Articles
Multilevel
Planning for Strengthening Mathematical
Competencies in Rural Primary Education
Planeación
multinivel y fortalecimiento de competencias
matemáticas en educación primaria rural
Itzel Natalia Lendechy Velázquez 1
ORCID:
https://orcid.org/0000-0002-1672-9061
Jessica Garizurieta Bernabe 2
ORCID:
https://orcid.org/0000-0002-1443-4737
Universidad
Veracruzana, Sistema de Enseñanza Abierta (SEA). Xalapa-México 1
Universidad
Veracruzana, Facultad de Contaduría y Administración. Xalapa-México 2
Corresponding autor
jgarizurieya@uv.mx
Received: 25-06-2026
Accepted: 19-10-2026
Available online: 20-10-2026
Abstract
The objective of
the study was to analyze the effect of an intervention based on multilevel
planning on strengthening basic mathematical competencies among fifth- and
sixth-grade students at a rural primary school in Veracruz, Mexico. The
research was conducted using a mixed-methods approach, with an action research
design and a quasi-experimental scope involving measurements before and after
the intervention. Thirty-nine students who completed both assessments
participated in the study. Over ten weeks, a workshop-based course was implemented
using differentiated activities, manipulatives, constructivist strategies, and
contextualized problem-solving tasks. Data were collected through a pretest,
posttest, classroom observations, teacher interviews, and monitoring logs. The
results showed a significant increase in mathematical performance, accompanied
by improvements in participation, autonomy, and confidence in solving problems.
These findings indicated that organizing instruction through different levels
of support and complexity promoted learning in heterogeneous groups. It was
concluded that multilevel planning constitutes a relevant pedagogical strategy
for strengthening basic mathematical competencies and helping reduce learning
gaps in rural contexts.
Keywords: Mathematical competencies, multilevel planning, primary education,
pedagogical intervention, rural education.
Resumen
El objetivo del estudio fue analizar el efecto de una intervención
basada en planeación multinivel sobre el fortalecimiento de las competencias
matemáticas básicas en estudiantes de quinto y sexto grado de una escuela
primaria rural de Veracruz, México. La investigación se desarrolló mediante un
enfoque mixto, con diseño de investigación-acción y alcance cuasi experimental
con mediciones antes y después de la intervención. Participaron 39 estudiantes
que completaron ambas evaluaciones. Durante diez semanas se implementó un
curso-taller con actividades diferenciadas, recursos manipulativos, estrategias
constructivistas y resolución de problemas contextualizados. La información se
obtuvo mediante pretest, post-test, observación de aula, entrevistas a docentes
y bitácoras de seguimiento. Los resultados evidenciaron un incremento
significativo en el desempeño matemático, acompañado de mejoras en la participación,
la autonomía y la confianza para resolver problemas. Estos hallazgos indicaron
que la organización de la enseñanza mediante distintos niveles de apoyo y
complejidad favoreció el aprendizaje en grupos heterogéneos. Se concluyó que la
planeación multinivel constituye una estrategia pedagógica pertinente para
fortalecer las competencias matemáticas básicas y contribuir a disminuir el
rezago en contextos rurales.
Palabras clave: Competencias matemáticas,
planeación multinivel, educación primaria, intervención pedagógica, educación
rural.
Introduction
Mathematics learning during
primary education is an essential process for the development of logical
reasoning, information interpretation, and the ability to solve problems
encountered in everyday life. Beyond mastering algorithms, mathematical
competencies involve understanding numerical relationships, selecting
appropriate procedures, justifying answers, and transferring knowledge to new
situations. These abilities provide the foundation for subsequent learning and
for individuals’ active participation in different social contexts. However,
international assessments continue to show that a substantial proportion of
students experience difficulties in reaching satisfactory levels of
mathematical performance. The results of PISA 2022 indicate a decline in
performance compared with previous cycles and show that gaps associated with
socioeconomic background remain one of the main challenges faced by education
systems (OECD, 2023).
In Mexico, the 2022 Curriculum incorporates
mathematical thinking into the formative field of Knowledge and Scientific
Thinking and proposes that students construct knowledge through
problem-solving, argumentation, and the analysis of contextualized situations
(SEP, 2022). Nevertheless, teaching practice continues to rely heavily on
activities focused on the repetition of procedures and the memorization of
rules, with limited opportunities to promote conceptual understanding. Several
studies indicate that learning improves when students participate actively,
explain procedures, analyze errors, and develop cognitive strategies for
solving problems (Son et al., 2020).
