Mental computation and mathematical reasoning are two intertwined top-level mental activities. In deciding which strategy to use when doing mental computing, mathematical reasoning is essential. From this reciprocal influence, the current study aims at examining the relationship between mental computation and mathematical reasoning. The study was…

The current study investigated college students' content knowledge and cognitive abilities as factors associated with their algebra performance, and examined how combinations of content knowledge and cognitive abilities related to their algebra performance. Specifically, the investigation examined the content knowledge factors of computational…

Concerns regarding the dominance of the traditional written algorithms in schools have been raised by many mathematics educators, yet the teaching of these procedures remains a dominant focus in in primary schools. This paper reports on a project in one school where the staff agreed to put the teaching of the traditional written algorithm aside,…

This dataset contains the results of a quasi-experiment, testing Karl Pearson's "drunkard's walk" analogy for an abstract random walk. Inspired by the alternate hypothesis that drunkards stumble to the side of their dominant hand, it includes data on intoxicated test subjects walking a 10' line. Variables include: the…

According to national mathematics standards, algebra instruction should begin at kindergarten and continue through elementary school. Most often, teachers address algebra in the elementary grades with problems related to solving equations or understanding functions. With 789 second-grade students, we administered: (1) measures of calculations and…

The following report describes an assessment instrument called the Mathematics Performance and Cognition (MPAC) interview. The MPAC interview was designed to measure two outcomes of interest. It was designed to measure first and second graders' mathematics achievement in number, operations, and equality, and it was also designed to gather…

This report provides an overview of the development, implementation, and psychometric properties of a student mathematics interview designed to assess first- and second-grade student achievement and thinking processes. The student interview was conducted with 622 first- or second-grade students in 22 schools located in two public school districts…

In the context of a department of applied mathematics, a program assessment was conducted to assess the departmental goal of enabling undergraduate students to recognize, appreciate, and apply the power of computational tools in solving mathematical problems that cannot be solved by hand, or would require extensive and tedious hand computation. A…

In operational equating, frequency estimation (FE) equipercentile equating is often excluded from consideration when the old and new groups have a large ability difference. This convention may, in some instances, cause the exclusion of one competitive equating method from the set of methods under consideration. In this report, we study the…

A method called the Remainder Method is proposed for the calculation of sample quantiles of a given order, for example, quartiles, hexatiles, octatiles, deciles and percentiles assuming that all the observations are distinct. Proof is given for a special case of deciles. The criterion "equisegmentation" is proposed, namely that the number of…

The usual formula for variance depending on rounding off the sample mean lacks precision, especially when computer programs are used for the calculation. The well-known simplification of the total sums of squares does not always give benefit. Since the variance of two observations is easily calculated without the use of a sample mean, and the…