Early Mathematical Competence Research Articles

Exploring the potential of a game-based preschool assessment of mathematical competencies

BackgroundEarly mathematical competencies are foundational for later academical development. There is a need for valid and resource-saving approaches to assess those skills. The House of Numbers (HoN) is a newly developed linear board game that allows the assessment of preschool early mathematical competencies. This article aims to examine aspects of this 24-item screening such as its reliability and validity, and whether it can successfully identify children at risk of developing math difficulties. It also aims to explore children’s perceptions of the game-based HoN compared to a typical preschool math test.MethodsA sample of 147 German preschoolers (Mage = 5 years 10 months, SDage = 5 months) was evaluated with the HoN and with a standard instrument for assessing early mathematical competencies (MARKO-D). Additionally, a subsample of n = 47 children rated their perception of both tools.ResultsThe results speak against an effect of the game-setting on the children’s performance. Regarding the aspects of the reliability and the validity of the HoN, both tools were sensitive to age differences between 5- and 6-year-old children. The high correlation between the two assessments speaks for the convergent validity of the HoN. Furthermore, an item analysis based on the Rasch model showed excellent results for all items of the new game-based approach. The distribution of the items on the logit measurement ruler of the Person-Item Map confirms, with only a few explainable exceptions, the developmental levels of the model the HoN is based on. A high person and item reliability confirm the internal consistency of the HoN. Regarding the diagnostic validity of the HoN, running a receiver operating characteristic curve resulted in a superior discrimination area under the curve. A sample relevant cut-off z-score was specified. Using this score as an indicator of low math performance resulted in high sensitivity, specificity and a high relative improvement over chance index. In addition, children’s explorative assessment of perception speaks in favor of the game-based assessment.ConclusionAll in all, the findings suggest, that the game-based measurement HoN can be a reliable, valid, time-saving, and attractive option for assessing early mathematical competencies in preschool settings.

A teacher's choice: Preschool teachers’ selection and use of picture books for mathematics instruction

Preschool teachers’ selection and use of instructional materials play an important role in their provision of qualitative mathematics instruction. Picture books were recently shown effective for supporting early mathematical competencies. Picture book features further contributed to their effectiveness. The current study aimed to investigate teachers’ selection and use of picture books for mathematics instruction with special attention for their evaluation of picture book features. We also analyzed the contribution of teachers’ beliefs and children's age to teachers’ picture book selection and use. Sixty-six preschool teachers participated in an online interview about (a) their picture book use for (mathematics) instruction and (b) the domain-specific (i.e., numeracy) and general features they rate important when selecting a picture book for mathematics instruction. Teachers also filled in a questionnaire regarding their beliefs about mathematics and learning and teaching mathematics. Results showed that more than 90 % of the teachers used picture books for mathematics instruction. About 40 % used them at least once and maximum four times a week and 6 % used them on a daily basis. When selecting picture books for mathematics instruction, teachers rated general features more important than domain-specific features and features related to basic mathematical content more important than features related to complex mathematical content. Teachers’ instruction and scheme and formalism beliefs contributed to their preference for Arabic numerals and comparisons between quantities. Children's age was positively related to teachers’ preference for complex mathematical content. The limited focus on mathematical content when selecting and using picture books points to the importance of teacher professional development on the selection and use of picture books for enhancing early mathematical competencies.

Early Mathematical Competencies and Key Context Features That Promote Their Development

The main aim of this review is to systematize and present evidence from recent scientific studies regarding the role of early mathematical competencies in later mathematics achievement, as well as to analyze characteristics of educational and family environments that facilitate the development of these competencies in children. Presented longitudinal studies provide clear evidence that early math competencies significantly predict later mathematical outcomes. Reviewed studies also suggest that how adults and children interact in terms of mathematics activities is related to children’s mathematics development. In both formal education and family environment, adults who use everyday situations and activities for reasoning, communicating, and mathematical thinking seem to be the most important factor for fostering early math competencies. These findings are also discussed in the context of BiH where most children do not attend formal early education.

