Integer arithmetic is difficult for students worldwide. Although students' integer thinking has frequently been studied, little is known about typical instructional practice for this difficult topic. Thus, to investigate what resources teachers use, we surveyed U.S. middle-grade teachers who teach negative numbers. About half the teachers said…

Mathematical understanding in early childhood lays the foundation for children's later academic achievement, yet little is known about individual differences in U.S. early childhood educators' mathematics instruction in preschool classrooms. The present study explored the range of intentional mathematics instruction occurring in early childhood…

This study sought to understand how students activate number sense in determining the position of fractions on a number line and identify how the natural number bias and number sense influences students' thinking processes. The study utilized the Cognitive Task Analysis (CTA), involving four fifth-grade elementary students as the research…

Background: In response to persistent challenges in early grade mathematics achievement in South Africa, two intervention projects -- Base-Ten Thinking (BTT) and the Mental Starters Assessment Project (MSAP) -- were implemented to enhance number sense through mental mathematics in Grades 2 and 3. These projects integrate Freudenthal's theory of…

Estimation supports the development of higher level mathematical thinking and reasoning; however, has received relatively little research attention. We examined whether making predictions influences the accuracy of numerosity estimates in elementary-aged children, and whether the amount of information available to the estimator determines the…

Background: People report negative attitudes towards fractions and percentages relative to whole numbers (WNs, Sidney, Thompson, Fitzsimmons, & Taber, 2021), and these attitudes may relate to an individual's interpretation of what experiences with these number types signify. Because fractions are challenging, individual differences related to…

After making a lineup identification, eyewitnesses remember being more confident in their identification and having a better view of the initial crime if they are told they correctly identified the suspect compared to witnesses not given this feedback. The present studies investigated whether this effect of feedback occurs similarly when witnesses…

Is the natural number 7 rational? Is it complex? We argue that the answers to these questions relate to the ways numbers are taught. Commonly, a new kind of numbers is presented as an expansion of a previously familiar kind of numbers, which results in a nested image of the relations between number sets. In this article, we introduce an…

Numerosity perception has been studied for at least 150 years and its psychophysics have been well characterized by experimental work. However, the origins of many of its key properties remain obscure. For instance, people estimate the numerosity of small sets (up to four) much more rapidly and accurately than larger sets; people tend to…

In this paper, we first focus on the sum of powers of the first n positive odd integers, T[subscript k](n)=1[superscript k]+3[superscript k]+5[superscript k]+...+(2n-1)[superscript k], and derive in an elementary way a polynomial formula for T[subscript k](n) in terms of a specific type of generalized Stirling numbers. Then we consider the sum of…

This article presents a case study of two Grade 5 boys' argumentation concerning addition and subtraction of negative numbers while using an interactive tablet-based application simulating positive and negative tiles. We examine the properties of integers they conjectured, and the kinds of evidence and arguments they used to support their…

Reimagining elementary mathematics pedagogy using a three-step process--See It, Say It, Symbolize It--author Patrick L. Sullivan provides a guide for developing a dynamic and flexible understanding of numbers and operations. By helping students develop a language that is consistent across concepts and connecting it to what is seen and symbolized,…

Textbook is one of the most tangible resources for teaching and learning mathematics, offering valuable opportunities for both teachers and students. This study compared the mathematical tasks in 6th-grade textbooks from the United States and Turkey, focusing on three dimensions of the tasks: representation, contextual features, and cognitive…

This study identifies language specific errors made with transcoding tasks to inform possible future pedagogic decisions regarding the language used when teaching early number. We compared children aged 5-7 years from Kuwait and England. The spoken Arabic language of Kuwait gave the opportunity to compare not only languages where the tens and…

This study explored the utilisation of GeoGebra as a modelling tool to develop undergraduate engineering mathematics students' conceptual and procedural knowledge of complex numbers. This mission was accomplished by implementing GeoGebra-enriched activities, which provided carefully designed representational support to mediate between students'…