z =3D Estimate <=
/span>Std .=
Error =3D1 y su valor “p”, conside=
rando
p < 0.05, como nivel de significancia.
Validació=
;n
del modelo
Se evaluaron los residuos de Pearson y residuo=
s de
deviance , confirmando media cero y varianza
constante.
La razón , indicó=
un
adecuado ajuste del modelo. Se verificaron los supuestos de independencia de
observaciones y de adecuación de la distribución binomial
negativa para los conteos.
Interpretaci&oa=
cute;n
e implementación
Se identificaron las variables más
influyentes (edad, sexo femenino, comunidad, escolaridad de la madre y del
padre, actividades escolares) sobre la preservación de saberes
matemáticos comunitarios y ancestrales.
Los hallazgos ofrecen una base para el
diseño de secuencias didácticas contextualizadas que integren
instrumentos y prácticas tradicionales en la enseñanza de med=
idas
de longitud.
Los resultados se tradujeron en recomendaciones
pedagógicas, como destacar la comunidad como factor clave, adaptar l=
as
secuencias didácticas para integrar instrumentos y prácticas
tradicionales y orientar políticas educativas interculturales que
valoren los saberes matemáticos comunitarios y ancestrales en el apr=
endizaje
formal.
Desarrollo del
modelo
Modelo de saberes matemáticos comunitar=
ios
y ancestrales sobre longitud. Se plantea un modelo en que la variable respu=
esta
Y1 , es la probabilidad esperada de que se manif=
iesten
conocimientos matemáticos comunitarios y ancestrales acerca de la
longitud, la cual depende de once predictores (X1 a X11 ):
Y1 =3D f (X1 , X2 , X3 ,
X4 , X5 , X6 , X7 , X8 ,
X9 , X10, X11 )
(2)
Donde:
Y1 =3D es el valor esperado de la probabi=
lidad
de ocurrencia de dichos saberes.
n =3D es el total de estudiantes de la muestra=
.
X1 =3D es la edad del estudiante (añ=
;os).
X2 =3D es el sexo (M=3Dmujer; H=3Dhombre)=
.
X3 =3D es la comunidad de origen (valores=
1-9
para distintas localidades).
X4 =3D es el municipio (AXT =3DAcaxochitlán,
ZMP =3DZempoala, PCH =
=3DPachuca).
X5 , X6 , X7 =3D es la actividad económica de la comunid=
ad, de
los padres y de los abuelos, respectivamente (se codifica en categorí=
;as
como agricultura, comercio, ganadería, construcción, hogar,
empleado y sus combinaciones).
X8 , X9 , X10 =
=3D es el
nivel de escolaridad de madre, padre y abuelos (1=3Dprimaria, …,
4=3Dlicenciatura).
X11 =3D es el tipo de actividades escolares
(juntas, fiestas, entrevistas, desayunos, faenas).
Especificación del modelo, se ajusta un=
GLM con distribución binomial negativa y enlac=
e de
raíz cuadrada:
g(μi =
) =3D ni
=3D Xi′β, con E(yi ) =3D μi
(3)
Este enfoque se elige cuando los conteos prese=
ntan
sobredispersión (la varianza supera la m=
edia),
situación en la cual la distribución de Poisson no es adecuad=
a.
La variable dependiente real queda transformada como (=
Yn1+3 )
para evitar ceros o valores negativos al ajustar el modelo. La fórmu=
la
final programando en lenguaje R fue:
β j <=
/i>:
H0 :
H0 :
Estadíst=
ico: .
Si los grados de libertad se aproximan a los
residuales de la desviación indica buen ajuste.
Reducció=
n de
deviance : ((220.57-173.09) /220.57) =3D 0.2152, m=
uestra
una mejora notable al incluir los predictores.
AIC y BIC: <=
/b> métricas
que equilibran ajuste y complejidad; se prefiere el modelo con los valores
más bajos.
Resultados
principales
Intercepto ( : valor de cuando todos los Xj =3D 0.
