Exploring the Educational Potential of a Game-Based Math Competition

The main aim of this article was to investigate the educational potential of a game-based math game competition to engage students in training rational numbers. Finnish fourth (n = 59; Mage = 10.36) and sixth graders (n = 105; Mage = 12.34) participated in a math game competition relying on intra-classroom cooperation and inter-classroom competition. During a three-week period, the students were allowed to play a digital rational number game, which is founded on number line estimation task mechanics. The results indicated that students benefited significantly from participating in the competition and playing behaviour could be used to assess students rational number knowledge. Moreover, students were engaged in the competition and the results revealed that intrinsically motivating factors such as enjoyment and perceived learning gains predicted students' willingness to participate in math game competitions again. This article provides empirical support that educational game competition can be an effective, engaging, and a fair instructional approach.

Strategie szacowania miejsca liczb na osi u dzieci z dyskalkulią i typowo rozwijających się

CelCelem badań była ocena wpływu deficytów poznawczych obecnych w specyficznym zaburzeniu w uczeniu się matematyki, na operowanie mentalną osią liczbową przy użyciu jednocyfrowych liczb prezentowanych w formacie symbolicznym i niesymbolicznym. MetodaZbadano zdolność szacowania miejsca liczb na osi (ang. Number Line Estimation, NLE) u 20 dzieci z zaburzeniami w zakresie nauki matematyki (mathematical learning disabilities, MLD) i 27 ich typowo rozwijających się rówieśników (typically developing, TD). Wykorzystano w tym celu zadanie szacowania miejsca liczb na osi dla liczb z zakresu 1–9 przedstawianych w formacie symbolicznym i niesymbolicznym. WynikiW przypadku wszystkich dzieci większą wartość błędu szacowania uzyskano dla liczb ze środka osi liczbowej, aczkolwiek efekt był bardziej wyraźny w grupie z zaburzeniami. Co więcej, dzieci z obu grup w podobnym stopniu przeszacowywały, zaś różniły się pod względem niedoszacowywania miejsca liczb. Dzieci z grupy MLD ujawniły większe odchylenie w lewo niż dzieci z grupy TD w przypadku prawie wszystkich liczb, z wyjątkiem 7 i 8. Ocena wielkości błędu szacowania miejsca dla każdej liczby oddzielnie pozwoliła na opisanie profilu rozkładu wartości tego błędu, a co za tym idzie, prawdopodobnych strategii tego szacowania stosowanych przez dzieci z obu grup. WnioskiJak się wydaje, grupa MLD, przejawia tendencję do szacowania segmentów osi liczbowej, zaczynając od punktu odniesienia na lewym krańcu osi. Wyznaczanie kolejnego w jej centrum, nie ułatwia im poprawnego szacowania miejsca liczb 4 i 6. Ponadto u wszystkich dzieci odnotowano większy błąd szacowania w przypadku formatu niesymbolicznego (zbiory kropek), szczególnie dla wysokich wartości liczbowych, co można interpretować, zarówno jako przejaw błędów w szacowaniu miejsca liczb, jak i w przeliczaniu.

Conceptual replication and extension of the relation between the number line estimation task and mathematical competence across seven studies

A recent meta-analysis demonstrated the overall correlation between the number line estimation (NLE) task and children’s mathematical competence was r = .44 (positively recoded), and this relation increased with age. The goal of the current study was to conceptually replicate and extend these results by further synthesizing this correlation utilizing studies not present in the meta-analysis. Across seven studies, 954 participants, ranging from 3 to 11 years old (Age M = 6.02 years, SD = 1.57), the overall estimation-competence correlations were similar to those of the meta-analysis and ranged from r = −.40 to −.35. The current conceptual replication demonstrated that the meta-analysis captured a stable overall relation between performance on the NLE task and mathematical competence. However, the current study failed to replicate the same moderation of age group presented in the meta-analysis. Furthermore, the current study extended results by assessing the stability and predictive validity of the NLE task while controlling for covariates. Results suggested that the NLE task demonstrated poor stability and predictive validity in the seven samples present in this study. Thus, although concurrent relations replicated, the differential age moderation, lack of stability, and lack of predictive validity in these studies require a more nuanced approach to understanding the utility of the NLE task. Future research should focus on understanding the connection between children’s developmental progression and NLE measurement before further investigating the predictive and diagnostic importance of the task for broader mathematical competence.

