Teacher Tools Related to Mathematics
Building Initial Mathematical Understanding

ConcretetoRepresentationaltoAbstract Instruction
CRA instruction insures that students first develop a concrete level of understanding for a new mathematics concept or skill. Later, they can use this foundation to link their conceptual understanding to abstract mathematical learning activities. 
Explicitly Model Mathematics Concepts/Skills & Problem Solving Strategies
The purpose of explicitly modeling mathematics concepts/skills and problem solving strategies is twofold. First, explicit modeling of a target mathematics concept/skill provides students a clear and accessible format for initially acquiring an understanding of the mathematics concept/skill. Second, by explicitly modeling effective strategies for approaching particular problem solving situations, you provide students a process for becoming independent learners and problem solvers. 
Creating Authentic Mathematics Learning Contexts
By creating authentic mathematics learning contexts when teaching mathematics, the teacher explicitly connects the target math concept/skill/strategy to a relevant and meaningful context, therefore promoting a deeper level of understanding for students. Creating authentic mathematics contexts can be a wonderful way to make mathematics meaningful to all students.
Extending Mathematical Understanding

Provide Structured Language Experiences
Providing structured language experiences involves creating a wellstructured learning activity where students have abundant opportunities to use language to describe their mathematical understanding. It is also an excellent way to help students move from a concrete or representational level of understanding to an abstract level of understanding.
Building Mathematical Proficiency

Instructional Games
Mathematics instructional games are learning activities that encourage students to perform target mathematics concepts, skills, or strategies in a game format. By engaging students in practice using instructional games, teachers provide a motivational way for students to respond multiple times to prompts requiring them to apply their newly acquired mathematical understanding.
Evaluating Student Needs & Making Effective Mathematics Instructional Decisions

Dynamic Mathematics Assessment
Dynamic Mathematics Assessment combines principles of CRA Assessment, Error Pattern Analysis, and the Flexible Mathematics Interview to provide teachers with an indepth, instructionally relevant picture of a student's mathematical understanding. 
Continuous Monitoring of Student Mathematics Understandings & Skills
Continuous Monitoring of Student Mathematics Understandings and Skills is a simple yet powerful way to evaluate students’ learning on a daytoday basis. It involves creating short learning probes that ask students to respond to target mathematics concepts, skills, and strategies. Students should be able to complete any probe in 5 minutes or less, and students may chart their progress. 
Mathematics Instructional DecisionMaking Inventory
The Mathematics Instructional Decisionmaking Inventory (MIDMI) provides a structured, practical way to plan mathematics instruction for a class, for small groups of students, or for individual students. By using the MIDMI, the teacher is able to create a general picture of the type of mathematics instruction that would be the most beneficial for the students.
Developed by:
David Allsopp, Ph.D.,
University of South Florida