Edad ( : a mayor edad,
mayor probabilidad de usar esos saberes, ya que Y1 va disminuyendo y se ace=
rca
a la categorización de los saberes sobre longitud: =
Tabla 1
Categorizaci&oa=
cute;n
de los saberes matemáticos ancestrales y comunitarios sobre longitud=
Categor&iacut=
e;a
Significado
Categor&iacut=
e;a
Significado
L1
metro
L36
báscula,
metro, litro
L2
regla
L37
metro,
regla, pies, pasos
L3
flexómetro
L38
mano,
regla, metro, vara
L4
machete
L39
regla,
lazo, cinta, metro
L5
cinta
métrica
L40
metro,
regla, paso, cuerda
L6
pies
L41
metro,
regla, cuerda, lazo
L7
báscula
L42
metro,
regla, paso, lazo
L8
cazo
de carnitas
L43
regla,
metro, pies, cinta métrica
L9
cuarta
L44
regla,
manos, piedras, escoba
L10
sardina
L45
pasos,
regla, metro, cinta métrica
L11
pasos
L46
metro,
pasos, manos, regla
L12
cuartillo,
sardina
L47
metro,
palos, manos, regla
L13
teléfono,
computadora
L48
cinta
métrica, flexómetro, espejos, regla
L14
metro,
kilogramo
L49
metro,
regla, manos, pies
L15
cubeta,
sardina
L50
metro,
regla, cintra métrica, báscula
L16
lazo,
hilo
L51
metro,
regla, cinta métrica, pasos
L17
metro,
regla
L52
regla,
escuadra, lazo, cuarta, vara
L18
metro,
centímetro
L53
metro,
regla, lazo, mano, vara
L19
litro,
cinta métrica
L54
metro,
regla, lazo, mano, vara
L20
metro,
cinta métrica
L55
lazo,
hilo, cinta métrica, metro, vara
L21
regla,
cinta métrica
L56
metro,
regla, paso, cuerda, lazo
L22
metro,
juego geométrico
L57
metro,
regla, cinta métrica, cuartas, pasos
L23
metro,
Báscula
L58
metro,
regla, cinta métrica, flexómetro, manos, lazos =
span>
L24
cinta
métrica, báscula
L59
metro,
regla, cinta métrica, flexómetro, varas, lazos =
span>
L25
metro,
regla, cinta métrica
L60
metro,
regla, piedras, flexómetro, varas, lazos
L26
regla,
cinta métrica, flexómetro
L61
metro,
regla, cinta métrica, flexómetro, varas, piedras =
L27
pasos,
cuarta, metro
L62
metro,
lazo, sardina, cuartillo, kilo, costal
L28
pasos,
regla, dedos
L63
metro,
regla, cinta métrica, brazadas, cuartas, pasos =
p>
L29
regla,
metro, pasos
L64
metro,
regla, cinta métrica, lazos, pasos, piedras
L30
metro,
regla, pies
L65
metro,
pasos, manos, regla, cinta métrica, escuadra
L31
regla,
ramas, metro
L66
metro,
regla, cinta métrica, flexómetro, varas, piedras, lazos
L32
metro,
regla, cuartas
L67
metro,
regla, cinta métrica, pasos, varas, lazos, abrazada
L33
metro,
cinta métrica, pie
L68
metro,
regla, cinta métrica, flexómetro, manos, brazos, palos, laz=
os
L34
cinta
métrica, cuartas, pasos
L69
metro,
regla, cinta métrica, manos, cable, varas, pasos, lazos =
L35
flexómetro,
regla, cinta métrica
Fuente: elaboración propia.
Sexo femenino : las mujeres
presentan un efecto reductor sobre .
Comunidad : las localidad=
es
presentan mayor uso de estos saberes.
Escolaridad de la madre : mayor escolar=
idad
materna aumenta , lo que dismin=
uye
la representatividad de los saberes, de acuerdo=
a la
categorización.
Escolaridad del padre : mayor escolar=
idad
paterna reduce .
Actividades escolares : ciertas
actividades vinculan positivamente los saberes.
Por tanto, el modelo es:
Y 1 <=
/m:sSub>=3D <=
m:sSupPr> =
m:dPr>9.50 2 <=
/m:sSup>=3D90.25 Y 1 <=
/m:sSub>=3D <=
m:sSupPr> =
m:dPr>9.50-0.09 =
10 =
2 <=
/m:sSup>=3D73.96 ( X <=
/i>2 <=
/i>=3D1) y 10 años de edad: Y <=
/i>1 <=
/i>=3D61.62 .
