Project PAR: Promoting Algebra Readiness

By Dawn Woods, RME Elementary Mathematics Coordinator

Many students appear to be on-track for mathematics achievement in 4th grade, but exit 8th grade without having developed critical skills in the area of rational numbers (National Center for Education Statistics, 2009). Conceptual understanding of rational numbers, as well as, their symbolic representations is a critical component for understanding everyday situations in algebra. Students must master these foundational skills and concepts at the elementary and middle school levels. Project PAR: Promoting Algebra Readiness is an intervention curriculum designed to build this rational number understanding.

Project PAR is a three-year, Institute of Educational Sciences (IES) funded research study that is working to develop a strategic intervention on rational number concepts that use evidence based strategies. The purpose of this project is to promote algebra readiness for sixth grade students by developing students’ conceptual understanding of rational numbers on a number line. The project team consists of researchers and curriculum experts from the University of Oregon (UO) and Research in Mathematics Education (RME) at Southern Methodist University who have extensive experience designing math interventions for a range of student learners as well as vast teaching experience in the mathematics classroom.

Project PAR is completing the development phase of this study where curriculum writers from the UO and RME have designed the scope and sequence for the intervention, developed approximately 100 print-based lessons, and conducted preliminary feasibility testing of individual lessons. The project is now moving into the implementation phase where classroom intervention teachers in Texas and Oregon are teaching the lessons. At this time curriculum writers and researchers will determine if the lessons have realistic expectations and goals for classroom use as the teachers use the lessons and provide critical feedback. This summer, curriculum writers will revise the curriculum based on the results of the feasibility study in preparation for the pilot study scheduled for the 2014-2015 school year. During the pilot study, the potential promise of the intervention increasing student achievement will be examined.

RME would like to thank the sixth grade math teachers Bush Middle School in Carrollton-Farmers Branch ISD who opened up their classrooms for the preliminary feasibility testing as well as the sixth grade math teachers at Fowler Middle School in Frisco ISD who are implementing the PAR curriculum during the feasibility study. We could not do our work with out the support of great teachers at great schools who are putting evidence- based strategies into practice!

National Center for Education Statistics (2009). The nation’s report card: Mathematics 2009. Washington, DC: National Center for Education Statistics

Focus on Research: A Discussion on Learning Progressions for Instruction and Assessent

By Dr. Deni Basaraba, RME Assessment Coordinator

The need for differentiated instruction to meet the needs of all learners is one source of evidence that students’ learning is not linear and that not all students follow the same learning pathway to mastering content. Learning progressions can be used to describe the successively more sophisticated ways student think about an idea as a student learns, providing a description in words and using examples of what it means to move over time toward a more “expert” understanding of a given topic or content area (Duschl, Schweingruber, & Shouse, 2007).

In addition to including descriptions of students’ understanding as they move from novice to expert understanding, learning progressions also often include descriptions of common misconceptions students may have about the content of interest that may hinder or impede their understanding; these misconceptions can then provide the focus for targeted instruction (Alonzo & Gearhart, 2006).

The complexity associated with learning new content, because it is not linear or the same for every student, is best represented graphically as a complex map or network of connections and interactions rather than a linear path; this complex map allows for the fact that there is no “best” pathway and that some students may take one path in their learning than others to attain proficiency with the same content. A map of a sample learning progression will show not only the development and sophistication of students’ thinking as they move in the learning progression (i.e., increasing in sophistication of their skills and understanding) but will also represents an interaction and integration of knowledge.

In addition to relatedness among constructs in the learning progression, there are also connections of the knowledge and skills between one skill and the next. For example, if the target strategy for a level of a learning progression is the ability to recall multiple
strategies for single-digit addition (e.g., making tens, doubles), the perquisite skill might be a count on strategy whereby students can count on from an initial term (e.g., 5) to make a larger number (e.g., 5, 6, 7, 8). Finally, the most foundational skill in this hypothesized learning progression might be the ability to count all, that is, start from counting at 1 all the way to the desired sum (e.g., When asked what 5 + 3 equals the student starts counting from one – 1, 2, 3, 4, 5, 6, 7, 8).

How can learning progressions inform instruction and assessment?
Learning progressions can be a critical cog in the machinery of instruction and assessment. If, for example, we know that learning progressions provide ordered descriptions’ of students’ understanding, we can then use that information to help identify the “landmarks” or essential knowledge and skills students will need to learn as part of the math content, which can be used to help with instructional planning (e.g., what content to teach and when to teach it).

In addition, because learning progressions often include descriptions of the target knowledge and skills as well as common misconceptions or errors in students’ thinking we hypothesize may be interfering with students’ acquisition of a particular skill or mastery with specific content, learning progressions can provide valuable insights to how students think about the content of the learning progression. Together, these pieces of information can be used to help determine an appropriate sequence for the content of instruction (e.g., focusing first on foundational, prerequisite skills that gradually increase in complexity) as well as to develop classroom-based assessment items that focus on knowledge and skills that have been taught during instruction.

Alonzo, A. C., & Gearhart, M. (2006). Considering learning progressions from a classroom assessment perspective. Measurement: Interdisciplinary Research & Practice, 14(1-2), 99-104.

Duschl, R. A., Schweingruber, H. A., & Shouse, A. W. (Eds.) (2007). Taking science to school: Learning and teaching science in grades K-8. Washington, DC: National Academies Press.

