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 suggest 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 students 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, multigrade classrooms have less OTL; (c) OTL, as defined earlier, is positively associated with achievement.

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“…It seems that the data reiterate Zhu et al’s above argument. According to Cueto et al (2006), we should be cautious about expecting learners to respond correctly to all assignments. In learning mathematics, it was found that sixth grade students were able to solve only about 44% of mathematics assignments correctly (Cueto et al, 2006).…”

“…According to Cueto et al (2006), we should be cautious about expecting learners to respond correctly to all assignments. In learning mathematics, it was found that sixth grade students were able to solve only about 44% of mathematics assignments correctly (Cueto et al, 2006). The evidence from the current study shows a positive, predictive association between rigorous cognitive assignments and achievement of learning cognitive knowledge.…”

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“…For instance, international comparative studies have found that opportunity to learn the content on international assessments (such as the Trends in International Math and Science Study) is associated with nation-level performance (e.g., Schmidt et al, 2001) and with differences in performance across U.S. states (Schmidt et al, 2011). At the classroom level, numerous studies have indicated associations of OTL variables with student performance (e.g., Cueto, Ramirez, & Leon, 2006;D'Agostino, Welsh, & Corson, 2007;Ruiz-Primo, Shavelson, Hamilton, & Klein, 2002). In some cases, the effects of OTL are so large that there is no statistically significant residual between-course level (e.g., between general and honors levels) variation in achievement gains after controlling for OTL (e.g., Gamoran et al, 1997;Yoon & Resnick, 1998).…”

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“…However, to improve learning in Math and Language, there is a need for high-quality instruction. From previous studies, this does not seem the norm in public schools in Peru, where much rote learning takes place (Cueto et al, 2006;Cueto, Ramírez and León, 2006).…”