Intensified Algebra

Key Design Features

The key design features of Intensified Algebra I—derived from two years of planning and proof-of-concept development by the project's design team—are described below.

• Rigorous algebra curriculum targeting students' conceptual understanding, associated skills, and related problem-solving and reasoning capabilities. The core algebra instruction is built upon a technology-based delivery system developed by Agile Mind. The curriculum includes rigorous treatment of topics that are most critical for success in algebra and future mathematics courses, and targets students' conceptual understanding, associated skills, and related problem-solving and reasoning capabilities. Intensified Algebra I uses technology-based representations—visualizations, animations, and simulations—to allow students to explore algebra situations, increase their attention to mathematically important aspects of those situations, explicitly show relationships, and connect ideas.
• Efficient and effective review/repair strategies. Connecting new learning with prior knowledge involves both engaging students in tasks and activities that help them access relevant prior knowledge when they need it and "repairing" misconceptions they might have related to that knowledge. Intensified Algebra I takes a "just in time" approach to review/repair; based upon research with struggling learners, review tasks are strategically placed to help students access prerequisite knowledge and preview upcoming content in the algebra core. Our "repair" strategy is based on research that indicates that learning increases when common mistakes and misconceptions are systematically exposed, challenged, and discussed. In this approach, instructional tasks are designed so that learners confront inconsistencies between their existing beliefs and classroom experiences, then resolve the conflict through targeted practice and reflective discussion. Course developers draw upon the research literature on algebra teaching and learning to identify common misconceptions and prerequisite knowledge to be addressed.
• Ongoing, distributed practice. Struggling students need extra practice opportunities. Intensified Algebra I includes several means to promote ongoing practice of skills, concepts, and principles through tasks and problems. Our approach for such practice is based upon long-standing research that supports the use of distributed practice in mathematics. Practice and review in Intensified Algebra I are incorporated within the program's curriculum spiral, in homework assignments, and in daily "Staying Sharps"—short problem sets assigned each day that review previously learned material and reinforce prerequisite skills.
• Social-psychological interventions. Student motivation, views of intelligence, and engagement are addressed in the Intensified Algebra I course. As an example, students’ beliefs about their intelligence—as a fixed trait (fixed mindset) or one that can grow over time (malleable mindset)—influence their motivation to engage in academic tasks, and consequently, their success, especially in challenging subjects. Malleable-mindset interventions, which explicitly teach students about the brain, its functions, and that intellectual development is the result of effort and learning, have increased students' achievement in middle school mathematics. Building on these findings, Intensified Algebra I incorporates theories of malleable intelligence as well as strategies for goal setting and effective effort; how to learn; and effective communication. These activities have been strategically incorporated into the program.
• Supports for teachers for enactment of high cognitive demand tasks. Teachers facilitate students' conceptual development when they engage students in problems and contexts with important mathematics and high cognitive demand tasks and draw explicit attention to connections among ideas, facts, and procedures. A critical element is the extent to which students are actually cognitively engaged with the task at hand and the mathematics they are learning. A key challenge for all teachers, especially those with less experience, is to learn how to enact tasks so that the level of cognitive demand is retained, then orchestrate discussions using students' responses to advance the mathematical learning of the whole class. Intensified Algebra I assists teachers with this process by embedding questions and prompts within the student materials that help students get started on activities and focus on important mathematical ideas and relationships. Instructional tasks primarily are designed for partner work (rather than individual or small group work) to promote reflection, discussion and explanations. In addition, the Advice for Instruction (teacher guides) provides detailed information for teachers to support task enactments, e.g., key discussion questions.
• Tools that help students organize information and support metacognitive awareness. Metacognitive and cognitive strategies that support students becoming self-directed learners promote students' problem solving capabilities and mathematics achievement. However, struggling learners have difficulty organizing and interpreting information and complex processes. Thus, a key feature of Intensified Algebra I is a set of well-defined routines and tools that assists students in making connections within algebra, organizing information, and making their mathematical thinking "visible" to them and to their teachers. For example, the daily routine for introducing homework helps students to summarize learning and make explicit the connections between understandings from the day’s lesson that are needed to successfully complete the homework assignment.
• Enhanced formative assessments strategies. The positive effects of formative assessment on mathematics learning are well established. A key aspect of formative assessment involves effectively utilizing evidence gathered about students' learning to adjust instruction to meet students' learning needs. Other key aspects involve teachers' abilities to ask effective questions and engineer high-quality classroom discussions; use mathematics tasks that elicit evidence of learning; and provide feedback that moves learners forward. Typically, individual teachers are responsible for formative assessment. In contrast, Intensified Algebra I "offloads" some responsibility for formative assessment onto student and teacher materials. Lessons provide multiple means for students to communicate their thinking, and student and teacher materials contain questions and prompts to help teachers probe students’ understanding and link responses to suggested next steps in instruction. Students complete online assessments, receiving guidance in way of hints and immediate feedback; the Agile Mind reporting tools provide both educators and student with information about task performance. In short, Intensified Algebra I contains a comprehensive set of formative assessment activities and tools that provide struggling learners and their teachers with regular and targeted feedback to help them monitor progress, address sources of confusion, and build on the strengths in students’ mathematical knowledge to move them toward more advanced thinking and toward regulation of their own learning.
• Explicit supports for literacy and language development. Researchers have begun to understand how literacy and language issues impact learning in mathematics and science classes, particularly with struggling learners, and how to support content learning through the use of simple strategies and tools for language and literacy development. The program promotes better algebra understanding through the use of tools and routines—such as language notes and double- or triple-entry journals, and explicit reading comprehension strategies—to help students build essential academic vocabulary, comprehend and analyze key elements of mathematics problems, explicitly connect different representations of mathematical situations, and reflect upon and communicate their understandings.