Decimal numbers are generally assumed to be a straightforward extension of the base-ten system for whole numbers given their shared place value structure. However, in decimal notation, unlike whole numbers, the same magnitude can be expressed in multiple ways (e.g., 0.8, 0.80, 0.800, etc.). Here, we used a number line task with carefully selected…

Meta-analyses have become the gold standard for synthesizing evidence from multiple clinical trials, and they are especially useful when outcomes are rare or adverse since individual trials often lack sufficient power to detect a treatment effect. However, when zero events are observed in one or both treatment arms in a trial, commonly used…

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;…

Functions and formulas in spreadsheets provide an instructional opportunity to help students build their skills in identifying errors in their own work and identifying a path to go about correcting the errors. This paper provides examples of functions and equations used to create two approaches to calculating the solution to one problem, such as a…

Solving systems of linear equations is a core concept in linear algebra and a wide variety of problems found in the sciences and engineering can be formulated as linear equations. This study sought to explore undergraduate students' development of the schema for solving systems of linear equations. The triad framework was used to describe the…

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…

Studies on children's understanding of counting examine when and how children acquire the cardinal principle: the idea that the last word in a counted set reflects the cardinal value of the set. Using Wynn's (1990) Give-N Task, researchers classify children who can count to generate large sets as having acquired the cardinal principle…

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…

Subject-verb agreement errors are common in sentence production. Many studies have used experimental paradigms targeting the production of subject-verb agreement from a sentence preamble ("The key to the cabinets") and eliciting verb errors (… "*were shiny"). Through reanalysis of previous data (50 experiments; 102,369…

Collaborative learning offers numerous benefits to learners, largely due to the dialogue that is unfolding between them. However, there is still much to learn about the structure of collaborative dialogue, and especially little is known about co-creative dialogues during learning. This paper reports on a study with learners engaged in co-creative…

Block programming has been suggested as a way of engaging young learners with the foundations of programming and computational thinking in a syntax-free manner. Indeed, syntax errors--which form one of two broad categories of errors in programming, the other one being logic errors--are omitted while block programming. However, this does not mean…

Orlando and Thissen (2000) introduced the "S - X[superscript 2]" item-fit index for testing goodness-of-fit with dichotomous item response theory (IRT) models. This study considers and evaluates an alternative approach for computing "S - X[superscript 2]" values and other factors associated with collapsing tables of observed…

Contextual interference is an established phenomenon in learning research; random practice schedules are associated with poorer performance, but superior learning, compared with blocked practice schedules. We present a secondary analysis of N = 84 healthy young adults, replicating the contextual interference effect in a time estimation task. We…

Presenters' pedagogical choices are strongly affected by whether they view knowledge as coherent or fragmented. This mixed-methods survey study seeks to contribute to epistemological discussions and associated pedagogical suggestions in the context of mole ratio related mistakes evident in stoichiometry calculations performed by in-service…

Several studies have shown that children do not only erroneously use additive reasoning in proportional word problems, but also erroneously use proportional reasoning in additive word problems. Traditionally, these errors were contributed to a lack of calculation and discrimination skills. Recent research evidence puts forward an additional…