We report on results of a classroom teaching experiment in a mathematics content course for prospective elementary teachers. A local instruction theory for the development of number sense, which was previously applied to whole-number mental computation, was extended to inform instruction concerning reasoning about fraction magnitude. We found that…

Students with emotional and behavioral disorders (EBD) demonstrate significant academic deficits across content areas (Coutinho, 1986; Lane, Barton-Arwood, Nelson, & Wehby, 2008; Nelson, Benner, Lane, & Smith, 2004; Reid, Gonzalez, Nordness, Trout, & Epstein, 2004; Ruhl & Berlinghoff, 1992). Mathematics, however, appears to be especially…

Multiplication facts are difficult to teach. Therefore many researchers have put a great deal of effort into finding multiplication strategies. Sherin and Fuson (2005) provided a good survey paper on the multiplication strategies research area. Kolpas (2002), Rendtorff (1908), Dabell (2001), Musser (1966) and Markarian (2009) proposed the finger…

Depending on task combination, dual-tasking can either be performed successfully or can lead to performance decrements in one or both tasks. Interference is believed to be caused by limitations in central processing, i.e. structural interference between the neural activation patterns associated with each task. In the present study, single- and…

An essential component of skill acquisition is learning the environmental conditions in which that skill is relevant. This article proposes and tests a neurobiologically detailed theory of how such learning is mediated. The theory assumes that a key component of this learning is provided by the cholinergic interneurons in the striatum known as…

Research literature is reviewed, identifying a need to design instruction to support multi-digit mental computation and critiquing conventional place value instruction. A distinctive instructional domain is proposed, called conceptual place value (CPV)--incrementing and decrementing numbers by units of ones, tens and hundreds. A design research…

Proton beams have been colliding at 7 TeV in the Large Hadron Collider (LHC) since 30 March 2010, meaning that the LHC research programme is underway. Particle physicists around the world are looking forward to using the data from these collisions, as the LHC is running at an energy three and a half times higher than previously achieved at any…

Exploring number systems of other cultures can be an enjoyable learning experience that enriches students' knowledge of numbers and number systems in important ways. It helps students deepen mental computation fluency, knowledge of place value, and equivalent representations for numbers. This article describes how the author designed her…

The most common question the author's students ask is, "When will I ever use this in real life?" To address this question in her geometry classes, the author sought to create a project that would incorporate a real-world business situation with their lesson series on the surface area and volume of three-dimensional objects--specifically, prisms,…

The process-component approach has become quite popular for examining many psychological concepts. A typical example is the model with internal restrictions on item difficulty (MIRID) described by Butter (1994) and Butter, De Boeck, and Verhelst (1998). This study proposes a hierarchical generalized random-situation random-weight MIRID. The…

This study investigated curriculum influences on student mathematics achievement by following two groups of students from fifth to sixth grade that were taught either the reformed curriculum or the conventional curriculum. Analyses with three-level modeling were conducted to examine learning outcomes of the students who were assessed three times…

The article considers a test of specification for quantile regressions. The test relies on the increase of the objective function and the worsening of the fit when unnecessary constraints are imposed. It compares the objective functions of restricted and unrestricted models and, in its different formulations, it verifies (a) forecast ability, (b)…

The article extends and applies previous approaches by Klauer and Fischer to the statistical evaluation of ability changes in tests conforming to the Rasch model (RM). Exact uniformly most powerful unbiased (UMPU) hypothesis tests and uniformly most accurate (UMA) confidence intervals (CIs) for the amount of change can be constructed for each…

This study examines how audiovisual signals are combined in time for a temporal analogue of the ventriloquist effect in a purely temporal context, that is, no spatial grounding of signals or other spatial facilitation. Observers were presented with two successive intervals, each defined by a 1250-ms tone, and indicated in which interval a brief…

Researchers have been making use of ecological momentary assessment (EMA) and other study designs that sample feelings and behaviors in real time and in naturalistic settings to study temporal dynamics and contextual factors of a wide variety of psychological, physiological, and behavioral processes. As EMA designs become more widespread,…