Researchers collaborated with a team of third-grade teachers in an urban district in the Upper Midwest to examine misunderstandings among students when using the number line as a model for fractions. Researchers looked closely at how the number line can be used as a model to build meaning for fractions for third-grade students. This article…

Automatic essay scoring (AES) refers to the process of scoring free text responses to given prompts, considering human grader scores as the gold standard. Writing such essays is an essential component of many language and aptitude exams. Hence, AES became an active and established area of research, and there are many proprietary systems used in…

This paper attempts to quantify the accuracy limit of "nextitem-correct" prediction by using numerical optimization to estimate the student's probability of getting each question correct given a complete sequence of item responses. This optimization is performed without an explicit parameterized model of student behavior, but with the…

Henson (1996) provided a number of demonstrations of error patterns in serial recall that contradict chaining models. Chaining models predict that when participants erroneously recall an item too early, recall should proceed from the point of error. In contradiction to such a prediction, Henson found evidence for a fill-in effect: participants…

Many people from Turkey emigrated to European countries as a result of the bilateral agreements signed between Turkey and related countries after the 1950s. The temporary travels to these countries left their place to permanent settlements, and the Turkish children living there were faced with the danger of alienation from their mother tongue and…

The time required to determine the larger of 2 digits decreases with their numerical distance, and, for a given distance, increases with their magnitude (Moyer & Landauer, 1967). One detailed quantitative framework to account for these effects is provided by random walk models. These chronometric models describe how number-related noisy…

Phonotactics--constraints on the position and combination of speech sounds within syllables--are subject to statistical differences that gradiently affect speaker and listener behavior (e.g., Vitevitch & Luce, 1999). What statistical properties drive the acquisition of such constraints? Because they are naturally highly correlated, previous…

Many children fail to master fraction arithmetic even after years of instruction, a failure that hinders their learning of more advanced mathematics as well as their occupational success. To test hypotheses about why children have so many difficulties in this area, we created a computational model of fraction arithmetic learning and presented it…

Memory for spatial location is typically biased, with errors trending toward the center of a surrounding region. According to the category adjustment model (CAM), this bias reflects the optimal, Bayesian combination of fine-grained and categorical representations of a location. However, there is disagreement about whether categories are malleable.…

The ideas behind the constraint-based modeling (CBM) approach to the design of intelligent tutoring systems (ITSs) grew out of attempts in the 1980's to clarify how declarative and procedural knowledge interact during skill acquisition. The learning theory that underpins CBM was based on two conceptual innovations. The first innovation was to…

Research indicates that learning from erroneous examples (EE) is superior to correct examples because errors may provide students with a stimulus to spontaneously produce more self-explanations, leading to better learning outcomes. However, because most studies were conducted in individual settings, it remains an open question whether the…

Counselors should have the counseling skills necessary for making adequate therapeutic progress through counseling sessions. Counselors start learning skills and knowledge for counseling in their undergraduate education. During this critical period, the time, form, and quality of the process of gaining core competencies in counseling differ…

Memories for spatial locations often show systematic errors toward the central value of the surrounding region. The Category Adjustment (CA) model suggests that this bias is due to a Bayesian combination of categorical and metric information, which offers an optimal solution under conditions of uncertainty (Huttenlocher, Hedges, & Duncan,…

The processing of morphological information during Chinese word memorization was investigated in the present study. Participants were asked to study words presented to them on a computer screen in the studying phase and then judge whether presented words were old or new in the test phase. In addition to parent words (i.e. the words studied in the…

The purpose of this study was to apply a random item mixture nominal item response model (RIM-MixNRM) for investigating instruction effects. The host study design was a pre-test-and-post-test, school-based cluster randomized trial. A RIM-MixNRM was used to identify students' error patterns in mathematics at the pre-test and the post-test.…