Relating End-of-Course Assessment Scores to Course Grades and College Readiness

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1 Relating End-of-Course ssessment Scores to Course Grades and College Readiness Introduction CT QualityCore end-of-course (EOC) assessments are built to measure mastery of rigorous course standards for core high school courses. The assessments are aligned to the Common Core State Standards 1 and measure the learning outcomes all students need to attain in order to succeed in college and in their careers. In this report, we provide information about CT QualityCore EOC assessment scores that can be used to guide grading standards and inform standard setting. For each CT QualityCore course, we present four types of empirical evidence: n Relationships of CT QualityCore EOC scores and concurrent high school course grades n Predictive relationships of CT QualityCore EOC scores and future high school course grades n Predictive relationships of CT QualityCore EOC scores and meeting the CT College Readiness Benchmarks n Percentile ranks for CT QualityCore EOC scores reflecting the population of high school graduates The report findings are intended to be used for three general purposes: n To guide grading practices from EOC assessments. To assign grades based on EOC assessment scores, educators must understand the meaning of the scores across the entire score range. n To provide empirical evidence useful to educators and policymakers seeking to set cutoff scores on CT QualityCore assessments for various purposes. n To provide enhanced score interpretation for all stakeholders who need to understand the meaning of CT QualityCore scores. This report updates a version published in Changes reflect updates to the CT College Readiness Benchmarks and an additional year of data tracking CT QualityCore-tested students.

2 Relating End-of-Course ssessment Scores to Course Grades and College Readiness Data and Methods This study is based on students who took one or more CT QualityCore EOC assessments as well as the CT college readiness assessment. Students are asked to report their grades in core high school courses when they register for the CT. The courses are presented in Table 1 along with the number of students and high schools represented. Student sample sizes are presented for three outcomes: current course grade, next course grade, and college readiness (based on the CT College Readiness Benchmarks). Note that the student sample sizes vary for current course grade and next course grade because not all students reported grades for both sets of courses. Table 1. Courses Studied and Sample Sizes N students Course N schools Current Next Course Grade Course Grade College Readiness English ,922 18,119 18,578 English ,888 45,237 61,511 English ,999 4,982 28,220 English ,306 N 7,282 lgebra I ,113 12,674 11,503 Geometry ,708 21,039 15,236 lgebra II ,202 20,429 57,994 Precalculus 127 6,585 2,003 9,657 U.S. History ,661 47,176 69,720 Biology ,986 38,373 39,880 Chemistry ,754 6,228 19,330 Physics 95 2,128 N 4,364 Table 2 provides, for each course, the next high school courses that were used for the predictive analyses as well as the most closely related CT Benchmark and subject area test. For each course, we list the grade level for which the course is usually taught. For English 12 and Physics, the college readiness analyses used students from grades 11 and 12. For the other courses, the college readiness analyses only used students from the most common grade level by CT, Inc. ll rights reserved. The CT is a registered trademark of CT, Inc., in the US and other countries. CT QualityCore is a registered trademark of CT, Inc., in the US

3 Table 2. dditional Course Information Course Primary Grade Level Next Course(s) CT Benchmark English 9 9 English (English) English English (English) English English (English) English N 18 (English) lgebra I 9 Geometry 22 (Mathematics) Geometry 10 lgebra 2 22 (Mathematics) lgebra II 11 Trigonometry, Other Math Beyond lgebra 2 22 (Mathematics) Precalculus 11 Calculus 22 (Mathematics) U.S. History 11 Government, Civics, Citizenship, Economics 22 (Reading) Biology 10 Chemistry 23 (Science) Chemistry 11 Physics 23 (Science) Physics 12 N 23 (Science) The sample used for each course is not necessarily representative of the population of high school students in terms of academic achievement. Therefore, the sample data for each course was weighted by CT Composite score to make it more closely resemble the national population of high school graduates. 2 When students register to take the CT, they are asked to report their grades in several high school courses, including the core subject area courses that are supported by CT QualityCore. Students are encouraged to provide accurate data; 3 prior research has shown that student-reported grades and CT scores are jointly predictive of college outcomes. 4 For each course, students indicated whether they earned an, B, C, D, or F. nalyses for each course were conducted to estimate relationships between CT QualityCore EOC assessment scores and three outcomes: n Concurrent high school course grades n Future high school course grades (in the next course) n Meeting the CT College Readiness Benchmark in the same subject area For the course grade analyses, we estimated the probability of earning an (and B or higher) across the CT QualityCore score range. The results of these analyses can help educators better understand the meaning and predictive nature of CT QualityCore scores. 3

