Frequency of behaviors or amounts of variables of interest are essential topics in many surveys. The use of heuristics might cause rounded answers, resulting in the increased occurrence of end-digits (called heaping or digit-preference). For web surveys (or CASI), we propose using a conditional prompt as input validation if digits indicating…

Every application of integration by parts can be done with a tabular method. The trick is to identify and consider each new integral in the table before deciding how to proceed. This paper supplements a classic introduction to integration by parts with a particular tabular method called Row Integration by Parts (RIP). Approaches to tabular methods…

To understand misconceptions with rational numbers (i.e., fractions, decimals, and percentages), we administered an assessment of rational numbers to 331 undergraduate students from a 4-year university. The assessment included 41 items categorized as measuring foundational understanding, calculations, or word problems. We coded each student's…

Children's ability to discriminate nonsymbolic number (e.g. the number of items in a set) is a commonly studied predictor of later math skills. Number discrimination improves throughout development, but what drives this improvement is unclear. Competing theories suggest it may be due to a sharpening numerical representation or an improved ability…

This paper examines the meaning-making practices of Latinx bilingual students with a challenging mathematics task involving exponential growth. Our aim is to draw a better understanding of how learning takes place among a group of Latinx bilingual students who participate in official and unofficial social spaces in the classroom. Studying the…

Math language plays a crucial role in early math skill development. However, previous studies have measured math language using children's knowledge or the environmental input of mathematical language, often limiting the scope to specific types of mathematical language. This study examined both numerical (e.g., number-related) and non-numerical…

This paper explores the tensions between two influences that currently shape the design of textbooks and other teaching resources. Through a textual analysis of primary school curricula from Australia and Mexico, we document a "curricular trend" in which number is framed almost exclusively in terms of counting. We explain that this trend…

This study investigated the influence of spontaneous focusing on numerosity (SFON) tendency on the performance and estimation patterns on number line estimation (NLE). To examine this question, 147 preschoolers (3.51-4.52 years) completed two types of SFON task (referenced SFON task and non-referenced SFON task) and three conditions of NLE…

In a pre-service mathematics methods class I taught, in which we mathematized political districting (first horizontally, then vertically), student questions led to engaging mathematics, in particular, the development of a new number sequence.

We describe the development and initial validation of the "ASL Fingerspelling and Number Comprehension Test" (ASL FaN-CT), a test of recognition proficiency for fingerspelled words in American Sign Language (ASL). Despite the relative frequency of fingerspelling in ASL discourse, learners commonly struggle to produce and perceive…

The present study examined patterns of number-related utterances and actions directed to 9-month-old infants by their parents. An ethnically and economically diverse sample of 86 families participated in structured play sessions conducted separately with the mothers and fathers of each infant. Data were coded for eight math talk categories, and…

The study investigates the acquisition of Hebrew zero and pronominal subjects in the context of first and second person. We provide distributional evidence relative to verb tense, number, person, and conversational utterance type, in a peer-talk corpus (2;0-8;0 years). Findings show that acquisition starts early on, that verb inflectional…

Informal Australian discussion suggests that calculators are still widely regarded as devices for calculation, consistent with their naming, and are rarely recognised as potentially helpful to support students learning mathematics. In this paper, Barry Kissane explores some of the ways in which modern calculators might support students learning…

This study reports the results of 4 experiments that addressed whether the domains of deictic time and number exert a cross-domain link. Such a link would be consistent with A Theory of Magnitude (i.e., ATOM). In contrast, no link between the two domains would support the conceptual metaphor theory (CMT), which assumes that each domain is only…

Cover, Copy, Compare (CCC) has been shown to be an effective intervention at improving single-digit multiplication fluency within the academic intervention literature. The application of the three-term contingency trial embedded within CCC provides the intervention with several key components of evidence-based interventions. Given that teachers…