​​​​NAEP Technical DocumentationIndex Scoring for the 2019 Grade 8 Mathematics Indices

Recoding of polytomous items for scaling, grade 8 mathematics combined national and state assessment, by index: 2019
Item Index Reason for decision Disposition
U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2019 Mathematics Assessment.
B034901 Persistence in learning To improve model-data fit Collapse categories: 1,2,3,4,5 becomes 1,1,2,3,4
B034902 Persistence in learning To improve model-data fit Collapse categories: 1,2,3,4,5 becomes 1,1,2,3,4
B034903 Persistence in learning To improve model-data fit Collapse categories: 1,2,3,4,5 becomes 1,1,2,3,4
B034904 Persistence in learning To improve model-data fit Collapse categories: 1,2,3,4,5 becomes 1,1,2,3,4
B035001 Academic self-discipline To improve model-data fit Collapse categories: 1,2,3,4,5 becomes 1,1,2,3,4
B035002 Academic self-discipline To improve model-data fit Collapse categories: 1,2,3,4,5 becomes 1,1,2,3,4
B035003 Academic self-discipline To improve model-data fit Collapse categories: 1,2,3,4,5 becomes 1,1,2,3,4
B035004 Academic self-discipline To improve model-data fit Collapse categories: 1,2,3,4,5 becomes 1,1,2,3,4
B035101 Enjoyment of complex problems To improve model-data fit Collapse categories: 1,2,3,4,5 becomes 1,1,2,3,4
B035102 Enjoyment of complex problems To improve model-data fit Collapse categories: 1,2,3,4,5 becomes 1,1,2,3,4
B035103 Enjoyment of complex problems To improve model-data fit Collapse categories: 1,2,3,4,5 becomes 1,1,2,3,4
B035104 Enjoyment of complex problems To improve model-data fit Collapse categories: 1,2,3,4,5 becomes 1,1,2,3,4
M831403 Confidence in mathematics knowledge and skills To improve model-data fit Collapse categories: 1,2,3,4,5 becomes 1,1,2,3,4
M831405 Confidence in mathematics knowledge and skills To improve model-data fit Collapse categories: 1,2,3,4,5 becomes 1,1,2,3,4
M831407 Confidence in mathematics knowledge and skills To improve model-data fit Collapse categories: 1,2,3,4,5 becomes 1,1,2,3,4
M831408 Confidence in mathematics knowledge and skills To improve model-data fit Collapse categories: 1,2,3,4,5 becomes 1,1,2,3,4
M831409 Confidence in mathematics knowledge and skills To improve model-data fit Collapse categories: 1,2,3,4,5 becomes 1,1,2,3,4
M831410 Confidence in mathematics knowledge and skills To improve model-data fit Collapse categories: 1,2,3,4,5 becomes 1,1,2,3,4
M831411 Confidence in mathematics knowledge and skills To improve model-data fit Collapse categories: 1,2,3,4,5 becomes 1,1,2,3,4
M831901 Interest/enjoyment in mathematics To improve model-data fit Collapse categories: 1,2,3,4,5 becomes 1,1,2,3,4
M831902 Interest/enjoyment in mathematics To improve model-data fit Collapse categories: 1,2,3,4,5 becomes 1,1,2,3,4
M831903 Interest/enjoyment in mathematics To improve model-data fit Collapse categories: 1,2,3,4,5 becomes 1,1,2,3,4
M831904 Interest/enjoyment in mathematics To improve model-data fit Collapse categories: 1,2,3,4,5 becomes 1,1,2,3,4
M831905 Interest/enjoyment in mathematics To improve model-data fit Collapse categories: 1,2,3,4,5 becomes 1,1,2,3,4
M831906 Interest/enjoyment in mathematics To improve model-data fit Collapse categories: 1,2,3,4,5 becomes 1,1,2,3,4
M831504 Mastery goals in mathematics To improve model-data fit Collapse categories: 1,2,3,4,5 becomes 1,1,2,3,4
M831505 Mastery goals in mathematics To improve model-data fit Collapse categories: 1,2,3,4,5 becomes 1,1,2,3,4
M831506 Mastery goals in mathematics To improve model-data fit Collapse categories: 1,2,3,4,5 becomes 1,1,2,3,4
M834102 Mastery goals in mathematics To improve model-data fit Collapse categories: 1,2,3,4,5 becomes 1,1,2,3,4
​