Basic mathematical competencies
integrate numerical knowledge, procedures, and reasoning skills that enable
students to interpret information and respond to diverse situations. During
primary education, students are expected to consolidate fundamental operations,
fractions, decimal numbers, elementary geometry, and problem-solving. These
competencies support later learning; therefore, difficulties that arise at this
stage tend to accumulate and negatively influence future academic performance
(OECD, 2023). From a constructivist perspective, such learning is strengthened
when students reorganize their prior knowledge through interaction with
materials, peers, and teachers in environments where the explanation and
discussion of procedures form part of the teaching process. In this regard,
Bermejo et al. (2021) demonstrated that constructivist interventions support
mathematical performance when content is presented progressively and teachers
act as mediators of learning.
Within this approach,
problem-solving constitutes a central instructional strategy because it
promotes the interpretation of information, the selection of procedures, and
the justification of results. Rather than being viewed solely as an application
activity, it serves as a means of developing conceptual understanding and
autonomy. According to Son et al. (2020), teaching approaches that incorporate
problem-solving and active student participation produce significant
improvements in mathematical performance. Likewise, the meta-analysis conducted
by Vessonen et al. (2025) found that interventions are more effective when they
include a structured instructional sequence, teacher support, and consistent
implementation.
The need to strengthen these
competencies is particularly relevant in rural schools, where socioeconomic
conditions, the availability of educational resources, and opportunities for
family support are often heterogeneous. UNESCO (2023) states that responding to
these differences requires inclusive pedagogical approaches capable of adapting
instruction to students’ characteristics. In this context, multilevel planning
is a strategy that organizes a common learning objective through activities
with different levels of support and complexity, allowing all students to
engage with the same content without lowering learning expectations. This
approach shares principles with differentiated instruction, which adjusts resources,
processes, and forms of participation to respond to classroom diversity. Bal
(2023) found that such strategies can improve both mathematical achievement and
attitudes toward the subject when activities address students’ learning needs.
Although research has examined
differentiated instruction, problem-solving, and constructivist learning, the
available evidence on pedagogical interventions that integrate these components
through multilevel planning in rural primary education remains limited, particularly
in the Mexican context. Most studies analyze these strategies independently or
in urban settings; therefore, evidence concerning their combined application in
rural schools with heterogeneous groups is still scarce. Rather than confirming
an absolute knowledge gap, this situation highlights the need to document
contextualized experiences that help explain how such approaches can be
implemented under real teaching conditions.
At José María Morelos y Pavón
Primary School, located in Acajete, Veracruz, an institutional assessment
conducted at the beginning of the school year through a mathematical competency
test administered to fifth- and sixth-grade students showed an average of 9.21
correct answers out of a maximum of 30 items, equivalent to 30.68% performance.
The greatest difficulties were found in fractions, decimal numbers, and
contextualized problem-solving. These results indicated low performance in
basic mathematical competencies rather than educational underachievement in a
broader sense and justified the implementation of a pedagogical intervention
aimed at strengthening these areas of learning.
Based on the foregoing, the
objective of the present study was to evaluate changes in the basic
mathematical competencies of fifth- and sixth-grade students at a rural primary
school after a pedagogical intervention based on multilevel planning.
Methodology
The study employed a
mixed-methods approach with a quantitative emphasis and a complementary
qualitative component. The quantitative component followed a one-group
pre-experimental design with pretest and posttest measurements, as all
participants received the workshop-based intervention and no comparison group
or random assignment was available. Accordingly, the design made it possible to
assess changes in basic mathematical competencies between the pretest and
posttest; however, it did not allow those changes to be attributed exclusively
or causally to the intervention. The qualitative component was used to broaden
the interpretation of the quantitative findings through information related to
participation, autonomy, collaborative work, academic confidence,
problem-solving strategies, and persistent difficulties.
The study was conducted during
the 2024–2025 academic year at José María Morelos y Pavón Primary School, which
belongs to Xalapa-Foráneas School Zone 012 and is located in Acajete, Veracruz,
Mexico. The school had an enrollment of 141 students distributed across 11
classes from first through sixth grade. The eligible population consisted of 48
fifth- and sixth-grade students: 10 from Grade 5, Group A; nine from Grade 5,
Group B; 14 from Grade 6, Group A; and 15 from Grade 6, Group B. A
non-probability purposive sampling procedure was used because these grades
represent the final stage of primary education, during which students are
expected to consolidate fundamental operations, fractions, decimal numbers,
elementary geometry, and problem-solving skills before entering secondary
education.
Of the 48 students initially
considered, 45 produced valid pretest records, and 39 completed both the
intervention and the two assessments. The three students without valid
diagnostic records were not included in the initial database, whereas six of
the 45 students assessed at baseline did not complete the posttest because of
absences or changes in school attendance during the final assessment period.