App-based learning for kindergarten children at home (Learning4Kids): Study protocol for cohort 2 and the school assessments

Children's early literacy and mathematical competencies are very important predictors for their later success in school and their educational attainment in general. However, not all children are able to develop to their full potential and some are at risk of failing to reach sufficient competence levels. The project "App-based learning for kindergarten children at home" (Learning4Kids) is designed as a longitudinal intervention study that tests the potential impact of a computer tablet-based intervention for kindergarten children and their families before school entry. Here, the focus lies on both, potential short-term and long-term influences on children's competencies development in kindergarten and school. Learning4Kids uses a multi-method intervention approach and draws on expertise from different fields such as psychology, education, informatics, and didactics. It combines child test assessments with parental, educator, and teacher surveys and checklists, interviews as well as observations in the families to measure child competencies and their behaviour, and to assess family characteristics. The participating children and their families will be visited and assessed altogether seven times, starting in the second-last year of kindergarten until children are at the end of Grade 2. In cohort 1, 190 families participated in this project, whereas in cohort 2 another 310 families joined the Learning4Kids project. For the school assessments, standardized and curriculum-based tests will be used to assess children's mathematical and literacy competencies. In addition, cognitive and non-cognitive child abilities will be assessed. Learning4Kids offers substantive advances for the scientific fields of psychology and education, and also provides implications for policy and practice in the long term. Improving young children's learning trajectories and analysing these trajectories from kindergarten to primary school is both a social and economic imperative as it contributes to greater individual success and thus to societal prosperity.

Adding family math to the equation: Promoting Head Start preschoolers’ mathematics learning at home and school

Differences in children's mathematics knowledge are evident at kindergarten entry, favoring children who have greater access to economic resources. Fostering preschoolers’ mathematics learning at home and in classroom settings, through games and other developmentally appropriate activities, is of great interest to educators, early childhood leaders, and policymakers. This cluster randomized trial examined the effects of a naturalistic, game-based mathematics intervention implemented in Head Start classrooms and examined whether including a family math component added value. A total of 573 children (64% Hispanic; 60% multilingual) were included from 66 classrooms which were randomly assigned to Classroom Math (CM), Classroom Math + Family Math (CM+FM), or business-as-usual (BAU). Results indicated that the family math component did add value to the classroom-based intervention as CM+FM resulted in a significant positive impact on children's mathematics knowledge relative to BAU, but CM alone did not. For preschoolers age 50+ months, both interventions had significant effects on children's mathematics knowledge relative to BAU, but CM+FM had a stronger effect (d = .36). The number of math games played was significantly associated with higher mathematics scores and the number of family math mini-books returned had a significant impact on children's spring scores, over and above the number of games played. The CM+FM intervention also had a significant effect on teachers’ instructional practice (d =.79). Adding a family math component to a game-based classroom intervention resulted in positive impacts for preschoolers and seems to be an effective, ecologically valid intervention that fosters early mathematical competencies.

Contributions of the psychology of mathematical cognition in early childhood education using apps.

Educational interventions are necessary to develop mathematical competence at early ages and prevent widespread mathematics learning failure in the education system as indicated by the results of European reports. Numerous studies agree that domain-specific predictors related to mathematics are symbolic and non-symbolic magnitude comparison, as well as, number line estimation. The goal of this study was to design 4 digital learning app games to train specific cognitive bases of mathematical learning in order to create resources and promote the use of these technologies in the educational community and to promote effective scientific transfer and increase the research visibility. This study involved 193 preschoolers aged 57–79 months. A quasi-experimental design was carried out with 3 groups created after scores were obtained in a standardised mathematical competence assessment test, i.e., low-performance group (N = 49), high-performance group (N = 21), and control group (N = 123). The results show that training with the 4 digital learning app games focusing on magnitude, subitizing, number facts, and estimation tasks improved the numerical skills of the experimental groups, compared to the control group. The implications of the study were, on the one hand, provided verified technological tools for teaching early mathematical competence. On the other hand, this study supports other studies on the importance of cognitive precursors in mathematics performance.

Socio-Economic and Cultural Context in the Development of Early Mathematical Competencies: A Comparative Study of Specific Educational Contexts in Chile and Spain.

