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Longitudinal/Cross-Sectional Study of the Impact of Mathematics in Context on Student Performance
Classroom Achievement for Mathematics in Context Classrooms for1997-1998
(Technical Report #33)
Thomas Romberg, David Webb, and Lorene Folgert, University of Wisconsin-Madison
Mary Shafer, Northern Illinois University
Romberg, T. A., Webb, D.C., Folgert, L., & Shafer, M.C. (2003) Classroom achievement for Mathematics in Context classrooms for 1997-1998. (Mathematics in Context Longitudinal/Cross-Sectional Study Tech. Rep. No. 33). Madison, WI: University of Wisconsin, Wisconsin Center for Education Research.
The research reported in this paper was supported in part by the National Science Foundation #REC-9553889 and #REC-0087511 and by the Wisconsin Center for Education Research, School of Education, University of Wisconsin-Madison and the Northern Illinois University. The views expressed here are those of the authors and do not necessarily reflect the views of the funding agency.
Introduction
The purposes of the longitudinal/cross-sectional study of the impact of Mathematics in Context (MiC; National Center for Research in Mathematical Sciences Education & Freudenthal Institute, 1997–1998) on student performance are (a) to determine the mathematical knowledge, understanding, attitudes, and levels of student performance as a consequence of studying MiC for over three years; and (b) to compare student knowledge, understanding, attitudes, and levels of performance of students using MiC with those using conventional mathematics curricula. The research model for this study is an adaptation of a structural model for monitoring changes in school mathematics (Romberg, 1987). For this study, information is being gathered on 14 variables over a 3-year period for three groups of students (those in Grades 5, 6, and 7 in 1997). The variables have been organized in five categories (prior, independent, intervening, outcome, and consequent). (See Figure 1 for variables and hypothesized relationships.)
Student Background
Social Context
Teacher Background
Support Environment
Teacher Knowledge
Teacher Professional
Responsibility
Classroom Events
Pedagogical Decisions
Knowledge andUnderstanding
Application
Attitudes
Further Pursuits Student
Pursuits
Prior Independent Intervening Outcome Consequent
Curricular Content and
Materials
Figure 1. Revised model for the monitoring of school mathematics.
2
Overview The data in this Technical Report contain the general results for the eight grade-level-by-year studies shown as white ellipses in Figure 2. The summary data has been derived from each student’s weighted item scores on the Classroom Achievement Index (CA) (see Appendix A).
Grade 7Grade 7
Cross-Grade
Grade 5
Grade 6
Grade 7
Grade 6
Grade 8
Grade 7
Grade 8
Cross-Year
Cross-Year
Cross-Year
Cross-Grade
Cross-Grade
L o n g i t u d i n a l
L o n g i t u d i n a l
L o n g i t u d i n a l
1 9 9 7 - 1 9 9 8 1 9 9 8 - 1 9 9 9 1 9 9 9 - 2 0 0 0 Figure 2. Sources of Data and Planned Comparisons of the MiC Longitudinal/Cross-Sectional Study
In each case the summary data has been displayed in terms of Tables that include the number of students, mean, standard deviation, both lower and upper 95% confidence intervals, and score distributions for the 95%tile, 75%tile, 25%tile, and 5%tile, then a Progress Map has been constructed to portray that data.1
The following Tables and Maps have been organized in terms of each of the eight year-by-grade studies. Within each study the data on student performance is then organized first across all districts, second for each district separately, and then by teachers within districts.
1 Progress Maps were not made if N < 10.
3
Grade 5 All Districts
Table 1.5.1 MiC Classroom Achievement in All Districts, Grade 5, in 1997-1998, by Gender, by Ethnic Group, and by Content Strand
N Mean SD Lower Upper 95%tile 75%tile 25%tile 5%tileOverall 448 255.2 43.7 251.1 259.2 330.7 281.6 228.5 185.0
Male 229 257.1 45.7 251.2 263.0 336.1 284.4 228.5 185.0Female 219 253.1 41.6 247.6 258.6 324.8 278.7 224.5 185.0
White 215 268.2 43.7 262.4 274.1 338.3 298.5 239.8 194.8African-American 50 229.4 35.0 219.7 239.1 265.4 253.9 196.3 175.1Hispanic 96 238.4 34.4 231.5 245.3 296.4 263.5 211.5 185.0Other 87 256.1 45.1 246.7 265.6 333.6 284.4 224.5 186.9
Number 448 256.8 45.0 252.6 260.9 332.2 286.9 227.7 181.4Algebra 448 258.1 46.4 253.8 262.4 320.0 293.4 225.0 184.1Geometry 448 251.9 46.1 247.6 256.1 318.6 287.5 234.8 173.5Statistics 448 249.8 48.8 245.2 254.3 332.5 282.8 213.7 166.5
95% Confidence Interval Score distribution percentiles
4
Figure 2. Distribution of Classroom Achievement in MiC Classrooms in All Districts, Grade 5, in 1997-1998, by Gender, by Ethnic Group, and
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
N = 448 N = 229 N = 219 N = 215 N = 50 N = 96 N = 87 N = 448 N = 448 N = 448 N = 448
Band 1
Band 5
Band 4
Band 3
Band 2
400
250
100
All Gender Ethnic Group Content Strands
Male Female White Afr-Am Hisp Other Number Alg Geom Stat
by Content Strand
5
Table 1.5.2 MiC Classroom Achievement, Grade 5, in 1997-1998, by District
N Mean SD Lower Upper 95%tile 75%tile 25%tile 5%tileOverall 448 255.2 43.7 251.1 259.2 330.7 281.6 228.5 185.0
District 1 153 266.9 44.6 259.8 274.0 337.5 301.3 236.4 191.2District 2 168 235.0 37.2 229.4 240.7 298.5 258.1 210.3 174.4District 3 127 267.6 41.0 260.5 274.8 342.7 284.4 241.5 208.0
95% Confidence Interval Score distribution percentiles
6
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
N = 448 N = 153 N = 168 N = 127
Band 1
Band 5
Band 4
Band 3
Band 2
400
250
100 All District 1 District 3District 2
Figure 3. Distribution of Classroom Achievement in MiC Classrooms, Grade 5, in 1997-1998, by District
7
Table 1.5.3 MiC Classroom Achievement in All Districts, Grade 5, in 1997-1998, by Gender
N Mean SD Lower Upper 95%tile 75%tile 25%tile 5%tileOverall
Male 229 257.1 45.7 251.2 263.0 336.1 284.4 228.5 185.0Female 219 253.1 41.6 247.6 258.6 324.8 278.7 224.5 185.0
District 1Male 80 266.6 47.1 256.3 277.0 337.5 301.3 232.4 190.9
Female 73 263.6 52.0 251.7 275.4 333.4 298.5 243.2 194.3District 2
Male 84 236.5 39.3 228.1 244.9 298.5 258.8 210.3 173.0Female 84 233.6 35.1 226.1 241.1 289.7 258.1 210.3 178.8
District 3Male 65 272.1 42.3 261.8 282.3 346.4 284.4 243.2 212.4
Female 62 263.0 39.4 253.2 272.8 340.0 283.7 236.4 206.7
95% Confidence Interval Score distribution percentiles
8
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
N = 229 N = 219 N = 80 N = 73 N = 84 N = 84 N = 65 N = 62
Band 1
Band 5
Band 4
Band 3
Band 2
400
250
100
All District 1 District 2 District 3
Male Female Male Female Male Female Male Female
Figure 4. Distribution of Classroom Achievement in MiC Classrooms in All Districts, Grade 5, in 1997-1998, by Gender
9
Table 1.5.4 MiC Classroom Achievement in All Districts, Grade 5, in 1997-1998, by Ethnic Group
N Mean SD Lower Upper 95%tile 75%tile 25%tile 5%tileOverall
White 215 268.2 43.7 262.4 274.1 338.3 298.5 239.8 194.8African American 50 229.4 35.0 219.7 239.1 265.4 253.9 196.3 175.1
Hispanic 96 238.4 34.4 231.5 245.3 296.4 263.5 211.5 185.0Other 87 256.1 45.1 246.7 265.6 333.6 284.4 224.5 186.9
District 1White 79 283.7 38.9 275.1 292.3 337.5 309.8 259.0 224.5
African American 40 232.2 34.3 221.5 242.8 265.1 255.6 203.9 178.4Hispanic 9 240.4 37.0 216.2 264.6 294.2 266.9 216.1 195.5
Other 25 278.9 44.5 261.5 296.3 342.4 316.0 243.2 199.3District 2
White 37 236.4 42.7 222.7 250.2 299.6 263.5 206.5 164.1African American 10 218.3 37.4 195.1 241.5 265.4 251.2 192.5 168.8
Hispanic 83 236.8 34.3 229.4 244.2 287.4 260.7 211.5 185.0Other 38 234.2 37.6 222.2 246.2 299.4 249.7 216.1 172.0
District 3White 99 267.8 41.6 259.6 276.0 340.6 284.4 243.2 205.4
African American 0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0Hispanic 4 266.6 22.0 245.1 288.1 293.3 272.2 253.0 251.0
Other 24 267.2 42.3 250.3 284.1 343.7 294.3 232.4 211.5
95% Confidence Interval Score distribution percentiles
10
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
N = 215 N = 50 N = 96 N = 87 N = 79 N = 40 N = 9 N = 25 N = 37 N = 10 N = 83 N = 38 N = 99 N = 0 N = 4 N = 24
Band 1
Band 5
Band 4
Band 3
Band 2
400
250
100
District 1 District 2 District 3
White Afr-Am Hisp Other White Afr-Am Hisp Other White Afr-Am Hisp Other White Afr-Am Hisp Other
All
Figure 5. Distribution of Classroom Achievement in MiC Classrooms in All Districts, Grade 5, in 1997-1998, by Ethnic Group
11
Table 1.5.5 MiC Classroom Achievement in All Districts, Grade 5, in 1997-1998, by Content Strand
N Mean SD Lower Upper 95%tile 75%tile 25%tile 5%tileOverall
Number 448 256.8 45.0 252.6 260.9 332.2 286.9 227.7 181.4Algebra 448 258.1 46.4 253.8 262.4 320.0 293.4 225.0 184.1
Geometry 448 251.9 46.1 247.6 256.1 318.6 287.5 234.8 173.5Statistics 448 249.8 48.8 245.2 254.3 332.5 282.8 213.7 166.5
District 1Number 153 272.1 45.5 264.9 279.3 345.5 307.1 236.1 208.5Algebra 153 263.1 47.6 255.5 270.6 320.0 293.4 250.3 184.1
Geometry 153 257.4 46.2 250.1 264.7 324.6 287.5 234.8 173.5Statistics 153 258.8 52.3 250.5 267.1 332.5 292.9 225.1 166.5
District 2Number 168 236.0 40.6 229.9 242.1 300.7 266.2 208.5 161.2Algebra 168 249.1 43.5 242.6 255.7 309.4 285.8 225.0 184.1
Geometry 168 238.7 41.1 232.5 245.0 303.3 271.2 210.9 173.5Statistics 168 229.5 41.1 223.3 235.7 292.9 253.7 201.5 166.5
District 3Number 127 265.8 39.6 258.9 272.7 332.2 286.9 240.1 208.5Algebra 127 263.8 47.3 255.6 272.1 333.4 293.4 225.0 184.1
Geometry 127 262.6 48.4 254.1 271.0 333.5 287.5 234.8 173.5Statistics 127 265.6 45.1 257.7 273.4 345.5 292.9 239.8 205.1
95% Confidence Interval Score distribution percentiles
12
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
N =448
N =448
N =448
N =448
N =153
N =153
N =153
N =153
N =168
N =168
N =168
N =168
N =127
N =127
N =127
N =127
Band 1
Band 5
Band 4
Band 3
Band 2
400
250
100
District 1 District 2 District 3 District 4
Number Alg Geom Stat Number Alg Geom Stat Number Alg Geom Stat Number Alg Geom Stat
Figure 6. Distribution of Classroom Achievement in MiC Classrooms in All Districts, Grade 5, in 1997-1998, by Content Strand
13
District 1
Table 1.5.6 MiC Classroom Achievement in District 1, Grade 5, in 1997-1998, by Gender, by Ethnic Group, and by Content Strand
Sample Mean SD Lower Upper 95%tile 75%tile 25%tile 5%tileOverall 153 266.9 44.6 259.8 274.0 337.5 301.3 236.4 191.2