The statistical analysis was therefore conducted exclusively with the 39
matched cases included in the comparative database. These participants
represented 86.7% of those who completed the pretest and 81.3% of the initially
selected population, as shown in Table 1.
Table 1
Participant flow throughout the study
|
Stage
|
Students
|
Percentage of
the initial population
|
|
Students
initially selected
|
48
|
100.0%
|
|
Students with a
valid pretest
|
45
|
93.8%
|
|
Students with
complete pretest and posttest data
|
39
|
81.3%
|
|
Records excluded
from the paired analysis
|
9
|
18.7%
|
Source. Authors’
own elaboration. Three students did not have a valid diagnostic record, and six
did not complete the final assessment.
As shown in Table 2, the
analytical sample consisted of eight students from Grade 5, Group A; eight from
Grade 5, Group B; 11 from Grade 6, Group A; and 12 from Grade 6, Group B. All
39 participants included in the final analysis attended 100% of the scheduled
workshop sessions. Age and sex were not collected during data gathering and
were therefore not included in the sample characterization. The four classroom
teachers also participated through semi-structured interviews.
Table 2
Distribution
of the analytical sample by grade and class group
|
Grade and group
|
Frequency
|
Porcentage
|
|
5.º A
|
8
|
20.5%
|
|
5.º B
|
8
|
20.5%
|
|
6.º A
|
11
|
28.2%
|
|
6.º B
|
12
|
30.8%
|
|
Total
|
39
|
100.0%
|
Source. Authors’
own elaboration based on the matched cases.
The inclusion criteria were enrollment
in fifth or sixth grade, parental authorization and student assent,
participation in the sessions, and availability of complete scores for both
assessments. Cases without either a pretest or posttest score were excluded
from the analysis. The baseline mean for the 45 students who completed the
initial assessment was 9.24 points, whereas the corresponding mean for the 39
matched cases was 9.21 points. The difference of 0.03 points indicated that
participant attrition did not substantially alter the initial group mean,
although the possibility of attrition bias could not be completely ruled out.
Quantitative measurement was
conducted using a 30-item test developed specifically for the study. The
characteristics of the instrument are presented in Table 3. The test was
administered face-to-face in paper-and-pencil format. Responses were
subsequently entered into Google Forms and exported to Microsoft Excel. Each
correct answer was awarded one point, whereas incorrect or unanswered items
received zero points, resulting in a possible total score ranging from 0 to 30.
Table 3
Test
specifications for mathematical competencies
|
Area assessed
|
Content included
|
Items
|
Possible score
|
|
Numbers and basic operations
|
Number reading, rounding, ordering, addition, and
subtraction
|
1-5
|
0-5
|
|
Multiplication
|
Algorithms, mental calculation, error
identification, and application
|
6-10
|
0-5
|
|
Division
|
Algorithms, remainders, verification, and sharing
problems
|
11-15
|
0-5
|
|
Fractions and decimals
|
Equivalence, ordering, conversion, and operations
|
16-20
|
0-5
|
|
Geometry and measurement
|
Shapes, perimeter, area, and unit conversion
|
21-25
|
0-5
|
|
Integrated problems
|
Selection and combination of operations
|
26-30
|
0-5
|
|
Total
|
|
30
|
0-30
|
Source. Authors’
own elaboration based on the research instrument.
Three performance levels were
established to interpret the scores: low, from 0 to 17 points; medium, from 18
to 23 points; and high, from 24 to 30 points. These categories served a
descriptive purpose and were not intended as individual diagnostic
classifications.
Before its final administration,
the test was piloted with 20 students whose characteristics were similar to
those of the target population. The pilot study made it possible to revise the wording
of several items. Internal consistency in the pilot administration was α = .84.
Cronbach’s alpha was .91 for the pretest and .80 for the posttest.
The test was also reviewed by
three specialists in mathematics education and educational assessment, who
evaluated the clarity, relevance, and alignment of the items. Interrater
agreement reached a Fleiss’ kappa of κ = .81, which was interpreted as almost
perfect agreement according to Landis and Koch (1977). Pretest item difficulty
indices ranged from .00 to .62, with a mean of .31, while corrected item–total
correlations ranged from .21 to .75, with a mean of .48. Item 18 received no
correct responses and therefore lacked sufficient variability to estimate its
discriminatory capacity. Its revision was consequently considered necessary for
future applications.
