SANTIAGO CUETO, CECILIA RAMIREZ and JUAN LEON OPPORTUNITIES TO LEARN AND ACHIEVEMENT IN MATHEMATICS IN A SAMPLE OF SIXTH GRADE STUDENTS IN LIMA, PERU * ABSTRACT. In recent years, the mathematics achievement of Peruvian students has been evaluated in three national and two international studies. The results in all cases sug- gest very poor learning. A similar situation is found in many developing countries. In this study, we analyzed the opportunities to learn (OTL) mathematics of sixth grade stu- dents from 22 public schools in Lima, Peru. OTL were defined in this study as curriculum coverage, cognitive demand of the tasks posed to the students, percent of mathematical exercises that were correct and quality of feedback. These variables were coded in the workbooks and notebooks of the students, which were gathered at the end of the school year (at the same time, the mathematics achievement test was administered). The results show that: (a) regarding OTL, less than half of the exercises available in the workbooks were solved, teachers overemphasize some topics of the national curriculum (i.e. related to Number and Number Sense), they pose tasks that are at very low levels of cognitive demand, and it is common to find mistakes in the students’ answers to problems that have no feedback (or even worse, the feedback is wrong); (b) students in relatively poorer, multi- grade classrooms have less OTL; (c) OTL, as defined earlier, is positively associated with achievement. KEY WORDS: achievement in mathematics, cognitive demand, curriculum coverage, feed- back, opportunities to learn, Peru 1. INTRODUCTION In recent years, educational enrollment in Peru, and most Latin American countries, has risen so that currently almost all students in age to attend an elementary school do so (Guadalupe, 2000). But a series of studies (e.g. World Bank, 1999) and public statements by local specialists (e.g. Foro Educativo, 2000) have agreed in pointing out that the quality of the educational system is very low. We will not attempt to define educational quality here (as it is not defined in a precise way in the documents mentioned earlier), but we will explore one of the aspects commonly associated with educational quality, i.e. achievement in standardized tests. ∗ A preliminary version of this paper received the Research Medal in the category Knowl- edge, Education and Technology at the Annual Meeting of the Global Development Network (GDN) in Cairo, in January 2003. Educational Studies in Mathematics (2006) 62: 25–55 DOI: 10.1007/s10649-006-7922-2 C  Springer 2006