In this work we examined the content of approximately 950 mathematics questions used in measuring achievement among 4th, 5th and 6th graders in the US in an attempt to determine how the current standardized examinations, which were developed to reflect new national curricular mandates, compared to the old measures used for the same purpose. Using…

This report will determine to what degree the AP Physics 1 and 2 and AP Calculus AB and BC frameworks are aligned with the Trends in International Mathematics and Science Study (TIMSS) Advanced Physics and Mathematics frameworks. This will enable an exploration of any differences in content coverage and levels of complexity, and will set the stage…

There is a lack of knowledge in whether there is a difference in results for students on paper and pencil high stakes assessments and computer-based high stakes assessments when considering race and/or free and reduced lunch status. The purpose of this study was to add new knowledge to this field of study by determining whether there is a…

The Partnership for Assessment of Readiness for College and Careers (PARCC) is a state-led consortium working to develop next-generation assessments that more accurately, compared to previous assessments, measure student progress toward college and career readiness. The PARCC assessments include both English Language Arts/Literacy (ELA/L) and…

Identifying the skills that determine the success or failure to exercises and question items is a difficult task. Multiple skills may be involved at various degree of importance, and skills may overlap and correlate. In an effort towards the goal of finding the skills behind a set of items, we investigate two techniques to determine the number of…

We show that there are exactly four quadratic polynomials, Q(x) = x [superscript 2] + ax + b, such that (x[superscript 2] + ax + b) (x[superscript 2] - ax + b) = (x[superscript 4] + ax[superscript 2] + b). For n = 1, 2, ..., these quadratic polynomials can be written as the product of N = 2[superscript n] quadratic polynomials in x[superscript…

In this paper we discuss an interesting class of noncommutative rings which can be constructed using finite directed graphs. This construction also creates a vector space. These structures provide undergraduate students connections between ring theory and graph theory and, among other things, allow them to see a ring unity element that looks quite…

We use a concept of framing to explain 3 cases in which participants initially lacked mutual understanding but then achieved significant mutual understanding. The cases were all consistent with a pattern of "positional framing" that includes a human participant who is inquiring, which we call a "listener", and a "source", which may be another…

In order to be treated quantitatively, subjective gains and losses (utilities/disutilities) must be psychologically measured. If legitimate comparisons are sought between them, measurement must be at least interval level, with a common unit. If comparisons of absolute magnitudes across gains and losses are further sought, as in standard…

In this note, a new method for computing the partial fraction decomposition of rational functions with irreducible quadratic factors in the denominators is presented. This method involves polynomial divisions and substitutions only, without having to solve for the complex roots of the irreducible quadratic polynomial or to solve a system of linear…

In this qualitative study, we explored how oral interviews can inform instructors about students' understanding of abstract algebra and their ability to construct a proof in this setting. Our findings indicate that some students had a good understanding of the ideas needed for a subgroup proof, but could not write a coherent proof. On the other…

This study investigated middle school students' conceptual understanding of algebraic equations. 257 sixth- and seventh-grade students solved algebraic equations and generated story problems to correspond with given equations. Aspects of the equations' structures, including number of operations and position of the unknown, influenced students'…

Karina Wilkie discusses functional thinking in the primary classroom. She provides a useful learning progression with sample responses to a growing pattern task.

The proportion of eighth graders in United States public schools enrolled in algebra or a more advanced mathematics course doubled between 1990 and 2011. This article uses Early Childhood Longitudinal Study's Kindergarten Cohort data to consider the selection process into advanced middle school mathematics courses and estimate the effects of…

The purpose of this paper is to report the results of a two-part study. Study 1 was conducted to refine and validate a survey instrument, SELMA (Hodges, 2008), used to measure learners' self-efficacy toward learning mathematics in online or technology-intensive, asynchronous learning environments. Study 2 was conducted to investigate the…