In the spirit of the networking of didactical theories, it is advocated in this presentation in favor of a mixed networking of philosophical theories, namely Husserlian phenomenology and hermeneutics, and didactical theories to produce a fertile interplay between philosophy and mathematics education. The cross-analysis of students' work on a…

A vectorial representation of the full sequence of events occurring during the 2D-NMR heteronuclear single-quantum correlation (HSQC) experiment is presented. The proposed vectorial representation conveys an understanding of the magnetization evolution during the HSQC pulse sequence for those who have little or no quantum mechanical background.…

Since the introduction of the Common Core State Standards for Mathematics (CCSSM) in 2010, stakeholders in adopting states have engaged in a variety of activities to understand CCSSM standards and transition from previous state standards. These efforts include research, professional development, assessment and modification of curriculum resources,…

One option for length of individual mathematics class periods is the schedule type selected for Algebra I classes. This study examined the relationship between student achievement, as indicated by Algebra I Criterion-Referenced Test scores, and the schedule type for Algebra I classes. Data obtained from the Utah State Office of Education included…

Much of the work on teacher knowledge suggests that content knowledge shapes pedagogical content knowledge, and in fact is primary in the relationship between the two forms of knowledge. In this paper we challenge this view, arguing from a situated perspective on knowledge and learning, that pedagogical content knowledge strongly shapes content…

We describe methods for assessing all possible criteria (i.e., dependent variables) and subsets of criteria for regression models with a fixed set of predictors, x (where x is an n x 1 vector of independent variables). Our methods build upon the geometry of regression coefficients (hereafter called regression weights) in n-dimensional space. For a…

Between 1990 and 2012, the percentage of 13-year-olds (most of whom are 8th graders) taking algebra more than doubled, from 15% to 34% (National Center for Education Statistics, 2013). Yet recent education policy changes suggest that this movement to encourage algebra-taking in 8th grade has begun to reverse course. Existing research suggests that…

Field experiments that involve nested structures frequently assign treatment conditions to entire groups (such as schools). A key aspect of the design of such experiments includes knowledge of the clustering effects that are often expressed via intraclass correlation. This study provides methods for constructing a more powerful test for the…

The authors review what is known about early and universal algebra, including who is getting access to algebra and student outcomes associated with algebra course taking in general and specifically with universal algebra policies. The findings indicate that increasing numbers of students, some of whom are underprepared, are taking algebra earlier.…

This article presents the results of a study focused on the issue of how proctored testing affects student test scores in a formal Intermediate Algebra course setting. The study follows a model of assessment in which students in one group have taken two of their five unit exams as proctored tests along with a proctored comprehensive final exam,…

Using data from an existing pre-algebra computer-based tutor, we analyzed the covariance of item-types with the goal of describing a more effective way to assign skill labels to item-types. Analyzing covariance is important because it allows us to place the skills in a related network in which we can identify the role each skill plays in learning…

Research has suggested that musicians process music in the same cortical regions that adolescents process algebra. An early adolescence synaptogenesis might present a window of opportunity during middle school for music to create and strengthen enduring neural connections in those regions. Six school districts across Maryland provided scores from…

The educational standards, instruction, and testing of mathematics remain a controversial subject in the United States. Given the significant and growing need for mathematics remediation, it is reasonable to question how well individual states are preparing its high school students to succeed. This evaluation examines the correlation between the…

This study investigates whether the functions linking number-correct scores to the College-Level Examination Program (CLEP) scaled scores remain invariant over gender groups, using test data on the 16 testlet-based forms of the CLEP College Algebra exam. To be consistent with the operational practice, linking of various test forms to a common…

Mathematics is often thought of as a purely intellectual and unemotional activity. Recently, researchers have begun to question the validity of this approach, arguing that emotions and cognition are intertwined. The emotions expressed during mathematics work may be linked to mathematics achievement. We used behavioral measures to identify the…