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IES Grant

Title: Promoting Algebra Readiness: Developing a Strategic Intervention On Rational Number Concepts (Project PAR)
Center: NCSER Year: 2012
Principal Investigator: Clarke, Ben Awardee: University of Oregon
Program: Science, Technology, Engineering, and Mathematics      [Program Details]
Award Period: 06/01/2012–05/31/2015 Award Amount: $1,499,966
Type: Development and Innovation Award Number: R324A120115

Co-Principal Investigators: Fine, Hank; Baker, Scott K.; Ketterlin-Geller, Leanne

Purpose: Algebra competence is of particular concern for secondary students with disabilities who are participating in general education mathematics courses in growing numbers and facing curriculum standards and graduation requirements that demand mastery of algebra. The purpose of this project is to develop the curriculum Promoting Algebra Readiness for sixth-grade students with or at risk for learning disabilities in mathematics. Promoting Algebra Readiness will be designed to include instructional features appropriate for this population, including optimal sequencing of lessons, pre-teaching prerequisite knowledge, and providing opportunities for practice. There are two major aims of the project: (a) develop a 100-lesson algebra readiness intervention focusing on conceptual understanding and procedural fluency with rational numbers and equivalent representations for students at risk for math learning difficulties and disabilities, and (b) assess the feasibility and the promise of intervention effectiveness.

Project Activities: The project team will develop the 100-lesson algebra readiness intervention program through multiple "design experiments," which are iterative cycles of development, observation, analysis, and refinement. Two experts in instructional design and mathematics instruction will conduct an extensive content analysis to determine scope and sequence of the lessons, build instructional templates, and complete lesson sets for the implementation phase. The project team will then conduct small-scale implementation studies with teacher-researchers (teachers who are heavily involved in the research) to explore feasibility and potential efficacy. Two feasibility studies with six sixth-grade teachers will be conducted (with a revision phase in between) to determine teacher satisfaction with the intervention, delivery of lesson content, and student responsiveness. In the final year, the project team will conduct a pilot study in which all 100 lessons will be implemented by 12 teachers to determine if the intervention is operating as intended. Data collection in the treatment condition and matched comparison condition will include surveys and focus groups, direct observations, and proximal and distal outcome measures of student learning. The project concludes with a final revision phase.

Products: The products of this project include a fully developed Project Algebra Readiness intervention, a classroom observation system addressing fidelity of implementation, published reports, and presentations.

Structured Abstract

Setting: The research takes place in middle schools in Oregon and Texas.

Sample: Participants include sixth-grade students with mathematics learning disabilities and students who are at risk for mathematics learning disabilities from the classrooms of approximately 25 teachers. Students will be in Title I schools and the researchers will oversample English language learners.

Intervention: The Promoting Algebra Readiness (PAR) intervention includes two major components. The first is mathematics content, which focuses on rational number concepts and includes four strands: (a) generalization of key whole number concepts to rational numbers, (b) conceptual development of fractions, (c) understanding of equivalent representations, and (d) conceptual understanding and procedural fluency of operations with fractions. The second component encompasses research-based instructional design and delivery features. These include an explicit focus on the instructional sequence, pre-teaching prerequisite knowledge, opportunities for practice to improve fluency, and developing mathematical models. PAR will be taught in groups of four to six students for 30 minutes per day, 4–5 days per week.

Research Design and Methods: The researchers will use "design experiments" in all phases of the project. Design experiments offer a methodological structure for developing instructional interventions through iterative cycles of development, observation, analysis, and refinement. The design experiments involve frequent observations of teaching and a range of measures to determine the feasibility of the intervention and to examine the potential promise of the intervention for improving student mathematics achievement. A small pilot study in the final year of the project will examine the potential promise of the PAR intervention for increasing student achievement.

Control Condition: The control condition for the pilot study is a business-as-usual condition. During the pilot study, a matched comparison group of 60 students will be screened into the study from 12 additional classrooms.

Key Measures: Proximal measures and a distal measure (Stanford Achievement Test-Tenth Edition) will be used to examine the promise of the PAR intervention. Proximal measures include the AIMSweb Math Computation Probes, the Conceptual Understanding of Algebraic Reasoning Skills and Knowledge measure, and the Conceptual Understanding of Fractions measure. The researchers will also use teacher focus groups, teacher surveys (including the Mathematical Knowledge for Teaching survey), and a classroom observation system focusing on fidelity and instructional quality to inform revisions to the intervention.

Data Analytic Strategy: Descriptive data from teacher surveys, classroom observations, and student mathematics performance will be used to iteratively revise the intervention, determine feasibility, and examine the potential impact of the intervention on student mathematics achievement. Focus group data will be analyzed qualitatively and used in intervention revision. Differential gains between treatment and control groups on student mathematics achievement measures will be analyzed using a mixed-model analysis of covariance. Correlation and other strength of association methods will be used to test hypotheses related to implementation fidelity and quality of teacher-student instructional interactions.