Male 80 266.6 47.1 256.3 277.0 337.5 301.3 232.4 190.9Female 73 263.6 52.0 251.7 275.4 333.4 298.5 243.2 194.3
White 79 283.7 38.9 275.1 292.3 337.5 309.8 259.0 224.5African American 40 232.2 34.3 221.5 242.8 265.1 255.6 203.9 178.4Hispanic 9 240.4 37.0 216.2 264.6 294.2 266.9 216.1 195.5Other 25 278.9 44.5 261.5 296.3 342.4 316.0 243.2 199.3
Number 153 272.1 45.5 264.9 279.3 345.5 307.1 236.1 208.5Algebra 153 263.1 47.6 255.5 270.6 320.0 293.4 250.3 184.1Geometry 153 257.4 46.2 250.1 264.7 324.6 287.5 234.8 173.5Statistics 153 258.8 52.3 250.5 267.1 332.5 292.9 225.1 166.5
Confidence Interval Score distribution percentiles
14
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
N = 153 N = 80 N = 73 N = 79 N = 40 N = 9 N = 25 N = 153 N = 153 N = 153 N = 153
Band 1
Band 5
Band 4
Band 3
Band 2
400
250
100 Male Female White Afr-Am Hisp Other Number Alg Geom Stat
All Gender Ethnic Group Content Strands
Figure 7. Distribution of Classroom Achievement in MiC Classrooms in District 1, Grade 5, in 1997-1998, by Gender, Ethnic Group, and by Content Strand
15
Table 1.5.7 MiC Classroom Achievement in District 1, Grade 5, in 1997-1998, by Teacher
Teacher ID Sample Mean SD Lower Upper 95%tile 75%tile 25%tile 5%tile4 15 252.6 23.0 240.9 264.2 282.4 262.1 247.1 214.514 53 239.0 41.7 227.7 250.2 306.4 266.9 216.1 176.119 26 291.5 26.6 281.2 301.7 333.5 310.5 278.7 249.127 19 252.6 36.0 236.4 268.8 307.9 268.6 234.4 196.331 31 316.8 21.0 309.4 324.2 348.8 332.4 299.9 287.849 9 242.5 21.9 228.2 256.8 262.4 257.3 236.4 207.7
Confidence Interval Score distribution percentiles
16
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
N = 15 N = 53 N = 26 N = 19 N = 31 N = 9
Band 1
Band 5
Band 4
Band 3
Band 2
400
250
100 Teacher 4 Teacher 14 Teacher 19 Teacher 27 Teacher 31 Teacher 49
Figure 8. Distribution of Classroom Achievement in MiC Classrooms in District 1, Grade 5, in 1997-1998, by Teacher
17
Table 1.5.8 MiC Classroom Achievement in Number, District 1, Grade 5, in 1997-1998, by Teacher
Teacher ID Sample Mean SD Lower Upper 95%tile 75%tile 25%tile 5%tile4 15 251.3 24.9 238.7 263.9 288.9 269.6 231.9 218.414 53 246.1 44.8 234.0 258.2 321.0 280.0 218.4 173.319 26 295.5 26.9 285.1 305.8 343.8 311.9 274.8 260.627 19 262.6 34.9 246.9 278.3 320.5 286.9 240.1 217.431 31 321.9 21.7 314.2 329.5 352.4 335.4 307.1 286.949 9 240.4 19.1 227.9 252.8 267.3 251.4 227.7 216.2
Confidence Interval Score distribution percentiles
18
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
N = 15 N = 53 N = 26 N = 19 N = 31 N = 9
Band 1
Band 5
Band 4
Band 3
Band 2
400
250
100 Teacher 4 Teacher 14 Teacher 19 Teacher 27 Teacher 31 Teacher 49
Figure 9. Distribution of Classroom Achievement in Number, MiC Classrooms in District 1, Grade 5, in 1997-1998, by Teacher
19
Table 1.5.9 MiC Classroom Achievement in Algebra, District 1, Grade 5, in 1997-1998, by Teacher
Teacher ID Sample Mean SD Lower Upper 95%tile 75%tile 25%tile 5%tile4 15 273.0 36.7 254.5 291.6 320.0 297.2 250.3 212.714 53 232.4 50.7 218.8 246.1 300.9 266.3 184.1 133.019 26 287.7 33.8 274.7 300.8 330.0 309.4 277.4 225.027 19 258.2 40.2 240.1 276.2 310.4 289.6 250.3 184.131 31 288.6 31.8 277.4 299.8 342.7 305.2 266.3 237.649 9 278.2 42.4 250.5 305.9 323.8 300.9 277.4 210.6
Confidence Interval Score distribution percentiles
20
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
N = 15 N = 53 N = 26 N = 19 N = 31 N = 9
Band 1
Band 5
Band 4
Band 3
Band 2
400
250
100 Teacher 4 Teacher 14 Teacher 19 Teacher 27 Teacher 31 Teacher 49
Figure 10. Distribution of Classroom Achievement in Algebra, MiC Classrooms in District 1, Grade 5, in 1997-1998, by Teacher
21
Table 1.5.10 MiC Classroom Achievement in Geometry, District 1, Grade 5, in 1997-1998, by Teacher
Teacher ID Sample Mean SD Lower Upper 95%tile 75%tile 25%tile 5%tile4 15 236.7 30.1 221.5 251.9 287.5 244.4 222.9 199.714 53 231.5 44.3 219.6 243.5 303.3 254.0 210.9 173.519 26 282.6 21.8 274.3 291.0 318.6 303.3 271.2 254.027 19 247.3 44.1 227.4 267.1 304.8 271.2 222.9 202.331 31 301.2 35.0 288.9 313.5 348.3 318.6 287.5 244.449 9 241.9 22.6 227.1 256.6 271.2 254.0 234.8 210.9
Confidence Interval Score distribution percentiles
22
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
N = 15 N = 53 N = 26 N = 19 N = 31 N = 9
Band 1
Band 5
Band 4
Band 3
Band 2
400
250
100 Teacher 4 Teacher 14 Teacher 19 Teacher 27 Teacher 31 Teacher 49
Figure 11. Distribution of Classroom Achievement in Geometry, MiC Classrooms in District 1, Grade 5, in 1997-1998, by Teacher
23
Table 1.5.11 MiC Classroom Achievement in Statistics, District 1, Grade 5, in 1997-1998, by Teacher
Teacher ID Sample Mean SD Lower Upper 95%tile 75%tile 25%tile 5%tile4 15 242.8 37.5 223.9 261.8 275.7 267.8 239.8 181.314 53 240.4 46.8 227.8 253.0 309.9 272.7 225.1 153.519 26 269.0 43.9 252.1 285.8 317.7 292.9 246.8 183.727 19 234.8 47.8 213.3 256.3 294.1 263.0 213.7 159.131 31 314.4 39.4 300.6 328.3 394.0 325.1 298.8 253.749 9 223.4 20.5 210.1 236.8 250.0 244.4 201.5 201.5
Confidence Interval Score distribution percentiles
24
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
N = 15 N = 53 N = 26 N = 19 N = 31 N = 9
Band 1
Band 5
Band 4
Band 3
Band 2
400
250
100 Teacher 4 Teacher 14 Teacher 19 Teacher 27 Teacher 31 Teacher 49
Figure 12. Distribution of Classroom Achievement in Statistics, MiC Classrooms in District 1, Grade 5, in 1997-1998, by Teacher
25
District 2
Table 1.5.12 MiC Classroom Achievement in District 2, Grade 5, in 1997-1998, by Gender, by Ethnic Group, and by Content Strand
Sample Mean SD Lower Upper 95%tile 75%tile 25%tile 5%tileOverall 168 235.0 37.2 229.4 240.7 298.5 258.1 210.3 174.4
Male 84 236.5 39.3 228.1 244.9 298.5 258.8 210.3 173.0Female 84 233.6 35.1 226.1 241.1 289.7 258.1 210.3 178.8
White 37 236.4 42.7 222.7 250.2 299.6 263.5 206.5 164.1African American 10 218.3 37.4 195.1 241.5 265.4 251.2 192.5 168.8Hispanic 83 236.8 34.3 229.4 244.2 287.4 260.7 211.5 185.0Other 38 234.2 37.6 222.2 246.2 299.4 249.7 216.1 172.0
Number 168 236.0 40.6 229.9 242.1 300.7 266.2 208.5 161.2Algebra 168 249.1 43.5 242.6 255.7 309.4 285.8 225.0 184.1Geometry 168 238.7 41.1 232.5 245.0 303.3 271.2 210.9 173.5Statistics 168 229.5 41.1 223.3 235.7 292.9 253.7 201.5 166.5
Confidence Interval Score distribution percentiles
26
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
N = 168 N = 84 N = 84 N = 37 N = 10 N = 83 N = 38 N = 168 N = 168 N = 168 N = 168
Band 1
Band 5
Band 4
Band 3
Band 2
400
250
100
All Gender Ethnic Group Content Strands
Male Female White Afr-Am Hisp Other Number Alg Geom Stat
Figure 13. Distribution of MiC Classroom Achievement in District 2, Grade 5, in 1997-1998, by Gender, by Ethnic Group, and by Content Strand
27
Table 1.5.13 MiC Classroom Achievement in District 2, Grade 5, in 1997-1998, by Teacher
Teacher ID Sample Mean SD Lower Upper 95%tile 75%tile 25%tile 5%tile2 32 231.9 34.8 219.9 244.0 282.8 257.3 196.3 185.012 41 222.1 35.8 211.2 233.1 275.9 247.1 196.3 172.022 23 241.1 39.0 225.2 257.1 297.1 255.6 230.5 164.926 72 241.8 36.9 233.3 250.4 304.2 265.9 216.1 185.0
Confidence Interval Score distribution percentiles
28
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
N = 32 N = 41 N = 23 N = 72
Band 1
Band 5
Band 4
Band 3
Band 2
400
250
100 Teacher 2 Teacher 12 Teacher 22 Teacher 26
Figure 14. Distribution of Classroom Achievement in MiC Classrooms in District 2, Grade 5, in 1997-1998, by Teacher
29
Table 1.5.14 MiC Classroom Achievement in Number, District 2, Grade 5, in 1997-1998, by Teacher
Teacher ID Sample Mean SD Lower Upper 95%tile 75%tile 25%tile 5%tile2 32 242.7 35.8 230.3 255.1 296.9 267.9 218.4 189.612 41 230.2 39.5 218.1 242.3 293.8 258.8 208.5 161.222 23 243.6 36.2 228.8 258.4 286.2 266.2 218.4 181.426 72 233.9 44.3 223.7 244.2 309.9 253.2 208.5 172.3
Confidence Interval Score distribution percentiles
30
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
N = 32 N = 41 N = 23 N = 72
Band 1
Band 5
Band 4
Band 3
Band 2
400
250
100 Teacher 2 Teacher 12 Teacher 22 Teacher 26
Figure 15. Distribution of Classroom Achievement in Number, MiC Classrooms in District 2, Grade 5, in 1997-1998, by Teacher
31
Table 1.5.15 MiC Classroom Achievement in Algebra, District 2, Grade 5, in 1997-1998, by Teacher
Teacher ID Sample Mean SD Lower Upper 95%tile 75%tile 25%tile 5%tile2 32 241.9 39.3 228.3 255.5 285.8 266.3 225.0 184.112 41 238.9 50.2 223.6 254.3 300.9 277.4 225.0 133.022 23 258.8 35.6 244.2 273.3 309.4 289.6 225.0 225.026 72 255.0 42.5 245.2 264.9 314.2 293.4 225.0 184.1
Confidence Interval Score distribution percentiles
32
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
N = 32 N = 41 N = 23 N = 72
Band 1
Band 5
Band 4
Band 3
Band 2
400
250
100 Teacher 2 Teacher 12 Teacher 22 Teacher 26
Figure 16. Distribution of Classroom Achievement in Algebra, MiC Classrooms in District 2, Grade 5, in 1997-1998, by Teacher
33
Table 1.5.16 MiC Classroom Achievement in Geometry, District 2, Grade 5, in 1997-1998, by Teacher
Teacher ID Sample Mean SD Lower Upper 95%tile 75%tile 25%tile 5%tile2 32 236.8 44.3 221.4 252.2 303.3 258.3 210.9 173.512 41 229.2 41.7 216.4 241.9 271.2 254.0 210.9 125.222 23 236.7 46.6 217.7 255.7 300.1 254.0 222.9 130.026 72 245.7 36.9 237.2 254.2 294.6 271.2 210.9 173.5
Confidence Interval Score distribution percentiles
34
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
N = 32 N = 41 N = 23 N = 72
Band 1
Band 5
Band 4
Band 3
Band 2
400
250
100 Teacher 2 Teacher 12 Teacher 22 Teacher 26
Figure 17. Distribution of Classroom Achievement in Geometry, MiC Classrooms in District 2, Grade 5, in 1997-1998, by Teacher
35
Table 1.5.17 MiC Classroom Achievement in Statistics, District 2, Grade 5, in 1997-1998, by Teacher
Teacher ID Sample Mean SD Lower Upper 95%tile 75%tile 25%tile 5%tile2 32 219.3 37.2 206.4 232.2 272.7 244.4 186.3 166.512 41 209.0 38.0 197.4 220.7 253.7 225.1 186.3 166.522 23 233.9 40.7 217.2 250.5 282.8 253.7 225.1 139.326 72 244.4 39.0 235.4 253.4 292.9 263.0 213.7 201.5
Confidence Interval Score distribution percentiles
36
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
N = 32 N = 41 N = 23 N = 72
Band 1
Band 5
Band 4
Band 3
Band 2
400
250
100 Teacher 2 Teacher 12 Teacher 22 Teacher 26
Figure 18. Distribution of Classroom Achievement in Statistics, MiC Classrooms in District 2, Grade 5, in 1997-1998, by Teacher
37
District 3
Table 1.5.18 MiC Classroom Achievement in District 3, Grade 5, in 1997-1998, by Gender, by Ethnic Group, and by Content Strand
