engineering.One point of interestwithinthe
project is the evaluation process in the higher education
system. According to the author, the evaluation should serve
to improve the teaching- learningprocessasawhole,andnot
only to obtain a numerical measurement of the result
expected by the students. In this context, the use of rubrics
for the evaluation of academic performance is proposed.
2. DEVELOPMENT
A useful tool for student evaluation, which provides the
teacher with information that goes beyondtheassessmentof
the level of knowledge reached on a given topic, is the rubric,
which is a tool for assessing learning assessment.
Alsina et al. (2013, p.8) point out that "A rubric is an
instrument whose main purpose is to share the criteria for
performing learning and evaluation tasks with students and
among teachers." Gatica-Lara andUribarren-Berrueta(2012,
p. 1) indicate that "they are tables that disclose student
performancelevels in a givenarea,withspecificperformance
criteria. They indicate the achievement of the curricular
objectives and the expectationsoftheteachers."Torres,J.and
Perero, V. (2010, p. 142) define the rubric as "an evaluation
instrument based on a quantitative and / or qualitative scale
associated To pre-established criteria that measure the
actions of students on the aspects of the task or activity that
will be evaluated."
From the definitions given, wecan observe the repetition
of the following concepts: instrument, evaluation, criteria. A
definition that integrates the criteria of the authors
mentioned would start by saying that a rubric is an
evaluation tool based on criteria. The selection of the
evaluation criteria, as well as the way in which these criteria
will be evaluated, is the starting point fortheuseoftherubric
as part of a support system in the teaching - learning process
of Geometry in Higher Education.
Regarding the evaluation process itself, the RAE points
out, among its definitions, that evaluating is "Estimating the
knowledge, skills and performance of students" (2016).
Gvirtz and Palamidessi, indicate that "an evaluation intends
to prove, to verify something relative to the expected
qualities of a person or athing"(2006),andindicatethatsuch
evaluation can occur within two models:
 Model 1: assess is to measurelearningproductstoqualify
apprentices. Its function is to qualify the student with a
grade.
 Model 2: Evaluation is a complex judgment about
learners' performance and teaching strategies. It
evaluates the student, the action of the teacher, the
teaching systems and the curriculum.
In the "Evaluation of students in Higher Education", the
Permanent Training Service of the University of Valencia
(2007, p.18) points out that evaluation should also involve
teaching self-assessment.Inthissense,theauthorsarguethat
"the time we dedicate to correcting and explaining to a
student the reasons and arguments of a judgment about a
work, examination orintervention,isteaching",andindicates
that there are two types of evaluation: summativeevaluation
and Formative evaluation. Summative assessment is
performed at the end of a period and is intended to "qualify
according to the appreciated performance, ie, certify the
performance or performance at the end of that period." The
formative evaluation is "the issuance of judgments that are
carried out throughout a period of teaching and that aim to

inform the student and the teacher about the progressive
achievements of the student in order to improve both
teaching and learning." (P.19)
The author's position in this document is that the
evaluation should be formative, seeking to improve both
teaching and learning. Taking the semantic definition, this
formative evaluation must also serve to estimate the
performance of the students.
The rubric, in this context, should specify the criteria
necessary to evaluate the performance of the student, and
also find the shortcomings of the student and the curricula,
the teacher and the teaching process, so that learning can
improve.
Torres and Perera coincide with Gatica-Lara and
Uribarren-Berrueta, pointing out that there are two types of
rubrics: global rubrics and analytical rubrics. The authors
point outthatglobal,comprehensiveorholisticrubricsassess
learning or competence from a global view, without
determining the components of the process or topic
evaluated, while the analytical rubrics focus onspecificareas
of learning and break down their components to obtain a
total grade.
Goodrich (2005, p. 2) points out that a rubric is
instructional if it is "co-createdwithstudents,delivered,used
to facilitate peer review and self-assessment and teacher
feedback, and only then used to grade." Inthissense,arubric,
whether analytical or comprehensive, must be designed to
meet other learning requirements first, before being used in
the evaluation itself. Gatica-Lara and Uribarren-Berrueta
(2013) present examples of comprehensive and analytical
rubrics, which are shown in Tables 1 and 2.
Table 1: Example of comprehensive rubric
Scale Description
5 Full understanding of the problem is
evident. Includes all the elements required
in the activity.
4 Understanding of the problem is evident. It
includes a high percentage of the elements
required in the activity.
3 Partial understanding of the problem is
evident. It includes some elements required
in the activity
2 The evidence indicates little understanding
of the problem. Does not include the
elements required in the activity.
1 The activity was not understood
0 Nothing was done
Source: Gattica-Lara y Uribarren-Berrueta (2013).
Table 2: Example of analytical rubric
Criteria Level
4.
Excellen
t
3.
Satisfact
ory
2.
Improva
ble
1.
Inapprop
riate
Supports
used in
the
presentat
ion on the
subject.
Sources
of
biomedic
al
informati
on
The
student
uses
different
resource
s that
strength
en the
presenta
tion of
the
subject
He/she
uses few
resource
s that
strength
en the
presenta
tion of
the
subject
He/she
uses one
or two
resource
s but the
presenta
tion of
the
subject is
deficient
He/she
does not
use
additional
resources
in
presentin
g the
subject
Understa
nding of
the
subject.
Sources
of
biomedic
al
informati
on
He/she
answers
precisely
all the
question
s
propose
d from
the
subject
He/she
answers
with
precision
the
majority
of the
question
s
propose
d from
the
subject
He/she
answers
accuratel
y some
question
s on the
subject
He/she
does not
answer
the
questions
proposed
from the
subject
Mastery
of
biomedic
al
informati
on search
strategies
He/she
demonst
rates
mastery
of search
strategie
s
He/she
demonst
rates a
satisfact
ory level
of
proficien
cy in
search
strategie
s
He/she
demonst
rates
mastery
of some
search
strategie
s
He/she
does not
dominate
search
strategies
Source: Gattica-Lara and Uribarren-Berrueta (2013).
In either case, it should be clear what are the learning
objectives and the criteria to be evaluated. And as in any
evaluation, determine the weight of each criterion. Goodrich
points outthefollowingadvantagesofaninstructionalrubric:
it helps students to understand the goal of an assignment,
helps the teacher to provide feedback, in an individualized
manner and in an acceptable time, and even though it does
not correspond to the grade, it also allows students to
generate a self-assessment and a peer evaluation, which
makes them aware of their areas of failure. As for the
disadvantages, the authors of the tables presented indicate