Qualitative information was
collected through direct observation, weekly field logs, and semi-structured
interviews with the four classroom teachers. The observations focused on
students’ comprehension of instructions, mathematical procedures, reliance on
manual counting, selection of operations, review of results, concentration,
confidence in participating, and collaboration with peers. The field logs
documented the difficulties encountered, the progress observed, and the
adjustments introduced during the sessions.
The interview guide consisted of
11 questions addressing mathematical performance, recurring errors,
instructional strategies, motivation, attendance, family support, and the need
for educational resources. This information complemented the diagnostic
assessment and informed the selection of intervention content and support
strategies.
As shown in Table 4, the
intervention consisted of a 10-week workshop-based course implemented by the
lead researcher with support from the classroom teachers. One session per week
was conducted in each of the four groups, resulting in 10 sessions per group
and 40 group-based sessions overall. Session length was adjusted according to
the objectives established for each week. In lesson plans that included a
detailed time allocation, sessions consisted of 15 to 20 minutes of activation
activities, approximately 60 minutes of development, and 20 minutes of closure
or conceptual introduction.
Table 4
Organization
of the workshop-based intervention
|
Weeks
|
Purpose
|
Content
|
Strategies
|
|
1-4
|
Consolidate basic operations and understand
remainders
|
Addition, subtraction, multiplication, division,
grouping, and remainders
|
Formative assessment, modeling, mental calculation,
linked exercises, and sharing problems
|
|
5-8
|
Broaden students’ understanding of numbers
|
Fractions, equivalence, operations with fractions,
decimals, and place value
|
Manipulatives, graphic representations, progressive
exercises, and collaborative work
|
|
9-10
|
Integrate learning
|
Measurement, decimal numbers, perimeter, area, and
integrated problems
|
Problem-solving, graphic representation, guided
review, and independent work
|
Source. Authors’
own elaboration based on the workshop lesson plans.
Multilevel planning maintained
common learning objectives while varying the degree of support, the number of
exercises, and the complexity of the tasks. Students who experienced greater
difficulties received step-by-step modeling, worked examples, concrete
resources, and visual support. Students with an intermediate level of mastery
completed activities with less guidance and were required to explain their
procedures, whereas those demonstrating more advanced performance solved
integrated problems and completed tasks requiring mathematical argumentation
and knowledge transfer.
Support was assigned flexibly on
the basis of pretest performance, classroom observations, and students’
performance in each area of content. In fifth grade, greater emphasis was
placed on modeling and reinforcing basic operations. During the fourth week,
both fifth-grade groups received extended support in grouping, multiplication,
division, and interpretation of remainders. In the final integrative activity,
fifth-grade students solved one comprehensive problem, whereas sixth-grade
students completed two problems combining operations, fractions, decimals,
measurement, and geometry.
Implementation fidelity was
documented through lesson plans, field logs, and evidence of the activities
completed. The records included the objectives, content, strategies,
difficulties encountered, and instructional adaptations implemented. No
standardized fidelity scale was administered, and no quantitative fidelity
percentage was calculated; therefore, implementation monitoring was based on
systematic documentary review.
The quantitative analysis was
conducted using the 39 matched cases. Frequencies, percentages, means, medians,
standard deviations, and minimum and maximum values were calculated. The
normality of the difference scores was examined using the Shapiro–Wilk test.
The result, 
, 
, supported the use of a paired-samples
Student’s 
test, with statistical significance
established at 
.
The magnitude of change was
estimated using Cohen’s 
, which is appropriate for repeated
measurements. The mean difference was 7.79 points, and the standard deviation
of the difference scores was 6.08, resulting in 
. The database was organized in Microsoft Excel,
and inferential analyses were performed using IBM SPSS Statistics, version 29.
The qualitative analysis followed
a descriptive thematic procedure. Meaning units were grouped into five
categories: participation, autonomy, collaboration, attitudes toward mathematics,
and problem-solving. The interviews, observations, and field logs were
subsequently compared to identify similarities and differences. Integration was
conducted by relating quantitative changes to qualitative records indicating
reduced reliance on manual counting, greater confidence, improved selection of
operations, and increased autonomy.
Before the intervention began,
authorization was obtained from the school authorities. With their support,
parents and legal guardians were invited to a meeting at which the study
objectives, activities, instruments, voluntary nature of participation, and
confidential use of the information were explained. Those who authorized
participation signed an approval agreement. Students received an
age-appropriate explanation of the study and provided their assent. The data
were coded and reported in aggregate form, and the authorization documents
remained under the custody of the school.
Results
The results comprised descriptive and inferential
analyses of the 39 matched cases, together with qualitative information derived
from classroom observations, teacher interviews, and field logs.
