Date of Completion
differentiated curricula, mathematics curricula, enrichment learning, multilevel models, gifted education
E. Jean Gubbins
D. Betsy McCoach
Sally M. Reis
H. Jane Rogers
Field of Study
Doctor of Philosophy
The research literatures on mathematics education and gifted and talented education share many common conclusions about effective practices for strengthening students’ cognitive engagement and deep conceptual understandings. Enrichment learning and differentiated instruction comprise two broad approaches long advocated by proponents of gifted education. Enrichment learning shares many conceptual parallels with process standards advocated in mathematics education. Yet the effectiveness of applying curricular and pedagogical principles initially developed for gifted education/talent development programs to heterogeneous elementary school mathematics classrooms has received little research attention. Therefore, it is difficult to determine if these principles should be disseminated and implemented more frequently in mixed-ability classrooms, and if so, what student and contextual factors predict positive learning outcomes when using enriched and pre-differentiated instructional units in mathematics. To investigate this line of inquiry, The National Research Center on the Gifted and Talented (NRC/GT) created a series of three enriched and pre-differentiated grade 3 mathematics units. The NRC/GT subsequently conducted a multisite cluster-randomized control trial to study the overall causal impact of implementing these units on students’ mathematical achievement, with performance on the Problem Solving and Data Interpretation subtest of the Iowa Test of Basic Skills (ITBS) as the outcome measure.
In addition to completing the ITBS measure, treatment students completed researcher-developed pretests and posttests for each of the three units to measure learning gains on specific content within the curricular units. The present study used multilevel models to clarify to what extent student-level factors (quantitative ability, gender, prior mathematics achievement, and status as a “high learning potential” nominee) and contextual factors (class average quantitative ability, class average prior mathematics achievement, teacher responses to the curriculum, and school aggregate SES) predicted treatment students’ outcomes on the researcher-developed tests. Student scores on composite unit pretests, unit posttests, and on the difference scores from pretest to posttest were regressed on these predictors in a series of two-level models. Further, three-level models were tested with a measurement model at level-1 that examined each unit test as a subscale component of the composite test.
Results indicate that quantitative ability, prior achievement, and being nominated as having high learning potential were predictive of composite pretest and posttest scores, but gender was not. Student gains were predicted by quantitative ability and nomination status, but not by gender and prior achievement. Classroom mean gains from pretest to posttest varied across the classrooms in the study, but only one relationship between a student-level variable and an outcome varied significantly. Consequently, no significant cross-level interactions were apparent from the two-level models. The three-level hierarchical multivariate linear models confirmed the standard HLM covariance structure was appropriate for the posttest, but suggested the pretest was more adequately modeled with heterogeneous level-1 variances. Several student-level and cluster-level predictors explained the variance in particular subscales even though these effects were not found when modeling the composite measures.
Foreman, Jennifer, "Multilevel Impacts on Mathematical Learning Using Differentiated Curricula" (2013). Doctoral Dissertations. 40.