This research presents the findings of a comparative study of mathematical competence among 130 students (M = 54.08months; SD = 2.57) from vulnerable school contexts in Chile and the Spanish public school system. The study analyses a set of general and specific domain precursors for which evidence of socioeconomic background exists. Using multivariate regression and discriminant analysis techniques, we calculated similarities and differences between groups by comparing these precursors. Significant differences were found between the Spanish and Chilean groups (p < .05); however, no differences were observed in non-symbolic comparison and receptive vocabulary. Possible reasons for the existence and extent of these differences are discussed in terms of socio-cultural and educational contexts.

App-based learning for kindergarten children at home (Learning4Kids): study protocol for cohort 1 and the kindergarten assessments

BackgroundChildren’s literacy and mathematical competencies are a critical platform for their successful functioning as individuals in society. However, many children, in particular those with low socio-economic status (SES) backgrounds who may not receive the home support needed to develop to their full potential, are at risk of not reaching sufficient competence levels. The overall aim of this project is to develop innovative computer tablet applications (‘apps’) and test whether the apps support parents in the provision of high-quality home learning environments (HLEs) and impact positively on the short- and long-term development of children’s competencies.Altogether, “App-based learning for kindergarten children at home” (Learning4Kids) is a 5-year longitudinal study funded by the EU and designed to assess the potential impact of a tablet-based family intervention on children’s learning, development, social inclusion and well-being.Methods/designThis study uses a multi-method intervention approach and draws on expertise from psychology, education, informatics, and didactics to evaluate the effectiveness of learning apps and the intervention approach. It also exploits new technological possibilities afforded by tablet computers that are very common nowadays in families. Learning4Kids sets out to measure the quality of the HLE, children’s early mathematical, literacy, and cognitive competencies and their behaviour. Here, data will be gathered via standardized tests, observations, and parental and educator surveys and checklists. Data collection also includes the assessment of app usage times via mobile sensing. In cohort 1, 190 families are assigned to one of four groups. One business-as-usual group will only participate in the child assessments, whereas the three remaining groups are provided with tablets for about 10 months. Two intervention groups will receive mathematical or literacy learning apps as well as parental information about these topics and the tablet-control-group will receive similar apps and information that focus on general child development, but not on mathematics or literacy.DiscussionWhilst offering substantive advances for the scientific fields of psychology and education, the Learning4Kids study also has broad societal implications. Improving young children’s learning trajectories is both a social and economic imperative as it equips them to achieve greater individual success and to contribute to societal prosperity.

Modulation of general and specific cognitive precursors to early mathematical competencies in preschool children

The main goal of this study was to analyze the contribution of predictors of both domain-general (working memory, processing speed, and receptive vocabulary) and domain-specific variable (estimation and magnitude comparison) processes to informal mathematical performance (numbering, comparison, calculation, and understanding of concepts) in preschoolers. In order to reach this, a structural equation modeling was used. A total of 158 preschool students (ages ranging from 52 to 64 months) participated in the investigation. Students were assessed with informal tasks measuring mathematical thinking, numerical estimation, symbolic and non-symbolic comparison making, coding, receptive vocabulary, and backward digit span. Results showed that domain-general (specially working memory) was the highest impact of the general-domain predictors on informal mathematical competencies and a limited specific-domain factor effects for magnitude comparison. The consequences for mathematics learning in initial school years are discussed.

The relevance of the early years home and institutional learning environments for early mathematical competencies

Journal for educational research online 12 (2020) 3, S. 103-125 Padagogische Teildisziplin: Empirische Bildungsforschung; Padagogik der fruhen Kindheit;

Spontaneous focusing on Arabic number symbols and its association with early mathematical competencies

Many studies have investigated the association between children’s spontaneous attention to number and their early mathematical abilities. This work has presented number in a non-symbolic format by exclusively using numerosities as their stimuli. Therefore, little is known about children’s spontaneous attention for Arabic number symbols. We aimed to address this gap by exploring, for the first time, whether we can observe individual differences in young children’s tendency to spontaneously focus their attention on Arabic number symbols (SFONS) using a newly developed Picture task. We investigated SFONS and its association with spontaneous focusing on numerosity (SFON), numerical abilities, and teacher ratings of mathematical competence in the three years of Flemish kindergarten. One hundred and eleven kindergartners (2 years 4 months – 6 years 2 months of age) completed a battery of tasks to measure their SFONS and SFON, as well as a range of numerical abilities (i.e., Arabic numeral identification, verbal counting, and counting objects). Kindergarten teachers were asked to rate their children’s mathematical competence on a 4-point Likert scale. Findings revealed that children in the three kindergarten years under study largely differed in their tendency to spontaneously attend to Arabic number symbols in the pictures they had to describe. We also observed differences in the levels of SFONS and SFON between the three kindergarten years. Although SFONS and SFON were not strongly associated in the three kindergarten years, significant associations were found between children’s SFONS and their numerical abilities in kindergarten year 1 and 2, and teacher ratings of their mathematical competence in kindergarten year 3. Together, these results suggest that SFONS is a relevant component of children’s early mathematical development.