IRT parameters for items in the index of eighth-grade students' persistence in learning, grade 8 mathematics combined national and state assessment: 2019
Item b d d d
The number of d parameters is one less than the number of categories for the item. For items scaled with the partial credit model, parameters a and c are not estimated. The a parameter value is exactly one and the c parameter is exactly zero. For item j, b represents a location parameter related to item difficulty, and d represents the category threshold parameter for category i of item j; d may not sum to zero because of rounding.
U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2019 Mathematics Assessment.
B034901 -0.28 1.02 0.05 -1.07
B034902 -0.50 0.81 0.05 -0.86
B034903 -0.31 0.77 0.01 -0.78
B034904 -0.73 0.63 0.03 -0.66
​

IRT parameters for items in the index of eighth-grade students' enjoyment of complex problems, grade 8 mathematics combined national and state assessment: 2019
Item b d d d
The number of d parameters is one less than the number of categories for the item. For items scaled with the partial credit model, parameters a and c are not estimated. The a parameter value is exactly one and the c parameter is exactly zero. For item j, b represents a location parameter related to item difficulty, and d represents the category threshold parameter for category i of item j; d may not sum to zero because of rounding.
U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2019 Mathematics Assessment.
B035101 0.65 0.77 -0.05 -0.72
B035102 0.07 0.73 -0.02 -0.71
B035103 0.13 0.75 -0.01 -0.74
B035104 0.08 0.64 -0.02 -0.62
​

IRT parameters for items in the index of eighth-grade students' academic self-discipline, grade 8 mathematics combined national and state assessment: 2019
Item b d d d
The number of d parameters is one less than the number of categories for the item. For items scaled with the partial credit model, parameters a and c are not estimated. The a parameter value is exactly one and the c parameter is exactly zero. For item j, b represents a location parameter related to item difficulty, and d represents the category threshold parameter for category i of item j; d may not sum to zero because of rounding.
U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2019 Mathematics Assessment.
B035001 0.10 0.74 -0.02 -0.72
B035002 -0.06 0.87 0.10 -0.96
B035003 -0.35 0.68 0.05 -0.73
B035004 -0.20 0.69 0.05 -0.74
​

IRT parameters for items in the index of eighth-grade students' confidence in mathematics knowledge and skills, grade 8 mathematics combined national and state assessment: 2019
Item b d d d
The number of d parameters is one less than the number of categories for the item. For items scaled with the partial credit model, parameters a and c are not estimated. The a parameter value is exactly one and the c parameter is exactly zero. For item j, b represents a location parameter related to item difficulty, and d represents the category threshold parameter for category i of item j; d may not sum to zero because of rounding.
U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2019 Mathematics Assessment.
M831403 -0.05 0.63 -0.13 -0.50
M831405 -0.42 0.63 -0.10 -0.52
M831407 -0.18 0.81 -0.16 -0.65
M831408 -0.14 0.68 0.00 -0.68
M831409 -0.40 0.84 -0.04 -0.80
M831410 -0.60 0.66 -0.03 -0.63
M831411 -0.48 0.83 -0.09 -0.74
​

IRT parameters for items in the index of eighth-grade students' performance goals in mathematics, grade 8 mathematics combined national and state assessment: 2019
Item b d d d d
The number of d parameters is one less than the number of categories for the item. For items scaled with the partial credit model, parameters a and c are not estimated. The a parameter value is exactly one and the c parameter is exactly zero. For item j, b represents a location parameter related to item difficulty, and d represents the category threshold parameter for category i of item j; d may not sum to zero because of rounding.
U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2019 Mathematics Assessment.
M831501 -0.07 0.78 0.64 -0.32 -1.10
M831502 0.25 0.78 0.53 -0.36 -0.94
M831503 0.18 0.58 0.45 -0.28 -0.75
M834004 -0.57 0.71 0.36 -0.31 -0.76
​

