Teacher Tools Related to Mathematics

Building Initial Mathematical Understanding

  • Concrete-to-Representational-to-Abstract Instruction
    C-R-A 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 well-structured 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 in-depth, 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 day-to-day 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 Decision-Making Inventory
    The Mathematics Instructional Decision-making 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

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