Opportunities to Learn and Achievement in Mathematics in

a sample of sixth grade students in Lima, Peru

Santiago Cueto, Cecilia Ramírez, Juan León & Oscar

PainGRADE

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)

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

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

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?

Number of public schools in the sample by type of school and location

 Full

GradeMultigrad

e

Lima City 8 3

Lima (other urban and rural areas)

7 4

Total 15 7

Characteristics of the students in the sample by type of school

Full Grade Multigrade

Male 46% 55%Average age (in years) 11.52 12.15*SD (0.95) (1.55)

Average of persons living at home 5.63 5.91SD (3.07) (1.88)

Percent of students who have spanish as their mother's tongue

98% 95%

SD (15%) (23%)

Mother lives at home 94% 85% *SD (23%) (36%)

Father lives at home 83% 77%SD (37%) (42%)

Percent of homes with a car 20% 11% *SD (40%) (31%)

Percent of homes with a refrigerator 65% 53%SD (48%) (50%)

Percent of homes with a color TV 79% 64% *SD (41%) (48%)

Percent of homes with a telephone 48% 20% *SD (50%) (40%)

Average daily attendance in 2001 96% 92% *SD (7%) (14%)

Percent of children that work 41% 72% *SD (49%) (45%)N 295 74

* p>0.05 (t-test for independent groups)

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%

Percent of tasks solved by students by competency in workbooks and notebooks.

  WORKBOOK NOTEBOOK

COMPETENCIESAverag

eFull

GradeMultigrad

eAverag

eFull

GradeMultigra

de

Statistics 2% 3% 1% 1% 1% 1%

Geometry 9% 9% 9% 5% 6% 2%

Measurement 5% 5% 4% 6% 7% 2%

Number and Number Sense

78% 77% 81% 70% 69% 73%

Problems 5% 5% 5% 11% 13% 7%

Not in curriculum   7% 5% 13%

Total 100% 100% 100% 100% 100% 100%

Number of Tasks

763 824 658 657 742 524

Percent of tasks solved by level of cognitive demand in workbooks and notebooks

WORKBOOK NOTEBOOK

NUMBER SENSE, MEASUREMENT, GEOMETRY AND STATISTICS

AverageFull

GradeMultigrad

eAverag

eFull

GradeMultigrad

e

Memorization 25% 24% 25% 22% 20% 26%

Procedures without connections

62% 62% 63% 65% 67% 66%

Procedures with connection

8% 9% 8% 2% 0% 1%

Doing math 0% 0% 0% 0% 0% 0%

PROBLEMS

Procedures without connections

5% 5% 4% 11% 13% 7%

Procedures with connections

0% 0% 0% 1% 0% 0%

Doing math 0% 0% 0% 0% 0% 0%

Total 100% 100% 100% 100% 100% 100%

Number and percent of tasks with a correct answer by type of school and competency.

  WORKBOOK NOTEBOOK

COMPETENCIES  Average

Full Grade

Multigrade

  Average Full GradeMultigrad

e

Statistics  67% 64% 100%   85% 85% 100%

  18 / 27 17 / 26 1 / 1   11 / 13 10 / 12 1 / 1

Geometry  64% 66% 60%   86% 86% 86%

  85 / 133 51 / 77 34 / 56   79 / 92 66 / 77 13 / 15

Measurement  48% 58% 26%   80% 79% 90%

  32 / 67 27 / 47 5 / 20   44 / 55 39 / 49 05-Jun

Number and Number sense

  68% 74% 60%   87% 87% 86%

 771 /

1132 482 / 650 289 / 482   745 / 857 405 / 463 340 / 394

Problems  51% 65% 37%   83% 83% 84%

  40 / 78 29 / 49 11 / 29   104 / 125 76 / 92 28 / 33

Not in curriculum 

 

  86% 85% 88%

    81 / 94 34 / 40 47 / 54             

Total  66% 71% 58%   86% 86% 86%

 946 /

1437 606 / 849 340 / 588  1064 /

1236 630 / 733 434 / 503

Correlation matrix of OTL, SES and achievement in the test (Spearman).

Achievement in the

testSES

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+

**p<0.001, *p<0.05, +p<0.10

Hierarchical Linear Model of achievement, including OTL

1.95 ** 1.33 * 1.65 * 0.99 * 0.75 * 7.01 **(Standard error) (0.65) (0.53) (0.67) (0.43) (0.38) (2.52)

-0.38 -0.30 -0.38 -0.24 -0.09 -1.42(Standard error) (0.28) (0.23) (0.29) (0.20) (0.18) (1.10)

-0.03 0.51 2.11 3.46 0.37 0.00(Standard error) (5.97) (4.80) (6.18) (4.97) (3.43) (22.86)

1.65 * 1.48 ** 1.80 * 0.67 0.94 * 6.43 *(Standard error) (0.67) (0.54) (0.69) (0.43) (0.37) (2.59)

-0.09 -0.08 -0.10 -0.06 -0.04 -0.38(Standard error) (0.11) (0.09) (0.11) (0.07) (0.06) (0.42)

0.57 0.45 0.64 0.45 + 0.32 2.18(Standard error) (0.39) (0.31) (0.39) (0.25) (0.22) (1.48)

20.94 ** 13.24 ** 15.91 ** 10.19 ** 11.37 ** 70.97 **(Standard error) (1.78) (1.34) (1.68) (1.02) (1.07) (6.18)

0.78 1.46 -0.41 -2.26 + -1.41 -3.62(Standard error) (2.17) (1.59) (1.99) (1.11) (1.09) (7.46)

6.65 0.52 5.01 3.90 * 7.53 * 14.13(Standard error) (6.34) (4.81) (2.93) (1.55) (3.18) (24.24)

7.11 18.67 + 16.51 + 1.72 -0.60 48.34 *(Standard error) (5.12) (8.81) (8.82) (1.82) (0.89) (21.86)

Students 276 276 276 224 206 276Schools 18 18 18 14 12 18

Level 1 - Variance 24.73 16.05 26.25 8.71 6.13 368.22Level 2 - Variance 11.51 ** 6.20 ** 9.62 ** 0.87 ** 0.53 ** 124.01 **

32% 28% 27% 9% 8% 25%0.84 0.82 0.81 0.58 0.56 0.80

**p<0.01, *p<0.05, +p<0.10Reliability

Geo

metr

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Nu

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Nu

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Sen

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Pro

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Measu

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Age (In Years)

Attendance rate in 2001

Sta

tisti

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To

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Sco

re

Level 1: Student variablesGender (1=Male, 0=Female)

Math is preffered subject (1=Yes, 0=No)

Number of persons living at home

SES

Level 2: School and classroom variables

Percent of Variance between schools

Intercept Bo

Type of School (1=Full grade, 0=Multigrade)

Curriculum coverage

Cognitive Demand

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.