Por tanto, la comunidad es el factor que
más peso tiene para mantener vivos los saberes matemáticos
comunitarios y ancestrales sobre longitud, seguido de la edad el sexo (muje=
res)
y la escolaridad paterna.
DESARROLLO
Antecedentes
La presente investigación se enmarca en=
un
contexto educativo caracterizado por marcadas desigualdades sociales y
limitaciones estructurales. La población objeto de estudio est&aacut=
e;
compuesta por estudiantes de sexto año de educación primaria,
tanto de escuelas generales como indígenas, ubicadas en zonas rurales
del estado de Hidalgo. Estas localidades presentan una baja densidad
poblacional, así como restricciones en el acceso a servicios
básicos, infraestructura y oportunidades educativas, factores que
inciden directamente en el desarrollo de los procesos de enseñanza y
aprendizaje (INEGI, 2020).
La muestra se conformó por 160 estudian=
tes
provenientes de nueve escuelas primarias distribuidas en tres municipios
representativos: Acaxochitlán, Zempoala y Pachuca. En
Acaxochitlán, se seleccionaron cuatro escuelas indígenas (de =
un
total de 23), con 62 estudiantes; en Zempoala, cuatro escuelas generales (de
28) aportaron 77 estudiantes; y en Pachuca, una escuela general ubicada en =
una
comunidad rural participó con 21 estudiantes. Esta muestra se extraj=
o de
una población total estimada de 134 escuelas y 5421 estudiantes de s=
exto
grado, lo que garantiza una representación diversa en términos
culturales, lingüísticos y socioeconómicos. <=
/span>
El estudio se fundamenta en la necesidad de
reconocer e integrar los saberes comunitarios y ancestrales en la
enseñanza formal de las matemáticas, particularmente en lo que
respecta a las medidas de longitud. La propuesta didáctica implement=
ada
se sustenta en la teoría de situaciones didácticas de Michele
Artigue, la cual favorece la construcción activa del conocimiento a
través de situaciones contextualizadas que promueven la reflexi&oacu=
te;n
y el diálogo matemáticos. Esta metodología se
organizó en cuatro etapas: detección, puesta en escena,
explotación y análisis/consolidación (Artigue, 1995).<=
o:p>
Para la recolección de la
información se emplearon técnicas cualitativas y cuantitativa=
s,
tales como entrevistas semiestructuradas y cuestionarios de respuesta abier=
ta,
permitiendo explorar las percepciones, experiencias y conocimientos previos=
de
los estudiantes (Lesh y Do=
err ,
2003) (Katayama, 2014). Durante la implementación de la secuencia
didáctica, se observó un alto nivel de participación
interés y apropiaciones de los contenidos por parte del alumnado,
especialmente en aquellas actividades que involucran instrumentos de
medición tradicionales como la vara, el lazo, la cuerda y otros obje=
tos
utilizados cotidianamente en sus comunidades.
Asimismo, las entrevistas con docentes y
directivos escolares revelaron una actitud favorable hacia la
incorporación de estrategias pedagógicas innovadoras que resp=
eten
los marcos normativos locales y respondan a las características
particulares de cada comunidad. La experiencia acumulada permitió af=
inar
tanto la secuencia didáctica como los instrumentos de evaluaci&oacut=
e;n,
consolidado una base de datos de 160 estudiantes y 11 variables (edad, sexo,
comunidad, municipio, actividad económica de la comunidad, padres y
abuelos, escolaridad de la madre, del padre y de los abuelos y las activida=
des
escolares).
RESULTADOS
En este estudio se documentaron los saberes
matemáticos comunitarios y ancestrales relacionados con la
medición de longitud en una muestra de 160 estudiantes y sus familia=
s.
La información recopilada incluye veintiocho variables que abarcan c=
aracterísticas
demográficas, contextuales y culturales, así como los diferen=
tes
instrumentos de medición, convencionales y tradicionales, utilizados=
por
los estudiantes, sus padres y abuelos.
Descripción de la base de datos, la bas=
e de
datos en la cual se basó el modelo consta de 160 registros (estudian=
tes)
y 28 variables:
Demográf=
icas
y contextuales: edad, sexo, comunidad de origen, municipio.
Actividad
económica: de la comunidad, de los padres y de los abuelos. =
Nivel educativo=
: de padres y
abuelos.