that rubrics require time in their elaboration and that the
teacher training for its design and use is necessary.
3. RESULTS
The proposal of this document is that, since Geometry is
an initial subject, the rubric can be used in two moments
during the course:
 Intermediate, to assess the evaluation of continuous
learning throughout the course
 Final, to assess the evaluation of general course learning
For the realization of these rubrics some componentsare
needed:
- Academic: the contents of the geometry program
(intermediate and final moment)
- Spatial visualization of the student at the beginning of
the course. The author proposes theVanHielemodel,ascited
by Crowley (1987) for being commonly used in the course of
Geometry.
- Use on the part of the students of the computer support
available to them, mainly new information and
communication technologies, ICT.
There is also an initial moment, when the student enters
the course, and there is no material to evaluate. The author's
position is that at the beginning of the course should be used
a support instrument, similar to a rubric of a comprehensive
type, referring only to academic performance. The results of
this instrument can serve the teacher to know which are the
subjects of the course on which should be focused at the
beginning in order to facilitate the success of the learning. A
proposal is presented in Table 3.
Table 3: Proposal of an assessment instrument – Initial
moment
Scale Description
4 He/she has exceptional knowledge about Basic
Mathematics taught at school.
3 His/her knowledge about Basic Mathematics is
very good.
2 His/her knowledge about Basic Mathematics is
acceptable.
2 He/she brings a lot of Basic Mathematics failures
from school.
1 His/her initial level is deficient and will not allow
him/her to continue with the course.
Table 4: Example of analytical rubric – Intermediate
and final moment
Criteria Level
4.
Excellent
3. Very
good
2. Good 1.
Regular
0.
Deficien
t
Underst
anding
the
content
of the
course
His/her
knowledg
e is
widely
demonstr
ated in
problem
solving
and in
his/her
theoretic
al
knowledg
e.
He/she
solves
problems
by
demonstrati
ng clear
theoretical
knowledge.
However,
answers are
not
accurate.
His/her
lack of
theoreti
cal
knowle
dge is
evident
in the
impreci
sion of
his/her
answers
.
Howeve
r,
he/she
seeks to
find a
way
towards
a
solution
.
He/she
does
not find
ways to
solve
the
problem
s raised.
Scarcely
handles
theoreti
cal
informa
tion
His/her
theoretic
al
knowled
ge and
practical
applicati
on are
absent
Visualiz
ation
(Van
Hiele
model)
Rigor Deduction Informa
l
deducti
on
Analysis Visualiza
tion
(básic
level)
Use of
ICT as
support
to the
best
perform
ance of
the
course
He/she
masters
the ICT
that allow
him/her
to take
full
advantag
e of the
course
He/she
knows
some ICT
and tries to
use them in
the course
He/she
is
learning
some
ICT and
uses the
one
he/she
knows
in the
best
manner
He/she
knows
few ICT
and
does
not
know
how to
use
them in
the
course.
He/she
does not
know
ICT
For the following levels, it is proposed to evaluate the
criteria indicated, according to the rubric shown in Table 4.
This rubric can be useful to the following actors:
Student: allows him/her to know the faults in each of the
criteria.
Teacher: allows him/her to locate student failures,
according to the different criteria, and at the same time, to
generate a possible correlation between said failures.
Educational institution: Applyingrubricsaccordingtothe
different contents of the course, allowsidentifyingareaswith
major deficiencies, which could be due to the structureofthe
program, or to the teacher.
4. DISCUSSION
Since rubrics are an evaluation tool that measure across
diverse criteria, the accuracy with which these criteria are

