Numerical understanding and arithmetic skills are easier to acquire for whole numbers than fractions. The "integrated theory of numerical development" posits that, in addition to these differences, whole numbers and fractions also have important commonalities. In both, students need to learn how to interpret number symbols in terms of…

Fraction and decimal arithmetic are crucial for later mathematics achievement and for ability to succeed in many professions. Unfortunately, these capabilities pose large difficulties for many children and adults, and students' proficiency in them has shown little sign of improvement over the past three decades. To summarize what is known about…

Although restating part of a student's correct response correlates with learning and various types of restatements have been incorporated into tutorial dialogue systems, this tactic has not been tested in isolation to determine if it causally contributes to learning. When we explored the effect of tutor restatements that support inference on…

The current study explored a possible continuum of spelling features that children receiving literacy instruction in Spanish might be expected to master in Grades 1-3. We administered a developmental spelling inventory representing nine distinct Spanish spelling features to 864 students in bilingual and dual language schools across the U.S.…

As learning technologies proliferate, it is important for research to address how to best align instruction to educational goals. For example, recent evidence indicates that working collaboratively may have unique benefits for facilitating the acquisition of conceptual understanding, as opposed to procedural fluency (Mullins, Rummel & Spada,…

We examined relations between symbolic and non-symbolic numerical magnitude representations, between whole number and fraction representations, and between these representations and overall mathematics achievement in fifth graders. Fraction and whole number symbolic and non-symbolic numerical magnitude understandings were measured using both…

Post-problem reflective tutorial dialogues between human tutors and students are examined to predict when the tutor changed the level of abstraction from the student's preceding turn (i.e., used more general terms or more specific terms); such changes correlate with learning. Prior work examined lexical changes in abstraction. In this work, we…

Implementing evidence-based practices (EBPs) for children with autism is challenging for teachers because these practices are often complex, requiring significant training and resources that are not available in most school settings. This brief investigation was designed to identify areas of strength and difficulty for teachers implementing one…

We examined developmental and individual differences in 6th and 8th graders' fraction arithmetic and overall mathematics achievement and related them to differences in understanding of fraction magnitudes, whole number division, executive functioning, and metacognitive judgments within a crosssectional design. Results indicated that the difference…

For some time, it has been clear that students who are tutored generally learn more than students who experience classroom instruction (e.g., Bloom, 1984). Much research has been devoted to identifying features of tutorial dialogue that can explain its effectiveness, so that these features can be simulated in natural-language tutoring systems. One…

We investigated the relation between children's numerical-magnitude representations and their memory for numbers. Results of three experiments indicated that the more linear children's magnitude representations were, the more closely their memory of the numbers approximated the numbers presented. This relation was present for preschoolers and…