Influence of initial mathematical competencies on the effectiveness of a classroom‐based intervention

Cueli, Marisol; Areces, Débora; García, Trinidad; Rodríguez, Celestino; Vallejo, Guillermo; Castro, Paloma González

doi:10.1111/bjep.12239

Cited by 6 publications

(8 citation statements)

References 31 publications

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“…The purpose of this section is to provide a comparison of the MBF without missing data, the LD-MBF, and the MI-MBF tests based upon a subset of the data described in Cueli et al (2019). Missing data were generated under a non-monotone MCAR process, deleting 10% of all values in the dataset.…”

Section: Empirical Illustration Using Real Datamentioning

confidence: 99%

“…Table 6 shows the results obtained after applying the MBF without missing data, LD-MBF, and MI-MBF procedures to the data of Cueli et al (2019) to check the individual effects of the types of treatment and levels of mathematics competency, as well as the effect of the two factors in combination, when the four formal dependent variables were considered simultaneously. In Table 6, the F-values, P-values and the associated degrees of freedom of all the tests were computed using the Fapproximation statistic for the Wilks' lambda, which is extensively used by data analysts.…”

Section: Empirical Illustration Using Real Datamentioning

confidence: 99%

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Combination rules for homoscedastic and heteroscedastic MANOVA models from multiply imputed datasets

2020

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Classical MANOVA tests do not pose any difficulty when the assumptions on which they are based are satisfied, while the modified Brown-Forsythe (MBF) procedure has low sensitivity to the lack of multivariate normality and homogeneity of covariance matrices. Both methods assume complete data for all subjects. In this paper, we present combination rules for the MANOVA and MBF procedures with multiply imputed datasets. These rules are illustrated by pooling the results obtained with a two-factor multivariate design after applying the two approaches to each of the imputed datasets when the covariance matrices were equal (MI-MANOVA) and when the covariance matrices were unequal (MI-MBF). A Monte-Carlo study was carried out to compare the proposed solution, in terms of type I error rates and statistical power, with the MANOVA and MBF approaches without missing data, and with listwise deletion of missing data followed by the MANOVA approach (LD-MANOVA) and listwise deletion followed by the MBF procedure (LD-MBF). Simulations showed that the type I error rates in all analyses on datasets with missing values (with or without imputation) were well controlled. We also found that the MI-MANOVA approach was substantially more powerful than LD-MANOVA. Moreover, the power of the MI-MANOVA was generally comparable to that of its complete data counterpart. Similar results were obtained for the MI-MBF procedure when covariance matrices were unequal. We conclude, based on the current evidence, that the solution presented performs well and could be of practical use. We illustrate the application of combination rules using a real dataset.

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Section: Empirical Illustration Using Real Datamentioning

confidence: 99%

Section: Empirical Illustration Using Real Datamentioning

confidence: 99%

Combination rules for homoscedastic and heteroscedastic MANOVA models from multiply imputed datasets

2020

Self Cite

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“…The official educational curriculum in Spain and other countries establishes the need to accurately estimate collections or quantities of continuous subjects. Despite not finding statistically significant differences in the use of the app, in terms of magnitude comparison, this task should be relevant to be taught through this instructional programme due to its potential importance in improving mathematics skills (Laski and Siegler, 2007 ; De Smedt et al, 2009 ; Matejko and Ansari, 2016 ; Xenidou-Dervou et al, 2017 ; Cueli et al, 2019a ). Comparing quantities development becomes relevant for improving mathematics learning as this task is part of the ANS for non-symbolic comparison and the PNS for symbolic comparison.…”

Section: Discussionmentioning

confidence: 99%

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

Mera

Casas²,

Mendizábal³

et al. 2022

Front. Psychol.

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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.

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“…To illustrate the computational details of the above-considered rules for combining estimates after MI, the primary hypotheses for the modified two-way MANCOVA model based on the original data are compared with the primary hypotheses of the modified two-way MANCOVA model based on data completed by imputation. Data for this purpose were taken from an educational study reported in Cueli et al (2019). The chief aim of this study was to determine the influence of the initial level of mathematics competency in relation to performance gains after an intervention with integrated dynamic representation (IDR; González-Castro et al, 2014) in elementary school students.…”

Section: Real Data Examplementioning

confidence: 99%

“…covariates) measured before treatment assignment. The MANCOVA is used in a wide variety of disciplines, including the behavioral sciences (e.g., Cueli et al, 2019; Freire et al, 2018; Hyams et al, 2018). It is assumed that the covariates are related to the dependent variables, and that they represent a source of variation that must be controlled for to obtain valid conclusions when testing the potential effects in any design (Zimmermann et al, 2020).…”

mentioning

confidence: 99%

Multivariate analysis of covariance for heterogeneous and incomplete data.

Vallejo¹,

García²,

Livacic-Rojas³

2023

Psychological Methods

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Influence of initial mathematical competencies on the effectiveness of a classroom‐based intervention

Abstract: Although all the three competency levels of the EG improved, the progression was different for each level. Results showed that students with low competency level improved substantially more than the students with medium and/or high baseline competency level.

Cited by 6 publications

References 31 publications

Combination rules for homoscedastic and heteroscedastic MANOVA models from multiply imputed datasets

Combination rules for homoscedastic and heteroscedastic MANOVA models from multiply imputed datasets

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

Multivariate analysis of covariance for heterogeneous and incomplete data.

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