Intensified Algebra I: Research Base and Design Principles

• In Event: Intensified Algebra: A Design-Based Research and Development Project for Double-Period High School Algebra

Abstract

The design for Intensified Algebra (IA) is based on specific principles in the learning sciences from research on how people learn (Bransford, Brown, & Cocking, 2000), how students learn mathematics (Donovan & Bransford, 2005), and challenges in learning algebra (Kieran, 2007), along with established principles of mathematics learning and instruction (Henningson & Stein, 1997), literacy enhancements to facilitate understanding (Gomez & Gomez, 2007), and new approaches to assessment (Pellegrino, Chudowsky, & Glaser, 2001). Also foundational is research on learners with special needs (Bulgren & Schumaker, 2006), the social/emotional aspects of academic success (Elliott & Dweck, 2005), and on using representationally innovative technologies to promote conceptual understanding (Tatar et al., 2008).

Core principles from this research are instantiated in IA’s key design features:

• Rigorous algebra curriculum targeting conceptual understanding, skills, and problem-solving and reasoning. Core instruction is built upon Agile Mind’s technology-based delivery system, which provides technology-based representations – visualizations, animations, and simulations – to allow students to explore algebra situations, draw attention to mathematically important aspects of those situations, explicitly show relationships, and connect ideas.
• High cognitive demand tasks and supports for teachers’ enactment of them. IA uses a “launch-investigate-debrief” instructional model in which students solve challenging problems that explicitly connect ideas, facts, and procedures. Student and teacher materials support teachers’ enactment of such tasks.
• Efficient and effective review/repair strategies. Review tasks are strategically placed to help students access prerequisite knowledge and preview upcoming content. Our “repair” strategy includes having students analyze and discuss common mistakes and misconceptions.
• Ongoing, distributed practice with feedback is systemically incorporated into homework assignments and daily “Staying Sharps”.
• Social-psychological interventions address students’ motivation, views of intelligence, and engagement. For example, IA provides explicit instruction about the brain, its functions, and that intellectual development is the result of effort.
• A set of well-defined routines and tools help students organize information and support metacognitive awareness.
• Enhanced formative assessment strategies support teachers’ analysis of students’ learning and feedback to students.
• Explicit supports for literacy and language development, including language notes, double- or triple-entry journals, and reading comprehension strategies, are incorporated.

Our design-based research has iteratively informed the design of IA over the past two years. A small group of six intensive research classrooms are the focus of a descriptive study of teachers’ enactment of units, and of students’ academic, social and emotional learning outcomes through the use of interviews, classroom observations, and assessments. The broader group of implementing classrooms are used to validate emergent trends from our intensive classroom studies and to gather data via web-based surveys about specific program design and implementation issues.

Program revisions to date have been primarily informed by (a) teacher surveys from all classrooms, including end-of-unit surveys and a more general survey about teachers’ perceptions of the program; (b) analysis of classroom observations/videos from intensive research classrooms, with special attention to teachers’ enactments of lessons compared to developers’ intended enactments.

The paper will describe details of how our design-based research informed IA design.

Authors

• Diane Briars, National Council of Supervisors of Mathematics

• Kathy Cook, Dana Center

• Timothy Matthew Stoelinga, University of Illinois at Chicago

• James Lynn, University of Illinois at Chicago