defined and the grades for eachareimportant.Thisdefinition
has to be based on the learning objectives of the academic
program, and in turn, these must be detachedfromtheobject
of the course. Thus, the usefulness of the rubric does notonly
depend on a good work done bytheteacher,butalsodepends
on the structure of the subject in which they will be used.
Here, it is important the interaction of the teacher with
the educational institution, for the elaboration of the
document that will be used with the student. In this
interaction, the student must also participate. This way, the
student will be enabled to know, in advance, which are the
criteria that will be part of the final evaluation. This goes
beyond the knowledge of thethematic units.Intheparticular
case of Geometry, it is beneficial to know the type of spatial
thinking with which the student initiates higher education.
There are scales for the measurement of this thought, which
are not the reason forthe present study.Also,bytheirnature,
ICT present a learning tool for the student,whichcanprovide
a better understanding of the object of study. The ability to
use these ICTs is also of interest for evaluation.
5. CONCLUSIONS
In the case of Geometry, for the design of the rubrics it is
important to generate a link with the content prior to the
course, that is, the subjects of higher education. The first
concern at the time of design is to identify the points of
contact betweentheBasicMathematicsofthehighschooland
Geometry. The author's position is that thesesubjectsshould
be evaluated in a global way, since it is knowledge not
provided by the institution or the teacher that applies the
initial rubric, and because in addition, it should be used only
as a tool of assessment of the diagnostic evaluation, which
cannot serve for a final grade.
The initial rubric should allow the teacher to know in a
global way the level of knowledge of Basic Mathematics with
which the student arrives at the course of Geometry. From
there, the teacher can give a new direction to the course, so
that the learning process is facilitated. For the rubrics
corresponding totheintermediateandfinalmoments,itmust
first be clear on which are the thematic units to be evaluated.
The rubrics should answer the following questions:
 Which are the thematic units that generate the greatest
learning difficulty
 How the level of visualizationaffectstheunderstandingof
the subject
 How is it possible to move from one level to the next, in
each criterion
 How the criteria may complement / affect each other
By answering these questions, the rubric becomes not
only a tool for assessing the learning evaluation but also a
support element for the improvement of the whole teaching
of the subject.
REFERENCES
[1] Alsina, J. et al (2013) Rúbricas para la evaluación de
competencias. ICE y Ediciones OCTAEDRO S.L.
Barcelona.
[2] Crowley, M. (1987). The Van Hiele model of the
development of geometricthought.TheNational Council
of Teachers of Mathematics, Inc. Reston, VA.
[3] Gatica-Lara, F.; Uribarren-Berrueta, T. (2013). ¿Cómo
elaborar una rúbrica? Investigación en Educación
Médica. Inv Ed Med 2013;2(1):61-65. México D.F.
Retrieved on December 2016 from
http://riem.facmed.unam.mx/sites/all/archivos/V2Nu
m01/10_PEM_GATICA.PDF
[4] Goodrich AH. Teaching with rubrics. The good, the bad
and the ugly. College Teaching 2005;53(1):27-30.
[5] Gvirtz, S., y Palamidessi, M. (2006). El ABC de la tarea
docente: curriculum y enseñanza. Buenos Aires: AIQUE
Grupo Editor S.A.
[6] Real Academia Española (2016). Diccionario de la
Lengua Española. (23.a Ed.) Madrid, España. Retrieved
on June 2016 from
http://www.rae.es/publicaciones/obras-
academicas/diccionarios-de-la-real-academia-espanola
[7] Reddy, M.; Andrade, H. (2010) A review of rubric use in
higher education. Assessment & Evaluation in Higher
Education Vol. 35, No. 4, July 2010, 435–448. Taylorand
Francis. Retrieved on December 2016 from
http://class.web.nthu.edu.tw/ezfiles/669/1669/img/13
81/6.Areviewofrubricuseinhighereducation.pdf
[8] Salinas, B.; Cotillas, C. (2007). La evaluación de los
estudiantes en la Educación Superior (pp.23-29).
Valencia: Universitat de Valencia. Servei de Formació
Permanent.
[9] Torres, J.; Perero, V. (2010). La rúbrica como
instrumento pedagógico para la tutorización y
evaluación de los aprendizajes en el foro online en
educación superior. Revista de Medios y Educación. Nº
36 Enero 2010 pp.141 – 149. Sevilla. Retrieved on
December 2016 from
http://acdc.sav.us.es/ojs/index.php/pixelbit/article/vie
w/436/172
BIOGRAPHY
Nancy Varela Terreros, P.E., M.B.A.
Full time professor at the Faculty
of Engineering of the Catholic
University of Santiago de
Guayaquil

Rubrics as an Alternative for the Teaching of Geometry at the Engineering Faculty at the Catholic University of Santiago De Guayaquil

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