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

Advance Organizer MDA at a glance Important concepts MDA description MDA video model Review Questions/Discussion MathVIDS information

MDA at a Glance instructional specific information focus on conceptual 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 Level of Cognitive Understanding Level of Expressive Understanding Mathematical Thinking Procedural Accuracy Instructional Hypothesis

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 In what manner can students show their understanding? Recognition (receptive level) Doing (expressive level)

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 Are students able to use effective algorithms/procedures in order to successfully compute? Algorithms Procedures

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 Hypothesis Components: Context What students can do What students cannot do Reason “Given ________, students can _______ students cannot ______, because __________.”

Mathematics Dynamic Assessment: Description Student Interest Inventory C-R-A Assessment Error Pattern Analysis Flexible Interview

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

Student Interest Inventory

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 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?

What Does the Error Pattern Mean? a+5a= a=7 a=5 24 x ? ? ?

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 MDA video Four clips: Introduction/Overview Organization of classroom Implementation Results

MDA Video Clip 1: Overview/Introduction

Reflection: What Did You Learn?

MDA Video Clip 2: Organization of Classroom & Materials

C-R-A Assessment Planning Form

C-R-A Assessment Response Sheet Example Concrete- Expressiv e student response

C-R-A Assessment Response Sheet-Example Abstract- Receptiv e student response

Reflection: What Did You Learn?

MDA Video Clip 3: Implementation

Reflection: What Did You Learn?

MDA Video Clip 4: Results

C-R-A Assessment Results level of cognitive understanding level of expressive understanding M -mastery I - instructional F -frustration

Error Pattern Analysis & Flexible Interview Observations

Reflection: What Did You Learn?

Instructional Hypothesis

Review 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?

Discussion/Questions