The purpose of the current study was to examine dimensionality and concurrent validity evidence of the EARLI numeracy measures (DiPerna, Morgan, & Lei, 2007), which were developed to assess key skills such as number identification, counting, and basic arithmetic. Two methods (NOHARM with approximate chi-square test and DIMTEST with DETECT…

This study reports the neurophysiological and behavioral correlates of digital memory retrieval features in Chinese individuals with and without dyscalculia. A total of 18 children with dyscalculia (ages 11.5-13.5) and 18 controls were tested, and their event-related potentials were digitally recorded simultaneously with behavior measurement.…

We studied the acquisition of the ordinal meaning of number words and examined its development relative to the acquisition of the cardinal meaning. Three groups of 3-, 4-, and 5-year-old children were tested in two tasks requiring the use of number words in both cardinal and ordinal contexts. Understanding of the counting principles was also…

Adult proficiency in numeracy in the United States lags that of other developed nations, and the nonselective institutions that dominate the higher education sector struggle to address the learning needs of the sizeable proportion of students who enroll in their institutions and are deemed academically underprepared in mathematics. Research on…

These proceedings are a written record of the research presented at the 41st annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (PME-NA) held in St. Louis, Missouri, November 14-17, 2019. This year's conference theme is "...against a new horizon." The papers comprise 67…

Nearly all studies aiming to determine the effect of modern teaching methods on academic success using an experimental design contain control groups in which traditional methods are used. Effect of traditional methods in geometry and numbers learning domains on academic achievement has not been conclusively studied by researchers yet. On the other…

While early childhood practitioners have long been asked to have complex understandings of child development and provide rich, meaningful educational experiences for children, focusing on mathematics marks new terrain. Consequently, teacher educators are now tasked with figuring out how to communicate new ideas about early mathematics education to…

While early childhood practitioners have long been asked to have complex understandings of child development and provide rich, meaningful educational experiences for children, focusing on mathematics marks new terrain. Consequently, teacher educators are now tasked with figuring out how to communicate new ideas about early mathematics education to…

The transition from whole numbers to integers involves challenges for both students and teachers. Leadership in mathematics education calls for an ability to translate depth of understanding into effective teaching methods, and this landscape includes alternative treatments of familiar topics. Noting the multiple meanings associated with the…

A pair of 6-sided dice cannot be relabeled to make the sums 2, 3,...., 12 equally likely. It is possible to label seven, 10-sided dice so that the sums 7. 8,..., 70 occur equally often. We investigate such relabelings for "pq"-sided dice, where "p" and "q" are distinct primes, and show that these relabelings usually…

We give an elementary solution to the famous Basel Problem, originally solved by Euler in 1735. We square the well-known series for arctan(1) due to Leibniz, and use a surprising relation among the re-arranged terms of this squared series.

Humans rely on two main systems of quantification; one is nonsymbolic and involves approximate number representations (known as the approximate number system or ANS), and the other is symbolic and allows for exact calculations of number. Despite the pervasiveness of the ANS across development, recent studies with adolescents and school-aged…

Anthropological approaches to studying the contextual specificity of mathematical thought and practice in schools can productively inform descriptions and analyses of mathematical practices within and across different teaching and learning contexts. In this paper I argue for an anthropological methodological orientation that takes into…

Tablet computers (tablets) are positioned to be powerful, innovative, effective, and motivating research and assessment tools. We addressed two questions critical for evaluating the appropriateness of using tablets to study number-line estimation, a skill associated with math achievement and argued to be central to numerical cognition. First, is…

Treatment dose is an understudied aspect of treatment effectiveness. This study compared the frequency with which a small-group mathematics intervention was delivered weekly (i.e., four times, twice, once) with a control condition while controlling for total duration. 101 at-risk students in grades 2-4 were randomly assigned to a condition…