Relación entre el vocabulario comprensivo y la competencia matemática temprana en niños de 5 y 6 años

El presente estudio tiene como objetivo determinar la relación entre el vocabulario comprensivo y la competencia matemática temprana. Se empleó un tipo de investigación descriptivo correlacional, siendo la muestra de sujetos constituida por 45 niños de una institución educativa estatal. Los resultados indican que existe una correlación significativa entre vocabulario comprensivo y competencia matemática temprana (Rho=.617), además al se observó relación significativa entre vocabulario comprensivo y el componente de capacidad relacional (Rho=.661) y componente numérico (Rho=.441) estos resultados permiten concluir que el vocabulario comprensivo asociado a conceptos espaciales, cuantitativos, temporales, cualitativos, de tamaño y forma, se relacionan con la competencia matemática del número.

Early mathematical competencies and later achievement: insights from the Longitudinal Study of Australian Children

International research suggests that early mathematical competence predicts later mathematical achievement. In this article, we explore the relationship between mathematical competencies at 4–5 years, as measured by teacher ratings, and later results on Years 3, 5, 7 and 9 National Assessment Program – Literacy and Numeracy (NAPLAN) numeracy tests. Data from a nationally representative sample of 2343 children participating in the Longitudinal Study of Australian Children (LSAC) are examined. In line with international studies, we report moderate correlations between preschool-entry mathematics and later NAPLAN numeracy test results. However, analysis of individual growth trajectories indicates that early mathematics predicts the initial (Year 3) level, but not subsequent growth. This suggests that early mathematical competencies are important for enhancing achievement in early schooling, but that the quality of mathematics education provided in the schooling years is critical for future development.

IDENTIFICACIÓN Y ANÁLISIS DEL ÍNDICE DE COMPETENCIA MATEMÁTICA A TEMPRANA EDAD

Resumen.La teoría y la práctica sobre el desarrollo y enseñanza de los conceptos matemáticos en los niños/as pequeños ha estado fuertemente influida por este modelo de operaciones lógicas de Piaget y Szeminska (1941). La posición piagetiana apunta una fuerte relación entre las operaciones lógicas y los conceptos numéricos y también con las operaciones aritméticas. El modelo piagetiano ha recibido diversas críticas poniendo en duda el modelo lógico del número, puesto que proporcionaría una explicación incompleta de las competencias numéricas en el niño. Mayer et al., (2002) señalan la importancia del conteo en el desarrollo matemático. Por otro lado, Bryant y Nunes (2002) han sugerido que la base del desarrollo matemático es el pensamiento lógico, la enseñanza del sistema de numeración convencional y el aprendizaje significativo y contextualizado de los contenidos matemáticos. Otro punto de vista que denominamos interaccionista asume que las operaciones piagetianas y el conteo juntos contribuyen al desarrollo del número. Con este enfoque, el desarrollo del número es reformulado por el constructo denominado competencia matemática temprana (CMT). Un nivel suficiente de CMT es un requisito para ser capaz de seguir una educación matemática formal (Kroesbergen, et al., 2009), de ahí que resulte de alto interés poder lograr un procedimiento de evaluación de este tipo de competencia. En este sentido, el grupo de Van Luit ha desarrollado un procedimiento de evaluación exitoso a través del Early Numeracy Test-R (Van Luit et al., 2009). Esta prueba evalúa 9 componentes en niños de 4 a 7 años: Comparación, Clasificación, Correspondencia uno a uno, Seriación, Conteo verbal, Conteo estructurado, Conteo resultante o resultado del conteo (sin señalar), Conocimiento general de los números y Estimación. Para este trabajo se ha utilizado la versión española informatizada, con el objetivo de estandarizarla. Un total de 1391 alumnos participaron en este estudio (747 niños y 644 niñas). Los participantes evaluados tenían un rango de edad comprendido entre los 48 y los 95 meses. La prueba, (Alpha = 0.902) permite establecer un índice de la CMT en 6 niveles, teniendo en cuenta las características evolutivas de los participantes, concentrados en 10 grupos edad. Para cada uno de los niveles, la prueba sitúa al alumno en función del resultado en un valor cuantitativo y cualitativo respecto al grupo de edad de referencia. La ventaja de este índice de CMT es que tiene una considerable valor predictivo respecto al rendimiento matemático, permitiendo una detección temprana de las dificultades de aprendizaje.Palabras clave: Competencia Matemática Temprana, evaluación, Early Numeracy Test-r.