Participaci&oac=
ute;n
escolar:
tipo de actividades en las que los estudiantes participan (juntas, fiestas,
entrevistas, desayunos, faenas).
Instrumentos y
saberes:
para longitud, tanto convencionales (metro, regla, flexómetro, cinta
métrica, Vernier, nivel) como propios de la comunidad (varas, piedra=
s,
lazos, brazadas pasos , palos cuarta, hilos, cuer=
das).
Instrumentos y saberes de longitud, los
participantes utilizan, alternativamente o de forma complementaria instrume=
ntos
de medida convencionales y herramientas heredadas de generaciones anteriore=
s.
Convencionales:=
metro, regla,
flexómetro, cinta métrica, Vernier, nivel. <=
/p>
Tradicionales
Unidades de med=
ida: varas, piedras,
lazos, brazadas (para leña o ramos de flores), pasos, palos, cuarta,
hilo, cuerda, pies (como extremidad).
Aplicaciones: <=
/span> medición=
de
terrenos, tablas, plantas, puertas, troncos, construcciones (casas),
árboles, animales; útiles en faenas agrícolas y de
recolección.
Estás prácticas muestran la
permanencia de conocimientos etnomátematicos,
que, además de resolver necesidades cotidianas refuerzan la identidad
cultural.
Modelo estadístico de saberes de longit=
ud,
para profundizar en los factores que influyen en la manifestación de
estos saberes, se ajustó un modelo lineal generalizado de
distribución binomial negativa con enlace de raíz cuadrada. La
variable respuesta (Y1 ) es la probabilidad de
ocurrencia de los saberes de longitud y se definió en función=
de
once predictoras (X1 a X11=
),
que incluyen edad, sexo, comunidad escolaridad de padres ya vuelos y
actividades escolares entre otros.
En referencia a los resultados del programa en=
R,
en la siguiente tabla se observan las estimaciones de los coeficientes del
modelo. Se presentan los valores estimados, errores estándar, valore=
s z
y significancia estadística (p-valor) Un p-valor indica que el
coeficiente es estadísticamente significativo:
Tabla 2
Resultados del
modelo ajustado de los saberes matemáticos comunitarios y ancestrales
sobre longitud, en R
Variable=
Estimaci&oacu=
te;n
Error
estándar
z <=
/span>
p-valor<=
/o:p>
Intercept
9.50394
0.55521
17.118
< 2e -16<=
/o:p>
Edad
(X1 )
-0.09296
0.02959
-3.141
0.00168
Sexo
(Mujer, X2 )
-0.75965
0.30842
-2.463
0.01378
Comunidad
(X3 )
-1.15418
0.26801
-4.306
1.66e -05
Escolaridad
madre (X8 )
0.44410
0.18269
2.431
0.01507
Escolaridad
padre (X9 )
-0.35721
0.17572
-2.033
0.04207
Actividades
escolares (X11 )
0.48739
0.14872
3.277
0.00105
Fuente: elaboración propia.
Hallazgos
principales
Edad (X1 ): coeficiente negativo y significativo; los saberes se vuelven
más representativos a partir de cierta edad, al integrarse los
estudiantes en labores comunitarias.
Sexo (X2 ): el valor negativo de la variable “mujer” sugiere que l=
as
niñas tienden a retener y aplicar con mayor frecuencia estos saberes=
.
Comunidad (X3 ): el efecto más fuerte y negativo, reflejando que el arraigo
cultural y la identidad son fundamentales para la transmisión de
conocimientos matemáticos tradicionales.
Escolaridad de =
los
padres (X8 , X9 )
La escolaridad materna ejerce un efecto positi=
vo
en el modelo (mayor formación formal tiende a desplazar saberes
tradicionales).
La escolaridad paterna se asocia con un increm=
ento
en la probabilidad de conservar estos saberes.
Actividades
escolares (X11 ): también muestran un impacto
significativo, indicando que la participación en ciertos eventos
escolares puede coincidir con menor uso de los saberes ancestrales, aunque =
este
efecto es complelo de interpretar, posiblemente
ocurre porque la escuela como institución, motiva a los estudiantes a
seguir estudiando en niveles más avanzados, lo que lleva a estos a
desplazarse muchas veces fuera de su comunidad.
