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DOI: https://doi.org/1= 0.56712/latam.v6i3.4235

Estimación de los saberes matemáticos comunitarios y ancestrales sobre longitud en escuelas primarias indígenas y general= es de Hidalgo

Estimation of community and ancestral mathematical knowledge about length in indigenous a= nd general primary schools in Hidalgo

 

Miriam Martínez Vázquez

profe_6901@uaeh.edu.mx

https://orcid.org/0000-0003-4893-9175

Universidad Autónoma del Estado de Hidalgo

México

 

Juan Bacilio Guerrero Escamilla

juan_guerrero9464@uaeh.edu.mx

https://orcid.org/000-0002-0971-7564

Universidad Autónoma del Estado de Hidalgo

México

 

Aarón Víctor Reyes Rodríguez

aaronr@uaeh.edu.mx

https://orcid.org/0000-0001-8294-9022

Universidad Autónoma del Estado de Hidalgo

México

 

Artículo recibido: 30 de junio de 2025. Aceptado para publicación: 25 de juli= o de 2025.

Conflictos de Interés: Ninguno que declarar.

 

Resumen<= /o:p>

Los Modelos Lineales Generalizados (GLM) constituyen una extensión de los modelos lineales tradicionales, diseñados para analizar datos que no se ajustan a los supuestos clásicos de normalidad, homocedasticidad y linealidad. Su estructura permite modelar una amplia gama de situaciones donde la variable respuesta sigue distribuciones pertenecientes a la familia exponencial, como Poisson o binomial negativa. El objetivo de los GLM es identificar y cuantificar relaciones entre una variable dependiente y varios predictores, adaptándose a contextos donde las distribuciones normal= es no son adecuadas (Martínez y Morales, 2007). En el caso particular d= el estudio de saberes matemáticos comunitarios y ancestrales sobre longitud, se busca evaluar como factores socioculturales afectan la preservación de estos conocimientos en comunidades rurales. Se utilizó un GML con distribución binomial negativa y función de enlace raíz cuadrada para mode= lar datos de conteo con sobredispersión. Se analizaron once predictores: edad, sexo, comunidad, escolaridad familiar. La selección del modelo óptimo se basó en criterios de aj= uste (AIC, BiC) y reducción de la devianza. La estimaci&oa= cute;n de los parámetros se realizó por máxima verosimilitud mediante el algoritmo de Fisher-Scoring y se evaluó el ajuste con residuos de Pearson y de d= ieviance. En el modelo la reducción de deviance fu= e del 21.5% y el AIC fue el más bajo. Las vari= ables significativas (p<0.05) fueron: edad, sexo femenino, comunidad, escolari= dad de madre y padre, y actividades escolares. El modelo evidenció que e= stas variables son determinantes en la conservación de saberes matemáticos comunitarios y ancestrales. El arraigo comunitario resul= tó el principal factor para la conservación de los saberes matemáticos comunitarios y ancestrales, seguido del género y = la educación familiar. Los GLM permiten un análisis robusto y culturalmente contextualizado, para analizar dato= s de conteo socioculturales, facilitando interpretaciones significativas.

Palabras clave: modelos lineal= es generalizados, binomial negativa, saberes ancestrales, sobredispersión, factores socioculturales

 

Abstract

Generalized Linear Models (GLMs) are an extension of traditional linear models, designed to analyze data that do not conform to the classic assumptions of normality, homoscedasticity, and linearity. Their structure allows for modeling a wide range of situations w= here the response variable follows distributions belonging to the exponential family, such as Poisson or negative binomial. The objective of GLMs is to identify and quantify relationships betwee= n a dependent variable and several predictors, adapting to contexts where normal distributions are not adequate. In the specific case of the study of commun= ity and ancestral mathematical knowledge about longitude, the aim is to evaluate how sociocultural factors affect the preservation of this knowledge in rural communities. A GLM with a negative binomial distribution and square root link function was used to model overdispersed count data. Eleven predictors were anal= yzed: age, sex, community, and family education. The selection of the optimal mod= el was based on fit criteria (AIC, BiC) and devian= ce reduction. Parameter estimation was performed using maximum likelihood using the Fisher-Scoring algorithm, and the fit was assessed using Pearson residu= als and deviance. The model reduced deviance by 21.5%, and the AIC was the lowe= st. Significant variables (p<0.05) were age, female sex, community, mother's= and father's education, and school activities. The model showed that these variables are determinants in the preservation of community and ancestral mathematical knowledge. Community roots were the main factor for the preservation of community and ancestral mathematical knowledge, followed by gender and family education. GLMs allow for a r= obust and culturally contextualized analysis of sociocultural count data, facilitating meaningful interpretations.

