The author discusses fixing the "Iceberg Problem" of gaps and unfinished learning lurking beneath the surface of math students. Math is cumulative, with new learning resting atop earlier mastery. Year by year, students learn interconnected concepts in a coherent progression, building a foundational body of knowledge that undergirds new…

Strong prerequisite skills are essential to student success in the calculus sequence; however, many students arrive in Calculus I with weaknesses that are difficult for them to overcome. In this paper, we describe an approach to early incentivized remediation of prerequisite material in a Calculus I course. We present data that supports the idea…

To increase opportunities for students to take more advanced math courses in high school, many school districts enroll grade 8 students in Algebra I, a gateway course for advanced math. But students who take Algebra I in grade 8 and skip other math courses, such as grade 8 general math, might miss opportunities to develop the foundational…

Success in math is important to all students; it provides them with college and career options in the fields of science, technology, engineering, and mathematics. In the middle grades, students build upon the critical skills taught in elementary school and prepare for entry into algebra, which is considered a gateway to later achievement in school…

The collection of studies in this special issue make an important contribution to our understanding and measurement of the core cognitive and noncognitive factors that influence children's emerging quantitative competencies. The studies also illustrate how the field has matured, from a time when the quantitative competencies of infants and young…

ESOL teacher Barbara Gottshalk frequently hears well-intentioned but misinformed comments and questions about English language learners and her teaching field. In this article, she clarifies the misconceptions revealed by 10 common remarks--for example, "The students will never learn English if they don't speak it in their home,"…

The Woodcock-Johnson-Fourth edition (WJ IV; Schrank, McGrew, & Mather, 2014a) and the Wechsler Intelligence Scale for Children-Fifth edition (WISC-V; Wechsler, 2014) are two of the major tests of cognitive abilities used in school psychology. The complete WJ IV battery includes the Woodcock-Johnson IV Tests of Cognitive Abilities (Schrank,…

According to a variety of metrics (NAEP, PISA, TIMMS, college completion, etc.), the mathematics knowledge of U.S. students can be described, at best, as mediocre. In light of the growing importance of mathematics for both individual and national economic competitiveness, this weak performance has rightfully alarmed policymakers and the public.…

Stories that are presented through literature or popular media can be used to invite students into the world of math; stir their mathematical imaginations; and enhance their ability to read about, write about, and discuss math. This article explores how literature ("Flatland," the book and the movie) and an existing seventh-grade unit…

Ask a parent, politician, or school board member to describe the ideal qualifications of a math teacher, and most would probably rank having a college major in that subject high on the list. Yet when it comes to improving student learning in elementary and middle school, research shows that the value of that academic credential is limited--at…

In this Appendix, we provide details about the data used for the current study, the curricula used in the classrooms from which data were collected, and the current study's methodological approach. (Contains 14 tables and 5 footnotes.)[For full report, see ED544189.]

This conceptual article describes a model of a school-based, student-led initiative that uses peer tutoring to address underachievement in mathematics. The model is three pronged: a) it suggests a site-based approach to building on existing student excellence in mathematics to drive improved student mathematics achievement; b) it seeks to address…

Developed jointly by OECD member countries through the OECD's Directorate for Education, the Programme for International Student Assessment (PISA) aims to measure how far students approaching the end of compulsory education have acquired some of the knowledge and skills essential for full participation in the knowledge society. The assessment is…

There are more math classes than there are math teachers to teach them. School administrators often decide how to cover such classes by selecting a person from a pool of other teachers, counselors, and administrators. This can inhibit student progress in math because an appointed math teacher cannot do the job as well as a real math teacher.…

How knowledge of children's thinking in mathematics derived from a cognitive science research model was used by a first-grade teacher to make instructional decisions over four years is described. The curriculum, teacher expectations, and method for using research-based knowledge are reviewed, along with the teacher's knowledge and beliefs. (SLD)