IRT parameters for items in the index of eighth-grade students' mastery goals in mathematics, grade 8 mathematics combined national and state assessment: 2019
Item b d d d
The number of d parameters is one less than the number of categories for the item. For items scaled with the partial credit model, parameters a and c are not estimated. The a parameter value is exactly one and the c parameter is exactly zero. For item j, b represents a location parameter related to item difficulty, and d represents the category threshold parameter for category i of item j; d may not sum to zero because of rounding.
U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2019 Mathematics Assessment.
M831504 -0.41 0.89 0.01 -0.90
M831505 -0.99 0.71 0.07 -0.78
M831506 -1.03 0.68 0.03 -0.71
M834102 -0.31 0.78 -0.03 -0.75
​

IRT parameters for items in the index of eighth-grade students' interest/enjoyment in mathematics, grade 8 mathematics combined national and state assessment: 2019
Item b d d d
The number of d parameters is one less than the number of categories for the item. For items scaled with the partial credit model, parameters a and c are not estimated. The a parameter value is exactly one and the c parameter is exactly zero. For item j, b represents a location parameter related to item difficulty, and d represents the category threshold parameter for category i of item j; d may not sum to zero because of rounding.
U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2019 Mathematics Assessment.
M831901 0.33 0.60 0.05 -0.65
M831902 0.41 0.53 0.03 -0.56
M831903 0.32 0.65 0.01 -0.66
M831904 -0.30 0.72 0.06 -0.78
M831905 -0.20 0.53 0.00 -0.53
M831906 -0.73 0.58 0.00 -0.58
​

IRT parameters for items in the index of eighth-grade students' enjoyment of mathematics activities, grade 8 mathematics combined national and state assessment: 2019
Item b d d d d
The number of d parameters is one less than the number of categories for the item. For items scaled with the partial credit model, parameters a and c are not estimated. The a parameter value is exactly one and the c parameter is exactly zero. For item j, b represents a location parameter related to item difficulty, and d represents the category threshold parameter for category i of item j; d may not sum to zero because of rounding.
U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2019 Mathematics Assessment.
M834301 -0.59 0.66 0.48 -0.41 -0.73
M834302 -0.08 0.64 0.47 -0.38 -0.73
M834303 0.10 0.62 0.46 -0.39 -0.69
M834304 -0.19 0.52 0.40 -0.33 -0.58
M834305 0.06 0.57 0.41 -0.36 -0.62
M834306 0.08 0.54 0.43 -0.37 -0.60
​

​
Response averages and transformed scores for the index of eighth-grade students' persistence in learning, grade 8 mathematics combined national and state assessment, by classification: 2019
Response average Transformed score Percentage of students
Detail may not sum to totals because of rounding.
U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2019 Mathematics Assessment.
Low
1.00 5.8 3
1.25 6.6 3
1.50 7.2 4
1.75 7.8 5
Moderate
2.00 8.2 7
2.25 8.7 6
2.50 9.1 9
2.75 9.5 9
High
3.00 10.0 12
3.25 10.5 11
3.50 11.1 11
3.75 11.9 10
4.00 12.9 11
​

Response averages and transformed scores for the index of eighth-grade students' enjoyment of complex problems, grade 8 mathematics combined national and state assessment, by classification: 2019
Response average Transformed score Percentage of students
Detail may not sum to totals because of rounding.
U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2019 Mathematics Assessment.
Low
1.00 6.9 13
1.25 7.8 8
1.50 8.5 8
1.75 9.1 8
Moderate
2.00 9.5 10
2.25 10.0 8
2.50 10.4 9
2.75 10.8 8
High
3.00 11.2 8
3.25 11.7 6
3.50 12.2 5
3.75 12.8 4
4.00 13.7 6
​

