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Mathematics Dynamic Assessment: Finding Out What You Need To Know In Order To Make Effective Mathematical Instructional Decisions. David H. Allsopp, Ph.D. University of South Florida [email protected] Advance Organizer. MDA at a glance Important concepts MDA description

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Mathematics Dynamic Assessment:Finding Out What You Need To Know In Order To Make Effective Mathematical Instructional Decisions
advance organizer
Advance Organizer
  • MDA at a glance
  • Important concepts
  • MDA description
  • MDA video model
  • Review
  • Questions/Discussion
  • MathVIDS information
mda at a glance
MDA at a Glance
  • instructional specific information
  • focus onconceptual understanding, procedural accuracy, & mathematical thinking
  • incorporates 4 effective assessment practices
    • Student interest assessment
    • C-R-A assessment
    • Error pattern analysis
    • Flexible mathematics interview
  • can be completed in an ordinary classroom period
important concepts
Important Concepts
  • Level of Cognitive Understanding
  • Level of Expressive Understanding
  • Mathematical Thinking
  • Procedural Accuracy
  • Instructional Hypothesis
level of cognitive understanding
Level of Cognitive Understanding
  • At what level(s) do students understand the target mathematics?
  • Three levels:
    • concrete (objects/manipulatives)
    • representational (drawing)
    • abstract (numbers/symbols only)
level of expressive understanding
Level of Expressive Understanding
  • In what manner can students show their understanding?
  • Recognition (receptive level)
  • Doing (expressive level)
mathematical thinking
Mathematical Thinking
  • Are students able to think about mathematics in ways...
  • 1) that are reasonable?
  • 2) that show understandings of how relevant mathematics concepts/skills across the curriculum “fit” together in order to problem solve?
  • Reasoning
  • Approach to Problem Solving
procedural accuracy
Procedural Accuracy
  • Are students able to use effective algorithms/procedures in order to successfully compute?
  • Algorithms
  • Procedures
instructional hypothesis
Instructional Hypothesis
  • Provides you with a focused approach to teaching that specifically addresses the needs of your students based on the results of a mathematics dynamic assessment.
instructional hypothesis1
Instructional Hypothesis
  • Components:
    • Context
    • What students can do
    • What students cannot do
    • Reason

“Given ________,

students can _______

students cannot ______,

because __________.”

mathematics dynamic assessment description
Mathematics Dynamic Assessment: Description
  • Student Interest Inventory
  • C-R-A Assessment
  • Error Pattern Analysis
  • Flexible Interview
student interest inventory
Student Interest Inventory
  • Ask students to describe interests they have in a variety of areas in a format you can pick up and review. For example:
    • things they like to do with friends
    • things they like to do alone
    • things they do with their family
    • hobbies
    • interests or special talents they have
c r a assessment
C-R-A Assessment
  • Identify target concept (e.g., comparing fractions)
  • Develop 3-5 assessment items:
    • concrete, representational, abstract levels
    • recognition and expressive response formats
  • Create concrete, representational, & abstract centers
  • Develop process for students responding to and showing you their responses
  • Evaluate student performance at each level of understanding and response format
error pattern analysis
Error Pattern Analysis
  • Review student responses
  • Determine whether students consistently use faulty procedures for responses that are incorrect
  • Evaluate the meaning of the error pattern...
    • does it represent lack of conceptual understanding?
    • does it represent lack of pre-requisite knowledge?
    • does it represent sensory-motor problems?
    • does it represent impulsivity or distractibility?
flexible interview
Flexible Interview
  • “Listen” for student’s mathematical thinking based on problems to which they have responded...
  • ask them to describe to you how the solved the problem
  • ask them to “teach” you how to solve the problem
  • ask them to watch & listen as you solve the problem and to “catch” you doing something incorrect
  • use concrete materials or drawings to further explore student understandings
mathematics dynamic assessment model
Mathematics Dynamic Assessment: Model
  • MDA video
  • Four clips:
    • Introduction/Overview
    • Organization of classroom
    • Implementation
    • Results
mda video
MDA Video
  • Clip 1: Overview/Introduction
mda video1
MDA Video
  • Clip 2: Organization of Classroom & Materials
c r a assessment response sheet example
C-R-A Assessment Response Sheet Example


student response

c r a assessment response sheet example1
C-R-A Assessment Response Sheet-Example


student response

mda video2
MDA Video
  • Clip 3: Implementation
mda video3
MDA Video
  • Clip 4: Results
c r a assessment results
C-R-A Assessment Results

level of cognitive understanding

M -mastery

I -instructional

F -frustration

level of expressive understanding

  • Purpose of MDA?
  • 4 effective assessment practices the MDA integrates?
  • Important areas of mathematical understanding the MDA provides information on?
  • How can the MDA guide your mathematics instruction?
  • Where can the MDA video clips be accessed for further professional development?