N Mean SD Lower Upper 95%tile 75%tile 25%tile 5%tileOverall 127 267.6 41.0 260.5 274.8 342.7 284.4 241.5 208.0
Male 65 272.1 42.3 261.8 282.3 346.4 284.4 243.2 212.4Female 62 263.0 39.4 253.2 272.8 340.0 283.7 236.4 206.7
White 99 267.8 41.6 259.6 276.0 340.6 284.4 243.2 205.4African-American 0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0Hispanic 4 266.6 22.0 245.1 288.1 293.3 272.2 253.0 251.0Other 24 267.2 42.3 250.3 284.1 343.7 294.3 232.4 211.5
Number 127 265.8 39.6 258.9 272.7 332.2 286.9 240.1 208.5Algebra 127 263.8 47.3 255.6 272.1 333.4 293.4 225.0 184.1Geometry 127 262.6 48.4 254.1 271.0 333.5 287.5 234.8 173.5Statistics 127 265.6 45.1 257.7 273.4 345.5 292.9 239.8 205.1
95% Confidence Interval Score distribution percentiles
38
Figure 19. Distribution of Classroom Achievement in MiC Classrooms in District 3, Grade 5, in 1997-1998, by Gender, Ethnic Group, and by
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
N = 127 N = 65 N = 62 N = 99 N = 0 N = 4 N = 24 N = 127 N = 127 N = 127 N = 127
Band 1
Band 5
Band 4
Band 3
Band 2
400
250
100
All Gender Ethnic Group Content Strands
Male Female White Afr-Am Hisp Other Number Alg Geom Stat
Content Strand
39
Table 1.5.19 MiC Classroom Achievement in District 3, Grade 5, in 1997-1998, by Teacher
Teacher ID N Mean SD Lower Upper 95%tile 75%tile 25%tile 5%tile3 17 259.2 47.2 236.8 281.7 314.1 278.7 239.8 183.87 23 281.4 44.2 263.4 299.5 359.6 304.2 250.5 221.623 22 252.3 31.2 239.2 265.3 298.2 273.1 232.4 192.625 20 282.5 37.6 266.0 299.0 343.7 303.5 260.7 244.641 22 263.5 42.9 245.6 281.4 340.0 278.7 236.4 212.248 23 265.8 38.0 250.3 281.3 323.9 290.0 238.1 212.0
95% Confidence Interval Score distribution percentiles
40
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
N = 17 N = 23 N = 22 N = 20 N = 22 N = 23
Band 1
Band 5
Band 4
Band 3
Band 2
400
250
100 Teacher 3 Teacher 7 Teacher 23 Teacher 25 Teacher 41 Teacher 48
Figure 20. Distribution of Classroom Achievement in MiC Classrooms in District 3, Grade 5, in 1997-1998, by Teacher
41
Table 1.5.20 MiC Classroom Achievement in Number, District 3, Grade 5, in 1997-1998, by Teacher
Teacher ID Sample Mean SD Lower Upper 95%tile 75%tile 25%tile 5%tile3 17 264.6 44.2 243.6 285.6 314.5 280.0 236.1 199.17 23 279.9 37.0 264.8 295.1 344.2 300.7 255.1 236.123 22 252.8 36.6 237.5 268.1 318.9 273.1 229.8 197.325 20 274.4 38.0 257.7 291.0 320.8 295.5 258.8 239.941 22 261.4 43.0 243.4 279.4 331.6 278.2 229.8 209.048 23 261.8 37.8 246.4 277.2 324.6 280.0 240.1 227.7
Confidence Interval Score distribution percentiles
42
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
N = 17 N = 23 N = 22 N = 20 N = 22 N = 23
Band 1
Band 5
Band 4
Band 3
Band 2
400
250
100 Teacher 3 Teacher 7 Teacher 23 Teacher 25 Teacher 41 Teacher 48
Figure 21. Distribution of Classroom Achievement in Number, MiC Classrooms in District 3, Grade 5, in 1997-1998, by Teacher
43
Table 1.5.21 MiC Classroom Achievement in Algebra, District 3, Grade 5, in 1997-1998, by Teacher
Teacher ID Sample Mean SD Lower Upper 95%tile 75%tile 25%tile 5%tile3 17 270.8 45.3 249.3 292.3 338.6 285.8 250.3 225.07 23 276.1 45.5 257.4 294.7 350.2 305.2 250.3 188.223 22 248.2 34.4 233.9 262.6 300.2 277.4 225.0 186.125 20 266.6 59.6 240.5 292.7 334.3 309.4 225.0 181.541 22 247.8 48.1 227.7 267.9 319.5 274.6 225.0 184.148 23 274.3 45.4 255.8 292.9 350.2 293.4 258.3 188.2
Confidence Interval Score distribution percentiles
44
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
N = 17 N = 23 N = 22 N = 20 N = 22 N = 23
Band 1
Band 5
Band 4
Band 3
Band 2
400
250
100 Teacher 3 Teacher 7 Teacher 23 Teacher 25 Teacher 41 Teacher 48
Figure 22. Distribution of Classroom Achievement in Algebra, MiC Classrooms in District 3, Grade 5, in 1997-1998, by Teacher
45
Table 1.5.22 MiC Classroom Achievement in Geometry, District 3, Grade 5, in 1997-1998, by Teacher
Teacher ID Sample Mean SD Lower Upper 95%tile 75%tile 25%tile 5%tile3 17 247.2 47.7 224.6 269.9 309.3 271.2 234.8 163.97 23 281.6 46.2 262.8 300.5 363.0 295.4 254.0 213.323 22 256.5 46.3 237.1 275.8 332.7 287.5 234.8 175.425 20 279.1 37.9 262.5 295.7 334.2 307.1 254.0 233.641 22 252.6 47.3 232.8 272.3 332.7 266.9 234.8 175.448 23 255.8 56.6 232.7 278.9 332.0 287.5 222.9 173.5
Confidence Interval Score distribution percentiles
46
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
N = 17 N = 23 N = 22 N = 20 N = 22 N = 23
Band 1
Band 5
Band 4
Band 3
Band 2
400
250
100 Teacher 3 Teacher 7 Teacher 23 Teacher 25 Teacher 41 Teacher 48
Figure 23. Distribution of Classroom Achievement in Geometry, MiC Classrooms in District 3, Grade 5, in 1997-1998, by Teacher
47
Table 1.5.23 MiC Classroom Achievement in Statistics, District 3, Grade 5, in 1997-1998, by Teacher
Teacher ID Sample Mean SD Lower Upper 95%tile 75%tile 25%tile 5%tile3 17 244.9 61.4 215.7 274.1 309.3 272.7 235.2 125.87 23 270.9 42.3 253.6 288.1 331.0 305.3 235.2 214.823 22 251.4 29.1 239.3 263.6 292.4 272.7 227.6 202.125 20 286.0 37.8 269.5 302.6 334.6 308.0 260.7 234.741 22 276.5 48.7 256.1 296.8 351.0 292.9 244.4 214.848 23 260.9 41.5 244.0 277.9 329.7 282.8 234.8 202.7
Confidence Interval Score distribution percentiles
48
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
N = 17 N = 23 N = 22 N = 20 N = 22 N = 23
Band 1
Band 5
Band 4
Band 3
Band 2
400
250
100 Teacher 3 Teacher 7 Teacher 23 Teacher 25 Teacher 41 Teacher 48
Figure 24. Distribution of Classroom Achievement in Statistics, MiC Classrooms in District 3, Grade 5, in 1997-1998, by Teacher
49
Grade 6 All Districts
Table 1.6.1 MiC Classroom Achievement in All Districts, Grade 6, in 1997-1998, by Gender, by Ethnic Group, and by Content Strand
N Mean SD Lower Upper 95%tile 75%tile 25%tile 5%tileOverall 503 239.9 48.9 235.7 244.2 316.6 275.9 206.5 165.2
Male 229 236.1 49.1 230.3 241.9 312.9 266.3 206.5 144.9Female 274 243.1 48.6 236.8 249.4 317.4 282.1 206.5 165.2
White 226 260.28 45.07 254.41 266.16 325.05 292.72 229.05 184.43Afr-Am 85 201.10 42.12 192.15 210.05 266.32 234.13 175.39 121.18Hispanic 108 233.99 39.49 226.55 241.44 293.43 256.01 206.46 175.39Other 84 232.10 48.57 221.71 242.49 311.16 263.35 199.68 155.15
Number 503 239.7 48.5 235.5 243.9 311.5 274.1 214.4 139.1Algebra 503 242.3 47.3 238.2 246.4 308.5 275.6 218.3 133.0Geometry 503 247.7 49.2 243.4 252.0 316.7 289.9 202.7 158.7Stat&Prob 503 238.6 50.7 234.2 243.0 321.1 271.4 206.5 153.0
95% Confidence Interval Score distribution percentiles
50
Figure 25. Distribution of Classroom Achievement in MiC Classrooms in All Districts, Grade 6, in 1997-1998, by Gender, by Ethnic Group, and
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
N = 503 N = 229 N = 274 N = 226 N = 85 N = 108 N = 84 N = 503 N = 503 N = 503 N = 503
Band 1
Band 5
Band 4
Band 3
Band 2
400
250
100Male Female White Afr-Am Hisp Other Number Alg Geom Stat
All Gender Ethnic Group Content Strands
by Content Strand
51
Table 1.6.2 MiC Classroom Achievement, Grade 6, in 1997-1998, by District
N Mean SD Lower Upper 95%tile 75%tile 25%tile 5%tileOverall 503 239.9 48.9 235.7 244.2 316.6 275.9 206.5 165.2
District 1 118 213.6 45.1 205.5 221.8 282.1 246.1 184.4 121.2District 2 161 233.3 42.6 226.7 239.9 296.3 262.4 206.5 165.2District 3 148 279.2 39.0 272.9 285.5 338.4 307.1 258.0 206.2District 4 76 218.4 35.6 210.4 226.4 273.4 247.1 192.3 165.2
95% Confidence Interval Score distribution percentiles
52
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
N = 503 N = 118 N = 161 N = 148 N = 76
Band 1
Band 5
Band 4
Band 3
Band 2
400
250
100 All District 1 District 4District 3District 2
Figure 26. Distribution of Classroom Achievement in MiC Classrooms, Grade 6, in 1997-1998, by District
53
Table 1.6.3 Mi C Classroom Achievement in All Districts, Grade 6, in 1997-1998, by Gender
N Mean SD Lower Upper 95%tile 75%tile 25%tile 5%tileOverall
Male 274 236.1 49.1 230.3 241.9 312.9 266.3 206.5 144.9Female 229 243.1 48.6 236.8 249.4 317.4 282.1 206.5 165.2
District 1Male 58 211.3 40.1 201.0 221.6 282.6 238.6 184.4 151.3
Female 61 213.3 53.4 199.9 226.6 279.3 255.0 192.3 121.2District 2
Male 99 236.2 41.9 227.9 244.4 296.5 262.4 206.5 174.4Female 62 228.7 43.8 217.9 239.6 295.7 255.0 201.4 140.0
District 3Male 80 284.7 38.6 276.2 293.2 335.1 309.2 265.3 222.7
Female 68 272.7 38.7 263.5 281.9 338.4 297.0 247.1 201.4District 4
Male 37 221.7 35.2 210.4 233.1 273.2 247.1 192.3 173.4Female 39 215.2 36.1 203.8 226.5 269.0 238.6 192.3 164.0
95% Confidence Interval Score distribution percentiles
54
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
N = 274 N = 229 N = 60 N = 58 N = 62 N = 99 N = 68 N = 80 N = 39 N = 37
Band 1
Band 5
Band 4
Band 3
Band 2
400
250
100
All District 1 District 2 District 3
Male Female Male Female Male Female Male Female
District 4
Male Female
Figure 27. Distribution of Classroom Achievement in MiC Classrooms in All Districts, Grade 6, in 1997-1998, by Gender
55
Table 1.6.4 MiC Classroom Achievement in All Districts, Grade 6, in 1997-1998, by Ethnic Group
N Mean SD Lower Upper 95%tile 75%tile 25%tile 5%tileOverall
White 226 260.3 45.1 254.4 266.2 325.1 292.7 229.0 184.4African American 85 201.1 42.1 192.1 210.1 266.3 234.1 175.4 121.2
Hispanic 108 234.0 39.5 226.5 241.4 293.4 256.0 206.5 175.4Other 84 232.1 48.6 221.7 242.5 311.2 263.4 199.7 155.1
District 1White 64 228.3 39.5 218.6 238.0 284.5 256.0 206.5 155.1
African American 27 184.8 44.3 168.1 201.5 244.6 212.7 165.2 104.2Hispanic 11 198.7 37.8 176.3 221.0 242.9 231.3 175.4 148.3
Other 16 213.9 48.9 190.0 237.9 284.2 249.1 172.9 139.3District 2
White 25 249.9 49.7 230.4 269.4 311.0 279.3 234.1 161.2African American 20 200.2 40.5 182.5 217.9 267.0 216.8 182.2 138.3
Hispanic 81 233.6 35.3 226.0 241.3 285.0 255.0 212.7 184.4Other 35 239.6 45.7 224.5 254.7 301.5 275.9 209.6 161.7
District 3White 133 278.5 36.8 272.3 284.8 331.9 306.4 255.0 221.7
African American 0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0Hispanic 6 289.5 53.2 246.9 332.1 343.5 320.0 270.3 216.3
Other 9 281.6 61.4 241.5 321.7 344.9 311.5 259.0 181.6District 4
White 4 229.8 40.4 190.2 269.3 272.2 257.3 197.8 193.4African American 38 213.2 38.2 201.0 225.3 267.3 247.1 184.4 153.4
Hispanic 10 242.4 25.9 226.4 258.5 279.4 258.0 229.0 210.6Other 24 214.7 31.1 202.2 227.1 265.7 230.3 197.8 175.4
95% Confidence Interval Score distribution percentiles
56
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
