Numerical Training Videos and Early Numerical Achievement: A Study on 3-Year-Old Preschoolers

Early numerical abilities predict later math achievement and could be improved in children by using various training methods. As the literature on the use of training videos to develop numerical abilities is still surprisingly scant, the aim of the present study was to test the efficacy of a numerical training video on the development of counting and number line knowledge in 3-year-old preschoolers. Far transfer effects to cardinality and working memory were also examined. The study involved 86 children randomly assigned to two intervention groups: a numerical training group exposed to videos on counting and number lines; and a control group exposed to videos on colors and animal names in a foreign language. After the video training, there was an improvement in the numerical training group’s counting skills, but not in their number line knowledge, and this improvement persisted six months later. The numerical training group also showed a far-transfer enhancement of cardinality six months after the intervention. Based on our results, numerical training videos could be effective in helping to enhance early numeracy skills in very young preschoolers.

Senior high school students’ understanding of mathematical inequality

Mathematics inequality is an essential concept that students should fully understand since it is required in mathematical modeling and linear programming. However, students tend to perceive the solution of the inequalities problem without considering what the solution of inequality means. This study aims to describe students’ mistakes variations in solving mathematical inequality. It is necessary since solving inequality is a necessity for students to solve everyday problems modeled in mathematics. Thirty-eight female and male students of 12th-grade who have studied inequalities are involved in this study. They are given three inequality problems which are designed to find out students’ mistakes related to the change of inequality sign, determine the solution, and involve absolute value. All student work documents were analyzed for errors and misconceptions that emerged and then categorized based on the type of error, namely errors in applying inequality rules, errors in algebraic operations, or errors in determining the solution set, then described. The result shows that there were some errors and misconceptions that students made caused by still bringing the concept of equality when solving the inequalities problem. It made them did not aware of the inequality sign. Students are still less thorough in operating algebra and do not understand the number line concept in solving inequalities. The other factor was giving “fast strategy” to the students without considering the students’ understanding.

Learner-generated drawings by students with mathematical learning difficulties in finishing open number sentences

Although MLD students do not have good mathematical performance in completing addition and subtraction operations of integers, MLD students have suggestive ideas in the form of drawings produced in solving open number sentences questions. This study aims to classify the types and identify changes in the drawing produced by MLD students in solving open number sentences questions. This research method is qualitative with a micro generic study approach to understand students' thinking individually and explore drawing changes in solving open number sentences questions between sessions. The research subjects were 2 out of 20 MLD grade 5 elementary school students who produced the most varied drawings in solving open number sentences questions. Data collection techniques used are giving questions and interviews. The results showed that MLD students produced: discrete object drawings by focusing on the cardinality of the quantity of a number; transitions from objects to the number line by focusing on the magnitude of numbers; partitioning the number line using magnitude reasoning; number sentences; and others using verbal reasoning. Changes in the drawings produced by MLD students between sessions indicate the development of students' understanding towards a better direction in interpreting symbolic representations to visual representations. The results of this study contribute to the theory that although MLD students have low mathematical performance. However, MLD students can produce variations and changes in drawings with rich mathematical idea information representing integer operations.

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.

Uncertainty and Prior Assumptions, Rather Than Innate Logarithmic Encoding, Explain Nonlinear Number-to-Space Mapping

Mapping number to space is natural and spontaneous but often nonveridical, showing a clear compressive nonlinearity that is thought to reflect intrinsic logarithmic encoding of numerical values. We asked 78 adult participants to map dot arrays onto a number line across nine trials. Combining participant data, we confirmed that on the first trial, mapping was heavily compressed along the number line, but it became more linear across trials. Responses were well described by logarithmic compression but also by a parameter-free Bayesian model of central tendency, which quantitatively predicted the relationship between nonlinearity and number acuity. To experimentally test the Bayesian hypothesis, we asked 90 new participants to complete a color-line task in which they mapped noise-perturbed color patches to a “color line.” When there was more noise at the high end of the color line, the mapping was logarithmic, but it became exponential with noise at the low end. We conclude that the nonlinearity of both number and color mapping reflects contextual Bayesian inference processes rather than intrinsic logarithmic encoding.

On The Theory Of Perfect Numbers and Primes

This paper explores the properties of the set $\frac{n(n+1)}{2}$ and its implication on the distribution of perfect numbers. A major takeaway is a conjecture that all perfect numbers - even and odd lie on that line. It also describes primes arising from the perfect number line equation and equivalent statements of perfectness.

The SNARC effect: A preregistered study on the interaction of horizontal,vertical, and sagittal spatial-numerical associations

Small numbers are processed faster through left-sided than right-sided responses, whereas large numbers are processed faster through right-sided than left-sided responses (i.e., the Spatial-numerical Association of Response Codes [SNARC] effect). This effect suggests that small numbers are represented on the left side of space, whereas large numbers are represented on the right side of space, along a mental number line. The SNARC effect has been widely investigated along the horizontal Cartesian axis (i.e., left-right). Aleotti et al. (2020), however, have shown that the SNARC effect could also be observed along the vertical (i.e., small numbers-down side vs. large numbers-up side) and the sagittal axis (i.e., small numbers-near side vs. large numbers-far side). Here, we investigated whether the three Cartesian axes could interact to elicit the SNARC effect. Participants were asked to decide whether a centrally presented Arabic digit was odd or even. Responses were collected through an ad hoc-made response box on which the SNARC effect could be compatible for one, two, or three Cartesian axes. The results showed that the higher the number of SNARC-compatible Cartesian axes, the stronger the SNARC effect. We suggest that numbers are represented in a three-dimensional number space defined by interacting Cartesian axes.