Response averages and transformed scores for the index of eighth-grade students' academic self-discipline, grade 8 mathematics combined national and state assessment, by classification: 2019
Response average Transformed score Percentage of students
Detail may not sum to totals because of rounding.
U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2019 Mathematics Assessment.
Low
1.00 6.4 4
1.25 7.3 4
1.50 7.9 5
1.75 8.5 7
Moderate
2.00 8.9 9
2.25 9.3 8
2.50 9.8 10
2.75 10.2 10
High
3.00 10.6 11
3.25 11.1 9
3.50 11.6 8
3.75 12.3 7
4.00 13.3 6
​
​
Response averages and transformed scores for the index of eighth-grade students' confidence in mathematics knowledge and skills, grade 8 mathematics combined national and state assessment, by classification: 2019
Response average Transformed score Percentage of students
Detail may not sum to totals because of rounding.
U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2019 Mathematics Assessment.
Low
1.00 5.6 3
1.14 6.4 1
1.29 6.9 1
1.43 7.4 2
1.57 7.7 2
1.71 8.0 2
1.86 8.3 3
Moderate
2.00 8.6 8
2.14 8.8 4
2.29 9.1 5
2.43 9.3 5
2.57 9.5 5
2.71 9.8 6
2.86 10.0 6
High
3.00 10.3 7
3.14 10.5 6
3.29 10.8 6
3.43 11.1 6
3.57 11.5 6
3.71 11.9 5
3.86 12.5 5
4.00 13.4 8
​​

Response averages and transformed scores for the index of eighth-grade students' performance goals in mathematics, grade 8 mathematics combined national and state assessment, by classification: 2019
Response average Transformed score Percentage of students
Detail may not sum to totals because of rounding.
U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2019 Mathematics Assessment.
Low
1.00 6.3 5
1.25 7.1 3
1.50 7.7 4
1.75 8.1 5
2.00 8.5 7
2.25 8.9 6
2.50 9.2 7
2.75 9.5 6
Moderate
3.00 9.8 10
3.25 10.2 7
3.50 10.5 7
3.75 10.8 6
High
4.00 11.2 8
4.25 11.7 5
4.50 12.2 4
4.75 12.8 3
5.00 13.6 8
​

Response averages and transformed scores for the index of eighth-grade students' mastery goals in mathematics, grade 8 mathematics combined national and state assessment, by classification: 2019
Response average Transformed score Percentage of students
Detail may not sum to totals because of rounding.
U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2019 Mathematics Assessment.
Low
1.00 5.6 5
1.25 6.3 2
1.50 6.9 3
1.75 7.5 3
Moderate
2.00 7.9 8
2.25 8.4 4
2.50 8.8 7
2.75 9.2 7
High
3.00 9.7 12
3.25 10.2 7
3.50 10.8 8
3.75 11.6 7
4.00 12.6 27
​

Response averages and transformed scores for the index of eighth-grade students' interest/enjoyment in mathematics, grade 8 mathematics combined national and state assessment, by classification: 2019
Response average Transformed score Percentage of students
Detail may not sum to totals because of rounding.
U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2019 Mathematics Assessment.
Low
1.00 6.0 7
1.17 6.9 3
1.33 7.5 4
1.50 8.0 5
1.67 8.4 5
1.83 8.7 5
Moderate
2.00 9.0 8
2.17 9.3 5
2.33 9.6 6
2.50 9.9 6
2.67 10.2 6
2.83 10.5 6
High
3.00 10.8 7
3.17 11.1 5
3.33 11.4 4
3.50 11.8 4
3.67 12.3 4
3.83 12.9 3
4.00 13.7 8
​

Response averages and transformed scores for the index of eighth-grade students' enjoyment of mathematics activities, grade 8 mathematics combined national and state assessment, by classification: 2019
Response averageTransformed scorePercentage of students
Detail may not sum to totals because of rounding.
U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2019 Mathematics Assessment.
Low
1.006.14
1.176.81
1.337.31
1.507.72
1.678.02
1.838.32
2.008.64
2.178.83
2.339.04
2.509.24
2.679.45
2.839.65
Moderate
3.009.810
3.1710.06
3.3310.26
3.5010.46
3.6710.66
3.8310.85
High
4.0011.06
4.1711.34
4.3311.64
4.5011.93
4.6712.32
4.8312.91
5.0013.74
​
Last updated 31 March 2025 (SK)