N = 226 N = 85 N = 108 N = 84 N = 64 N = 27 N = 11 N = 16 N = 25 N = 20 N = 81 N = 35 N = 133 N = 0 N = 6 N = 9 N = 4 N = 38 N = 10 N = 24
Band 1
Band 5
Band 4
Band 3
Band 2
400
250
100
District 1 District 2 District 3 District 4
White AfrAm Hisp Other
All
White AfrAm Hisp Other White AfrAm Hisp Other White AfrAm Hisp Other White AfrAm Hisp Other
Figure 28. Distribution of Classroom Achievement in MiC Classrooms in All Districts, Grade 6, in 1997-1998, by Ethnic Group
57
Table 1.6.5 MiC Classroom Achievement in All Districts, Grade 6, in 1997-1998, by Content Strand
N Mean SD Lower Upper 95%tile 75%tile 25%tile 5%tileOverall
Number 503 239.7 48.5 235.5 243.9 311.5 274.1 214.4 139.1Algebra 503 242.3 47.3 238.2 246.4 308.5 275.6 218.3 133.0
Geometry 503 247.7 49.2 243.4 252.0 316.7 289.9 202.7 158.7Statistics 503 238.6 50.7 234.2 243.0 321.1 271.4 206.5 153.0
District 1Number 118 221.6 47.3 213.0 230.1 285.6 254.8 198.2 139.1Algebra 118 211.0 48.9 202.2 219.8 288.1 242.7 180.1 133.0
Geometry 118 232.2 42.1 224.6 239.8 292.1 270.7 202.7 158.7Statistics 118 214.4 42.8 206.6 222.1 271.4 236.0 185.9 153.0
District 2Number 161 231.1 44.3 224.3 238.0 294.3 261.7 198.2 139.1Algebra 161 246.1 40.5 239.9 252.4 308.5 275.6 218.3 180.1
Geometry 161 238.9 46.8 231.6 246.1 304.7 270.7 202.7 158.7Statistics 161 230.0 46.1 222.8 237.1 294.2 260.0 206.5 153.0
District 3Number 148 274.2 39.6 267.8 280.5 329.2 303.1 247.0 198.2Algebra 148 269.0 39.2 262.6 275.3 322.1 288.1 261.0 193.5
Geometry 148 277.8 47.8 270.1 285.5 347.4 316.7 243.9 202.7Statistics 148 277.3 45.1 270.0 284.5 359.0 306.8 248.2 206.5
District 4Number 76 218.9 39.1 210.1 227.7 275.4 248.9 198.2 139.1Algebra 76 230.8 40.2 221.8 239.9 288.1 261.0 218.3 180.1
Geometry 76 231.9 41.5 222.6 241.2 293.6 270.7 202.7 158.7Statistics 76 219.4 37.4 210.9 227.8 271.4 248.2 206.5 153.0
95% Confidence Interval Score distribution percentiles
58
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%400
N = 503 N = 503 N = 503 N = 503 N = 118 N = 118 N = 118 N = 118 N = 161 N = 161 N = 161 N = 161 N = 148 N = 148 N = 148 N = 148 N = 76 N = 76 N = 76 N = 76
Band 1
Band 5
Band 4
Band 3
Band 2
250
100
District 1 District 2 District 3 District 4
Number Alg Geom Stat
All
Number Alg Geom StatNumber Alg Geom StatNumber Alg Geom StatNumber Alg Geom Stat
Figure 29. Distribution of Classroom Achievement in MiC Classrooms in All Districts, Grade 6, in 1997-1998, by Content Strand
59
District 1
Table 1.6.6 MiC Classroom Achievement in District 1, Grade 6, in 1997-1998, by Gender, by Ethnic Group, and by Content Strand
Sample Mean SD Lower Upper 95%tile 75%tile 25%tile 5%tileOverall 118 213.6 45.1 205.5 221.8 282.1 246.1 184.4 121.2
Male 60 215.9 49.7 203.3 228.5 279.4 255.0 192.3 121.2Female 58 211.3 40.1 201.0 221.6 282.6 238.6 184.4 151.3
White 64 228.3 39.5 218.6 238.0 284.5 256.0 206.5 155.1African American 27 184.8 44.3 168.1 201.5 244.6 212.7 165.2 104.2Hispanic 11 198.7 37.8 176.3 221.0 242.9 231.3 175.4 148.3Other 16 213.9 48.9 190.0 237.9 284.2 249.1 172.9 139.3
Number 118 221.6 47.3 213.0 230.1 285.6 254.8 198.2 139.1Algebra 118 211.0 48.9 202.2 219.8 288.1 242.7 180.1 133.0Geometry 118 232.2 42.1 224.6 239.8 292.1 270.7 202.7 158.7Statistics 118 214.4 42.8 206.6 222.1 271.4 236.0 185.9 153.0
Confidence Interval Score distribution percentiles
60
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
N = 118 N = 60 N = 58 N = 64 N = 27 N = 11 N = 16 N = 118 N = 118 N = 118 N = 118
Band 1
Band 5
Band 4
Band 3
Band 2
400
250
100
Gender Ethnic Group Content Strands
Male Female White Afr-Am Hisp Other Number Alg Geom Stat
All
61
Figure 30. Distribution of Classroom Achievement in MiC Classrooms in District 1, Grade 6, in 1997-1998, by Gender, Ethnic Group, and by Content Strand
Table 1.6.7 MiC Classroom Achievement in District 1, Grade 6, in 1997-1998, by Teacher
Teacher ID Sample Mean SD Lower Upper 95%tile 75%tile 25%tile 5%tile30 8 232.9 27.7 213.7 252.1 267.1 250.9 221.1 194.333 54 215.4 47.4 202.8 228.1 282.1 253.0 184.4 139.338 56 209.1 44.6 197.5 220.8 273.5 243.2 190.4 121.2
Confidence Interval Score distribution percentiles
62
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
N = 8 N = 55 N = 56
Band 1
Band 5
Band 4
Band 3
Band 2
400
250
100 Teacher 30 Teacher 33 Teacher 38
63
Figure 31. Distribution of Classroom Achievement in MiC Classrooms in District 1, Grade 6, in 1997-1998, by Teacher
Table 1.6.8 MiC Classroom Achievement in Number, District 1, Grade 6, in 1997-1998, by Teacher
Teacher ID Sample Mean SD Lower Upper 95%tile 75%tile 25%tile 5%tile30 8 223.1 41.3 194.5 251.6 259.3 254.8 210.4 159.733 54 218.4 50.1 205.0 231.7 282.9 254.8 198.2 139.138 56 224.5 46.0 212.4 236.5 286.0 261.7 192.6 139.1
Confidence Interval Score distribution percentiles
64
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%400
N = 8 N = 54 N = 56
Band 1
Band 5
Band 4
Band 3
Band 2
250
100 Teacher 30 Teacher 33 Teacher 38
65
Figure 32. Distribution of Classroom Achievement in Number, MiC Classrooms in District 1, Grade 6, in 1997-1998, by Teacher
Table 1.6.9 MiC Classroom Achievement in Algebra, District 1, Grade 6, in 1997-1998, by Teacher
Teacher ID Sample Mean SD Lower Upper 95%tile 75%tile 25%tile 5%tile30 8 244.5 23.4 228.3 260.8 270.5 261.0 218.3 218.333 54 214.6 50.4 201.1 228.0 288.1 242.7 180.1 133.038 56 202.8 48.2 190.1 215.4 288.1 242.7 180.1 133.0
Confidence Interval Score distribution percentiles
66
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
N = 8 N = 54 N = 56
Band 1
Band 5
Band 4
Band 3
Band 2
400
250
100 Teacher 30 Teacher 33 Teacher 38
67
Figure 33. Distribution of Classroom Achievement in Algebra, MiC Classrooms in District 1, Grade 6, in 1997-1998, by Teacher
Table 1.6.10 MiC Classroom Achievement in Geometry, District 1, Grade 6, in 1997-1998, by Teacher
Teacher ID Sample Mean SD Lower Upper 95%tile 75%tile 25%tile 5%tile30 8 250.0 43.9 219.5 280.4 299.6 275.5 243.9 188.533 54 241.1 43.7 229.4 252.8 304.7 270.7 202.7 158.738 56 221.0 37.9 211.1 231.0 289.9 243.9 202.7 158.7
Confidence Interval Score distribution percentiles
68
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%400
N = 8 N = 54 N = 56
Band 1
Band 5
Band 4
Band 3
Band 2
250
100 Teacher 30 Teacher 33 Teacher 38
69
Figure 34. Distribution of Classroom Achievement in Geometry, MiC Classrooms in District 1, Grade 6, in 1997-1998, by Teacher
Table 1.6.11 MiC Classroom Achievement in Statistics, District 1, Grade 6, in 1997-1998, by Teacher
Teacher ID Sample Mean SD Lower Upper 95%tile 75%tile 25%tile 5%tile30 8 237.1 28.5 217.3 256.8 278.8 254.0 218.5 206.533 54 217.9 46.4 205.5 230.3 275.4 248.2 185.9 153.038 56 207.7 39.8 197.3 218.1 260.0 236.0 185.9 153.0
Confidence Interval Score distribution percentiles
70
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%400
N = 8 N = 54 N = 56
Band 1
Band 5
Band 4
Band 3
Band 2
250
100 Teacher 30 Teacher 33 Teacher 38
71
Figure 35. Distribution of Classroom Achievement in Statistics, MiC Classrooms in District 1, Grade 6, in 1997-1998, by Teacher
District 2
Table 1.6.12 MiC Classroom Achievement in District 2, Grade 6, in 1997-1998, by Gender, by Ethnic Group, and by Content Strand
Sample Mean SD Lower Upper 95%tile 75%tile 25%tile 5%tileOverall 161 233.3 42.6 226.7 239.9 296.3 262.4 206.5 165.2
Male 62 228.7 43.8 217.9 239.6 295.7 255.0 201.4 140.0Female 99 236.2 41.9 227.9 244.4 296.5 262.4 206.5 174.4
White 25 249.9 49.7 230.4 269.4 311.0 279.3 234.1 161.2African American 20 200.2 40.5 182.5 217.9 267.0 216.8 182.2 138.3Hispanic 81 233.6 35.3 226.0 241.3 285.0 255.0 212.7 184.4Other 35 239.6 45.7 224.5 254.7 301.5 275.9 209.6 161.7
Number 161 231.1 44.3 224.3 238.0 294.3 261.7 198.2 139.1Algebra 161 246.1 40.5 239.9 252.4 308.5 275.6 218.3 180.1Geometry 161 238.9 46.8 231.6 246.1 304.7 270.7 202.7 158.7Statistics 161 230.0 46.1 222.8 237.1 294.2 260.0 206.5 153.0
Confidence Interval Score distribution percentiles
72
0%
10%
20%
30%
40%
50%
60%
70%
80%
9
100%
73
Figure 36. Distribution of MiC Classroom Achievement in District 2, Grade 6, in 1997-1998, by Gender, by Ethnic Group, and by Content Strand
0%
N = 161 N = 62 N = 99 N = 25 N = 20 N = 81 N = 35 N = 161 N = 161 N = 161 N = 161
Band 1
Band 5
Band 4
Band 3
Band 2
400
250
Gender Ethnic Group Content Strands
Male Female White Afr-Am Hisp Other Number Alg Geom Stat
All
Table 1.6.13 MiC Classroom Achievement in District 2, Grade 6, in 1997-1998, by Teacher
Teacher ID Sample Mean SD Lower Upper 95%tile 75%tile 25%tile 5%tile37 45 228.0 34.4 218.0 238.1 280.2 251.1 199.7 177.245 36 267.2 36.2 255.4 279.0 316.2 287.8 247.1 206.551 47 231.9 38.9 220.8 243.1 282.1 259.0 209.6 150.152 33 205.5 41.4 191.4 219.6 285.0 234.1 184.4 140.5
Confidence Interval Score distribution percentiles
74
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
N = 45 N = 36 N = 47 N = 33
Band 1
Band 5
Band 4
Band 3
Band 2
400
250
100 Teacher 37 Teacher 45 Teacher 51 Teacher 52
Figure 37. Distribution of Classroom Achievement in MiC Classrooms in District 2, Grade 6, in 1997-1998, by Teacher
75
Table 1.6.14 MiC Classroom Achievement in Number, District 2, Grade 6, in 1997-1998, by Teacher
Teacher ID Sample Mean SD Lower Upper 95%tile 75%tile 25%tile 5%tile37 45 228.9 38.0 217.8 240.0 282.7 254.8 214.4 146.445 36 260.7 36.8 248.6 272.7 308.5 290.6 238.1 192.651 47 230.4 43.2 218.0 242.8 284.9 258.3 214.4 139.152 33 203.0 43.0 188.3 217.6 266.7 238.1 176.0 139.1
Confidence Interval Score distribution percentiles
76
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%400
N = 45 N = 36 N = 47 N = 33
Band 1
Band 5
Band 4
Band 3
Band 2
250
100 Teacher 37 Teacher 45 Teacher 51 Teacher 52
77
Figure 38. Distribution of Classroom Achievement in Number, MiC Classrooms in District 2, Grade 6, in 1997-1998, by Teacher
Table 1.6.15 MiC Classroom Achievement in Algebra, District 2, Grade 6, in 1997-1998, by Teacher
Teacher ID Sample Mean SD Lower Upper 95%tile 75%tile 25%tile 5%tile37 45 249.1 34.7 239.0 259.2 288.1 275.6 218.3 180.145 36 266.8 41.4 253.3 280.4 333.3 299.2 242.7 218.351 47 239.1 40.9 227.5 250.8 295.8 261.0 218.3 180.152 33 229.5 37.4 216.7 242.3 288.1 275.6 218.3 180.1
Confidence Interval Score distribution percentiles
78
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%400
N = 45 N = 36 N = 47 N = 33
Band 1
Band 5
Band 4
Band 3
Band 2
250
100 Teacher 37 Teacher 45 Teacher 51 Teacher 52
79
