Opportunities to Learn and Achievement in Mathematics in a sample of sixth grade students in Lima, Peru

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
Low level of cognitive demand Procedures without connections
   
High level of cognitive demand Procedures with connections
High level of cognitive demand 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 Grade Multigrade
Lima City 8 3
Lima (other urban and rural areas) 7 4

Total 15 7
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 Multigrade Full grade Average
Statistics 95 1 28 19
Geometry 188 30 41 37
Measurement 265 8 18 15
Number and Number Sense 1150 42 57 52
Problems 109 27 42 38
9
Percent of tasks solved by students by competency
in workbooks and notebooks.
  WORKBOOK WORKBOOK WORKBOOK WORKBOOK NOTEBOOK NOTEBOOK NOTEBOOK
COMPETENCIES Average Full Grade Multigrade Multigrade Average Full Grade Multigrade
Statistics 2 3 1 1 1 1 1
Geometry 9 9 9 9 5 6 2
Measurement 5 5 4 4 6 7 2
Number and Number Sense 78 77 81 81 70 69 73
Problems 5 5 5 5 11 13 7
Not in curriculum         7 5 13

Total 100 100 100 100 100 100 100
Number of Tasks 763 824 824 658 657 742 524
10
Percent of tasks solved by level of cognitive
demand in workbooks and notebooks
WORKBOOK WORKBOOK WORKBOOK NOTEBOOK NOTEBOOK NOTEBOOK
NUMBER SENSE, MEASUREMENT, GEOMETRY AND STATISTICS NUMBER SENSE, MEASUREMENT, GEOMETRY AND STATISTICS Average Full Grade Multigrade Average Full Grade Multigrade
Memorization Memorization 25 24 25 22 20 26
Procedures without connections Procedures without connections 62 62 63 65 67 66
Procedures with connection Procedures with connection 8 9 8 2 0 1
Doing math Doing math 0 0 0 0 0 0

PROBLEMS PROBLEMS
Procedures without connections Procedures without connections 5 5 4 11 13 7
Procedures with connections Procedures with connections 0 0 0 1 0 0
Doing math Doing math 0 0 0 0 0 0

Total Total 100 100 100 100 100 100
11
Number and percent of tasks with a correct answer
by type of school and competency.
  WORKBOOK WORKBOOK WORKBOOK NOTEBOOK NOTEBOOK NOTEBOOK
COMPETENCIES   Average Full Grade Multigrade   Average Full Grade Multigrade
Statistics   67 64 100   85 85 100
Statistics   18 / 27 17 / 26 1 / 1   11 / 13 10 / 12 1 / 1
Geometry   64 66 60   86 86 86
Geometry   85 / 133 51 / 77 34 / 56   79 / 92 66 / 77 13 / 15
Measurement   48 58 26   80 79 90
Measurement   32 / 67 27 / 47 5 / 20   44 / 55 39 / 49 05-Jun
Number and Number sense   68 74 60   87 87 86
Number and Number sense   771 / 1132 482 / 650 289 / 482   745 / 857 405 / 463 340 / 394
Problems   51 65 37   83 83 84
Problems   40 / 78 29 / 49 11 / 29   104 / 125 76 / 92 28 / 33
Not in curriculum           86 85 88
Not in curriculum           81 / 94 34 / 40 47 / 54
             
Total   66 71 58   86 86 86
Total   946 / 1437 606 / 849 340 / 588   1064 / 1236 630 / 733 434 / 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 0.21 0.33 0.49
Number of Tasks correct 0.43 0.54 0.88 0.40
plt0.001, plt0.05, plt0.10
13
Hierarchical Linear Model of achievement,
including OTL
14
(No Transcript)
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.