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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

  • David H. Allsopp, Ph.D.

  • University of South Florida

  • [email protected]

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?