Figure 39. Distribution of Classroom Achievement in Algebra, MiC Classrooms in District 2, Grade 6, in 1997-1998, by Teacher
Table 1.6.16 MiC Classroom Achievement in Geometry, District 2, Grade 6, in 1997-1998, by Teacher
Teacher ID Sample Mean SD Lower Upper 95%tile 75%tile 25%tile 5%tile37 45 227.7 44.9 214.6 240.9 301.8 270.7 202.7 158.745 36 273.2 38.9 260.4 285.9 316.7 304.7 264.0 202.751 47 233.4 42.0 221.4 245.5 289.9 270.7 202.7 158.752 33 224.4 47.4 208.2 240.6 289.9 270.7 202.7 158.7
Confidence Interval Score distribution percentiles
80
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%400
N = 45 N = 36 N = 47 N = 33
Band 1
Band 5
Band 4
Band 3
Band 2
250
100 Teacher 37 Teacher 45 Teacher 51 Teacher 52
81
Figure 40. Distribution of Classroom Achievement in Geometry, MiC Classrooms in District 2, Grade 6, in 1997-1998, by Teacher
Table 1.6.17 MiC Classroom Achievement in Statistics, District 2, Grade 6, in 1997-1998, by Teacher
Teacher ID Sample Mean SD Lower Upper 95%tile 75%tile 25%tile 5%tile37 45 220.9 37.6 209.9 231.9 271.4 248.2 206.5 153.045 36 256.0 42.2 242.2 269.8 321.1 274.3 236.0 218.551 47 235.9 41.6 224.0 247.8 294.2 260.0 206.5 185.952 33 205.4 52.1 187.6 223.2 280.5 236.0 185.9 109.6
Confidence Interval Score distribution percentiles
82
0%
10%
20%
30%
40%
50%
83
Figure 41. Distribution of Classroom Achievement in Statistics, MiC Classrooms in District 2, Grade 6, in 1997-1998, by Teacher
60%
70%
80%
90%
10
N = 45 N = 36 N = 47 N = 33
0%
Band 1
Band 5
Band 4
Band 3
Band 2
400
250
100 Teacher 37 Teacher 45 Teacher 51 Teacher 52
District 3
Table 1.6.18 MiC Classroom Achievement in District 3, Grade 6, in 1997-1998, by Gender, by Ethnic Group, and by Content Strand
N Mean SD Lower Upper 95%tile 75%tile 25%tile 5%tileOverall 148 279.2 39.0 272.9 285.5 338.4 307.1 258.0 206.2
Male 68 272.7 38.7 263.5 281.9 338.4 297.0 247.1 201.4Female 80 284.7 38.6 276.2 293.2 335.1 309.2 265.3 222.7
White 133 278.5 36.8 272.3 284.8 331.9 306.4 255.0 221.7African-American 0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0Hispanic 6 289.5 53.2 246.9 332.1 343.5 320.0 270.3 216.3Other 9 281.6 61.4 241.5 321.7 344.9 311.5 259.0 181.6
Number 148 274.2 39.6 267.8 280.5 329.2 303.1 247.0 198.2Algebra 148 269.0 39.2 262.6 275.3 322.1 288.1 261.0 193.5Geometry 148 277.8 47.8 270.1 285.5 347.4 316.7 243.9 202.7Statistics 148 277.3 45.1 270.0 284.5 359.0 306.8 248.2 206.5
95% Confidence Interval Score distribution percentiles
84
0%
10%
20%
30%
40%
50%
60%
70%
80%
9
100%400
0%
N = 148 N = 80 N = 68 N = 133 N = 0 N = 6 N = 9 N = 148 N = 148 N = 148 N = 148
Band 1
Band 5
Band 4
Band 3
Band 2
250
100
Gender Ethnic Group Content Strands
Male Female White Afr-Am Hisp Other Number Alg Geom Stat
All
85
Figure 42. Distribution of Classroom Achievement in MiC Classrooms in District 3, Grade 6, in 1997-1998, by Gender, Ethnic Group, and by Content Strand
Table 1.6.19 MiC Classroom Achievement in District 3, Grade 6, in 1997-1998, by Teacher
Teacher ID N Mean SD Lower Upper 95%tile 75%tile 25%tile 5%tile6 24 302.5 37.2 287.6 317.4 350.7 326.7 282.1 241.715 41 280.7 35.5 269.8 291.5 325.6 306.4 251.1 224.039 38 277.4 39.1 265.0 289.8 332.6 304.6 256.0 224.640 38 278.5 27.7 269.7 287.3 317.6 302.9 262.4 229.050 7 203.8 23.0 186.7 220.8 231.1 224.0 188.4 178.1
95% Confidence Interval Score distribution percentiles
86
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
N = 24 N = 41 N = 38 N = 38 N = 7
Band 1
Band 5
Band 4
Band 3
Band 2
400
250
100 Teacher 6 Teacher 15 Teacher 39 Teacher 40 Teacher 50
87
Figure 43. Distribution of Classroom Achievement in MiC Classrooms in District 3, Grade 6, in 1997-1998, by Teacher
Table 1.6.20
MiC Classroom Achievement in Number, District 3, Grade 6, in 1997-1998, by Teacher
Teacher ID Sample Mean SD Lower Upper 95%tile 75%tile 25%tile 5%tile6 24 289.9 39.0 274.3 305.6 329.2 318.1 274.1 228.915 41 276.7 38.7 264.9 288.5 329.2 303.1 247.0 214.439 38 272.5 39.9 259.8 285.2 331.5 306.4 247.0 208.740 38 275.8 28.2 266.8 284.7 320.4 294.3 261.7 236.550 7 205.3 34.6 179.7 230.9 238.1 232.7 198.2 156.8
Confidence Interval Score distribution percentiles
88
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%400
N = 24 N = 41 N = 38 N = 38 N = 7
Band 1
Band 5
Band 4
Band 3
Band 2
250
100 Teacher 6 Teacher 15 Teacher 39 Teacher 40 Teacher 50
89
Figure 44. Distribution of Classroom Achievement in Number, MiC Classrooms in District 3, Grade 6, in 1997-1998, by Teacher
Table 1.6.21 MiC Classroom Achievement in Algebra, District 3, Grade 6, in 1997-1998, by Teacher
Teacher ID Sample Mean SD Lower Upper 95%tile 75%tile 25%tile 5%tile6 24 292.9 30.4 280.7 305.0 337.3 310.6 275.6 261.015 41 264.8 38.9 252.9 276.7 308.5 288.1 261.0 180.139 38 274.2 36.3 262.6 285.7 318.1 288.1 261.0 218.340 38 263.9 34.8 252.9 275.0 308.5 288.1 242.7 218.350 7 210.2 42.2 179.0 241.5 255.5 230.5 199.2 147.1
Confidence Interval Score distribution percentiles
90
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
N = 24 N = 41 N = 38 N = 38 N = 7
Band 1
Band 5
Band 4
Band 3
Band 2
400
250
100 Teacher 6 Teacher 15 Teacher 39 Teacher 40 Teacher 50
91
Figure 45. Distribution of Classroom Achievement in Algebra, MiC Classrooms in District 3, Grade 6, in 1997-1998, by Teacher
Table 1.6.22 MiC Classroom Achievement in Geometry, District 3, Grade 6, in 1997-1998, by Teacher
Teacher ID Sample Mean SD Lower Upper 95%tile 75%tile 25%tile 5%tile6 24 306.6 33.2 293.4 319.9 356.3 327.3 289.9 243.915 41 286.7 44.8 272.9 300.4 347.4 316.7 243.9 202.739 38 264.0 44.8 249.8 278.3 316.7 289.9 243.9 202.740 38 278.8 43.4 265.0 292.6 338.8 304.7 250.6 202.750 7 195.6 38.4 167.2 224.1 243.9 223.3 158.7 158.7
Confidence Interval Score distribution percentiles
92
0%
10%
20%
30%
40%
50%
6
93
Figure 46. Distribution of Classroom Achievement in Geometry, MiC Classrooms in District 3, Grade 6, in 1997-1998, by Teacher
0%
70%
80%
90%
10
N = 24 N = 41 N = 38 N = 38 N = 7
0%
Band 1
Band 5
Band 4
Band 3
Band 2
400
250
100 Teacher 6 Teacher 15 Teacher 39 Teacher 40 Teacher 50
Table 1.6.23 MiC Classroom Achievement in Statistics, District 3, Grade 6, in 1997-1998, by Teacher
Teacher ID Sample Mean SD Lower Upper 95%tile 75%tile 25%tile 5%tile6 24 301.0 40.8 284.6 317.3 355.8 337.5 282.8 237.915 41 275.2 48.2 260.5 290.0 359.0 294.2 236.0 206.539 38 279.0 47.8 263.8 294.2 359.0 306.8 248.2 203.440 38 272.6 34.9 261.5 283.7 323.6 294.2 260.0 206.550 7 223.7 26.1 204.3 243.0 256.5 242.1 206.5 192.1
Confidence Interval Score distribution percentiles
94
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%400
N = 24 N = 41 N = 38 N = 38 N = 7
Band 1
Band 5
Band 4
Band 3
Band 2
250
100 Teacher 6 Teacher 15 Teacher 39 Teacher 40 Teacher 50
95
Figure 47. Distribution of Classroom Achievement in Statistics, MiC Classrooms in District 3, Grade 6, in 1997-1998, by Teacher
District 4
Table 1.6.24 MiC Classroom Achievement in District 4, Grade 6, in 1997-1998, by Gender, by Ethnic Group, and by Content Strand
N Mean SD Lower Upper 95%tile 75%tile 25%tile 5%tileOverall 76 218.4 35.6 210.4 226.4 273.4 247.1 192.3 165.2
Male 39 215.2 36.1 203.8 226.5 269.0 238.6 192.3 164.0Female 37 221.7 35.2 210.4 233.1 273.2 247.1 192.3 173.4
White 4 229.8 40.4 190.2 269.3 272.2 257.3 197.8 193.4African-American 38 213.2 38.2 201.0 225.3 267.3 247.1 184.4 153.4Hispanic 10 242.4 25.9 226.4 258.5 279.4 258.0 229.0 210.6Other 24 214.7 31.1 202.2 227.1 265.7 230.3 197.8 175.4
Number 76 218.9 39.1 210.1 227.7 275.4 248.9 198.2 139.1Algebra 76 230.8 40.2 221.8 239.9 288.1 261.0 218.3 180.1Geometry 76 231.9 41.5 222.6 241.2 293.6 270.7 202.7 158.7Statistics 76 219.4 37.4 210.9 227.8 271.4 248.2 206.5 153.0
95% Confidence Interval Score distribution percentiles
96
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%400
N = 76 N = 37 N = 39 N = 4 N = 38 N = 10 N = 24 N = 76 N = 76 N = 76 N = 76
Band 1
Band 5
Band 4
Band 3
Band 2
All Gender Ethnic Group Content Strands
250
100 Male Female White Afr-Am Hisp Other Number Alg Geom Stat
Figure 48. Distribution of Classroom Achievement in MiC Classrooms in District 4, Grade 6, in 1997-1998, by Gender, Ethnic Group, and by Content Strand
97
Table 1.6.25
MiC Classroom Achievement in District 4, Grade 6, in 1997-1998, by Teacher
Teacher ID N Mean SD Lower Upper 95%tile 75%tile 25%tile 5%tile29 46 208.5 36.5 197.9 219.0 265.3 237.5 184.4 156.346 30 233.6 28.5 223.4 243.8 274.4 255.0 214.1 188.0
95% Confidence Interval Score distribution percentiles
98
0%
10%
20%
30%
40%
50%
60%
70%
99
Figure 49. Distribution of Classroom Achievement in MiC Classrooms in District 4, Grade 6, in 1997-1998, by Teacher
80%
90%
10 %
N = 46 N = 30
0
Band 1
Band 5
Band 4
Band 3
Band 2
040
250
100 Teacher 29 Teacher 46
Table 1.6.26 MiC Classroom Achievement in Number in District 4, Grade 6, in 1997-1998, by Teacher
Teacher ID Sample Mean SD Lower Upper 95%tile 75%tile 25%tile 5%tile29 46 209.5 40.3 197.9 221.2 266.5 235.4 198.2 139.146 30 233.3 32.9 221.5 245.0 277.0 261.7 214.4 186.0
Confidence Interval Score distribution percentiles
100
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%400
N = 46 N = 30
Band 1
Band 5
Band 4
Band 3
Band 2
250
100 Teacher 29 Teacher 46
101
Figure 50. Distribution of Classroom Achievement in Number, MiC Classrooms in District 4, Grade 6, in 1997-1998, by Teacher
Table 1.6.27 MiC Classroom Achievement in Algebra, District 4, Grade 6, in 1997-1998, by Teacher
Teacher ID Sample Mean SD Lower Upper 95%tile 75%tile 25%tile 5%tile29 46 223.6 42.6 211.3 235.9 288.1 256.4 180.1 144.846 30 242.0 33.8 229.9 254.1 275.6 261.0 218.3 180.1
Confidence Interval Score distribution percentiles
102
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%400
N = 46 N = 30
Band 1
Band 5
Band 4
Band 3
Band 2
250
100 Teacher 29 Teacher 46
103
Figure 51. Distribution of Classroom Achievement in Algebra, MiC Classrooms in District 4, Grade 6, in 1997-1998, by Teacher
Table 1.6.28 MiC Classroom Achievement in Geometry, District 4, Grade 6, in 1997-1998, by Teacher
Teacher ID Sample Mean SD Lower Upper 95%tile 75%tile 25%tile 5%tile29 46 227.9 41.8 215.8 240.0 289.9 243.9 202.7 158.746 30 238.0 41.0 223.4 252.7 298.1 270.7 202.7 158.7
Confidence Interval Score distribution percentiles
104
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%400
N = 46 N = 30
Band 1
Band 5
Band 4
Band 3
Band 2
250
100 Teacher 29 Teacher 46
105
