This study investigated the developmental dynamics of mathematical performance during children's transition from preschool to Grade 2 and the cognitive antecedents of this development. 194 Finnish children were examined 6 times according to their math performance, twice during each year across a 3-year period. Cognitive antecedents, that is,…

This article extends and strengthens the knowledge in pieces perspective (diSessa, 1988, 1993) by applying core components to analyze how 5th-grade students with computational knowledge of whole-number multiplication and connections between multiplication and discrete arrays constructed understandings of area and ways of using representations to…

The authors extend the standard education production function and student time allocation analysis to focus on the interactions between student effort and performance over the semester. The purged instrumental variable technique is used to obtain consistent estimators of the structural parameters of the model using data from intermediate…

Simple slopes, regions of significance, and confidence bands are commonly used to evaluate interactions in multiple linear regression (MLR) models, and the use of these techniques has recently been extended to multilevel or hierarchical linear modeling (HLM) and latent curve analysis (LCA). However, conducting these tests and plotting the…

Three pieces of literature are used to launch mathematical investigations. The tasks provide opportunities for students to apply proportional reasoning skills, explore linear relationships, calculate a unit rate, and find the relationship between the volume of a cylinder and a cone. A poem, a short story, and a young adult novel are discussed.…

Spatial visualization is an important skill that deserves instructional attention. Strong evidence supports the claim that "measures of mathematical ability tend to be strongly correlated with spatial ability" (Anderson 2000). Thus, there is every reason to believe that time spent helping students develop their spatial visualization skills will…

This article describes a Monte Carlo study of 2 methods for treating incomplete nonnormal data. Skewed, kurtotic data sets conforming to a single structured model, but varying in sample size, percentage of data missing, and missing-data mechanism, were produced. An asymptotically distribution-free available-case (ADFAC) method and structured-model…

Three experiments attempted to clarify the effect of altering the spatial presentation of irrelevant auditory information. Previous research using serial recall tasks demonstrated a left-ear disadvantage for the presentation of irrelevant sounds (Hadlington, Bridges, & Darby, 2004). Experiments 1 and 2 examined the effects of manipulating the…

Computer-assisted instruction (CAI) has been shown to enhance rote memory skills and improve higher order critical thinking skills. The challenge now is to identify what aspects of CAI improve which specific higher-order skills. This study focuses on the effectiveness of using CAI to teach logarithmic graphing and dimensional analysis. Two groups…

In this article, the author describes a week of "timely" open-ended lessons with a high ability Y9 group of boys. He gives lessons that would give the students some sense of purpose, as they try to generate a mathematical entity to represent something they used regularly. He states that understanding metric time is something his students…

This study examines basic number processing (subitizing, automaticity, and magnitude representation) as the possible underpinning of mathematical difficulties often evidenced in deaf adults. Hearing and deaf participants completed tasks to assess the automaticity with which magnitude information was activated and retrieved from long-term memory…

Complex survey designs often employ multistage cluster sampling designs and oversample particular units to ensure more accurate population parameter estimates. These issues must be accommodated in the analysis to ensure accurate parameter estimation. Incorporation of sample weights in some statistical procedures has been studied. However, research…

A method for incorporating maximum likelihood (ML) estimation into reliability analyses with item-level missing data is outlined. An ML estimate of the covariance matrix is first obtained using the expectation maximization (EM) algorithm, and coefficient alpha is subsequently computed using standard formulae. A simulation study demonstrated that…

Ipsative data (individual scores subject to a constant-sum constraint), suggested to minimize response bias, are sometimes observed in behavioral sciences. Chan and Bentler (1993, 1996) proposed a method to analyze ipsative data in a single-group case. Cheung and Chan (2002) extended the method to multiple-group analysis. However, these methods…

When a professional engineer solves a mathematical problem using technology, he/she generally uses a single one-step "high-level" command of a readily available computer package to obtain the solution immediately. This should not happen during his/her learning cursus. In an engineering mathematics course, the educator should decompose the solution…