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…

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…

Rounding is a necessary step in many mathematical processes. We are taught early in our education about significant figures and how to properly round a number. So when we are given a data set and asked to find a regression line, we are inclined to offer the line with rounded coefficients to reflect our model. However, the effects are not as…

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…

This qualitative case study of emergent practices in a multi-paradigmatic field at one department in Norway explores how performance metrics in science intra-act with staff composition and resource allocation, potentially affecting paradigm trends. Inspired by agential realism, we discuss four key metrics as the material core of an assemblage…

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…

Ever since their serendipitous discovery by Italian mathematicians trying to solve cubic equations in the 16th century, imaginary and complex numbers have been difficult topics to understand. Here the word complex is used to describe something consisting of a number of interconnecting parts. The different parts of a complex number are the…

The present study examines the effect of visual scaffolding on promoting number sense skills (including number recognition, counting, ordinality, comparison, and calculation) of Egyptian autistic children mainstreamed in kindergartens. The participants were five autistic children, enrolled in the second level of kindergarten (ages 5-6).…

Building students' understanding of cardinality is fundamental for working with numbers and operations. Without these early mathematical foundations in place, students will fall behind. Consequently, it is imperative to build on students' strengths to address their weaknesses with the notion of cardinality.

It is widely acknowledged that the transition from informal, everyday knowledge to formal, school-taught knowledge is a critically important stage in children's mathematical development. Research highlights the importance of making connections between the different representations of mathematics and the value of children's own 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…

This article describes some of the essential mathematics that underpins the use of algorithms through a series of learning pathways. To begin, a graphic depicting the mathematical ideas and concepts that underpin the learning of algorithms for multiplication and division is provided. The understanding and use of algorithms is informed by two…

The present study aimed to assess the effect of two different types of digital technologies (computers and tablets) in early childhood students' understanding of numbers. Three hundred and sixty-five children (mean age in months, M = 62.0, SD = 5.5) from 21 kindergarten classes were randomly assigned to two intervention groups and a…

This article contributes to the research literature concerning prospective elementary teachers' mathematical thinking and learning with a focus on flexibility. We present a case study of a prospective elementary teachers' development of flexibility in mental addition and subtraction during a Number and Operations course. Building upon the…

Higher-level mathematics requires a connection between literal symbols (e.g., "x") and their mental representations. The current study probes the nature of mental representations for literal symbols using both the priming distance effect, in which ease of comparing a target number to a fixed standard is a function of prime-target…