COMPETENCIAS MATEMÁTICAS TEMPRANAS Y ACTITUD HACIA LAS TAREAS MATEMÁTICAS VARIABLES PREDICTORAS DEL RENDIMIENTO ACADÉMICO EN EDUCACIÓN PRIMARIA: RESULTADOS PRELIMINARES

Resumen.La investigación presenta el rol que poseen las Competencias Matemáticas Tempranas (CMT de aquí en adelante) respecto del rendimiento escolar, tanto en el ámbito general, como también específico en Matemáticas y Lenguaje de los estudiantes chilenos. De esta manera, se espera aportar antecedentes acerca del valor predictivo de la evaluación de las CMT respecto del éxito o fracaso escolar que el niño o niña tendrá posteriormente durante su itinerario escolar. A partir de los análisis realizados, se logró comprobar que las CMT se relacionan de manera significativa con los desempeños tanto en Matemática como en Lenguaje, así como en el rendimiento general, durante todos los años escolares posteriores a la evaluación, en todos los colegios donde se realizó el estudio. Del mismo modo, se evaluaron otras variables psicológicas y se integraron en un modelo de interacción de regresión lineal. Se encontró que la actitud hacia las tareas matemáticas posee un rol crucial en la explicación de la variabilidad de los rendimientos escolares, analizados en las diversas áreas de aprendizaje. Se destaca el rol que la inteligencia lógica posee al tener una relación estrecha con el rendimiento. Del mismo modo, se observa el rol de factores asociados con la convivencia escolar, observando que los aspectos de victimización, agresión, indisciplina y desidia docente, se relacionaban de forma significativa con el desempeño de los estudiantes. Se confirmó la hipótesis inicial referida a que en la medida que exista un mayor nivel de desarrollo de las CMT, el rendimiento académico de los participantes tiende a ser mejor, tendiendo además a alcanzar mejores puntuaciones en tareas de razonamiento lógico-inductivo. De acuerdo a los resultados obtenidos a través del análisis correlacional entre las CMT (evaluadas con el Test de Utrech,TEMT-U) y la actitud hacia las tareas matemáticas, se encuentra que en casi todas las dimensiones hay una relación estadísticamente significativa y de carácter inversamente proporcional. En general, los educandos que alcanzaron mayores niveles de CMT tienden a presentar puntuaciones más bajas en el Cuestionario de Actitud hacia las Tareas Matemáticas. Esto puede interpretarse como que los niños y niñas que tuvieron buenos resultados en el TEMT-U fueron los que, en general, presentaban una actitud favorable hacia las Tareas Matemáticas y viceversa.Palabras claves: Competencia Matemática Temprana, Inteligencia Lógica, Actitud hacia las Matemáticas, Convivencia Escolar.

