The Concrete - Representation - Abstract (CRA) Model:
- Enhances student performance
- Promotes student learning and retention of conceptual knowledge
- Supports understanding of underlying concepts before learning the “rules” of math
The Lesh Model
The Lesh translation model suggests that elementary mathematical ideas can be represented in five different modes: manipulatives, pictures, real-life contexts, verbal symbols, and written symbols. It stresses that understanding is reflected in the ability to represent mathematical ideas in multiple ways, plus the ability to make connections among the different embodiments; and, it emphasizes that translations within and between various modes of representation make ideas meaningful for students.
Five Easy Steps to a Balanced Math Program (FES) - See Resources for FES in SPPSapps
Step 1: Math Review and Mental Math (Computational Skills) is a specific and intentional process to build students’ number sense and computational skills through daily practice where students receive immediate and effective feedback by processing the problems as a class. Teachers and students process the problems and discuss common misconceptions and students articulate their understandings, or misunderstandings, through personal written reflections. This practice communicates the message to students that math intelligence is modifiable.
Step 2: Problem Solving which is an instructional practice that builds student's capacity to solve contextual problems independently similar to what is required on the MCAs. It embeds culturally responsive teaching through relationships, rigor, relevance, and realness and uses PBIS rituals and routines to strengthen students collaboration to solve complex problems.
Step 3: Conceptual Units are resources designed to support teaching the MN Math Standards & Benchmarks conceptually and are aligned to the MCA-III test specifications. These resources include prioritized standards, unwrapped benchmarks with concepts, skills, and Bloom's taxonomy, learning targets, big ideas, misconceptions, and sequencing guides.
Step 5: Common Formative Assessments are aligned to the prioritized benchmarks and the MCA-III test specifications. Each learning target has a beginning understanding item, developing understanding item, proficient understanding item, and exemplary understanding item. These learning targets can be progress monitor by teachers and students using the designed tools.
Step 4: Math Facts program that focuses on instruction that deliberately teaches students strategies for learning sets of facts. Students investigate the meaning of facts through hands-on-exploration to develop strong conceptual understanding of operations and number relationships. Varied instructional techniques are used to ensure that students experience facts in multiple ways, including use of manipulatives, visuals, literature, exploration, and discussions to reach fluency with the facts.