Arithmetic fluency is regarded as a foundational math skill, typically measured as a single construct with pencil-and-paper-based timed assessments. We introduce a tablet-based assessment of single-digit fluency that captures individual trial response times across several embedded experimental contrasts of interest. A large (n = 824) cohort of…

This study examines the conceptual understanding of numbers and operations among 372 fifth-grade students, based on their responses to an online three-tier test designed to assess their number sense, declarative knowledge, explanatory knowledge, and confidence. The results showed that most students had low performance and low number sense, with…

Decimal misconceptions are a persistent challenge in mathematics education, often hindering students' long-term understanding. This study examines how learning analytics (LA) can be effectively integrated into instructional sequences to address these misconceptions, providing teachers with real-time insights for formative assessment. Despite the…

Many U.S. students possess only a weak knowledge of fraction arithmetic. I hypothesize that textbooks are a critical reason for students' poor performance on fraction arithmetic. This is not because of what textbooks contain but rather because of what they lack. Distributions of fraction arithmetic problems in textbooks are imbalanced, with…

The intention of the study was to examine the effects of a fraction intervention in a whole-class environment. The intervention aimed to enhance students' conceptual fraction knowledge, with a major focus on fraction magnitude understanding. This study included 120 fifth-grade students in standard classroom settings. Utilizing a cluster randomized…

Mathematics anxiety hinders students' mathematical achievement already in primary school, but research on its effects beyond whole number knowledge is limited. The main aim of the current study is to examine how state and trait mathematics anxiety relate to performance across five tasks that are relevant for the development of mathematics in…

Fraction is considered one of the main topics in mathematics in the early years. Many students struggle to progress in fractions in the classrooms and on exams. Teaching strategies are among the most important factors affecting student learning of fractions. The objective of this study was to examine the effectiveness of virtual and concrete…

Studies on math learning programs are lacking that consider a wide set of outcome variables, and students' practice behavior. Therefore, we investigated whether an adaptive arithmetic learning program fosters students' math performance (addition and subtraction), math self-concept, and a reduction of math anxiety, and how practice behavior…

Although an increasing number of studies have suggested that students with low mathematics achievement (LMA) tend to perform worse in arithmetic strategy use than children with typical development, the potential reasons remain unclear. Accordingly, the current study investigated the potential impact of task switching on strategy use for children…

Reasoning about numerical magnitudes is a key aspect of mathematics learning. Most research examining the relation of magnitude understanding to general mathematics achievement has focused on whole number and fraction magnitudes. The present longitudinal study (N = 435) used a 3-step latent class analysis to examine reasoning about magnitudes on a…

The Say-All-Fast-Minute-Every-Day-Shuffled (SAFMEDS) strategy promotes fast and accurate recall. The existing literature suggests that the strategy can help learners improve academic outcomes. Through a cluster randomized controlled trial, we assessed the impact of implementation support on children's mathematics outcomes during a teacher-led…

Personal Best (PB) goals are defined as specific, challenging, and competitively self-referenced goals involving a level of performance or effort that meets or exceeds an individual's previous best. Much of the available research underpinning arguments for PB goal-setting is self-report-based; thus, the causal effect of PB goals on learning…

To meet increasingly complex mathematics standards in late elementary school, students must conceptually understand and be fluent in the operations of multiplication and division. This includes understanding the operations' inverse relation. The purpose of the study was to investigate the effects of alternating concrete-representational-abstract…

This study investigated the accuracy of three fraction measures (i.e., fraction number line estimation accuracy, general fraction concepts, and fraction arithmetic) for screening fourth graders who might be at risk for mathematics difficulties. Receiver operating characteristic (ROC) curve analyses assessed diagnostic accuracy of the fraction…

In the present study, we explored how linguistic skills (phonological and semantic) influence the multiple components of school arithmetic (numeration, computation, and word problems) by analyzing them sequentially. We studied a sample of 262 schoolchildren, aged 8 to 11, nested in 27 classrooms, using the following measures: semantic skills,…