Executive Function Skills, Early Mathematics, and Vocabulary in Head Start Preschool Children

ABSTRACTResearch Findings: The contribution of 3 executive function skills (shifting, inhibitory control, and working memory) and their relation to early mathematical skills was investigated with preschoolers attending 6 Head Start centers. Ninety-two children ranging in age from 3 years, 1 month, to 4 years, 11 months, who were native English or Spanish speakers were assessed for these executive function skills as well as their receptive vocabulary skills and early mathematical abilities using the Child Math Assessment (Starkey, Klein, & Wakeley, 2004), which captures an array of skills across 4 domains. Hierarchal regression analyses revealed that inhibitory control and working memory made unique contributions to children’s early mathematical abilities in the domains of numeracy, arithmetic, spatial/geometric reasoning, and patterning/logical relations after we controlled for age, receptive vocabulary, and previous Head Start experience. Furthermore, receptive vocabulary also accounted for significant variance in children’s early mathematical abilities above and beyond executive function skills. No group differences emerged between English-only and dual language learners on the fit of the regression models. Practice or Policy: These findings extend previous research highlighting the interface of executive function skills and mathematical learning in early childhood with further evidence to support this relationship beyond early numeracy and counting using a broad measure of critical early math skills. In addition, the intricate role of language in the development of early mathematical competence is considered. Implications of these findings for scaffolding executive function skills and vocabulary within prekindergarten math curricula are discussed, with particular consideration for children from low socioeconomic backgrounds.

Predictibilidad de las competencias matemáticas tempranas, predisposición desfavorable hacia la matemática, inteligencia lógica y factores de la convivencia escolar en el rendimiento académico en matemáticas

This research presents results about the degree of predictability of a set of psychoaffective variables related to students' performance in the subject of mathematics (N=669). It examines the role of previously assessed Early Mathematical Competencies (EMC) and other variables, such as logical intelligence, predisposition towards mathematics, and school environment factors, with respect to the grade point average that students received in the subject of mathematics during a period of four years. An inverse and significant relationship was found between a negative predisposition towards mathematics and performance in the subject. Moreover, a significant relationship was found between performance in mathematics and logical intelligence and EMC. This study also emphasizes that factors associated with the school environment, like victimization, aggression, lack of discipline, and teacher apathy, are significantly related to students' performance. The students that obtained the highest levels of EMC are also those who received the highest grade point average. Stepwise linear regression analysis allows us to infer that 47.2% of the variance of grade point averages can be explained by the variables included in the model and the important role of attitude towards mathematics and EMC.

Predictability of Early Mathematical Competencies, Negative Predisposition towards Mathematics, Logical Intelligence, and Educational Environment Factors in Mathematics Performance

Predictability of Early Mathematical Competencies, Negative Predisposition towards Mathematics, Logical Intelligence, and Educational Environment Factors in Mathematics Performance

Explanatory model of emotional-cognitive variables in school mathematics performance: a longitudinal study in primary school.

This study tested a structural model of cognitive-emotional explanatory variables to explain performance in mathematics. The predictor variables assessed were related to students’ level of development of early mathematical competencies (EMCs), specifically, relational and numerical competencies, predisposition toward mathematics, and the level of logical intelligence in a population of primary school Chilean students (n = 634). This longitudinal study also included the academic performance of the students during a period of 4 years as a variable. The sampled students were initially assessed by means of an Early Numeracy Test, and, subsequently, they were administered a Likert-type scale to measure their predisposition toward mathematics (EPMAT) and a basic test of logical intelligence. The results of these tests were used to analyse the interaction of all the aforementioned variables by means of a structural equations model. This combined interaction model was able to predict 64.3% of the variability of observed performance. Preschool students’ performance in EMCs was a strong predictor for achievement in mathematics for students between 8 and 11 years of age. Therefore, this paper highlights the importance of EMCs and the modulating role of predisposition toward mathematics. Also, this paper discusses the educational role of these findings, as well as possible ways to improve negative predispositions toward mathematical tasks in the school domain.

Relationship between Early Mathematical Competence, Gender and Social Background in Chilean Elementary School Population. [Relación entre los niveles de competencia matemática temprana, género y extracción social en la población escolar primaria en Chile

The article describes the levels of early mathematical competence shown by Chilean pre-schoolers and primary students related to relational and numerical competence (N = 1437) that were assessed by means of the Early Mathematical Evaluation Test in its Utrecht version (TEMT-U). The study confirms that there are significant differences concerning early mathematical competence with regard to the academic level and children’s chronological age; however, neither gender nor social backgrounds are relevant in that respect. Results show that social background and gender do not represent an explanatory factor related to mathematical competence in initial schooling levels; the opposite happens in later years, which suggests that perhaps it is the quality of the educational action what makes the difference.