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Article |
Julia Paola Viteri Palacios[*]
Segundo Daniel Viteri Palacios*
Milton Rafael Maridueña Arroyave*
Luz Marina Bejarano Ospina*
Abstract
This study aimed to design and validate a
differentiated assessment instrument mediated by Quizizz to assess competency
M.5.1.75 related to the logarithmic function among second-year upper-secondary
students. An applied, descriptive-propositional design was used. The diagnostic
phase combined a survey of 120 students, an interview with a mathematics
teacher, classroom observation, and a diagnostic assessment. Written tests
predominated (100%), technological resources were not used for assessment
(100%), and 58.33% of students perceived learning logarithmic functions as very
difficult. The main difficulties concerned mathematical procedures (48.33%) and
graphs/problems (42.50%). Based on these needs, a 12-item Quizizz instrument
was structured into basic, intermediate, and advanced performance levels. Three
experts validated the proposal, yielding an overall mean of 3.77/4. Curriculum
relevance, methodological coherence, mathematical relevance, mathematical
representation, item distribution, and feedback reached 4.00/4. The instrument
therefore shows adequate curricular and methodological coherence for pilot
implementation; however, its effectiveness on student learning remains to be
tested empirically.
Keywords: differentiated assessment; formative assessment;
Quizizz; logarithmic function; secondary education; educational technology.
Resumen
El estudio tuvo como objetivo
diseñar y validar un instrumento de evaluación diferenciada, mediado por
Quizizz, para valorar la destreza M.5.1.75 vinculada con la función logarítmica
en estudiantes de segundo año de Bachillerato General Unificado. Se desarrolló
una investigación aplicada de alcance descriptivo-propositivo. El diagnóstico
integró una encuesta a 120 estudiantes, entrevista a un docente de Matemática,
observación de aula y una evaluación diagnóstica. Los hallazgos mostraron
predominio de pruebas escritas (100 %), ausencia de recursos tecnológicos en la
evaluación (100 %) y elevada dificultad percibida en la función logarítmica:
58,33 % la calificó como muy alta; las principales dificultades se concentraron
en procedimientos (48,33 %) y gráficas/problemas (42,50 %). Con base en estas
necesidades se diseñó un instrumento de 12 reactivos en Quizizz, organizado en
tres niveles: básico, intermedio y avanzado. La validación mediante tres
expertos alcanzó una media global de 3,77/4. Los criterios de pertinencia
curricular, coherencia metodológica, pertinencia matemática, representación
matemática, distribución de reactivos y retroalimentación obtuvieron 4,00/4. Se
concluye que el instrumento presenta coherencia curricular y metodológica
suficiente para su implementación piloto, aunque su efectividad sobre el
aprendizaje deberá comprobarse en una aplicación posterior.
Palabras clave: evaluación diferenciada; evaluación formativa; Quizizz; función
logarítmica; Bachillerato; tecnología educativa.
Introduction
Contemporary educational assessment is conceived as
a process of gathering and interpreting evidence to guide pedagogical
decisions, beyond the assignment of a grade. Formative assessment takes on
special importance when the evidence gathered allows for providing feedback to
students and adjusting instruction (Black & Wiliam, 1998; Cruzado Saldaña,
2022; Boström & Palm, 2023). Within this framework, differentiated
assessment seeks to recognize different paces and levels of performance through
instruments capable of offering equivalent opportunities to demonstrate
learning (Díaz, 2021).
In mathematics, this need is particularly acute in
content that requires integration among symbolic, graphical, and contextualized
representations. The logarithmic function requires linking prior knowledge of
exponents and exponential functions to properties, domain, graphical
representation, and modeling. Studies on learning functions have documented
difficulties in connecting different forms of representation and solving
modeling tasks, while also highlighting the value of strategies that promote
understanding and contextualization (Araújo et al., 2022; Viseu et al., 2022;
Hernández Martínez et al., 2022).
Digital platforms can complement formative
assessment by facilitating interaction, response tracking, and immediate
feedback. In particular, Quizizz has been studied as a resource for
strengthening participation, motivation, and assessment in mathematics,
although its usefulness depends on the pedagogical purpose and the quality of
the items (Farfán-Pimentel et al., 2023; Hernanz et al., 2024; Balbi et al., 2024; Muchuweni et al., 2025).
At the “Ciudad de Caracas” Educational Unit, the
preliminary assessment revealed a predominance of written exams, limited use of
technology, and difficulties with procedures, graphing, and problem-solving
related to the logarithmic function. Therefore, the objective of this study was
to design and validate a differentiated assessment instrument using Quizizz,
structured by performance levels, to evaluate curricular skill M.5.1.75 in
second-year students of the Unified General High School program.
Materials and methods
An applied research study with a
descriptive-propositional scope was conducted. The diagnostic phase was carried
out with second-year students in the Unified General High School program at the
“Ciudad de Caracas” Educational Unit in Ecuador. A total of 120 students
participated. Complementary sources included an interview with a mathematics
teacher, a classroom observation, and the results of a diagnostic assessment.