Pretest Results
As shown in Table 5, the 39
students obtained a mean score of 9.21 correct responses out of a maximum of
30, equivalent to an average performance level of 30.68%. The standard
deviation of 5.85 indicated considerable variability across scores, which
ranged from 0 to 21 correct responses. These findings reflected a limited
initial level of mastery of the competencies assessed.
Table 5
Descriptive
results of the pretest
|
Indicator
|
Result
|
|
Valid participants
|
39
|
|
Maximum possible score
|
30
|
|
Mean
|
9.21
|
|
Standard deviation
|
5.85
|
|
Median
|
9.00
|
|
Minimum score
|
0
|
|
Maximum score obtained
|
21
|
|
Mean performance percentage
|
30.68%
|
Source: Authors’
own elaboration based on the matched cases.
Regarding performance levels, 34
students were classified at the low level and five at the intermediate level;
none reached the high level. The responses revealed greater difficulties in
fractions and decimal numbers, geometry, measurement, and integrated problems.
Observations conducted during the diagnostic assessment also documented
reliance on manual counting, errors in organizing algorithms, limited answer
checking, and insecurity when addressing problems involving multiple
instructions.
Posttest Results
At the end of the 10-week
intervention, the same test used for the initial assessment was administered
again. As shown in Table 6, the mean score increased to 17.00 correct
responses, equivalent to 56.67% of the maximum possible score. The standard
deviation was 5.12, and scores ranged from 9 to 26. The median score of 16
indicated that half of the students obtained at least this score.
Table 6
Descriptive
results of the posttest
|
Indicator
|
Result
|
|
Valid participants
|
39
|
|
Maximum possible score
|
30
|
|
Mean
|
17.00
|
|
Standard deviation
|
5.12
|
|
Median
|
16.00
|
|
Minimum score
|
9
|
|
Maximum score obtained
|
26
|
|
Mean performance percentage
|
56.67%
|
Source: Authors’
own elaboration based on the results of the 39 matched cases.
The most evident improvements
were observed in the use of multiplication and division, the interpretation of
remainders, and the selection of appropriate operations to solve problems.
Nevertheless, the activities and field logs showed that fractions and decimal
numbers continued to present difficulties, particularly when tasks required
students to establish equivalences, perform conversions, or combine procedures.
Performance Comparison
As shown in Table 7, all groups
increased their scores. The largest mean changes were found in Grade 5, Group A
and Grade 5, Group B, which had also recorded the lowest initial means.
Table 7
Results by
grade and group
|
Grade and group
|
n
|
Pretest mean
|
Posttest mean
|
Mean change
|
|
5.º A
|
8
|
6.88
|
17.50
|
10.63
|
|
5.º B
|
8
|
3.38
|
12.50
|
9.13
|
|
6.º A
|
11
|
10.45
|
18.18
|
7.73
|
|
6.º B
|
12
|
13.50
|
18.58
|
5.08
|
|
Total
|
39
|
9.21
|
17.00
|
7.79
|
Source:
Authors’ own elaboration based on the comparative dataset for the 39
participants.
The mean score increased from
9.21 to 17.00 correct responses, representing a difference of 7.79 points and
an increase of 25.99 percentage points in average performance. Table 8 presents
the overall comparison.
Table 8
Comparison of overall mean performance
|
Assessment
|
Mean number of correct responses
|
Performance percentage
|
|
Pretest
|
9.21 de 30
|
30.68%
|
|
Posttest
|
17.00 de 30
|
56.67%
|
|
Difference
|
7.79
|
25.99 percentage points
|
Source: Authors’
own elaboration based on the 39 matched cases.
Changes were also observed in the
distribution across performance levels. As shown in Table 9, 34 students were
classified at the low level and five at the intermediate level in the pretest.
After the intervention, 23 students remained at the low level, 10 were
classified at the intermediate level, and six reached the high level.
Accordingly, the proportion of students at the low level decreased by 28.2
percentage points, whereas the proportions at the intermediate and high levels
increased by 12.8 and 15.4 percentage points, respectively.
Table 9
Comparison
of performance levels
|
Level
|
Pretest, n (%)
|
Posttest, n (%)
|
Percentage-point difference
|
|
Low
|
34 (87.2%)
|
23 (59.0%)
|
−28.2
|
|
Intermediate
|
5 (12.8%)
|
10 (25.6%)
|
+12.8
|
|
High
|
0 (0.0%)
|
6 (15.4%)
|
+15.4
|
|
Total
|
39 (100%)
|
39 (100%)
|
—
|
Source: Authors’
own elaboration. Performance levels were classified as low, from 0 to 17
points; intermediate, from 18 to 23 points; and high, from 24 to 30 points.