Figure 52. Distribution of Classroom Achievement in Geometry, MiC Classrooms in District 4, Grade 6, in 1997-1998, by Teacher
Table 1.6.29 MiC Classroom Achievement in Statistics, District 4, Grade 6, in 1997-1998, by Teacher
Teacher ID Sample Mean SD Lower Upper 95%tile 75%tile 25%tile 5%tile29 46 209.3 39.1 198.0 220.6 271.4 236.0 185.9 153.046 30 234.8 29.0 224.4 245.2 266.3 248.2 222.5 206.5
Confidence Interval Score distribution percentiles
106
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%400
N = 46 N = 30
Band 1
Band 5
Band 4
Band 3
Band 2
250
100 Teacher 29 Teacher 46
107
Figure 53. Distribution of Classroom Achievement in Statistics, MiC Classrooms in District 4, Grade 6, in 1997-1998, by Teacher
Grade 7 All Districts
Table 1.7.1 MiC Classroom Achievement in All Districts, Grade 7, in 1997-1998, by Gender, by Ethnic Group, and by Content Strand
95% Confidence Interval Score distribution percentilesN Mean SD Lower Upper 95%tile 75%tile 25%tile 5%tile
Overall 507 252.8 49.2 248.5 257.1 326.2 285.0 221.7 170.3
Male 256 256.0 52.8 249.6 262.5 334.1 291.3 226.8 170.3Female 251 249.5 45.2 243.9 255.0 318.8 280.4 216.1 180.5
White 202 277.2 44.1 271.2 283.3 345.3 308.7 248.8 203.6Afr-Am 54 231.7 44.5 219.9 243.6 305.4 258.7 205.3 154.1Hispanic 129 232.8 40.9 225.8 239.9 294.8 263.5 203.6 170.3Other 122 242.7 50.4 233.7 251.6 313.4 275.9 210.4 144.9
Number 507 249.3 47.8 245.1 253.4 326.8 279.0 212.5 164.4Algebra 507 254.1 50.0 249.8 258.5 336.5 284.9 233.0 173.4Geometry 507 254.5 51.1 250.0 258.9 322.0 285.6 227.2 169.2Stat&Prob 507 249.5 48.3 245.3 253.7 326.2 287.8 209.1 174.9
108
Figure 54. Distribution of Classroom Achievement in MiC Classrooms in All Districts, Grade 7, in 1997-1998, by Gender, by Ethnic Group, and
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
N = 507 N = 256 N = 251 N = 202 N = 54 N = 129 N = 122 N = 507 N = 507 N = 507 N = 507
Band 1
Band 5
Band 4
Band 3
Band 2
400
250
100 Male Female White Afr-Am Hisp Other Number Alg Geom Stat
All Gender Ethnic Group Content Strands
by Content Strand
109
Table 1.7.2 MiC Classroom Achievement in All Districts, Grade 7, in 1997-1998, by District
N Mean SD Lower Upper 95%tile 75%tile 25%tile 5%tileOverall 507 252.8 49.2 248.5 257.1 326.2 285.0 221.7 170.3
District 1 88 247.2 43.9 238.1 256.4 310.5 282.8 216.1 170.3District 2 184 240.3 39.8 234.5 246.0 307.9 266.3 210.4 180.5District 3 127 293.4 40.5 286.4 300.5 365.7 321.1 263.5 231.9District 4 108 230.8 50.0 221.3 240.2 298.6 266.3 196.9 144.9
95% Confidence Interval Score distribution percentiles
110
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
N = 507 N = 88 N = 184 N = 127 N = 108
Band 1
Band 5
Band 4
Band 3
Band 2
400
250
100All District 1 District 3District 2 District 4
Figure 55. Distribution of Classroom Achievement in MiC Classrooms, Grade 7, in 1997-1998, by District
111
Table 1.7.3 Mi C Classroom Achievement in All Districts, Grade 7, in 1997-1998, by Gender
N Mean SD Lower Upper 95%tile 75%tile 25%tile 5%tileOverall
Male 256 256.0 52.8 249.6 262.5 334.1 291.3 226.8 170.3Female 251 249.5 45.2 243.9 255.0 318.8 280.4 216.1 180.5
District 1Male 43 250.05 49.75 235.18 264.92 317.82 293.43 218.88 170.31
Female 45 244.56 37.83 233.50 255.61 305.40 269.71 216.06 196.86District 2
Male 93 242.2 45.5 233.0 251.5 313.8 273.1 210.4 176.4Female 91 238.3 33.3 231.4 245.1 297.1 264.9 216.1 184.7
District 3Male 72 297.9 40.0 288.7 307.1 368.3 324.5 263.5 234.4
Female 55 287.6 40.7 276.8 298.3 345.3 316.6 264.9 228.8District 4
Male 48 225.3 48.7 211.5 239.1 282.1 263.5 194.9 144.9Female 60 235.1 51.0 222.2 248.0 306.5 271.3 201.9 144.0
95% Confidence Interval Score distribution percentiles
112
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
N = 256 N = 251 N = 43 N = 45 N = 93 N = 91 N = 72 N = 55 N = 48 N = 60
Band 1
Band 5
Band 4
Band 3
Band 2
400
250
100
All District 1 District 2 District 3
Male Female Male FemaleMale Female Male Female
District 4
Male Female
Figure 56. Distribution of Classroom Achievement in MiC Classrooms in All Districts, Grade 7, in 1997-1998, by Gender
113
Table 1.7.4 MiC Classroom Achievement in All Districts, Grade 7, in 1997-1998, by Ethnic Group
N Mean SD Lower Upper 95%tile 75%tile 25%tile 5%tileOverall
White 202 277.2 44.1 271.2 283.3 345.3 308.7 248.8 203.6African-American 54 231.7 44.5 219.9 243.6 305.4 258.7 205.3 154.1
Hispanic 129 232.8 40.9 225.8 239.9 294.8 263.5 203.6 170.3Other 122 242.7 50.4 233.7 251.6 313.4 275.9 210.4 144.9
District 1White 54 254.4 43.4 242.8 265.9 321.4 290.6 221.7 194.1
African American 12 216.6 45.9 190.6 242.5 283.8 237.5 194.9 144.8Hispanic 9 243.7 42.6 215.8 271.5 296.7 266.3 226.8 181.8
Other 13 248.4 36.7 228.5 268.4 302.2 266.3 236.4 190.3District 2
White 28 262.1 30.0 251.0 273.2 313.0 283.5 243.9 219.8African American 19 233.6 33.0 218.8 248.4 286.8 256.2 213.2 188.1
Hispanic 90 232.7 38.0 224.8 240.5 293.4 256.2 203.6 180.5Other 47 244.5 46.2 231.3 257.7 317.3 271.4 210.4 188.9
District 3White 116 292.8 41.2 285.3 300.3 365.7 321.1 263.5 231.9
African American 0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0Hispanic 2 309.8 20.0 282.1 337.5 322.5 316.9 302.7 297.1
Other 9 298.3 35.1 275.3 321.2 349.9 316.6 282.1 254.9District 4
White 4 242.0 35.6 207.2 276.9 277.7 260.1 226.5 202.8African American 23 238.1 51.6 217.0 259.2 311.2 275.9 212.7 147.4
Hispanic 28 224.2 45.5 207.4 241.1 279.0 260.5 194.9 144.9Other 53 230.2 53.0 215.9 244.5 296.6 269.7 196.9 137.9
95% Confidence Interval Score distribution percentiles
114
Figure 57. Distribution of Classroom Achievement in MiC Classrooms in All Districts, Grade 7, in 1997-1998, by Ethnic Group
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
N = 202 N = 54 N = 129 N = 122 N = 54 N = 12 N = 9 N = 13 N = 28 N = 19 N = 90 N = 47 N = 116 N = 0 N = 2 N = 9 N = 4 N = 23 N = 28 N = 53
Band 1
Band 5
Band 4
Band 3
Band 2
400
250
100
District 1 District 2 District 3
White AfrAm Hisp Other
All
White AfrAm Hisp OtherWhite AfrAm Hisp OtherWhite AfrAm Hisp OtherWhite AfrAm Hisp Other
District 4
115
Table 1.7.5 MiC Classroom Achievement in All Districts, Grade 7, in 1997-1998, by Content Strand
N Mean SD Lower Upper 95%tile 75%tile 25%tile 5%tileOverall
Number 507 249.3 47.8 245.1 253.4 326.8 279.0 212.5 164.4Algebra 507 254.1 50.0 249.8 258.5 336.5 284.9 233.0 173.4
Geometry 507 254.5 51.1 250.0 258.9 322.0 285.6 227.2 169.2Statistics 507 249.5 48.3 245.3 253.7 326.2 287.8 209.1 174.9
District 1Number 88 242.1 46.5 232.4 251.8 307.8 279.0 212.5 166.3Algebra 88 256.4 44.5 247.1 265.6 331.7 284.9 233.0 173.4
Geometry 88 246.3 44.5 237.0 255.6 301.4 277.0 227.2 169.2Statistics 88 245.4 45.9 235.8 255.0 308.3 275.2 209.1 174.9
District 2Number 184 233.0 43.5 226.7 239.3 302.6 261.7 212.5 153.3Algebra 184 244.0 44.2 237.6 250.4 308.9 275.2 209.9 173.4
Geo & Meas 184 249.0 43.2 242.8 255.3 308.6 277.0 227.2 169.2Prob & Stat 184 236.7 44.3 230.3 243.1 312.7 262.1 209.1 174.9
District 3Number 127 283.3 39.7 276.4 290.2 350.9 310.5 256.8 212.5Algebra 127 290.2 43.4 282.7 297.8 360.0 319.2 263.6 233.0
Geometry 127 292.6 36.0 286.3 298.8 346.4 315.8 277.0 243.0Statistics 127 281.5 43.3 273.9 289.0 341.3 312.7 247.8 209.1
District 4Number 108 242.8 45.3 234.2 251.3 310.5 270.6 212.5 153.3Algebra 108 227.0 46.6 218.2 235.8 290.4 263.6 209.9 124.1
Geometry 108 225.6 57.8 214.7 236.5 293.7 277.0 169.2 120.4Statistics 108 236.8 45.8 228.2 245.5 300.1 262.1 209.1 174.9
95% Confidence Interval Score distribution percentiles
116
Figure 58. Distribution of Classroom Achievement in MiC Classrooms in All Districts, Grade 7, in 1997-1998, by Content Strand
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
N = 507 N = 507 N = 507 N = 507 N = 88 N = 88 N = 88 N = 88 N = 184 N = 184 N = 184 N = 184 N = 127 N = 127 N = 127 N = 127 N = 108 N = 108 N = 108 N = 108
Band 1
Band 5
Band 4
Band 3
Band 2
400
250
100
District 1 District 2 District 3 District 4
Number All Geo Stat
All Districts
Number Alg Geo Stat Number Alg Geo StatNumber Alg Geo Stat Number Alg Geo Stat
117
District 1
Table 1.7.6 MiC Classroom Achievement in District 1, Grade 7, in 1997-1998, by Gender, by Ethnic Group, and by Content Strand
Sample Mean SD Lower Upper 95%tile 75%tile 25%tile 5%tileOverall 88 247.2 43.9 238.1 256.4 310.5 282.8 216.1 170.3
Male 43 250.0 49.7 235.2 264.9 317.8 293.4 218.9 170.3Female 45 244.6 37.8 233.5 255.6 305.4 269.7 216.1 196.9
White 54 254.4 43.4 242.8 265.9 321.4 290.6 221.7 194.1African American 12 216.6 45.9 190.6 242.5 283.8 237.5 194.9 144.8Hispanic 9 243.7 42.6 215.8 271.5 296.7 266.3 226.8 181.8Other 13 248.4 36.7 228.5 268.4 302.2 266.3 236.4 190.3
Number 88 242.10 46.52 232.38 251.82 307.75 278.98 212.46 166.27Algebra 88 256.36 44.48 247.06 265.65 331.66 284.95 232.97 173.44Geometry 88 246.28 44.47 236.99 255.57 301.39 276.97 227.16 169.22Statistics 88 245.41 45.88 235.82 254.99 308.27 275.20 209.06 174.94
Confidence Interval Score distribution percentiles
118
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
N = 88 N = 43 N = 45 N = 54 N = 12 N = 9 N = 13 N = 88 N = 88 N = 88 N = 88
Band 1
Band 5
Band 4
Band 3
Band 2
400
250
100
All Gender Ethnic Group Content Strands
Male Female White Afr-Am Hisp Other Number Alg Geom Stat
119
Figure 59. Distribution of Classroom Achievement in MiC Classrooms in District 1, Grade 7, in 1997-1998, by Gender, Ethnic Group, and by Content Strand
Table 1.7.7 MiC Classroom Achievement in District 1, Grade 7, in 1997-1998, by Teacher
Teacher ID Sample Mean SD Lower Upper 95%tile 75%tile 25%tile 5%tile8 38 250.9 38.4 238.7 263.1 309.1 280.6 228.1 196.944 50 244.4 47.9 231.2 257.7 318.3 283.3 210.4 164.1
Confidence Interval Score distribution percentiles
120
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
N = 38 N = 50
Band 1
Band 5
Band 4
Band 3
Band 2
400
250
100 Teacher 8 Teacher 44
Figure 60. Distribution of Classroom Achievement in MiC Classrooms in District 1, Grade 7, in 1997-1998, by Teacher
121
by Teacher Table 1.7.8
MiC Classroom Achievement in Number, District 1, Grade 7, in 1997-1998,
Teacher ID Sample Mean SD Lower Upper 95%tile 75%tile 25%tile 5%tile8 38 263.8 49.2 248.2 279.5 335.1 294.7 243.7 184.744 50 239.0 52.1 224.6 253.4 310.5 279.0 195.8 153.3
Confidence Interval Score distribution percentiles
122
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
N = 38 N = 50
Band 1
Band 5
Band 4
Band 3
Band 2
400
250
100 Teacher 8 Teacher 44