Keywords: generalized li= near models, negative binomial, ancestral knowledge, overdispersion, sociocultur= al factors

 

 

 

 

 

 

 

 

 

 

T= odo el contenido de LATAM Revista Latinoamericana de Ciencias Sociales y Humanidades, publicado en este sitio está disponibles bajo Licencia Creative Commons.= = <= o:p>

Cómo citar:  Martínez Vázquez , M., Guerrero Escamilla , J. B., & Reyes Rodríguez, A. V. (2025). Estimación de los saberes matemáticos comunitarios y ancestrales sobre longitud en escuelas primarias indígenas y general= es de Hidalgo. LATAM Revista Latinoame= ricana de Ciencias Sociales y Humanidades 6 (3), 3859 – 3870. https://doi.or= g/10.56712/latam.v6i3.4235

 

INTRODUCCIÓN

En el análisis estadístico, seleccionar el modelo adecuado es esencial para comprender cómo una variable respuesta se relaciona con un conjunto de predictores. Tradicionalmente, los modelos lineales clásicos han sido la herramie= nta principal para este fin, sin embargo, sus supuestos de normalidad, homocedasticidad y linealidad frecuentemente no se cumplen en la práctica, especialmente cuando se trabaja con datos de conteo o proporciones. Para superar estas limitaciones, los Modelos Lineales General= izados (GLM) ofrecen una estructura flexible que permi= te modelar variables respuesta que siguen distribuciones pertenecientes a la familia exponencial, como Poisson o Binomial Negativa.

Los GLM se caracte= rizan por tres componentes clave: la especificación de una distribuci&oacu= te;n para la variable respuesta, una función de enlace que conecta la med= ia de la respuesta con un predictor lineal y una función de varianza que defina cómo varía la respuesta. La regresión de Poisso= n es útil para modelar conteos, aunque suponer que la media y la varianza= son iguales puede ser restrictivo. En casos de sobredisper= sión, la regresión binomial negativa proporciona un ajuste más adecuado. Estos modelos se estiman mediante máxima verosimilitud usa= ndo algoritmos iterativos como Fisher-Scoring. Además, se evalúa el ajuste mediante residuos y la deviance (Martínez y Morales, 2007).

El presente estudio tiene como objetivo analiz= ar la relación entre diversos factores socioculturales y la presencia de saberes matemáticos comunitarios y ancestrales relacionados con la noción de longitud en comunidades rurales. Estos saberes, transmitid= os de generación en generación forman parte del acervo cultural = de muchas comunidades y se expresan en prácticas cotidianas vinculadas = a la agricultura, la construcción, el comercio y otras actividades tradicionales.

Para modelar esta relación, se construyó un modelo estadístico basado en una regresión binomial negativa, adecuado para datos de conteo con s= obredispersión, lo que permitió evaluar la influencia de variables como la edad, el sexo, la comunidad de origen, el municipio, las actividades económic= as familiares, el nivel educativo de padres y abuelos, así como las actividades escolares en las que participan los estudiantes. La formulación del modelo busca estimar la probabilidad de ocurrencia y representatividad de estos saberes (variable dependiente) en función= de once variables explicativas, mediante una función de enlace basada e= n la raíz cuadrada.

La selección del modelo más adec= uado se realizó comparando distritos enfoques (Poisson, Cuasi-Poisson, Binomial Negativa), resultando en la elección del modelo M11E con enlace sqrt, al = mostrar un mejor ajuste según criterios como la devianc= e, el AIC y el BIC. A través del aná= lisis de los coeficientes estimados y sus significados estadísticos, se identifican las variables con mayor impacto sobre la conservación y debilitamiento de estos saberes, destacando la comunidad, la edad, el sexo,= la escolaridad de los padres y la participación en actividades escolares como los factores más influyentes. Este enfoque permite comprender c= on mayor precisión cómo influyen los contextos comunitarios, familiares y escolares en la transmisión de conocimientos ancestrale= s, ofreciendo así elementos clave para el diseño de polít= icas educativas interculturales que reconozcan y fortalezcan estos saberes en la formación de los estudiantes.

METODOLOGÍA

Para estructurar y resolver el modelo de los saberes matemáticos comunitarios y ancestrales sobre longitud se empleó la metodología de Investigación de Operaciones = (IO) propuesta por Taha (2012), complementada con técnicas de modelado estadístico. Se siguieron las siguientes fases:

Definició= ;n del problema: Se delimitó el objetivo, el cual fue identificar las variab= les socioculturales que influyen en la preservación de saberes de longit= ud entre estudiantes de primaria en zonas rurales de Hidalgo. Se estableci&oac= ute; la población muestra (n=3D160 estudiantes de sexto año) y las características contextuales (baja densidad, pobreza y rezago educativo).

Variable respue= sta: Yn1, conteo de eventos que reflejan la presencia de s= aberes comunitarios y ancestrales sobre longitud entre “n” estudiantes= de sexto año de primaria.

Variables explicativas: X1, X2, X3, X4, X5, X6, X7, X8, X9, X10, X11o, que representan la edad, sexo, comunidad de origen, municipio, actividad económica de la comunidad, padres y abuelos escolaridad de madre, pa= dre y abuelos y tipo de actividades escolares.

Los datos se obtuvieron mediante cuestionarios abiertos y entrevistas semiestructuradas aplicado a una muestra de 160 estudiantes de nuevas escuelas indígenas y generales de comunidades rurales en Acaxochitlán, Zempoala y Pachuca, Hidalgo.

Construcci&oacu= te;n del modelo:

Se formuló un Modelo Lineal Generalizad= o de la forma:

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:

βj<= /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

L24

cinta métrica, báscula

L59

metro, regla, cinta métrica, flexómetro, varas, lazos

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

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:

Y1<= /m:sSub>=3D<= m:sSupPr>9.502<= /m:sSup>=3D90.25Y1<= /m:sSub>=3D<= m:sSupPr>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 3D"https://revistacientifica.uamericana.edu.py/public/site/images/aduar=.

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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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