The descriptive results showed a
shift toward higher performance categories. However, given the one-group
pre-experimental design, these changes should be interpreted as differences
observed after the intervention rather than as definitive causal evidence.
Inferential Analysis
The Shapiro–Wilk test did not
indicate a statistically significant departure from normality, , . The mean score increased from 9.21 points on
the pretest (
) to 17.00 points on the posttest (
). The mean difference was 7.79 points (
), with a 95% confidence interval ranging from
5.82 to 9.77. The paired-samples test confirmed a statistically significant
difference between the two assessments, 
, 
.
The magnitude of change was
large, . Although this value indicated practical
relevance, the pre-experimental design did not allow the intervention to be
identified as the sole cause of the observed difference.
Table 10
Inferential comparison between pretest and posttest scores
|
Indicator
|
Result
|
|
n
|
39
|
|
Pretest
mean
|
9.21
|
|
Pretest
standard deviation
|
5.85
|
|
Posttest
mean
|
17.00
|
|
Posttest
standard deviation
|
5.12
|
|
Mean
difference
|
7.79
|
|
Standard
deviation of the difference scores
|
6.08
|
|
95%
confidence interval
|
[5.82, 9.77]
|
|
t
|
8.01
|
|
Degrees
of freedom
|
38
|
|
p
|
<
.001
|
|
Cohen’s 
|
1.28
|
Source: Authors’
own elaboration based on the analysis of the 39 paired observations.
Qualitative Findings
The observations, teacher
interviews, and field logs made it possible to identify changes in
participation, autonomy, collaboration, attitudes toward mathematics, and
problem-solving. Because the records were descriptive rather than verbatim
transcripts, the findings are presented as analytical summaries.
Table 11
Summary of qualitative findings
|
Category
|
Initial
situation
|
Changes
observed
|
Persistent
difficulties
|
|
Participation
|
Insecurity and
limited involvement
|
Greater
willingness to respond and explain
|
Uneven
participation in complex tasks
|
|
Autonomy
|
Dependence on
the teacher and manual counting
|
More independent
problem-solving and greater review of procedures
|
Continued need
for modeling in abstract content
|
|
Collaboration
|
Limited
interaction
|
Increased peer
support and exchange of strategies
|
Dependence on
higher-performing students
|
|
Attitudes toward
mathematics
|
Fear of making
mistakes and low confidence
|
Greater
confidence and interest in contextualized activities
|
Insecurity
regarding fractions and decimals
|
|
Problem-solving
|
Difficulty
interpreting instructions and selecting operations
|
Improved
identification of data and procedures
|
Problems involving
multiple conditions and conversions
|
Source: Authors’ own elaboration based on classroom
observations, teacher interviews, and field logs.
The qualitative findings were
consistent with the increase in scores, as they indicated greater participation,
autonomy, and confidence. However, they also showed that progress was not
uniform across all areas. Fundamental operations and some contextualized
problems showed clear improvements, whereas fractions and decimal numbers
continued to require greater instructional support. The findings should
therefore be interpreted in light of the contextual nature of the study and the
absence of a comparison group.
Discussion
The findings suggest that the
observed improvement was not limited to a quantitative shift in test scores,
but also involved a transformation in the way students engaged with
mathematical activity. The increase in the overall mean, together with
observational evidence of reduced reliance on manual counting, greater
willingness to participate, and increased confidence in explaining procedures,
suggests that the intervention influenced both procedural mastery and the
progressive appropriation of mathematical reasoning practices. This
interpretation is consistent with Bermejo et al. (2021), who documented that
constructivist interventions in mathematics yield better outcomes when students
assume an active role, teachers mediate the learning process, content is
meaningfully sequenced, and classroom work promotes cooperation and contextualization.
There is also a clear connection
with recent literature emphasizing that the quality of mathematics instruction
depends on the underlying structures of classroom practice rather than solely
on visible formats or isolated resources. Given that high-quality mathematics
teaching is organized around five principles cognitive demand, conceptual
focus, student orientation and adaptivity, longitudinal coherence, and enriched
mathematical communication (Prediger et al., 2022) the improvements observed in
this study, particularly in operations, problem interpretation, and oral
participation, may be understood as indications that the intervention succeeded
in simultaneously sustaining several of these principles. This is especially
relevant in heterogeneous groups, particularly because the most consistent
improvement programs do not rely on fragmented actions but rather on coherent
frameworks shared by those responsible for teaching and supporting professional
development processes (Prediger et al., 2024).