4 Relating End-of-Course ssessment Scores to Course Grades and College Readiness To develop suggested score ranges for assigning grades from the CT QualityCore EOC assessment scores, we first tabulated the distribution of CT QualityCore EOC assessment scores for three levels of concurrent course grades:, B, and C or lower. We defined a suggested score range for grades of, B, and C or lower according to the percentage of students predicted to be successful (in their next course and in meeting the CT College Readiness Benchmark) and also accounted for the regions of the score range for which each course grade had the largest probability distribution (relative to the other course grades). Suggested score ranges for EOC assessment results were defined as: n The range included scores for which the percentage of students meeting the CT College Readiness Benchmark was at least 67%, the percentage of students earning an in their next course was at least 5, and the grade score distribution had the largest probability distribution (relative to the B and C or lower distributions). Course grade data for the next high school course are not available for English 12 and Physics. For these courses, the range requires that the percentage of students earning an in the concurrent course is at least 5. n The B range included scores not included in the range for which the percentage of students meeting the CT College Readiness Benchmark was at least 33% and either the grade or B score distributions had the largest probability distribution (relative to the C or lower distributions). n The C or lower range included scores below the B range. Limitations There are some important limitations to this study that should be understood before interpreting the results: n The study results include general guidance for assigning grades from CT QualityCore EOC assessments, but states, districts, and schools should adopt the grading standards that are most reasonable for their unique setting. n While the data represent hundreds of high schools, a majority of the schools are from three states. It is possible that the results would shift if all states were equally represented. n The study relied on students self-reported course grades. Self-reported coursework and grades collected during CT registration have been found to be accurate relative to information provided on student transcripts. However, there is a tendency of students to overreport grades; the average difference between transcript-obtained and self-reported course grades has been documented at 0.23 on the typical four-point grading scale. 5 4

5 Results In the pages that follow, we present selected results for each course. One page is devoted to each course and notes are provided to guide correct interpretation of the results. Included in these results are: n CT QualityCore EOC score distributions by grade earned in the same (concurrent) course n Predictive relationship between CT QualityCore EOC scores and college readiness (meeting the CT Benchmark) n Predictive relationship between CT QualityCore EOC scores and concurrent course grades dditional results, including percentile ranks and predictive relationships for future courses, are presented in Tables 1 12 in the appendix, one table per course. 5

6 Relating End-of-Course ssessment Scores to Course Grades and College Readiness Score Distributions by Grade Earned English 9 Predictive Relationships with Concurrent Grades and College Readiness 9% 10 8% 9 7% 8 6% 7 5% 4% B C or lower College Readiness or B 3% 3 2% 2 1% 1 CT QualityCore Score CT QualityCore Score Course Grade CT QualityCore Score Percentiles 25th 50th 75th Largest Probability Range B C or lower Example Interpretation: mong students who earned an in English 9, the score distribution was centered at 161. The probability distribution for students who earned an was greater than the other two distributions for scores of 158 and higher. The probability distribution for students who earned a B was largest between scores of 155 and 157. Note: Values not plotted for scores with small sample size. Values also given in Table 1. Example Interpretation: mong students with a score of 158, 55% earned an in English 9; 92% earned at least a B. Of the 9th graders with a score of 158, 86% went on to later meet the CT College Readiness Benchmark in English. mong students with a score of 155, 41% earned an in English 9; 87% earned at least a B. Of the 9th graders with a score of 155, 74% went on to meet the CT College Readiness Benchmark in English. 6