Four sources of information were used: (a) a
10-question student survey on assessment practices, difficulties with
logarithmic functions, feedback, and attitudes toward digital platforms; (b) a
semi-structured interview with the teacher; (c) a classroom observation form
with 10 indicators; and (d) a pre-test diagnostic assessment. The analysis was
descriptive, using frequencies and percentages. The triangulation of these
sources allowed for the construction of a needs matrix that guided the design
of the assessment instrument.
The instrument was aligned with skill M.5.1.75 and
indicator I.M.5.3.5 (I.3). Twelve items were designed in Quizizz and
distributed progressively: four at the basic level, four at the intermediate
level, and four at the advanced level. Content validation was conducted through
expert judgment by three experts, who rated ten criteria on a scale from 1 (not
relevant) to 4 (very relevant). Averages were calculated for each criterion and
an overall average was determined. Qualitative observations were used to adjust
time limits and instructions.
Figure 1. Methodological structure of the differentiated
assessment instrument. Developed based on the thesis project.
Results
The survey revealed a predominantly traditional
assessment practice: all 120 students indicated that math assessments are
always conducted through written tests and that technological resources are
never used for assessment. Furthermore, 89.17% noted that exercises with
varying levels of difficulty appear only occasionally, and 10.83% indicated
that they are never included. Classroom observations were consistent with this
pattern: written tests predominated, the use of technology for assessment was
nonexistent, and contextualized problems appeared rarely.
Figure 2. Selected diagnostic findings. The percentages
correspond to different indicators and are not mutually exclusive categories.
The perceived difficulty was high: 58.33% rated the
difficulty of learning the logarithmic function as very high, 20.83% as high,
and 20.83% as moderate. Regarding the type of difficulty, 48.33% identified
mathematical procedures and 42.50% identified graphs and problems; only 9.17%
cited properties as the main difficulty. These results are consistent with the
literature describing difficulties in articulating representations and
developing modeling processes when learning functions (Araújo et al., 2022; Viseu
et al., 2022).
There was broad acceptance of differentiated
assessment: 83.33% strongly agreed and 16.67% agreed with organizing assessment
by levels; 100% considered immediate feedback useful. Furthermore, all students
reported not having previously used Quizizz or any other digital platform for
assessment, but expressed a favorable view of interactive platforms and of
Quizizz for level-based assessment. This contrast between limited technological
experience and high willingness reinforces the importance of guided
implementation, without assuming that the digital tool alone will lead to
improvements. This caution aligns with Balbi et al. (2024), who emphasize that
technology must be integrated into a coherent instructional design.
Table 2. Technical organization of the 12 items by performance levels.
|
Nivel |
Reactivos |
Desempeño esperado |
Tipo / tiempo |
|
Básico |
1–4 |
Reconocimiento
de la función logarítmica, base, dominio, restricciones y propiedades
básicas. |
Opción
múltiple; 45 s por ítem |
|
Intermedio |
5–8 |
Aplicación de propiedades, procedimientos, dominio,
ceros e interpretación gráfica. |
Selección múltiple / respuesta matemática; 120–180 s |
|
Avanzado |
9–12 |
Análisis,
resolución y modelación de situaciones contextualizadas. |
Problemas
contextualizados / respuesta numérica; hasta 5 min |
The progressive structure integrates conceptual
understanding, procedural application, and interpretation/modeling. The use of
Quizizz is intended as a means to digitize the items, record responses, and
support feedback—not as a substitute for teacher judgment. The proposal also
includes a matrix showing the alignment between skills, curriculum indicators,
assessment criteria, performance levels, and evidence generated by the
platform.
The assessment identified a gap between current
assessment practices and the needs expressed by students. Written tests
predominated, and technology was largely absent from assessment, while the
greatest difficulties with logarithmic functions were concentrated in
procedures, graphical interpretation, and problem-solving.
The methodological response was a 12-item assessment
tool aligned with skill M.5.1.75 and organized into basic, intermediate, and
advanced levels. This structure allows for linking types of evidence to
different degrees of cognitive complexity and provides a basis for
differentiated feedback.
The evaluation by three experts yielded an overall
average of 3.77/4 and allowed for specific adjustments to clarity and
completion time. Consequently, the instrument provides preliminary evidence of
curricular, mathematical, methodological, and technological relevance for a
pilot application.
The main limitation is that the instrument has not
yet been used as an intervention to measure changes in learning. Future
research should examine its reliability, item performance, performance by
level, and potential effects on learning through pretest–posttest or
comparative designs, in addition to considering connectivity conditions and
access to devices.
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Universidad
Bolivariana del Ecuador (UBE), Ecuador
Universidad
Bolivariana del Ecuador (UBE), Ecuador
Universidad
Bolivariana del Ecuador (UBE), Ecuador
0000-0002-8876-1896
Universidad
Bolivariana del Ecuador (UBE), Ecuador
0009-0005-7040-7249