1. DEVELOPING ALGEBRA-READY STUDENTS FOR MIDDLE SCHOOL: EXPLORING THE IMPACT OF EARLY ALGEBRA PRINCIPAL INVESTIGATORS:Maria L. Blanton, University of Massachusetts DartmouthEric Knuth, University of Wisconsin Madison mblanton@umassd.eduknuth@education.wisc.edu http://www.kaputcenter.umassd.edu/associates/people/blantonm/http://www.education.wisc.edu/ci/mathed This is a 3-year project designed to build the preliminary components for investigating the impacts of early algebra education on students’ algebra readiness in middle grades. The project goals are 1.To coordinate research, curricular, and mathematical perspectives to design a curricular learning progression [CLP] that identifies core algebraic concepts and their progression in children’s thinking across upper elementary and middle grades (grades 3-8). We expect the CLP to be based on core algebra areas involving variable, functions, equality, expressions and equations, proportional reasoning, and number and operation. 2.Using the CLP, to design grade-based assessments of students’ algebra understanding for upper elementary and middle grades (grades 3-7) and to validate these assessments through psychometric testing. 3.To conduct a preliminary study concerning the impact of an early algebra intervention based on the CLP and measured by the assessments developed in Project Goal 2. 4.To use the CLP and associated tasks to identify appropriate tasks for content-based teacher professional development [TPD] and to refine this through implementation of the TPD. RESEARCH OBJECTIVES RATIONALE FOR THE PROJECT Teaching and learning algebra has undergone a critical transformation in the US over the last two decades. Recognizing that historical paths to algebra have been largely unsuccessful in terms of students’ achievement in algebra, numerous conferences have convened to examine challenges in traditional algebra education and identify possible solutions. As a result, scholars have increasingly advocated that algebra be re- conceptualized in school mathematics as a longitudinal, grades K-12 strand of thinking so that students have long-term, sustained algebra experiences in school mathematics, beginning in the elementary grades, that build their natural, informal intuitions about structure and relationships into formalized ways of mathematical thinking. Along these lines, early algebra research has provided us with important evidence regarding children’s ability to think algebraically. However, a great deal of that evidence is still local in nature. As such, an open question in early algebra research involves understanding the impact a sustained, longitudinal early algebra experience has on students’ achievement in middle school and beyond. One of the essential reasons that impacts of early algebra education have not been explored extensively is that the curricular connections between early algebra and algebra in later grades have not been clearly articulated and appropriate assessments have not been developed and validated to examine student understanding of the skills within this domain. This project aims to address this work. RESEARCH METHODS & DESIGN Project Goal 2: Assessments for grades 3-7 will be developed using the CLP. Psychometric properties of the assessments will be evaluated in the following ways: (1)Internal consistency estimates of reliability will be calculated for each assessment. Individual items will be evaluated with respect to test reliability, item difficulty, variance, and item-total correlations. Each assessment will also be compared against state assessment scores to help establish construct validity. (2)We will evaluate item difficulties in relation to our (and the advisory board’s as expert panel) predictions of item difficulty and correlate our predicted item difficulties with those actually observed in our validation samples for evidence of test validity, construct validity and cognitive diagnostic assessment. (3)The project’s advisory board will provide expert evaluation of our individual items and overall assessments as a means to ensure content validity. Project Goal 3: We will conduct teaching experiments in grades 3-5 in one elementary school. Data will include students’ written work and student interviews. Assessments will be administered to students in experimental and control sites. Analysis will focus on students’ understanding of algebra concepts identified in the CLP. Results will be used to refine algebra assessments and the CLP. Student responses to the assessments will be analyzed for differences in student performance between control and experimental groups as a way to establish preliminary results of the teaching experiment and how it supports student progress within the CLP. Project Goal 4: Teachers in the experimental school will participate in TPD based on the CLP. We will use the TPD to explore how teachers understand the teaching experiment tasks, how they adapt these in their classroom practice, and how they interpret and use students’ thinking about the tasks in instruction. Data will include teacher reflections and responses to a questionnaire focusing on (1) teachers’ perceived appropriateness of the task for their students, (2) issues of implementing the tasks in their classroom, (3) whether the format for the TPD was reasonable and appropriate, and (4) what they learned about impacts of the tasks on children’s algebraic thinking. We will informally validate the questionnaires by interviewing selected teachers to ascertain why they responded as they did. Results will be used to refine the TPD for use in sustained, teacher-led early algebra interventions. Project Staff Angela Murphy Gardiner, University of Massachusetts Dartmouth Ana Stephens, University of Wisconsin Madison Courtney Koestler, University of Wisconsin Madison Dan McGinn, University of Wisconsin Madison