7 Score Distributions by Grade Earned English 10 Predictive Relationships with Concurrent Grades and College Readiness 9% 10 8% 9 7% 8 6% 7 5% 4% 3% B C or lower College Readiness or B 2% 3 1% 2 Course Grade CT QualityCore Score CT QualityCore Score Percentiles 25th 50th 75th Largest Probability Range B C or lower Example Interpretation: mong students who earned an in English 10, the score distribution was centered at 159. The probability distribution for students who earned an was greater than the other two distributions for scores of 158 and higher. The probability distribution for students who earned a B was largest between scores of 153 and CT QualityCore Score Note: Values not plotted for scores with small sample size. Values also given in Table 2. Example Interpretation: mong students with a score of 158, 51% earned an in English 10; 89% earned at least a B. Of the 10th graders with a score of 158, 82% went on to later meet the CT College Readiness Benchmark in English. mong students with a score of 153, 26% earned an in English 10; 74% earned at least a B. Of the 10th graders with a score of 153, 57% went on to meet the CT College Readiness Benchmark in English. 7

8 Relating End-of-Course ssessment Scores to Course Grades and College Readiness Score Distributions by Grade Earned English 11 Predictive Relationships with Concurrent Grades and College Readiness 7% 10 6% 9 8 5% 7 4% 3% 2% B C or lower College Readiness or B 1% 2 1 CT QualityCore Score CT QualityCore Score Course Grade CT QualityCore Score Percentiles 25th 50th 75th Largest Probability Range B C or lower Example Interpretation: mong students who earned an in English 11, the score distribution was centered at 158. The probability distribution for students who earned an was greater than the other two distributions for scores of 157 and higher. The probability distribution for students who earned a B was largest between scores of 153 and 156. Note: Values not plotted for scores with small sample size. Values also given in Table 3. Example Interpretation: mong students with a score of 157, 49% earned an in English 11; 89% earned at least a B. Of the 11th graders with a score of 157, 87% met the CT College Readiness Benchmark in English. mong students with a score of 153, 37% earned an in English 11; 83% earned at least a B. Of the 11th graders with a score of 153, 7 met the CT College Readiness Benchmark in English. 8

9 Score Distributions by Grade Earned English 12 Predictive Relationships with Concurrent Grades and College Readiness 8% 10 7% 9 8 6% 7 5% 4% 3% B C or lower College Readiness or B 2% 3 2 1% 1 CT QualityCore Score CT QualityCore Score Course Grade CT QualityCore Score Percentiles 25th 50th 75th Largest Probability Range B C or lower Example Interpretation: mong students who earned an in English 12, the score distribution was centered at 155. The probability distribution for students who earned an was greater than the other two distributions for scores of 153 and higher. The probability distribution for students who earned a B was largest between scores of 150 and 152. Note: Values not plotted for scores with small sample size. Values also given in Table 4. Example Interpretation: mong students with a score of 153, 51% earned an in English 12; 88% earned at least a B. Of the students with a score of 153, 77% met the CT College Readiness Benchmark in English. mong students with a score of 150, 41% earned an in English 12; 83% earned at least a B. Of the students with a score of 150, 59% met the CT College Readiness Benchmark in English. 9

10 Relating End-of-Course ssessment Scores to Course Grades and College Readiness Score Distributions by Grade Earned lgebra I Predictive Relationships with Concurrent Grades and College Readiness 12% % 7 6% 4% B C or lower College Readiness or B 3 2% 2 1 Course Grade CT QualityCore Score CT QualityCore Score Percentiles 25th 50th 75th Largest Probability Range B C or lower Example Interpretation: mong students who earned an in lgebra I, the score distribution was centered at 149. The probability distribution for students who earned an was greater than the other two distributions for scores of 148 and higher. The probability distribution for students who earned a B was largest for a score of 147. CT QualityCore Score Note: Values not plotted for scores with small sample size. Values also given in Table 5. Example Interpretation: mong students with a score of 148, 44% earned an in lgebra I; 82% earned at least a B. Of the 9th graders with a score of 148, 41% went on to later meet the CT College Readiness Benchmark in Mathematics. mong students with a score of 147, 39% earned an in lgebra I; 77% earned at least a B. Of the 9th graders with a score of 147, 34% went on to meet the CT College Readiness Benchmark in Mathematics. 10

