The purpose of this development project funded by the Institute of Education Sciences is to develop a mathematics intervention focused on properties and operations with whole and rational numbers to support the mathematics learning of sixth grade students who are at-risk and not at-risk for mathematics learning difficulties. This intervention is designed for use within a prevention-oriented, multi-tiered instructional model of service delivery.


Institute for Education Sciences



Principal Investigator

Dr. Leanne Ketterlin Geller


The purpose of the PAR project is to twofold: (1) to develop a 100-lesson mathematics intervention for sixth grade students that focuses on key algebra readiness concepts, such as properties and operations with whole and rational numbers, and (2) to document the feasibility and potential efficacy of the intervention through multiple implementation studies.


Three phases comprise the PAR project: (1) curriculum development, (2) a small-scale feasibility study, and (3) a pilot study. All phases of this study incorporate principles of design-based research as each phase will cycle through development, observation, analysis, and refinement.

The curriculum was developed not only to address the call put forth by the National Mathematics Advisory Panel (2008) and the Common Core Standards Initiative (NGA, 2001) for more focused mathematics program that are not “a mile wide and an inch deep” but is also organized around four strands that align explicitly with the Common Core State Standards in Mathematics: (1) multiplication and division with whole numbers, (2) understanding fractions as numbers, (3) addition and subtraction of fractions, and multiplication and division of fractions.

The two-part feasibility study is designed to field test and conduct ongoing evaluation of lessons revised based on data about how well the instructional design and delivery features functioned during initial implementation. The purpose of this study is to examine how well the prototypes of the initial intervention function in the classroom. Data will be collected during the first part of the feasibility study with the first half of the lessons (1-50), followed by a major revision cycle, and then the remaining revised 50 lessons of the intervention will be implemented in a small number of sixth grade classrooms.

All 100 lessons of the PAR intervention will be implemented during the pilot study in the final year of the project. The intervention will be delivered to small groups of 4-6 students identified as needing additional instructional support for 30 minutes per day, 4-5 days per week. During the pilot study, data will be collected in treatment and comparison classrooms using multiple measures including (but not limited to) observations, teacher surveys, and mathematics measures to examine the potential promise of the PAR intervention for increasing student achievement.


The primary outcome from this project is a 100 lesson mathematics intervention focused on properties and operations with whole and rational numbers to support sixth grade students’ understanding of key algebra readiness concepts. A secondary outcome is an observation system that focuses on research-based fidelity of implementation indicators and instructional interaction variables that may mediate the effect of the intervention on student achievement.


Ketterlin-Geller, L. R., Nelson-Walker, N., Clarke, B., & Jungjohann, K. J. (October 2014). Preparing students for algebra: Intervening with fractions. Panel presented at the 36th International Council on Learning Disabilities Conference: Philadelphia, PA.

Nelson-Walker, N., Ketterlin-Geller, L R., Woods, D., & Zachary, S. (April, 2014). Promoting algebra readiness: Developing a 6th grade rational number curriculum. Paper presented at the 2014 Council for Exceptional Children Conference and Expo: Philadelphia, PA.