# Promoting Rigorous Outcomes in Mathematics and Science Education: Connecting Curriculum Sensitive Assessment With Teacher Professional Development and Student Learning Outcomes Authors: William H. Schmidt, Neelam Kher, Richard T. Houang, Leland Cogan, Kathleen Wight To illustrate the use of curriculum-specific assessment in PROM/SE, the results presented here focus on the topic of fractions. However, similar analyses are conducted for all broad topics/strands in mathematics and science.

Data from the topic trace map indicated that state standards have identified the topics of ordering fractions and equivalent fractions in third grade. Our analytical framework allows us to determine if the intended curriculum as reflected in the standards is aligned with the implemented and attained curriculum.

PROM/SE student assessments revealed that at grade 3, 24% percent of students in participating districts pass the fractions subtest; at grade 4 about half of the students (49%) pass the subtest and by grade 5, the pass rate increases to 64% of the students. Thus, by the end of elementary school, about one-third of PROM/SE students in Michigan and Ohio do not pass the fractions assessment. At 6th grade the pass rate drops to 56% of the students.

The performance on the fractions subtest can be further disaggregated by topic areas. In the topic areas of equivalent fractions, ordering fractions, adding and subtracting fractions and word problems a similar pattern of performance appears across the grades: Third graders pass about one-quarter of the items (23-26%); fourth graders' pass rate ranges from 46% to 49%; fifth grade students pass 60% to 62% of the items. Models of fractions area is passed by 61% of third graders; 81% of fourth graders and 88% of fifth graders. Common denominators and multiplying fractions seem to difficult topics for all three grade levels. Five and 10%, respectively of third grade students pass the subtest areas; 13% and 23%, respectively of fourth graders; 23% and 35%, respectively, of fifth graders.

When we compare fourth grade students' performance on common denominators and equivalent fraction we find that the topic of common denominators seems to present more difficulty than the topic of equivalent fractions. This finding is somewhat surprising because the two topics are conceptually related and raises the question of curricular coherence. In the classroom, curricular coherence would be evident in the degree to which the logical structure of mathematics is preserved in instructional activities by linking various fractions topics and making the connections transparent for the students.

To determine the variation in topic coverage we used the difference in percent time devoted to fractions topics between the ninety-fifth percentile and fifth percentile. For the topic of common fractions the range for grades 3, 4, and 5, respectively was approximately 10.6 %, 11% and 9.9%. For the topic of decimal fractions the range was 5.7%, 7.2% and 10.3% respectively. Similar ranges were obtained for the topics of percentages, properties of common and decimal fractions, and common and decimal fraction relations. The data indicated that at even at the fifth percentile there were classrooms in all three grade levels where decimal fractions, percentages and properties of common and decimal fractions were not covered at all.

Relational analysis using IGP and student achievement (PROM/SE assessments) in mathematics were conducted at the district level. Data, adjusted for social-economic status show a positive relationship (R=0.53) between IGP and student achievement at the fifth grade level.