In this study, the authors wanted to examine whether success on items testing basic equivalence knowledge, such as the meaning of the equal sign and ability to solve problems such as 3 + 5 = 4 + _, predicted success on items testing more advanced algebraic thinking (i.e. principles of equality and solving equations that use letter variables). This…

How can schools respond to the call to equip all students with the math skills required in college and the workforce when students are working at widely varying skill levels? Offering extended instructional time in algebra, or double-dose instruction, offers one potential solution to this dilemma and has become an increasingly popular approach for…

The No Child Left Behind Act of 2001 requires states to test students in reading and math and identify them as below proficient, proficient, or advanced. Schools are held accountable only for ensuring that students test proficient or better (both considered passing), leading to concerns that a focus on increasing the percentage of students testing…

Textbooks, like many other resources teachers have at hand, are meant to be an aid for instruction; however there is little research with textbooks or on their potential to develop metacognitive knowledge. Metacognitive knowledge has received substantial attention in the literature, in particular for its relationship with problem-solving in…

In the past year, there was an overall decrease in dropouts at all grade levels in Maryland, with the largest decrease occurring among students in grade 12. Not surprisingly, principals across the state discovered that alternative assessment strategies that were designed to help students from special populations actually worked for all students.…

In a small-scale, 8-month teaching experiment, the author aimed to establish and maintain "mathematical caring relations" (MCRs) (Hackenberg, 2005c) with 4 6th-grade students. From a teacher's perspective, establishing MCRs involves holding the work of orchestrating mathematical learning for students together with an orientation to…

This correspondence reports on a case study conducted in the Master's-level Machine Learning (ML) course at Blekinge Institute of Technology, Sweden. The students participated in a self-assessment test and a diagnostic test of prerequisite subjects, and their results on these tests are correlated with their achievement of the course's learning…

The current study identified socioeconomic status (SES) group differences in student performance on an eighth grade mathematics assessment derived from the Third/Trends in International Mathematics and Science Study (TIMSS) 2003. Differential item functioning (DIF) methodology was applied to examine SES group differences on item performance for…

Data on public secondary schools in Arkansas were gathered for two separate school years, 2005-2006 (N = 278) and 2006-2007 (N = 279), to determine if there was an association between athletic expenditures and student academic achievement. Prior to this research, there was little empirical evidence demonstrating any effect that athletic spending…

This study measured the amounts of different types of metacognitive statements made by students enrolled in Elementary Algebra courses at a community college in California. A total of 17 students were interviewed three times during the course of a semester. All interviews were coded for types of metacognitive statements that fell into one of three…

In this article the authors set out to examine the effect of tracking in mathematics. Previous analyses have shown it to be quite prevalent at 8th grade unlike much of the rest of the world. The US practices both between- and within-school tracking, leading to very different content coverage for different students. Without judging the merits of…

"Perspective" is a monthly e-newsletter presenting news and views from Achieve. This month's issue commences with a commentary assessing the meaning of college- and career-readiness. In doing so, it addresses some of the questions Achieve gets asked most frequently, including: What subjects are most important in defining "Readiness"? What does…

Comparing multiple examples typically supports learning and transfer in laboratory studies and is considered a key feature of high-quality mathematics instruction. This experimental study investigated the importance of prior knowledge in learning from comparison. Seventh- and 8th-grade students (N = 236) learned to solve equations by comparing…

Second-order latent growth curve models (S. C. Duncan & Duncan, 1996; McArdle, 1988) can be used to study group differences in change in latent constructs. We give exact formulas for the covariance matrix of the parameter estimates and an algebraic expression for the estimation of slope differences. Formulas for calculations of the required sample…

This article reports on work undertaken by schools as part of Qualifications and Curriculum Authority's (QCA's) "Engaging mathematics for all learners" project. The goal was to use in the classroom, materials and approaches from a Royal Institution (Ri) Year 10 master-class, "Number Sense", which was inspired by examples from…