In the same vein, the findings
move away from a reductionist understanding of differentiation in which
responding to diversity would imply lowering expectations for students
experiencing greater difficulties. One of the most common distortions of
adaptivity consists of providing low-performing or socially disadvantaged
students with impoverished learning opportunities characterized by low
cognitive demand and an excessive procedural focus (Prediger et al., 2022). The
pattern observed in the present study, however, reflects a different logic:
common content was maintained while levels of support, pacing, materials, and
forms of participation were diversified. This distinction is important because
it helps explain why the improvement was evident not only in the execution of
algorithms but also in the comprehension of instructions and the more
appropriate selection of mathematical operations.
The relevance of these
improvements becomes even more apparent when considered within the
international context. According to the OECD (2023), the recent decline in
mathematics achievement and the strong association between socioeconomic
background and academic performance show that socially disadvantaged students
remain considerably more likely to fail to reach the basic level of
mathematical proficiency. Within this context, the fact that an intervention
implemented in a rural primary school produced such notable descriptive gains
does not, of course, resolve the underlying structural problem. Nevertheless,
it provides evidence that low achievement should not be regarded as a fixed
condition and that the classroom can function as a meaningful space for
pedagogical compensation when consistent instructional mediation is provided.
Another major strength of the
study lies in demonstrating that multilevel planning can function as a strategy
for accessing the curriculum rather than merely as a means of adapting
activities for low-performing students. The increase in the overall mean score
and the movement of students from the low-performance category toward the
intermediate and high levels suggest that the diversification of activities contributed
to academic inclusion. It enabled a greater number of students to remain
engaged in a shared learning experience rather than being symbolically excluded
from the content through homogeneous teaching practices. This finding is
consistent with the principle of student orientation and adaptivity described
by Prediger et al. (2022), according to which teaching should begin with an
assessment of students’ learning levels and lead to instructional decisions
that maintain shared trajectories of progress while responding to heterogeneous
needs.
Particularly noteworthy is that
the improvement observed does not appear to have resulted from a simple
simplification of schoolwork, but rather from a more refined balance between
support and academic demand. The current QuaMath framework emphasizes that
cognitive demand becomes educationally meaningful only when all students are
able to participate in rich mathematical tasks, rather than when complexity is
reserved for only a few learners (Prediger et al., 2022). From this
perspective, the experience described in the study is valuable because it
suggests that multilevel planning was most effective when it did not replace
reasoning with repetition, but instead differentiated students’ entry points
into the content while sustaining understanding through materials,
contextualized activities, and close instructional support.
The field logs, in turn, provide
qualitative corroboration of this process. The transition from an initial
pattern characterized by insecurity, dependence on the teacher, and predominant
use of manual counting toward greater autonomy in solving and explaining tasks,
together with more active collaborative work, is consistent with what has been
described as “enriched mathematical communication.” In this form of
instruction, mathematical discourse is not treated as an ancillary feature, but
rather as a condition for deepening conceptual understanding (Bermejo et al.,
2021; Prediger et al., 2022).
At the same time, the study
itself shows that not all mathematical content responds at the same pace to a
10-week intervention. The fact that fractions and decimal numbers remained
areas of difficulty does not weaken the intervention; rather, it helps clarify
the areas in which its effects appear more immediate and those that require
greater continuity. Recent literature suggests that more abstract mathematical
learning requires longer developmental trajectories, a strong conceptual focus,
and explicit connections among representations, procedures, and meanings. Within
the QuaMath framework, this relates to two dimensions: conceptual understanding
and longitudinal coherence in learning. Both emphasize that practice alone is
insufficient and that continuity must be established across stages,
representations, and uses of mathematical knowledge (Prediger et al., 2022;
Prediger et al., 2024).
From a broader pedagogical
perspective, the study reinforces three instructional decisions that merit
particular attention. The first is to use diagnostic assessment as a genuine
starting point for teaching rather than as a mere entry requirement. The second
is to design tasks that preserve the same curricular horizon for the entire
group while providing differentiated levels of support, representation, and
instructional mediation. The third is to make the communicative dimension of
mathematics more explicit so that explaining, arguing, comparing procedures,
and discussing errors become part of the content itself rather than merely
components of the methodology. These orientations are consistent both with
Mexico’s 2022 Curriculum, which emphasizes contextualization, problematization,
and connections with the community, and with recent research associating better
learning opportunities with high-quality instruction, adaptive support, and
formative monitoring of student progress (SEP, 2022; Prediger et al., 2022).
