Seventh graders from a STEM school performed poorly with rational number concepts in the yearly standardized test. This research investigated the impact of a three-day professional development intervention focused on improving math teachers' self-efficacy when teaching rational numbers. The study employed a concurrent mixed-method research design…

This study presents the preliminary qualitative results of a larger mixed methods study. The qualitative phase utilized task-based clinical interviews to examine the non-symbolic and symbolic linear generalizations of middle-grades students. This investigation identified similarities and differences in the students' generalizations, and…

The Tchokwe people lived on the African continent, in Mozambique and Angola. The sona belong to their cultural tradition. The sona are drawings made in the sand by older members of the tribe to tell stories, essential in the youngests' formation. In this article, we show a relationship between the sona and the greatest common divisor (GCD) of two…

This study seeks to analyse the awareness of the pre-service teachers on the counting methods, systems and tools used in the prehistoric method and the Ancient period and to examine the distribution of this awareness by gender. A total of 42 sophomore-level students studying at a university in the Western Black Sea region, Turkey, participated in…

In this paper, we share details of a South African early grades' number intervention informed by aspects of Davydov's writing on early number teaching and learning. A key part of Davydov's approach to early number teaching involves starting with attention to relationships between quantities rather than with counting. The Structuring Number…

This article describes the results of an investigation based on a Models and Modeling Perspective [MMP]. We present the evolution of the models built by university students when solving a model development sequence designed to promote their learning of the exponential function. As a result, we observed that students' thinking was modified,…

Background/purpose: Investigation into the misconceptions of preschool students in mathematics and their differences between the ages of 4-5 and 5-6 years old helps form appropriate developmental mathematics teaching programs. However, although several studies have been conducted examining preschoolers' previous knowledge and misconceptions about…

Children learn math concepts long before they enter school. Across all cultures, children are exposed to number and spatial language to varying degrees during everyday home routines. Yet most studies of math talk occur in the lab and target non-Hispanic, English-speaking families. We expanded inquiry to the spontaneous math language (i.e., number…

The authors describe a lesson--"You Decide"--which challenges students but also provides opportunities for success for those who may struggle. They show how this lesson has been helpful for teachers in revealing some misconceptions that often exist in primary students' thinking. In this article, they share data on the apparent relative…

This study investigated in-service teachers' conceptualization of the pure imaginary number, within the Cartesian form, "a" + "ib" where "a" and "b" are real numbers and "i" is the imaginary unit. As part of a larger design-based research study, in which a professional development (PD) program was…

A test method is described for determining the divisibility of non-negative integers by a prime number. The test uses an integer multiplying factor that is defined for each prime, designated as [beta], to reduce the non-negative integer that is being tested by an order of magnitude in each of a sequence of steps to obtain a series of new numbers.…

Much research has examined the reciprocal relations between a child's spontaneous focus on number (SFON) in the preschool years and later mathematical achievement. However, this literature relies on several different tasks to assess SFON with distinct task demands, making it unclear to what extent these tasks measure the same underlying construct.…

This paper is concerned with developing a new class of generalized numbers. The main advantage of this class is that it generalizes the two classes of generalized Fibonacci numbers and generalized Pell numbers. Some new identities involving these generalized numbers are obtained. In addition, the two well-known identities of Sury and Marques which…

Arguably one of the most under-appreciated, yet ubiquitous and frequently utilized aspects of modern, globalized society, our number system exemplifies how we are inextricably interconnected. Indeed, without a universal number system, there would be no global collaboration and no global solutions.

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…