Recent work reveals a left digit effect in number line estimation such that adults' and children's estimates for three-digit numbers with different hundreds-place digits but nearly identical magnitudes are systematically different (e.g., 398 is placed too far to the left of 401 on a 0-1000 line, despite their almost indistinguishable magnitudes;…

Interrupted time series (ITS) studies are frequently used to examine the impact of population-level interventions or exposures. Systematic reviews with meta-analyses including ITS designs may inform public health and policy decision-making. Re-analysis of ITS may be required for inclusion in meta-analysis. While publications of ITS rarely provide…

Children's early accuracy on place value (PV) tasks longitudinally predicts their later multidigit calculation skills. However, another window into children's emerging base-ten concepts is the pattern of errors -- "smart errors" -- they exhibit on these measures. Past research has speculated that these smart errors -- similar to invented…

Explanatory item response models (EIRMs) have been applied to investigate the effects of person covariates, item covariates, and their interactions in the fields of reading education and psycholinguistics. In practice, it is often assumed that the relationships between the covariates and the logit transformation of item response probability are…

Explanatory item response models (EIRMs) have been applied to investigate the effects of person covariates, item covariates, and their interactions in the fields of reading education and psycholinguistics. In practice, it is often assumed that the relationships between the covariates and the logit transformation of item response probability are…

We discuss the limits of the equation of the period of a simple pendulum, T[subscript s] = 2[pi][square root]l/g, frequently used in high-school and university classrooms to measure the acceleration of gravity. We evaluate the relative error in determining the acceleration of gravity with this simple equation instead of a more realistic one,…

Fraction arithmetic facility is fundamental to learning more advanced math topics. However, attaining the ability to add and subtract fractions is hard for many students. The present longitudinal study examined students' growth on simple addition and subtraction word problems between fourth and sixth grades (N = 536). Latent class growth analyses…

To explain children's difficulties learning fraction arithmetic, Braithwaite et al. (2017) proposed FARRA, a theory of fraction arithmetic implemented as a computational model. The present study tested predictions of the theory in a new domain, decimal arithmetic, and investigated children's use of conceptual knowledge in that domain. Sixth and…

Presenting novel numbers about climate change to people after they estimate those numbers can shift their attitudes and scientific conceptions. Prior research suggests that such science learning can be supported by encouraging learners to make use of given benchmark information, however there are several other numerical estimation skills that may…

Student growth percentiles (SGPs) are currently used by several states and school districts to provide information about individual students as well as to evaluate teachers, schools, and school districts. For SGPs to be defensible for these purposes, they should be reliable. In this study, we examine the amount of systematic and random error in…

The purpose of this research was to describe the positions and causes of students' errors in algebraic thinking based on the cognitive style. This study was qualitative research with subject consisting of twelve students. The results showed that (1) students with Field Independent type tended to make errors at the stage of comprehension,…

Adults use a variety of strategies to reason about fraction magnitudes, and this variability is adaptive. In two studies, we examined the relationships between mathematics anxiety, working memory, strategy variability and performance on two fraction tasks: fraction magnitude "comparison" and "estimation." Adults with higher…

Being able to estimate quantity is important in everyday life and for success in the STEM disciplines. However, people have difficulty reasoning about magnitudes outside of human perception (e.g., nanoseconds, geologic time). This study examines patterns of estimation errors across temporal and spatial magnitudes at large scales. We evaluated the…

Though proficiency with computation is highly emphasized in national mathematics standards, students with mathematics difficulty (MD) continue to struggle with computation. To learn more about the differences in computation error patterns between typically achieving students and students with MD, we assessed 478 third-grade students on a measure…

Though proficiency with computation is highly emphasized in national mathematics standards, students with mathematics difficulty (MD) continue to struggle with computation. To learn more about the differences in computation error patterns between typically achieving students and students with MD, we assessed 478 3rd-grade students on a measure of…