Research Base
The design for Intensified Algebra is based on specific principles in the learning sciences from research on how people learn and, specifically, how students learn mathematics. It also draws upon: established principles of mathematics learning and instruction; particular challenges in learning algebra; literacy enhancements to facilitate mathematics understanding, and new approaches to knowing what students know. This research emphasizes that all learners should:
- Engage with challenging tasks that involve students in actively meaning-making.
- Connect new learning with prior knowledge, and, in the process, address misconceptions.
- Acquire conceptual knowledge as well as skills, to enable them to organize their knowledge, transfer knowledge to new situations, and acquire new knowledge.
- Acquire facility for communicating using the language of algebra, which includes understanding the vocabulary, language structures, and mathematical representations of algebra.
- Socially construct knowledge through talk, activity, and interaction around meaningful problems.
- Receive timely feedback so they can revise their work, thinking, and understandings.
- Employ metacognitive awareness of their performance, e.g., self-monitoring when solving a problem.
- Practice the skills, concepts, and principles they acquire in tasks and situations that are close to the original learning situation as well as more distant from it.
Notably, our framework also includes principles from research on learners with special needs and on the social/emotional aspects of academic success. This literature indicates that learning is facilitated when students:
- Have access to routines and structures to help them access and organize critical mathematics content.
- Understand that intelligence is malleable, not fixed, and recognize the roles of effective effort, attribution of effort, sense of belonging, and motivation in learning mathematics.
Finally, we draw upon emerging research evidence regarding the use of innovative technologies that make use of various representations to deepen students’ conceptual understanding.
Download a file with a list of the research that informs Intensified Algebra I (pdf 231kb).