E. Jean Gubbins
D. Betsy McCoach
Jennifer L. Foreman
Cindy M. Gilson
Micah N. Bruce-Davis
Lisa DaVia Rubenstein
Jennifer Savino
Karen Rambo
Craig Waterman

Heterogeneous elementary school mathematics classrooms contain an astonishing array of student learning needs, including differences in abilities, cultures, and languages. Although many teachers strive to respond to student diversity, sensing that a “one-sizefits-all” curriculum fails to reach all learners, the time and knowledge demands of differentiation often preclude teachers from making meaningful adjustments that enhance learning. Consequently, effective differentiation of curriculum and instruction is absent in most classrooms in the United States.

Prior research found that providing teachers with professional development and predifferentiated and enriched curricula—developed according to exemplary practices in gifted education—has proven effective for students identified as mathematically talented. However, applying differentiation and enrichment strategies to all students has previously found mixed results. The impact of this type of curriculum intervention on teacher learning has also not been well-documented. In addition, in conjunction with professional development, educative curricular materials designed to provide teachers with guidance while promoting teacher learning offers promise in increasing the probability of effectively implementing pre-differentiated curricula. Therefore, the present study seeks to determine how exposure to pre-differentiated and enriched curricula incorporating educative curriculum materials affects students’ achievement as well as teacher and administrator responses to the intervention.

A 2-year multi-site cluster randomized control trial study (randomized by school for participants recruited during the first year and randomized by classroom for participants recruited during the second year) recruited a national sample of 4,530 grade 3 students in 216 classrooms from 62 schools across 17 states. All treatment teachers participated in professional development on differentiated instruction and enrichment practices, as well as specific training in using the components of the three differentiated mathematics units. Treatment and control students completed standardized pretest measures of cognitive abilities and mathematics achievement, as well as a standardized posttest measure of mathematics achievement. Students in the treatment group also completed unit pretests and posttests for each of the three differentiated mathematics units and selected items from the out-of-level grade 4 National Assessment of Educational Progress (NAEP). Researchers observed treatment and control classrooms to evaluate the fidelity of implementation of the curricular units. Treatment teachers completed logs with their responses to each of the units and participated in focus groups. Administrators completed open-ended questionnaires to assess their reactions to participating in the study.

Quantitative results did not show significant differences overall between treatment and control students on the standardized mathematics achievement test after accounting for pretest scores, although several measurement issues clouded the results, including a significant ceiling effect on the standardized posttest and a lack of content alignment between the standardized assessment and the treatment units. However, the multilevel analyses revealed significant three-way interaction effects between treatment, pretest scores, and school-average pretest achievement. The treatment appeared to be most effective for high achieving students in low achieving schools. Additionally and perhaps most importantly, replacing 16 weeks of traditional mathematics curriculum with highlevel investigative mathematics did not negatively impact student gains on traditional standardized mathematical assessments. Treatment students made substantial gains from pretest to posttest on the researcher-developed unit tests, and they scored above the national average on the out-of-level NAEP items.

Qualitative results demonstrated that the treatment teachers and administrators from participating schools responded positively to the curriculum intervention. Teachers and administrators appreciated how the mathematics units provided pre-differentiated lessons with guidance on forming instructional groups based upon preassessment data. This facilitated the implementation of differentiated and enriched instruction, as many teachers and administrators noted the benefits and ease of providing students with challenging lessons appropriately matched to students’ instructional levels. While many participants shared positive reactions to the curriculum intervention, some did express concerns over “covering” the state standards while also participating in the study. In comparison to control teachers, it was evident that treatment teachers engaged students more often in challenging, hands-on, and real-world lessons as well as in mathematical discourse through the use of higher-level divergent questioning. The educative nature of the intervention curriculum materials in conjunction with the provision of professional development for all participating treatment teachers indicated teacher change and learning in the areas of instructional practices, understanding of how students learn mathematics, and expectations of students. Administrators hoped that their teachers would continue to differentiate instruction, challenge students at all instructional levels, and apply authentic student learning to their lessons.

Reference:

What Works in Gifted Education Mathematics Study: Impact of Pre-Differentiated and Enriched Curricula on General Education Teachers and Their Students
E. Jean Gubbins
D. Betsy McCoach
Jennifer L. Foreman
Cindy M. Gilson
Micah N. Bruce-Davis
Lisa DaVia Rubenstein
Jennifer Savino
Karen Rambo
Craig Waterman
 

Conclusions

1. Treatment teachers who participated in the focus groups were positive in their reactions to implementing the What Works Mathematics Curricula with grade 3 students. They appreciated the embedded differentiation components and preferred the experimental curricula in algebra, geometry and measurement, and graphing and data analysis instead of their traditional textbooks.
2. Analysis of the administrators’ interviews and teacher focus groups revealed that as a result of participating in the study teachers were open to changing their instructional practices, learning and applying mathematical content knowledge, and implementing differentiated instructional practices.
3. Overall, administrators’ perceptions of the teachers’ and students’ responses to the What Works Mathematics Curricula were positive. The administrators discussed changes in teachers’ knowledge about instruction in addition to changes noted in the instructional climate of the classrooms.
4. Based upon the analysis of the treatment classroom observations, teachers engaged students in taking active roles as mathematicians in real-world learning experiences. Students had opportunities to participate in whole group and small group discourse. In addition, teachers perceived the What Works Mathematics Curricula to be challenging.
5. While the majority of comments were positive, some teachers expressed the challenges of teaching and learning the content in the units and adjusting to a new curriculum.
6. Quantitative results from the grade 3 Iowa Tests of Basic Skills subtests (math problems pretest compared to math problem solving and data interpretation posttest) did not show significant differences overall between treatment and control students on the standardized mathematics achievement test after accounting for pretest scores. Several measurement issues clouded the results, including a significant ceiling effect on the standardized posttest and a lack of content alignment between the standardized assessment and the treatment units.
7. The treatment appeared to be most effective for high achieving students in low achieving schools. Additionally and perhaps most importantly, replacing 16 weeks of traditional mathematics curriculum with high level investigative mathematics did not negatively impact student gains on traditional standardized mathematical assessments.
8. Students involved in the algebra, geometry and measurement, and graphing and data analysis units made substantial gains from pretest to posttest on the researcher-developed unit tests, and grade 3 students scored above the national average on the out-of-level National Assessment of Educational Progress (NAEP) items.