Using the basic properties of the base-b representation of rational numbers, we will give an elementary proof of Gauss's lemma: "Every real root of a monic polynomial with integer coefficients is either an integer or irrational." The paper offers a new perspective in understanding the meaning of 'irrational numbers' from a deeper…

We present a method to compute the power series expansions of e[superscript x] ln (1 + x), sin x, and cos x without relying on mathematical analysis. Using the properties of elementary functions, we determine the coefficients of each series through the method of undetermined coefficients. We have validated our formulae through the use of…

Imaginary latent variables are variables with negative variances and have been used to implement constraints in measurement models. This article aimed to advance this practice and rationalize the imaginary latent variables as a method to detect possible latent deficiencies in measurement models. This rationale is based on the theory of complex…

This article describes and analyzes the findings of children's observation records of block play with a focus on the wide range of mathematical outcomes resulting from children's block play. To this end, children's mathematical learning was analyzed in five areas: set and classification; pattern and symmetry; number and arithmetic; comparison and…

Mathematical problem-solving places heavy demands on children's developing working memory capacity. This review examines how offloading numerical information using embodied (e.g. finger counting) or external tools (e.g. manipulatives) can reduce cognitive load and improve mathematical task performance. Strategic offloading emerges in childhood;…

Students with learning disabilities in mathematics often struggle with the underlying concepts of multidigit addition and subtraction. To help students build a conceptual understanding of these computations, teachers can utilize evidence-based practices such as the concrete-semi-concrete-abstract framework and the use of multiple visual…

This work is a segment of an ongoing doctoral research in Brazil. The Leonardo numbers and the Leonardo sequence have gained attention from mathematicians and the academic community. Despite being a relatively new sequence within mathematical literature, its discussion has intensified over the past five years, giving rise to other branches, with…

Online learning affects students' curiosity, so it is important to develop students' curiosity during the pandemic. The purpose of this study is to describe and analyze students' curiosity about online learning. This study was conducted in the Department of Mathematics Education during the odd semester 2021/2022 with 106 students in three…

Empirical evidence suggests a phonological loop deficit associated with Down syndrome. A trisomy 21 may be associated with a narrowing of visual attention to fewer than four objects at a time too. In a study with computer tachistoscopy, the hypothesis was confirmed in all 194 persons with trisomy 21. The subitising limit of persons with trisomy 21…

This study aimed to examine whether a computational thinking (CT) intervention related to (a) number knowledge and arithmetic (b) algebra, and (c) geometry impacts students' learning performance in primary schools. To this end, a quasi-experimental, nonequivalent group design was employed, with 61 students assigned to the experimental group and 47…

The ability to solve mathematical problems has been an interesting research topic for several decades. Intuition is considered a part of higher-level thinking that can help improve mathematical problem-solving abilities. Although many studies have been conducted on mathematical problem-solving, research on intuition as a bridge in mathematical…

Studies show that indigenous languages have exhibited enormous impact on the evolution and didactics of counting and place value. However, Ghana systems have different perspectives and pose varied successes on the didactics of counting and place value. In this study, we explored a mixed methods design to examine the mismatch between Ghanaian and…

Children's mathematical knowledge at school entry varies considerably and predicts long-term achievement outcomes. Differences in children's exposure to math and number talk at home may help to explain variations in school-entry math ability. However, nearly all research on exposure to math and number talk has been conducted with parents and…

Recent studies show that English learning students are a growing population within the United States school system. Language barriers have been shown to negatively influence reading scores as well as math scores, and math scores are a predictor of future academic success in many subject areas. This qualitative action research study demonstrates…

Yupana Inca Tawa Pukllay (YITP) is a ludic didactic resource based on semiotic alternation that, using the reading of numbers in the Inca numeral system, improves its equivalent Indo-Arabic reading. Twelve children from first to fourth grade of a bilingual (Spanish-Quechua), multi-grade elementary school in a small rural Peruvian community were…