What’s in a Name? Think-a-Loud Protocol

By Dawn Woods, RME Elementary Mathematics Coordinator, and Marilea Jungman, RME Project Specialist

In January, Research in Mathematics (RME) conducted think-aloud protocols with second, third and fourth grade students at Nebbie Williams Elementary School in Rockwall ISD. The school volunteered to participate in the think-aloud protocol study that was designed to enrich the development of the ESTAR Universal Screener.

Background: What is the ESTAR Universal Screener?

The Elementary Students in Texas Algebra Ready, or ESTAR, is the latest intitative within the Texas Algebra Ready (TXAR framework) to support elementary students in the state of Texas to achieve a high level of preparedness in mathematics. The ESTAR Universal Screener is being designed to help educators identify students who may need additional support in becoming algebra-ready in the elementary grades and will be aligned with algebra-readiness knowledge and skills articulated in the revised Texas Response to the Curriculum Focal Points.

This document, based on the revised TEKS adopted in April 2012, identified critical areas of mathematics instruction in a framework for sequencing and developing curricula at each grade level. This document provides the content of the ESTAR Universal Screener and will be organized around foundational, bridging, and target knowledge and skill levels and simultaneously includes items written to target four levels of cognitive complexity - research indicates 4 areas critical for mathematics success: procedural understanding, conceptual understanding, strategic competence, and adaptive reasoning. Data generated from the screener will be reported in a format that helps teachers make informed decisions about the content and structure of mathematics instruction in the classroom.

Why is the ESTAR Universal Screener important?
Although performance standards are in process of being established for the State of Texas Assessments of Academic Readiness (STAAR), data from 2012 indicate that 3rd grade students responded, on average, to only 30 of 49 mathematics items correctly (61%) while 4th grade students responded, on average, to only 32 of 48 (or 66%) of mathematics items correctly (Texas Education Agency, 2012). These data speak to a need for early identification of students who may be struggling to learn critical mathematics content. One of the research steps in developing the Universal Screener is to conduct student interviews, also known as think-aloud protocols.

What is a Think-Aloud Protocol?
The purpose of a student interview or think-aloud protocol is to transform a student’s covert thinking process into an observable behavior so that the thinking process can be documented and analyzed (van Someren, Barnard, & Sandberg, 1994). Basically, we ask the student to work through a small number of math items appropriate to their grade level, and to “think-aloud” as they work. This concurrent data capture is maximized through the notes and reflections of the interviewer, the use of audio/visual, and a field observer dedicated to recording the student’s thoughts, hesitations, and gestures verbatim.

Once the student solves a math item, the interviewer asks the student to reflect on his or her thinking process after the task is completed. This is called retrospective data collection. Here, the interviewer uses questioning, prompting or dialogues to encourage the student to talk about his or her thoughts about the math item. The repetitive nature in the questioning allows student’s initial thoughts to be repositioned, and in many instances, a student alights on the correct answer after a first-round wrong choice.

We use the student interviews to verify and provide validity evidence of misconceptions captured in item designs as well as learn how metacognition (Flavell, 1979) plays a role in the planning and strategies students use in mathematical problem solving. Furthermore, student interviews also provide valuable information about students’ sense of self-efficacy, which may be correlated to student’s academic achievement (Hackett & Betz, 1989) and predicts later success for elementary school students (Bandura, 1997; Joet, Usher, & Bressoux, 2011).

Summing It Up
Think-aloud protocol is a valuable qualitative research method that enables researchers to uncover and map thinking processes. As we begin to analyze our data from our project at Nebbie Williams Elementary School, we hope to not only provide validity to our items for the ESTAR project, but gain valuable insight into how students think about math and how metacognition and self-efficacy play a role in students mathematics achievement.

Thank you again to the wonderful teachers that helped us with our project!

3rd Grade
Ms. Jennifer McCurry and Ms. Melody Carrilo

4th Grade
Ms. Christine Gregory and Ms. Lana Edwards

2nd Grade
Dr. Marcella J. Hodges and Ms. Kathleen Elam

Bandura, A. (1997). Self-efficacy: The exercise of control. U.S.A.: Macmillan.  

Flavell, J. H. (1979) Metacognition and cognitive monitoring: A new area of cognitive-developmental inquiry. American Psychologist 34(10). 906-911.  

Hackett, G. & Betz, N. E. (1989) An exploration of the mathematics self-efficacy/mathematics performance correspondence. Journal for Research in Mathematics Education 20(3). 261-273.  

van Someren, M. W., Barnard, Y. F., & Sandberg, J. A.C. (1994). The think aloud method: A practical guide to modeling cognitive processes. London: University of Amsterdam, Department of Social Science Informatics. 

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Welcome to Our Blog!

We are the Research in Mathematics Education (RME) unit at Southern Methodist University, located in Dallas, Texas.  Our goal as a research and outreach unit is to provide evidence-based support to improve students’ mathematics achievement in North Texas and across the country. 

Courtesy of Southern Methodist University.

We have launched this blog with the hope of cultivating a forum for discussing the critical issues that face educators and offering tools in the form of research, peer review and discussion, and professional outreach opportunities. You will hear from a variety of the faculty members, as well as research associates and master practitioners, all who have a deeply vested interest and broad experiences in mathematics education.

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