Teacher Figure 61. Distribution of Classroom Achievement in Number, MiC Classrooms in District 1, Grade 7, in 1997-1998, by
123
Table 1.7.9 MiC Classroom Achievement in Algebra, District 1, Grade 7, in 1997-1998, by Teacher
Teacher ID Sample Mean SD Lower Upper 95%tile 75%tile 25%tile 5%tile8 38 259.0 35.6 247.7 270.4 302.5 291.3 233.0 209.944 50 254.3 50.4 240.3 268.3 340.4 275.2 233.0 173.4
Confidence Interval Score distribution percentiles
124
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
N = 38 N = 50
Band 1
Band 5
Band 4
Band 3
Band 2
400
250
100 Teacher 8 Teacher 44
Figure 62. Distribution of Classroom Achievement in Algebra, MiC Classrooms in District 1, Grade 7, in 1997-1998, by Teacher
125
Table 1.7.10 om Achievement in Geometry, District 1, Grade 7, in 1997-1998, by Teacher MiC Classro
Teacher ID Sample Mean SD Lower Upper 95%tile 75%tile 25%tile 5%tile8 38 249.9 46.1 235.3 264.6 302.5 277.0 231.1 161.944 50 243.5 43.5 231.5 255.5 301.4 274.5 227.2 169.2
Confidence Interval Score distribution percentiles
126
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
N = 38 N = 50
Band 1
Band 5
Band 4
Band 3
Band 2
400
250
100 Teacher 8 Teacher 44
Figure 63. Distribution of Classroom Achievement in Geometry, MiC Classrooms in District 1, Grade 7, in 1997-1998, by Teacher
127
Table 1.7.11 MiC Classroom Achievement in Statistics, District 1, Grade 7, in 1997-1998, by Teacher
Teacher ID Sample Mean SD Lower Upper 95%tile 75%tile 25%tile 5%tile8 38 249.3 36.7 237.6 261.0 300.1 275.2 231.0 174.944 50 242.5 52.0 228.1 256.9 320.1 284.7 209.1 150.6
Confidence Interval Score distribution percentiles
128
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
N = 38 N = 50
Band 1
Band 5
Band 4
Band 3
Band 2
400
250
100 Teacher 8 Teacher 44
Figure 64. Distribution of Classroom Achievement in Statistics, MiC Classrooms in District 1, Grade 7, in 1997-1998, by Teacher
129
District
MiC Classroom Achievement in District 2, Grade 7, in 1997-1998, by Gender, by Ethnic Group, and by Content Strand
2
Table 1.7.12
Sample Mean SD Lower Upper 95%tile 75%tile 25%tile 5%tileOverall 184 240.3 39.8 234.5 246.0 307.9 266.3 210.4 180.5
Male 93 242.2 45.5 233.0 251.5 313.8 273.1 210.4 176.4Female 91 238.3 33.3 231.4 245.1 297.1 264.9 216.1 184.7
White 28 262.1 30.0 251.0 273.2 313.0 283.5 243.9 219.8African American 19 233.6 33.0 218.8 248.4 286.8 256.2 213.2 188.1Hispanic 90 232.7 38.0 224.8 240.5 293.4 256.2 203.6 180.5Other 47 244.5 46.2 231.3 257.7 317.3 271.4 210.4 188.9
Number 184 233.0 43.5 226.7 239.3 302.6 261.7 212.5 153.3Algebra 184 244.0 44.2 237.6 250.4 308.9 275.2 209.9 173.4Geometry 184 249.0 43.2 242.8 255.3 308.6 277.0 227.2 169.2Statistics 184 236.7 44.3 230.3 243.1 312.7 262.1 209.1 174.9
Confidence Interval Score distribution percentiles
130
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
N = 184 N = 93 N = 91 N = 28 N = 19 N = 90 N = 47 N = 184 N = 184 N = 184 N = 184
Band 1
Band 5
Band 4
Band 3
Band 2
400
250
100
All Gender Ethnic Group Content Strands
Male Female White Afr-Am Hisp Other Number Alg Geom Stat
Content Figure 65. Distribution of MiC Classroom Achievement in District 2, Grade 7, in 1997-1998, by Gender, by Ethnic Group, and by
Strand
131
Table 1.7.13 MiC Classroom Achievement in District 2, Grade 7, in 1997-1998, by Teacher
%tile11 41 217.0 35.5 206.1 227.9 278.7 231.9 196.9 180.520 45 256.3 35.4 246.0 266.7 313.8 278.7 231.9 203.635 50 249.1 46.4 236.3 262.0 315.5 281.3 213.2 192.547 48 235.9 29.3 227.6 244.2 280.9 256.2 214.6 188.9
Teacher ID Sample Mean SD Lower Upper 95%tile 75%tile 25%tile 5Confidence Interval Score distribution percentiles
132
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
N = 41 N = 45 N = 50 N = 48
Band 1
Band 5
Band 4
Band 3
Band 2
400
250
100 Teacher 11 Teacher 20 Teacher 35 Teacher 47
Figure 66. Distribution of Classroom Achievement in MiC Classrooms in District 2, Grade 7, in 1997-1998, by Teacher
133
Table 1.7.14
MiC Classroom Achievement in Number, District 2, Grade 7, in 1997-1998, by Teacher
Teacher ID Sample Mean SD Lower Upper 95%tile 75%tile 25%tile 5%tile11 41 212.4 48.7 197.5 227.3 279.0 251.9 190.3 101.620 45 239.6 44.9 226.4 252.7 302.6 270.6 212.5 153.335 50 241.8 42.7 230.0 253.7 310.5 270.6 212.5 170.047 48 235.3 32.5 226.1 244.5 284.1 261.7 212.5 190.3
Confidence Interval Score distribution percentiles
134
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
N = 41 N = 45 N = 50 N = 48
Band 1
Band 5
Band 4
Band 3
Band 2
400
250
100 Teacher 11 Teacher 20 Teacher 35 Teacher 47
Teacher Figure 67. Distribution of Classroom Achievement in Number, MiC Classrooms in District 2, Grade 7, in 1997-1998, by
135
Table 1.7.15 m Achievement in Algebra, District 2, Grade 7, in 1997-1998, by Teacher
MiC Classroo
Teacher ID Sample Mean SD Lower Upper 95%tile 75%tile 25%tile 5%tile11 41 224.0 36.2 212.9 235.1 263.6 250.3 209.9 173.420 45 269.6 30.3 260.7 278.4 315.6 293.4 250.3 209.935 50 245.8 53.2 231.0 260.5 322.7 284.9 209.9 173.447 48 235.3 40.6 223.9 246.8 293.4 263.6 209.9 173.4
Confidence Interval Score distribution percentiles
136
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
N = 41 N = 45 N = 50 N = 48
Band 1
Band 5
Band 4
Band 3
Band 2
400
250
100 Teacher 11 Teacher 20 Teacher 35 Teacher 47
Figure 68. Distribution of Classroom Achievement in Algebra, MiC Classrooms in District 2, Grade 7, in 1997-1998, by Teacher
137
Table 1.7.16 MiC Classroom Achievement in Geometry, District 2, Grade 7, in 1997-1998, by Teacher
Teacher ID Sample Mean SD Lower Upper 95%tile 75%tile 25%tile 5%tile11 41 229.7 43.3 216.5 243.0 293.7 256.4 205.1 169.220 45 256.8 38.6 245.5 268.1 307.1 285.6 227.2 205.135 50 261.8 44.6 249.5 274.2 316.0 291.7 243.0 185.447 48 244.8 40.4 233.4 256.3 285.6 266.9 227.2 169.2
Confidence Interval Score distribution percentiles
138
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
N = 41 N = 45 N = 50 N = 48
Band 1
Band 5
Band 4
Band 3
Band 2
400
250
100 Teacher 11 Teacher 20 Teacher 35 Teacher 47
r Figure 69. Distribution of Classroom Achievement in Geometry, MiC Classrooms in District 2, Grade 7, in 1997-1998, by Teache
139
Table 1.7.17 MiC Classroom Achievement in Statistics, District 2, Grade 7, in 1997-1998, by Teacher
Teacher ID Sample Mean SD Lower Upper 95%tile 75%tile 25%tile 5%tile11 41 214.5 41.4 201.8 227.1 287.8 231.0 174.9 174.920 45 256.6 40.0 244.9 268.3 312.7 287.8 231.0 209.135 50 244.2 45.1 231.7 256.7 320.1 271.9 209.1 174.947 48 229.4 40.5 217.9 240.9 275.2 262.1 209.1 146.2
Confidence Interval Score distribution percentiles
140
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
N = 41 N = 45 N = 50 N = 48
Band 1
Band 5
Band 4
Band 3
Band 2
400
250
100 Teacher 11 Teacher 20 Teacher 35 Teacher 47
Figure 70. Distribution of Classroom Achievement in Statistics, MiC Classrooms in District 2, Grade 7, in 1997-1998, by Teacher
141
District
Table 1.7.18 MiC Classroom Achievement in District 3, Grade 7, in 1997-1998, by Gender, by Ethnic Group, and by Content Strand
5.3 316.6 264.9 228.8
White 116 292.8 41.2 285.3 300.3 365.7 321.1 263.5 231.9African-American 0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0Hispanic 2 309.8 20.0 282.1 337.5 322.5 316.9 302.7 297.1Other 9 298.3 35.1 275.3 321.2 349.9 316.6 282.1 254.9
Number 127 283.3 39.7 276.4 290.2 350.9 310.5 256.8 212.5Algebra 127 290.2 43.4 282.7 297.8 360.0 319.2 263.6 233.0Geometry 127 292.6 36.0 286.3 298.8 346.4 315.8 277.0 243.0Statistics 127 281.5 43.3 273.9 289.0 341.3 312.7 247.8 209.1
95% Confidence Interval Score distribution percentiles
3
N Mean SD Lower Upper 95%tile 75%tile 25%tile 5%tileOverall 127 293.4 40.5 286.4 300.5 365.7 321.1 263.5 231.9
Male 72 297.9 40.0 288.7 307.1 368.3 324.5 263.5 234.4Female 55 287.6 40.7 276.8 298.3 34
142
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
N = 127 N = 72 N = 55 N = 116 N = 0 N = 2 N = 9 N = 127 N = 127 N = 127 N = 127
Band 1
Band 5
Band 4
Band 3
Band 2
400
250
100
All Gender Ethnic Group Content Strands
Male Female White Afr-Am Hisp Other Number Alg Geom Stat
up, and by Figure 71. Distribution of Classroom Achievement in MiC Classrooms in District 3, Grade 7, in 1997-1998, by Gender, Ethnic Gro
Content Strand
143
Table 1.7.19 MiC Classroom Achievement in District 3, Grade 7, in 1997-1998, by Teacher
Teacher ID N Mean SD Lower Upper 95%tile 75%tile 25%tile 595% Confidence Interval Score distribution percentiles
%tile9 1 231.9 231.9 231.9 231.9 231.916 126 293.9 40.3 286.9 300.9 365.7 321.1 264.2 231.9
144
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
N = 1 N = 126
Band 1
Band 5
Band 4
Band 3
Band 2
400
250
100 Teacher 9 Teacher 16
Figure 72. Distribution of Classroom Achievement in MiC Classrooms in District 3, Grade 7, in 1997-1998, by Teacher
145
Teacher Table 1.7.20
MiC Classroom Achievement in Number, District 3, Grade 7, in 1997-1998, by
Teacher ID Sample Mean SD Lower Upper 95%tile 75%tile 25%tile 5%tile9 1 228.2 228.2 228.2 228.2 228.216 126 283.7 39.6 276.8 290.6 351.4 310.5 261.7 212.5
Confidence Interval Score distribution percentiles
146
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
N = 1 N = 126
Band 1
Band 5
Band 4
Band 3
Band 2
400
250
100 Teacher 9 Teacher 16
Teacher Figure 73. Distribution of Classroom Achievement in Number, MiC Classrooms in District 3, Grade 7, in 1997-1998, by
147
Table 1.7.21 m Achievement in Algebra, District 3, Grade 7, in 1997-1998, by Teacher MiC Classroo
Teacher ID Sample Mean SD Lower Upper 95%tile 75%tile 25%tile 5%tile9 1 250.3 250.3 250.3 250.3 250.316 126 290.6 43.4 283.0 298.1 360.0 320.9 263.6 233.0
Confidence Interval Score distribution percentiles
148
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
N = 1 N = 126
Band 1
Band 5
Band 4
Band 3
Band 2
400
250
100 Teacher 9 Teacher 16
Figure 74. Distribution of Classroom Achievement in Algebra, MiC Classrooms in District 3, Grade 7, in 1997-1998, by Teacher
149
Table 1.7.22 MiC Classroom Achievement in Geometry, District 3, Grade 7, in 1997-1998,by Teacher
Teacher ID Sample Mean SD Lower Upper 95%tile 75%tile 25%tile 5%tile9 1 243.0 243.0 243.0 243.0 243.016 126 293.0 35.9 286.7 299.2 346.4 315.8 277.0 243.0
Confidence Interval Score distribution percentiles
150
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
N = 1 N = 126
Band 1
Band 5
Band 4
Band 3
Band 2
400
250
100 Teacher 9 Teacher 16
r Figure 75. Distribution of Classroom Achievement in Geometry, MiC Classrooms in District 3, Grade 7, in 1997-1998, by Teache