Left digit effects in numerical estimation across development

Number line estimation (NLE) tasks are widely used to investigate numerical cognition, learning, and development, and as an instructional tool. Interpretation of these tasks generally involves an implicit expectation that responses are driven by the overall magnitudes of target numerals, in the sense that the particular digits conveying those magnitudes are unimportant. However, recent evidence shows that numbers with similar magnitudes but different leftmost digits are estimated very differently. For example, “798” is placed systematically much too far to the left of “801” in a 0-1000 NLE task by children aged 7-11 and adults (Lai et al., 2018). Here we ask whether this left digit effect generalizes to two-digit numerals in a 0-100 NLE task and whether it emerges in younger children. Children aged 5-8 (Study 1, N = 73), adults (Study 2, N = 44), and children aged 9-11 (Study 3, N = 27) completed a standard 0-100 NLE task on a touchscreen tablet. We observed left digit effects for two-digit numerals in children aged 8-11 and adults, with large effect sizes, demonstrating that these effects generalize to smaller numerical ranges. Left digit effects were not apparent in 5- to 7-year-olds, suggesting that these effects do not emerge at younger ages for smaller, more familiar numerical ranges. We discuss developmental emergence of left digit effects in number line estimation and implications within and beyond the field of cognitive development.

Cognitive mediators of US—China differences in early symbolic arithmetic

Chinese children routinely outperform American peers in standardized tests of mathematics knowledge. To examine mediators of this effect, 95 Chinese and US 5-year-olds completed a test of overall symbolic arithmetic, an IQ subtest, and three tests each of symbolic and non-symbolic numerical magnitude knowledge (magnitude comparison, approximate addition, and number-line estimation). Overall Chinese children performed better in symbolic arithmetic than US children, and all measures of IQ and number knowledge predicted overall symbolic arithmetic. Chinese children were more accurate than US peers in symbolic numerical magnitude comparison, symbolic approximate addition, and both symbolic and non-symbolic number-line estimation; Chinese and U.S. children did not differ in IQ and non-symbolic magnitude comparison and approximate addition. A substantial amount of the nationality difference in overall symbolic arithmetic was mediated by performance on the symbolic and number-line tests.

EXPRESS: The Association of Basic Numerical Abilities and Math Achievement: The Mediating Role of Visuospatial and Arithmetical Abilities

Basic numerical abilities such as number line estimation have been observed repeatedly to be associated with mathematical achievement. Recently, it was argued that the association between basic numerical abilities and mathematical achievement is fully mediated by visuospatial abilities. However, arithmetical abilities have not yet been considered as influencing this association, even though solution strategies in number line estimation as well as mathematical achievement often involve arithmetical procedures. Therefore, we investigated the mediating role of arithmetical and visuospatial abilities on the association between number line estimation and mathematical achievement in a sample of n = 599 German elementary school students. Results indicated that arithmetical abilities as well as visuospatial abilities mediated the association between number line estimation and mathematical achievement. However, neither visuospatial nor arithmetical abilities fully mediated the association between number line estimation and mathematical achievement when considered in isolation. This substantiates the relevance of the intertwined development of visuospatial and arithemtical abilities as well as basic numerical abilities such as number line estimation (i.e. the combination of domain-specific numerical and domain-general abilities) driving mathematical achievement.

Imparare la matematica con Number Worlds: un intervento quinquennale nella scuola primaria

The Number Worlds (NW) program is based on Case’s theory of cognitive development and conceptual learning, and it promotes the learning of mathematical concepts through playful-manipulative activities and respecting children’s level of development. This five years-research is meant to develop an Italian adaptation of the program, compare it with traditional teaching, and determine the impact of working memory (WM) on math learning. 56 primary school children participated in the research. Since grade I, 13 pupils (controls) followed traditional teaching of math; 43 children worked with NW, 3 hours a week for 7 months. The pupils were assessed with two WM tests, the Number Knowledge Test (NKT), and the Number Line Estimation Task (NLET) at the beginning of Grade I and at the end of each Grade. At the end of Grade V, the AC-MT battery was also administered. The experimental group improved more than controls on the NKT and NLET from Grade I to IV. At the end of Grade V, both groups showed a «ceiling effect» in the NKT and NLET performance. However, a difference in favour of the experimental group was found in some AC-MT tasks. WM, together with the curriculum, was predictive of mathematics performance up to class IV.