David H. Allsopp, Ph.D. University of South Florida dallsopp@tempest.coeduf

1. 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 • dallsopp@tempest.coedu.usf.edu

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

3. 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

4. Important Concepts • Level of Cognitive Understanding • Level of Expressive Understanding • Mathematical Thinking • Procedural Accuracy • Instructional Hypothesis

5. 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)

6. Level of Expressive Understanding • In what manner can students show their understanding? • Recognition (receptive level) • Doing (expressive level)

7. 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

8. Procedural Accuracy • Are students able to use effective algorithms/procedures in order to successfully compute? • Algorithms • Procedures

9. 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.

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

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

12. 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

13. Student Interest Inventory

14. 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

15. 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?

16. What Does the Error Pattern Mean? ? ? ?

17. 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

18. Mathematics Dynamic Assessment: Model • MDA video • Four clips: • Introduction/Overview • Organization of classroom • Implementation • Results

19. MDA Video • Clip 1: Overview/Introduction

20. Clip 1: Overview/Introduction

21. Reflection: What Did You Learn?

22. MDA Video • Clip 2: Organization of Classroom & Materials

23. Clip 2: Organization of Classroom & Materials

24. C-R-A Assessment Planning Form

25. C-R-A Assessment Response Sheet Example Concrete-Expressive student response

26. C-R-A Assessment Response Sheet-Example Abstract-Receptive student response

27. Reflection: What Did You Learn?

28. MDA Video • Clip 3: Implementation

29. Clip 3: Implementation

30. Reflection: What Did You Learn?

31. MDA Video • Clip 4: Results

32. Clip 4: Results

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

34. Error Pattern Analysis & Flexible Interview Observations

35. Reflection: What Did You Learn?

36. Instructional Hypothesis

37. 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?

38. Discussion/Questions

39. http://coe.jmu.edu/mathvidsr