11 Score Distributions by Grade Earned Geometry Predictive Relationships with Concurrent Grades and College Readiness 12% % 7 6 6% 4% B C or lower 5 4 College Readiness or B 3 2% 2 1 Course Grade CT QualityCore Score CT QualityCore Score Percentiles 25th 50th 75th Largest Probability Range B C or lower Example Interpretation: mong students who earned an in Geometry, the score distribution was centered at 149. The probability distribution for students who earned an was greater than the other two distributions for scores of 148 and higher. The probability distribution for students who earned a B was largest for scores of 146 and 147. CT QualityCore Score Note: Values not plotted for scores with small sample size. Values also given in Table 6. Example Interpretation: mong students with a score of 148, 44% earned an in Geometry; 84% earned at least a B. Of the 10th graders with a score of 148, 54% went on to later meet the CT College Readiness Benchmark in Mathematics. mong students with a score of 146, 36% earned an in Geometry; 76% earned at least a B. Of the 10th graders with a score of 146, 37% went on to meet the CT College Readiness Benchmark in Mathematics. 11

12 Relating End-of-Course ssessment Scores to Course Grades and College Readiness Score Distributions by Grade Earned lgebra II Predictive Relationships with Concurrent Grades and College Readiness % 9 8% 8 7% 7 6% 5% 4% B C or lower College Readiness or B 3% 3 2% 2 1% 1 CT QualityCore Score CT QualityCore Score Course Grade CT QualityCore Score Percentiles 25th 50th 75th Largest Probability Range B C or lower Example Interpretation: mong students who earned an in lgebra II, the score distribution was centered at 149. The probability distribution for students who earned an was greater than the other two distributions for scores of 149 and higher. The probability distribution for students who earned a B was largest between scores of 146 and 148. Note: Values not plotted for scores with small sample size. Values also given in Table 7. Example Interpretation: mong students with a score of 149, 41% earned an in lgebra II; 79% earned at least a B. Of the 11th graders with a score of 149, 43% met the CT College Readiness Benchmark in Mathematics. mong students with a score of 146, 28% earned an in lgebra II; 7 earned at least a B. Of the 11th graders with a score of 146, 2 met the CT College Readiness Benchmark in Mathematics. 12

13 Score Distributions by Grade Earned Precalculus Predictive Relationships with Concurrent Grades and College Readiness 9% 10 8% 9 7% 8 6% 7 5% 4% 3% B C or lower College Readiness or B 2% 3 1% 2 Course Grade CT QualityCore Score CT QualityCore Score Percentiles 25th 50th 75th Largest Probability Range B C or lower Example Interpretation: mong students who earned an in Precalculus, the score distribution was centered at 151. The probability distribution for students who earned an was greater than the other two distributions for scores of 151 and higher. The probability distribution for students who earned a B was largest between scores of 148 and CT QualityCore Score Note: Values not plotted for scores with small sample size. Values also given in Table 8. Example Interpretation: mong students with a score of 151, 59% earned an in Precalculus; 93% earned at least a B. Of the 11th graders with a score of 151, 95% met the CT College Readiness Benchmark in Mathematics. mong students with a score of 148, 52% earned an in Precalculus; 91% earned at least a B. Of the 11th graders with a score of 148, 89% met the CT College Readiness Benchmark in Mathematics. 13