The rural context should not be
understood solely as a setting characterized by material deprivation, but
rather as an environment in which heterogeneous educational trajectories,
unequal learning paces, varying levels of family support, and institutional
limitations on sustained intensive support intersect. In this respect, perhaps
the study’s main contribution lies in showing that measurable improvement can
be achieved even in a school with accumulated difficulties in mathematics when
the intervention systematically organizes progression, support, and learning
expectations. However, scaling up experiences of this kind requires recognition
that local improvement often depends on a high intensity of instructional work
and carefully designed school-based support, both of which may not always be
structurally available in rural settings.
The OECD (2023) has warned that
education systems providing less timely support to students who fall behind and
reporting greater shortages of teaching staff face more adverse conditions for
sustaining mathematics achievement. This has clear implications for educational
policy, particularly because improvement in schools located in challenging
contexts depends less on standardized solutions than on context-sensitive
development frameworks, school networks, continuous professional learning,
additional resources, and cooperation among research, policy, and practice
(Holzer et al., 2025). This perspective aligns closely with the type of
intervention examined in the present study, which acquires its full meaning
precisely because it begins with a local diagnosis, designs specific forms of
support, and adjusts implementation according to classroom realities.
Therefore, the principal policy implication is not to replicate the workshop
mechanically, but rather to create the conditions that enable more schools to
develop their own responses with technical support, institutional time, and
appropriate materials.
Along the same lines, continuing
teacher education should move away from episodic, short-term workshop formats
and toward more sustained, collaborative models centered on problems of
practice. Large-scale programs with greater potential for sustainability are
those that articulate a shared vision of instructional quality, systematic
professional development, coherent materials, and networks of exchange among
schools and teacher educators (Prediger et al., 2024). The relevance of this
approach for rural contexts is evident: when teachers experience professional
isolation, heterogeneous classrooms, and limited external support,
collaborative networks and shared instructional resources cease to be
supplementary and instead become essential components of pedagogical
infrastructure.
In the case analyzed, the use of
contextualized problems appears to have supported both understanding and
participation. Accordingly, and in line with the 2022 Curriculum, which
explicitly proposes that problem-solving should be grounded in meaningful
contexts and in relationships among family, school, and community, a reasonable
recommendation for future interventions would be to deepen the territorial
contextualization of mathematical tasks and connect it more systematically with
family-based monitoring strategies, particularly in those areas identified as
more fragile in the present study, such as fractions and decimal numbers.
Finally, it is important to
emphasize that this study does not close the discussion regarding the effectiveness
of multilevel planning in rural contexts. Rather, it opens the discussion in a
meaningful way by showing that this approach warrants further examination
through comparative designs, measures of learning retention, and implementation
studies capable of distinguishing more clearly which components account for the
changes observed..
Conclusions
Following the multilevel
planning-based intervention, a statistically significant improvement was
observed in the overall mathematical performance of the 39 students who
completed both assessments. The mean posttest score was higher than the pretest
score, and the magnitude of change was large. These findings addressed the
objective of the study by demonstrating favorable differences between the
measurements conducted before and after the workshop-based intervention.
However, given the one-group pre-experimental design, the observed changes
cannot be attributed exclusively to the intervention.
Within the specific context of
the rural primary school examined, multilevel planning provided a feasible
approach for organizing common content through varying degrees of support,
instructional guidance, and task complexity. Observation records, field logs,
and teacher interviews suggested favorable changes in participation, autonomy,
and academic confidence among some students, although these improvements were
not uniform across all groups or content areas. Because the quantitative
analysis was based on the overall test score, it was not possible to determine
which specific mathematical competency or which component of the intervention
was most strongly associated with the observed improvement.
The findings should be
interpreted in light of the study’s limitations. The research was conducted in
a single institution, with a non-probability sample and no comparison group,
which limits the generalizability of the findings and the possibility of
establishing causal relationships. In addition, the use of the same instrument
for both the pretest and posttest may have produced a familiarity effect, while
regular classroom instruction and student maturation may also have influenced
the results. The 10-week duration of the intervention likewise did not allow
the persistence of the observed changes to be assessed over the medium or long
term.
Future research could incorporate
comparison groups, samples drawn from different rural schools, and follow-up
assessments to examine the stability of the findings over time. It would also
be relevant to analyze performance separately in operations, fractions, decimal
numbers, geometry, and problem-solving, as well as to evaluate the specific
contribution of visual supports, manipulatives, collaborative work, and
contextualized tasks. Such analyses would make it possible to determine more
precisely the scope of multilevel planning and the conditions under which it
may support mathematics learning in primary education.
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Funding
The authors received no funding
for the development of the research.
Conflict
of Interest
The authors declare that they
have no conflicts of interest.
Author
Contributions
The authors contributed to the
development of the manuscript.