151
Table 1.7.23 MiC Classroom Achievement in Statistics, District 3, Grade 7, in 1997-1998, by Teacher
Teacher ID Sample Mean SD Lower Upper 95%tile 75%tile 25%tile 5%tile9 1 231.0 231.0 231.0 231.0 231.016 126 281.9 43.3 274.3 289.4 341.3 312.7 247.8 209.1
Confidence Interval Score distribution percentiles
152
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
N = 1 N = 126
Band 1
Band 5
Band 4
Band 3
Band 2
400
250
100 Teacher 9 Teacher 16
Figure 76. Distribution of Classroom Achievement in Statistics, MiC Classrooms in District 3, Grade 7, in 1997-1998, by Teacher
153
District
MiC Classroom Achievement in District 4, Grade 7, in 1997-1998, by Gender, by Ethnic Group, and by Content Strand
4
Table 1.7.24
N Mean SD Lower Upper 95%tile 75%tile 25%tile 5%tileOverall 108 230.8 50.0 221.3 240.2 298.6 266.3 196.9 144.9
Male 48 225.3 48.7 211.5 239.1 282.1 263.5 194.9 144.9Female 60 235.1 51.0 222.2 248.0 306.5 271.3 201.9 144.0
White 4 242.0 35.6 207.2 276.9 277.7 260.1 226.5 202.8African-American 23 238.1 51.6 217.0 259.2 311.2 275.9 212.7 147.4Hispanic 28 224.2 45.5 207.4 241.1 279.0 260.5 194.9 144.9Other 53 230.2 53.0 215.9 244.5 296.6 269.7 196.9 137.9
Number 108 242.8 45.3 234.2 251.3 310.5 270.6 212.5 153.3Algebra 108 227.0 46.6 218.2 235.8 290.4 263.6 209.9 124.1Geometry 108 225.6 57.8 214.7 236.5 293.7 277.0 169.2 120.4Statistics 108 236.8 45.8 228.2 245.5 300.1 262.1 209.1 174.9
95% Confidence Interval Score distribution percentiles
154
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
N = 108 N = 48 N = 60 N = 4 N = 23 N = 28 N = 53 N = 108 N = 108 N = 108 N = 108
Band 1
Band 5
Band 4
Band 3
Band 2
400
250
100
All Gender Ethnic Group Content Strands
Male Female White Afr-Am Hisp Other Number Alg Geom Stat
Figure 77. Distribution of Classroom Achievement in MiC Classrooms in District 4, Grade 7, in 1997-1998, by Gender, Ethnic Gro Content Strand
up, and by
155
Table 1.7.25 MiC Classroom Achievement in District 4, Grade 7, in 1997-1998, by Teacher
Teacher ID N Mean SD Lower Upper 95%tile 75%tile 25%tile 595% Confidence Interval Score distribution percentiles
%tile28 35 191.5 47.8 175.7 207.3 262.1 226.8 144.9 127.434 29 248.3 36.4 235.0 261.5 302.6 282.1 221.7 202.336 44 250.5 41.1 238.3 262.6 300.1 273.8 247.8 170.3
156
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
N = 35 N = 29 N = 44
Band 1
Band 5
Band 4
Band 3
Band 2
400
250
100 Teacher 28 Teacher 34 Teacher 36
Figure 78. Distribution of Classroom Achievement in MiC Classrooms in District 4, Grade 7, in 1997-1998, by Teacher
157
Table 1.7.26 MiC Classroom Achievement in Number, District 4, Grade 7, in 1997-1998, by Teacher
Teacher ID Sample Mean SD Lower Upper 95%tile 75%tile 25%tile 5%tile28 35 211.5 48.1 195.6 227.4 264.4 246.5 190.3 137.834 29 250.8 38.1 237.0 264.7 312.1 270.6 228.2 190.336 44 262.3 33.2 252.5 272.1 310.5 279.0 251.9 190.3
Confidence Interval Score distribution percentiles
158
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
N = 35 N = 29 N = 44
Band 1
Band 5
Band 4
Band 3
Band 2
400
250
100 Teacher 28 Teacher 34 Teacher 36
Teacher Figure 79. Distribution of Classroom Achievement in Number, MiC Classrooms in District 4, Grade 7, in 1997-1998, by
159
Table 1.7.27 MiC Classroom Achievement in Algebra, District 4, Grade 7, in 1997-1998, by Teacher
Teacher ID Sample Mean SD Lower Upper 95%tile 75%tile 25%tile 5%tile28 35 199.6 47.0 184.1 215.2 263.6 221.4 173.4 124.134 29 239.3 39.9 224.8 253.8 290.0 263.6 209.9 173.436 44 240.7 41.4 228.5 253.0 300.2 263.6 209.9 173.4
Confidence Interval Score distribution percentiles
160
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
N = 35 N = 29 N = 44
Band 1
Band 5
Band 4
Band 3
Band 2
400
250
100 Teacher 28 Teacher 34 Teacher 36
Figure 80. Distribution of Classroom Achievement in Algebra, MiC Classrooms in District 4, Grade 7, in 1997-1998, by Teacher
161
Table 1.7.28 MiC Classroom Achievement in Geometry, District 4, Grade 7, in 1997-1998, by Teacher
Teacher ID Sample Mean SD Lower Upper 95%tile 75%tile 25%tile 5%tile28 35 182.2 49.2 165.9 198.5 265.1 205.1 144.8 120.434 29 250.5 49.2 232.6 268.4 308.6 285.6 227.2 169.236 44 243.6 50.4 228.7 258.5 293.7 285.6 221.7 127.7
Confidence Interval Score distribution percentiles
162
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
N = 35 N = 29 N = 44
Band 1
Band 5
Band 4
Band 3
Band 2
400
250
100 Teacher 28 Teacher 34 Teacher 36
r Figure 81. Distribution of Classroom Achievement in Geometry, MiC Classrooms in District 4, Grade 7, in 1997-1998, by Teache
163
Table 1.7.29 MiC Classroom Achievement in Statistics, District 4, Grade 7, in 1997-1998, by Teacher
Teacher ID Sample Mean SD Lower Upper 95%tile 75%tile 25%tile 5%tile28 35 209.2 45.1 194.2 224.1 279.0 239.4 174.9 130.734 29 246.1 43.1 230.4 261.8 312.7 262.1 209.1 174.936 44 252.7 38.3 241.4 264.0 300.1 287.8 231.0 174.9
Confidence Interval Score distribution percentiles
164
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
N = 35 N = 29 N = 44
Band 1
Band 5
Band 4
Band 3
Band 2
400
250
100 Teacher 28 Teacher 34 Teacher 36
Figure 82. Distribution of Classroom Achievement in Statistics, MiC Classrooms in District 4, Grade 7, in 1997-1998, by Teacher
165
Appendix A
166
The purposes of the longitudinal/cross-sectional study of the impact of Mathematics in Context (MiC) on student performance were (a) to determine the mathematical knowledge, understanding, attitudes, and levels of student performance as a consequence of studying MiC for over three years; and (b) to compare student knowledge, understanding, attitudes, and levels of performance of students using MiC with those using conventional mathematics curricula. The research model for this study was an adaptation of a structural model for monitoring changes in school mathematics (Romberg, 1987, described in Chapter 2). The outcome variables for this model are - knowledge and understanding, and application. For analytic purposes we assumed that variation in classroom achievement based on the measures developed for these variables can be captured in progress maps for classroom achievement. There were three questions that the study was designed to answer: 1. What is the impact of the MiC instructional approach on student performance? 2. How is this impact different from that of traditional instruction on students performance? 3. What variables associated with classroom instruction account for variation in student
performance? To answer these questions an analysis plan involving seven steps has been planned. Step One: Creating an Overall Progress Map The dependent variable used to answer each of the questions is an index of “Classroom Achievement (CA)” derived from data from student responses to eight tests {four External Assessments (EA) based on NAEP and TIMSS items, and four Problem Solving Assessments (PSA) developed by the staff of the Freudenthal Institute. One form of each test was given to students at each of the grades 5, 6, 7 and 8. From the raw scores on these tests the CA index was derived by the research team at the Australian Council for Educational Research (ACER) using “Rasch measurement models” that allow one to combine information from different tests administered at different times onto a single scale. The product of this step is a single CA scale. Step Two: Answering Question #1 – Grade-Level-by-Year As shown in Figure 1, the overall study involves seventeen studies: eight grade-level-by year studies that can be related for cross-sectional comparisons, three cross-grade studies, three cross-year studies, and three longitudinal comparisons.
167
Grade 7Grade 7
Cross-Grade
Grade 5
Grade 6
Grade 7
Grade 6
Grade 8
Grade 7
Grade 8
Cross-Year
Cross-Year
Cross-Year
Cross-Grade
Cross-Grade
L o n g i t u d i n a l
L o n g i t u d i n a l
L o n g i t u d i n a l
1 9 9 7 - 1 9 9 8 1 9 9 8 - 1 9 9 9 1 9 9 9 - 2 0 0 0
To answer “Question 1” the CA index was used to examine the performance of all MiC students in the four sites at each grade level (the eight grade-level-by-year descriptions of performance of all MiC students). Comparisons of performance on CA then was derived for the different sites, classes, teachers, gender of students, ethnicity of students, etc. Step Three: Answering Question #1 – Cross-Grade, Cross-Year From the analyses done in Step Two we made the three cross-grade comparisons, and the three cross-year cross-sectional studies indicated in Figure 1. These comparisons yield pictures of general student progress in performance as a consequence of instruction using MiC. Step Four: Answering Question #1 – Longitudinally Next we examined the three longitudinal descriptions also shown in Figure 1. However, since the student data-base must be restricted to those MiC students that participated in two or three years of the study (study transiency was high), several cohorts of students examined over the two (or three) years with respect to the overall index (CA). Step Five: Answering Question #2 To answer Question 2 only the MiC data from the two sites where similar data from students in classes using conventional instructional materials was gathered. The comparisions were with respect to the eight grade-level-by-year studies, followed by the cross-grade, cross-year, and longitudinal comparisions. Step Six: Answering Question #3 – Creating Composite Indices Data for both MiC and conventional students at the two sites were used to examine the relationship between variation in classroom achievement (CA), aggregated by strand, test, or total performance can be attributed to variations in opportunity to learn with understanding (OTLu), preceding achievement (PA), method of instruction (I), and school context (SC).
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Step Seven: Answering Question #3 – Analyses Since indices for each of these composite variables was constructed three different analyses were planned. First, for the grade-level-by-year studies we compared similar groups of students on CA. Second, linear regression was used to examine this relationship for the eight grade-level-by-year studies. Third, since the composite variables were constructed from several sources that reflect the original 14 variables structural model, we calculated path coefficients relating most of the variables in the model using structural equations.
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