14 Relating End-of-Course ssessment Scores to Course Grades and College Readiness Score Distributions by Grade Earned U.S. History Predictive Relationships with Concurrent Grades and College Readiness % 9 8% 8 7% 7 6% 5% 4% 3% B C or lower College Readiness or B 2% 2 1% 1 CT QualityCore Score CT QualityCore Score Course Grade CT QualityCore Score Percentiles 25th 50th 75th Largest Probability Range B C or lower Example Interpretation: mong students who earned an in U.S. History, the score distribution was centered at 150. The probability distribution for students who earned an was greater than the other two distributions for scores of 149 and higher. The probability distribution for students who earned a B was largest between scores of 146 and 148. Note: Values not plotted for scores with small sample size. Values also given in Table 9. Example Interpretation: mong students with a score of 149, 48% earned an in U.S. History; 84% earned at least a B. Of the 11th graders with a score of 149, 5 met the CT College Readiness Benchmark in Reading. mong students with a score of 146, 38% earned an in U.S. History; 78% earned at least a B. Of the 11th graders with a score of 146, 29% met the CT College Readiness Benchmark in Reading. 14

15 Score Distributions by Grade Earned Biology Predictive Relationships with Concurrent Grades and College Readiness 8% 10 7% 9 6% 8 7 5% 4% 3% B C or lower College Readiness or B 2% 3 1% 2 CT QualityCore Score 1 CT QualityCore Score Course Grade CT QualityCore Score Percentiles 25th 50th 75th Largest Probability Range B C or lower Example Interpretation: mong students who earned an in Biology, the score distribution was centered at 156. The probability distribution for students who earned an was greater than the other two distributions for scores of 154 and higher. The probability distribution for students who earned a B was largest between scores of 150 and 153. Note: Values not plotted for scores with small sample size. Values also given in Table 10. Example Interpretation: mong students with a score of 154, 42% earned an in Biology; 85% earned at least a B. Of the 10th graders with a score of 154, 4 went on to later meet the CT College Readiness Benchmark in Science. mong students with a score of 150, 27% earned an in Biology; 72% earned at least a B. Of the 10th graders with a score of 150, 18% went on to meet the CT College Readiness Benchmark in Science. 15

16 Relating End-of-Course ssessment Scores to Course Grades and College Readiness Score Distributions by Grade Earned Chemistry Predictive Relationships with Concurrent Grades and College Readiness 9% 10 8% 9 7% 8 6% 7 5% 4% 3% B C or lower College Readiness or B 2% 1% Course Grade CT QualityCore Score CT QualityCore Score Percentiles 25th 50th 75th Largest Probability Range B C or lower Example Interpretation: mong students who earned an in Chemistry, the score distribution was centered at 153. The probability distribution for students who earned an was greater than the other two distributions for scores of 152 and higher. The probability distribution for students who earned a B was largest between scores of 148 and CT QualityCore Score Note: Values not plotted for scores with small sample size. Values also given in Table 11. Example Interpretation: mong students with a score of 152, 51% earned an in Chemistry; 9 earned at least a B. Of the 11th graders with a score of 152, 65% met the CT College Readiness Benchmark in Science. mong students with a score of 148, 34% earned an in Chemistry; 79% earned at least a B. Of the 11th graders with a score of 148, 42% met the CT College Readiness Benchmark in Science. 16

17 Score Distributions by Grade Earned Physics Predictive Relationships with Concurrent Grades and College Readiness 12% % 7 6 6% 4% B C or lower 5 4 College Readiness or B 3 2% 2 1 Course Grade CT QualityCore Score CT QualityCore Score Percentiles 25th 50th 75th Largest Probability Range B C or lower Example Interpretation: mong students who earned an in Physics, the score distribution was centered at 147. The probability distribution for students who earned an was greater than the other two distributions for scores of 147 and higher. The probability distribution for students who earned a B was largest between scores of 145 and 146. CT QualityCore Score Note: Values not plotted for scores with small sample size. Values also given in Table 12. Example Interpretation: mong students with a score of 147, 59% earned an in Physics; 92% earned at least a B. Of the students with a score of 147, 67% met the CT College Readiness Benchmark in Science. mong students with a score of 145, 5 earned an in Physics; 88% earned at least a B. Of the students with a score of 145, 56% met the CT College Readiness Benchmark in Science. 17

