National mathematics achievement results show that elementary students in the United States are not increasing in cognitive ability or critical thinking skills (NAEP, 2020). For this increase, mathematically promising students require more opportunities for cognitively demanding mathematics instruction. As a result, this descriptive study focused…

At Haverford High School, a suburban high school in Haverford, Pennsylvania, a mathematical achievement gap exists for economically disadvantaged, special education, and Black students. Researchers have found that students in lower tracked classes often receive less rigorous tasks, tasks with lower cognitive demand, and fewer tasks that focus on…

Through the lenses of statistical investigations and cognitive demands, we examined bivariate data tasks offered in US high school mathematics textbook series--a popular representative of three curriculum types: traditional, integrated, and hybrid. We developed a framework grounded in literature of association topics for the inclusion and…

Many current policy initiatives focus on teacher qualifications and high-stakes assessments for students as a means to improve mathematics education in the United States, but this approach ignores the actual practice of teaching through which students have opportunities to learn mathematics. The present study is an effort to answer scholars'…

Using Young Lives longitudinal data from Peru, this paper explores the relationship between socioeconomic status (SES) measured at the age of one, opportunities to learn (OTL) and achievement in mathematics ten years later. Four variables of OTL were measured: hours of class per year, curriculum coverage, quality of teachers' feedback, and level…

A large body of research has shown that for novice learners, instruction that relies more heavily on worked examples than on problem solving, is more effective for learning as shown by higher test performance. Moreover, this beneficial effect is often obtained with less acquisition time and lower cognitive load during acquisition and test phase.…

Contemporary debates on effective pedagogies for K-12 mathematics have called for shifts in the way teachers and teacher educators conceptualise mathematics as a subject and how it should be taught. This is reflected by changes in the curriculum including the inclusion of a strand called Working Mathematically within K-12 mathematics curriculum…

To understand the difficulties that many students have with comprehension of mathematics, we must determine the cognitive functioning underlying the diversity of mathematical processes. What are the cognitive systems that are required to give access to mathematical objects? Are these systems common to all processes of knowledge or, on the…

Today, mathematics education faces two major challenges: raising the floor by expanding achievement for all, and lifting the ceiling of achievement to better prepare future leaders in mathematics, as well as in science, engineering, and technology. Many students lack access to higher-level mathematics courses and teaching at all levels of…