Does the timing of children's formal understanding of mathematical equivalence matter for algebra readiness? A change-resistance account (McNeil & Alibali, 2005) predicts that it is beneficial for children to construct a formal understanding of mathematical equivalence in the early grades before overly narrow operational patterns become…

Fractions are highly important. Therefore, it is crucial to understand the developmental trajectory of fraction knowledge and its main predictors and consequences. Our research team has proposed that we have a neurocognitive architecture dedicated to processing nonsymbolic ratios, which serves as a startup tool for fractions: the Ratio Processing…

The purpose of this non-experimental, cross-sectional, correlational study was to examine the influence, if any, of mathematical-instructional minutes on academic achievement as measured by the 2014 New Jersey Assessment of Skills and Knowledge (NJ ASK) 6, 7, and 8 mathematics scores. Additionally, the study accounted for other factors that…

Algebra I is a crucial course for middle and high school students for successful STEM related coursework. A key issue is whether students should take Algebra I in 8th versus 9th grade. Large-scale policy studies show conflicting results, and there are few (particularly longitudinal) individual difference studies. Here, 53 students were assessed in…

In spring 2015 Mississippi began testing the college readiness of all grade 11 public high school students and found that approximately 18 percent were ready for college math, a percentage that had changed little by 2017/18. This study examined: (1) the sequences of math courses that Mississippi students took in grades 6-11; (2) the math…

Description: Effective with the 2014/15 school year, Mississippi adopted new academic standards and courses aligned to these new standards. The new courses included both a subject-specific mathematics sequence (that is, algebra I, geometry, and algebra II) as well as an integrated mathematics sequence (that is, integrated I, integrated II, and…

Algebra is a prerequisite for access to STEM careers and occupational success (NMAP, 2008a), yet algebra is difficult for students through high school (US DOE, 2008). Growth in children's conceptual and procedural arithmetical knowledge is reciprocal, although conceptual knowledge has more impact on procedural knowledge than the reverse…

This report is a follow-up to "Gaining Ground in the Middle Grades" (Williams, Kirst, Haertel, et al., 2010). That study specified a comprehensive set of actionable practices that differentiated higher academic achievement among 303 middle grades schools in California. In doing so, the study provided a compelling and coherent account of…

Given its important role in mathematics as well as its role as a gatekeeper to future educational and employment opportunities, algebra has become a focal point of both reform and research efforts in mathematics education. Understanding and using algebra is dependent on understanding a number of fundamental concepts, one of which is the concept of…

This study contributes to the field by identifying a broad range of traditional and newer middle grade policies and practices, and determining in California which of these differentiate higher- from lower-performing schools serving similar student populations, with performance measured by the state's standards-based tests. Based on a sample of 303…

In the 2008-09 school year researchers from EdSource and Stanford University conducted a large-scale study of 303 middle grades schools in California. The team surveyed 303 principals, 3,752 English Language Arts (ELA) and math teachers in grades 6-8, and 157 superintendents of the districts and charter management organizations that oversee the…