18 Relating End-of-Course ssessment Scores to Course Grades and College Readiness Suggested Grading Standards The study results can be used to enhance interpretation of CT QualityCore EOC assessment scores and to inform grading practices. Table 3 gives the suggested CT QualityCore score ranges derived empirically using the method described earlier: n The range included scores for which the percentage of students meeting the CT College Readiness Benchmark was at least 67%, the percentage of students earning an in their next course was at least 5, and the grade historical score distribution had the largest probability distribution (relative to the B and C or lower distributions). n The B range included scores not included in the range for which the percentage of students meeting the CT College Readiness Benchmark was at least 33% and either the grade or B historical score distributions had the largest probability distribution (relative to the C or lower distributions). n The C or lower range included scores below the B range. For each suggested score range/course grade combination, we give the percentage of students in the sample who would have been assigned that grade, as well as the percentage of students who met the relevant CT College Readiness Benchmark (Table 3). Note that the percentages were derived after weighting the sample by CT Composite score to make it more representative of high school graduates nationally. 18

19 Table 3: Suggested EOC ssessment Grades Course Course Grade Suggested Score Range Percent ssigned Grade Percent Meeting Benchmark English 9 English 10 English 11 English 12 lgebra I Geometry lgebra II Precalculus U.S. History Biology Chemistry Physics B C or lower B C or lower B C or lower B C or lower B C or lower B C or lower B C or lower B C or lower B C or lower B C or lower B C or lower B C or lower

20 Relating End-of-Course ssessment Scores to Course Grades and College Readiness Predictive Relationships for Enhanced Score Interpretation Understanding how CT QualityCore score levels relate to probabilities of course success and college readiness is potentially useful for standard setting, where empirical and judgmental data are used to arrive at cutoff scores for various purposes. For each of the twelve CT QualityCore courses, Tables 1 12 in the appendix provide the following information across the score range: a. The probability of earning an in the concurrent high school course b. The probability of earning an or B in the concurrent high school course c. The probability of earning an in the next (future) high school course d. The probability of earning an or B in the next (future) high school course e. The probability of meeting the CT College Readiness Benchmark in the related subject area f. The estimated percentile rank associated with each score within the population of high school graduates (Note that parts a, b, and e were discussed on pages 6 17.) Because students can take the CT QualityCore assessments at different grade levels, it is important to note that the college readiness probabilities and percentile ranks are specific to students who take the CT QualityCore assessment in the primary grade level specified in Table 2. (The exception to this is English 12 and Physics, where the college readiness probabilities are based on students in grades 11 and 12.) For example, a score of 148 on the lgebra I assessment is at the 71st percentile for 9th graders, and the probability of later meeting the CT Mathematics Benchmark is The percentile rank and the college readiness probability would be smaller for a 10th grader with the same score. 20

21 Conclusion Using EOC assessment scores in course grading has potential to more evenly allocate accountability for course mastery among schools, teachers, and students. The study results provide guidance for assigning grades from CT QualityCore EOC assessments, but educators should adopt the grading standards that are most reasonable for their school and students. dditional considerations for developing grading standards include: n re the grading standards aligned with the school s goals for college and career readiness? n What portion of students final course grades will be determined from the EOC assessment? n Will the new grading standards cause a drastic change in the percentage of students who earn course grades of or B? Educators should consider these and other questions when adopting grading standards based on CT QualityCore EOC assessments. In the report appendix we provide the percentage of, B, and C or lower grades that are typically assigned to students in the courses studied (see Table 13). In most cases, the suggested EOC assessment grades based on CT QualityCore scores would result in fewer and B grades and more C or lower grades, relative to what is typically awarded for final course grades. This is especially true in mathematics and science courses, where relatively few students score high enough to have a 67% or higher chance of meeting the CT Benchmark, resulting in a small percentage of students who would be assigned an on the EOC assessment. (Nationally, only 44% of 2013 CT-tested graduates met the Mathematics Benchmark and 36% met the Science Benchmark. 6 ) Understanding the relationships between CT QualityCore scores and other educational outcomes such as course grades and college readiness is important for educators and policymakers who wish to set performance standards, as well as for students and parents who need information to make better informed choices and set goals. 21

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