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 Floridadallsopp@tempest.coedu.usf.edu

Advance OrganizerMDA at a glanceImportant conceptsMDA descriptionMDA video modelReviewQuestions/DiscussionMathVIDS information

MDA at a Glanceinstructional specific informationfocus on conceptual understanding, procedural accuracy, & mathematical thinkingincorporates 4 effective assessment practicesStudent interest assessmentC-R-A assessmentError pattern analysisFlexible mathematics interview

can be completed in an ordinary classroom period

Important ConceptsLevel of Cognitive UnderstandingLevel of Expressive UnderstandingMathematical ThinkingProcedural AccuracyInstructional Hypothesis

Level of Cognitive UnderstandingAt what level(s) do students understand the target mathematics?Three levels:concrete (objects/manipulatives)representational (drawing)abstract (numbers/symbols only)

Level of Expressive UnderstandingIn what manner can students show their understanding?Recognition (receptive level)Doing (expressive level)

Mathematical ThinkingAre 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?ReasoningApproach to Problem Solving

Procedural AccuracyAre students able to use effective algorithms/procedures in order to successfully compute?AlgorithmsProcedures

Instructional HypothesisProvides 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 HypothesisComponents:Context What students can do What students cannot do Reason Given ________,students can _______students cannot ______,because __________.

Mathematics Dynamic Assessment: Description Student Interest InventoryC-R-A AssessmentError Pattern AnalysisFlexible Interview

Student Interest InventoryAsk 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 friendsthings they like to do alonethings they do with their familyhobbiesinterests or special talents they have

Student Interest Inventory

C-R-A AssessmentIdentify target concept (e.g., comparing fractions)Develop 3-5 assessment items:concrete, representational, abstract levelsrecognition and expressive response formatsCreate concrete, representational, & abstract centersDevelop process for students responding to and showing you their responsesEvaluate student performance at each level of understanding and response format

Error Pattern AnalysisReview student responsesDetermine whether students consistently use faulty procedures for responses that are incorrectEvaluate 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????

392317

2a+5a=142a=7a=5

24x17 142824 1624

Flexible InterviewListen for students mathematical thinking based on problems to which they have responded...ask them to describe to you how the solved the problemask them to teach you how to solve the problemask them to watch & listen as you solve the problem and to catch you doing something incorrectuse concrete materials or drawings to further explore student understandings

Mathematics Dynamic Assessment: ModelMDA videoFour clips:Introduction/OverviewOrganization of classroomImplementationResults

MDA VideoClip 1: Overview/Introduction

Clip 1: Overview/Introduction

Reflection: What Did You Learn?

MDA VideoClip 2: Organization of Classroom & Materials

Clip 2: Organization of Classroom & Materials

C-R-A Assessment Planning Form

C-R-A Assessment Response Sheet ExampleConcrete-Expressivestudent response

C-R-A Assessment Response Sheet-ExampleAbstract-Receptivestudent response

Reflection: What Did You Learn?

MDA VideoClip 3: Implementation

Clip 3: Implementation

Reflection: What Did You Learn?

MDA VideoClip 4: Results

Clip 4: Results

C-R-A Assessment Resultslevel of cognitive understandinglevel of expressive understandingM -mastery I -instructionalF -frustration

Error Pattern Analysis & Flexible Interview Observations

Reflection: What Did You Learn?

Instructional Hypothesis

ReviewPurpose 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

http://coe.jmu.edu/mathvidsr