1. Opportunities to Learn and Achievement in Mathematics in a sample of sixth grade students in Lima, Peru Santiago Cueto, Cecilia Ramírez, Juan León & Oscar Pain GRADE

2. Opportunities to Learn (From TIMSS) Intended curriculum (National Curriculum approved by Congress) Implemented curriculum Attained curriculum (Achievement in tests developed by the Ministry of Education based on National Curriculum)

3. Implemented Curriculum Curriculum coverage. Cognitive Demand. Exercises solved correctly by the students. A new method to measure OTL through an analysis of workbooks and notebooks was developed

4. Cognitive Demand We analyzed the cognitive demand of the tasks solved by the students in their notebooks and workbooks. The tasks were classified as: Low level of cognitive demand Memorization Procedures without connections High level of cognitive demand Procedures with connections Doing Math

5. Research questions What curriculum are mathematics teachers using in sixth grade? What are the opportunities to learn the mathematics curriculum of students in the public school system in Lima? Is there a relationship between the average SES score of the students in a classroom and their OTL? Is there a relationship between OTL and achievement in standardized tests of mathematics?

6. Number of public schools in the sample by type of school and location Full GradeMultigrade Lima City83 Lima (other urban and rural areas) 74 Total157

7. Characteristics of the students in the sample by type of school

8. Percent of exercises from the workbook that had been solved by competency in the curriculum. Competencies Tasks available MultigradeFull gradeAverage Statistics 951%28%19% Geometry 18830%41%37% Measurement 2658%18%15% Number and Number Sense 115042%57%52% Problems 10927%42%38%

9. Percent of tasks solved by students by competency in workbooks and notebooks. WORKBOOKNOTEBOOK COMPETENCIESAverage Full Grade MultigradeAverage Full Grade Multigrade Statistics2%3%1% Geometry9% 5%6%2% Measurement5% 4%6%7%2% Number and Number Sense 78%77%81%70%69%73% Problems5% 11%13%7% Not in curriculum 7%5%13% Total100% Number of Tasks763824658657742524

10. Percent of tasks solved by level of cognitive demand in workbooks and notebooks WORKBOOKNOTEBOOK NUMBER SENSE, MEASUREMENT, GEOMETRY AND STATISTICS Average Full Grade MultigradeAverage Full Grade Multigrade Memorization 25%24%25%22%20%26% Procedures without connections 62% 63%65%67%66% Procedures with connection 8%9%8%2%0%1% Doing math 0% PROBLEMS Procedures without connections 5% 4%11%13%7% Procedures with connections 0% 1%0% Doing math 0% Total 100%

11. Number and percent of tasks with a correct answer by type of school and competency. WORKBOOKNOTEBOOK COMPETENCIES AverageFull GradeMultigrade AverageFull GradeMultigrade Statistics 67%64%100% 85% 100% 18 / 2717 / 261 / 1 11 / 1310 / 121 / 1 Geometry 64%66%60% 86% 85 / 13351 / 7734 / 56 79 / 9266 / 7713 / 15 Measurement 48%58%26% 80%79%90% 32 / 6727 / 475 / 20 44 / 5539 / 4905-Jun Number and Number sense 68%74%60% 87% 86% 771 / 1132482 / 650289 / 482 745 / 857405 / 463340 / 394 Problems 51%65%37% 83% 84% 40 / 7829 / 4911 / 29 104 / 12576 / 9228 / 33 Not in curriculum 86%85%88% 81 / 9434 / 4047 / 54 Total 66%71%58% 86% 946 / 1437606 / 849340 / 588 1064 / 1236630 / 733434 / 503

12. Correlation matrix of OTL, SES and achievement in the test (Spearman). Achievement in the test SES Curriculum Coverage Cognitive Demand SES 0.62** Curriculum Coverage 0.47* 0.49* Cognitive Demand 0.210.330.49* Number of Tasks correct 0.43+0.54 0.88**0.40+ **p<0.001, *p<0.05, +p<0.10

13. Hierarchical Linear Model of achievement, including OTL

15. Discussion A new method to measure OTL was developed, and found acceptable indicators of reliability and validity. The workbook distributed free by the government to all student was used infrequently (on average 32% of the tasks posed to the students were solved). OTL are associated positively with SES. The implemented curriculum showed poor coverage of topics, low levels of cognitive demand and frequent errors.