Los datos revelan una rica diversidad de saber=
es
matemáticos comunitarios y ancestrales empleados para medir longitud=
es.
La adopción simultánea de instrumentos convencionales y
tradicionales demuestra la flexibilidad de las prácticas etnomatemáticas . Además, las variables =
edad,
sexo, comunidad, escolaridad de los padres y actividades escolares emergen =
como
los principales determinantes de la transmisión y uso de estos saber=
es.
Estos hallazgos subrayan la relevancia de
incorporar el conocimiento local en programas educativos y de desarrollo
comunitario, con el fin de valorar las herencias culturales, fortalecer la
identidad colectiva y promover la continuidad intergeneracional de
prácticas ancestrales.
CONCLUSIONES
Los Modelos Lineales Generalizados (GLM ) y en particular la regresión binomial neg=
ativa
con enlace de raíz cuadrada, demostraron ser una herramienta adecuada
para analizar conteos de saberes matemáticos comunitarios y ancestra=
les
en contextos rurales. Gracias a su flexibilidad para manejar sobredispersión y distribuciones no normales,
permitió ajustar un modelo robusto y culturalmente pertinente. =
De los once predictores evaluados, resultados
estadísticamente significativos (p<0.05) la edad, el sexo femenin=
o,
la comunidad de origen, la escolaridad de la madre y del padre y las
actividades escolares. El arraigo comunitario emergió como el factor
más influyente seguido por las características
demográficas y la educación familiar, lo que evidencia la
importancia del entorno social y cultural en la trasmisión de
conocimientos.
El modelo seleccionado (M=
11E )
redujo la deviance en un 21.5% y presentó=
; el AIC más bajo entre las opciones consideradas
(Poisson, cuasi-Poisson, binomial negativa), lo cual confirma su capacidad =
para
explicar la variabilidad de los datos sin incurrir en sobreajuste.
Los hallazgos resaltan la necesidad de integrar
estos saberes en la enseñanza formal de las matemáticas.
Incorporar instrumentos y prácticas tradicionales en las secuencias
didácticas puede promover el reconocimiento de las herencias cultura=
les,
reforzar la identidad colectiva y favorecer la continuidad intergeneraciona=
l de
las prácticas etnomatemáticas . Se
sugiere replicar este enfoque en otras regiones y niveles educativos para
contrastar la influencia de distintos contextos socioculturales. =
REFERENCIAS
Artigue, M., DOUADY , R.
(1995). INGENIERÍA DIDÁCTICA EN EDUCACIÓN
MATEMÁTICA. Un esquema para la investigación y la
innovación en la enseñanza y el aprendizaje de las
matemáticas. Una empresa docente. Editorial Iberoamericana S.A de C.V. Bogotá. https://isfdajullon-lrj.infd.edu.ar/aula/archivos/repo=
sitorio/750/926/Ingenieria_didactica_de_Artigue_recorte.pdf
Instituto Nacional de Estadística y
Geografía (INEGI). (2020). Criterios de clasificación y
definiciones de localidades. Recuperado de https://<=
span
class=3DSpellE>www.inegi.org.mx /temas/localidades/ =
Katayama, O. R. J. (2014). Introducción=
a
la Investigación Cualitativa: Fundamentos, métodos, estrategi=
as y
técnicas. Fondo Editorial de la UIGV .
Lesh , R., y Doerr, H.
M. (2003). Foundations of a Models and Modeling Perspective on Mathematics
Teaching, Learning, and Problem Solving. En R. =
Lesh & H. M. Doerr (E=
ds.),
Beyond Constructivism: Models and Modeling Perspectives on Mathematics Prob=
lem
Solving
Martínez Mayoral, =
M.A .,
& Morales Socuéllamos, J. (2007). Modelos lineales generalizados.
Miguel Hernández.
Taha, H. A. (2012). Investigación de
operaciones. Pearson Educación.
Todo el contenido de LATAM Revista Latinoamericana de Ciencias Sociales y Humanidades ,
publicados en este sitio está disponibles bajo Licencia =
Creative Commons .
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LAT=
AM
Revista Latinoamericana de Ciencias Sociales y Humanidades, Asunción,
Paraguay.
ISSN en línea: 2789-3855, julio, 2025,
Volumen VI, Número 3 p 3858 .
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