ASSESSMENT AND CORRECTION MATHEMATICS EDUCATION: ECED 4251

1. ASSESSMENT AND CORRECTION MATHEMATICS EDUCATION: ECED 4251 Rosalind Duplechain, PhD University of West Georgia College of Education Introduction to D&C Process Module 1

2. Basic Structure of PPt • Lecture(slides 3-13) • Introduction to the D&C Process • Four Big Ideas: Some things to remember • Application(slide 14-15) • Another error pattern for your consideration • Homework - (See Course Calendar).

3. The D&C Process • The Diagnosing and Correcting Process • What is it? • What are the sub-processes that are involved? • What is the purpose of each sub-process in the D&C Process? • What are the goals of each sub-process in the D&C Process?

4. The D&C Process

5. The Four D&C Processes: Diagnose • There are five diagnosing steps: • Give a pretest and make sure student provides all of his/her work. • Analyze errors found on pre-test. • Make a pre-diagnosis of errors. • Interviewstudent. • Make a final diagnosisof errors.

6. The Four D&C Processes: Correct • There are a variety of correction steps depending on the errors found in a student’s work sample. • Specific correction steps will be provided for errors that involve • basic facts only, • violations of algorithms only, and • basic facts and violations of algorithms.

7. The Four D&C Processes: Evaluate • Give a post-test and make sure that student provides all of his/her work. • Ideally, use the same test you used to collect your pre-data. • Allow the same amount of time as you allowed for the pre-test. • Grade student’s work (Aim for at least 85%). • Diagnose all errors and ask yourself: • Are any of these errors like the original errors found on the pre-test? • Are any of these error new – unlike the original errors found on the pre-test?

8. The Four D&C Processes: Reflect • Use score from post-test to determine what to do next. • If <85%, repeat correction cycle. Student has not sufficiently mastered concepts and skills. • If ≥85%, this student is on his/her way to mastery. • Divide class instruction time into two blocks: • Drill time (15-20 minutes of every math lesson) • Use this as the time to re-teach and practice skills in order to keep these skills in the forefront of memory. • Instructional time (20-30 minutes of every math lesson) • Use this time to teach and re-teach concepts and skills in order to connect conceptual and procedural knowledge. • Never underestimate the time that could be used when students have completed assigned tasks earlier than their peers. • Have ready-to-go center activities that students can use to practice mathematics concepts and skills. These activities can be kept in baggies and stored in a consistent place in the classroom. They can be designed for individual students as well as small groups. • Aside from these learning opportunities, move on to work with more needy students or on other mathematical topics in mathematics curriculum.

9. 4 Big Ideas • What I’ve learned about the D&C Process… • Big Idea #1 • Big Idea #2 • Big Idea #3 • Big Idea #4

10. Big Idea #1 • Typical assessment procedures in elementary school classrooms • What exactly do teachers do with tests? • What do teachers do with test information? • Teachers are not using assessment data as effectively as they could.

11. Big Idea #2 • Diagnosing the results of an assessment can help teachers and students. • Assessments can be used in two ways: • to tell whether something is mastered after instruction (summative evaluation) • to use as information during instruction so as to provide better instruction (formative evaluation) • This course emphasizes formative evaluation. • The more specific my understanding of the error, the more specific my instruction can be. • The better my instruction, the more likely my students are to perform well.

12. Big Idea #3 • When diagnosing and correcting, until a student shows you that she knows something, do not assume the student does know. • To do otherwise, may cause you to miss something and thereby only correct part of the problem.

13. Big Idea #4 • Diagnosing and correcting is complex. • Gather information on the symptoms (collect pre-data), figure out why these symptoms exist (pre-diagnosis), test out our theory for the symptoms, implement a correction (correction steps), and collect post-data (post-test). • When we see doctors, we tell them symptoms and they make a pre-diagnosis. They order tests to rule out what is working what is working and to focus in on what is not working. They prescribe medication/surgery to correct problem. We follow the correction. They require a post-visit to see if correction worked. • When we see car mechanics, we tell them symptoms and they make a pre-diagnosis. They test-drive and/or look under the hood of the car in order to test out pre-diagnosis. They require us to buy or to pay for adjustments/removal of parts as a way to correct the problem. They make the correction. They take a final test-drive to see if correction worked. • Similarly, diagnosing and correcting mathematical errors is just as complex. • When students provide incorrect answers to mathematical problems, their errors are the symptoms. We study the errors and make a pre-diagnosis. We test our pre-diagnosis by interviewing the student about the errors. We provide corrective instruction. We use a post-test to see if problem is fixed.

14. Application: Error Patterns • Let’s review what we learned today about the D&C Process: • Rudolphe – See Instructional Materials and class notes. • Let’s apply what we’ve learned today about the D&C Process to another error pattern: • Rose – See Instructional Materials.

15. Application: Guidance Using each error pattern, one at a time, diagnose and plan correction. Refer to previous knowledge, textbook, and other resources as needed. Prepare to justify responses. • Ask yourself: • Did the diagnoser catch all of the errors in this work sample? If not, what did he/she miss? • Refer to the diagnosing checklist for whole numbers (right side of this slide) • Are all of the diagnoses correct? If not, what needs to be changed? • Refer to the diagnosing checklist for whole numbers (right side of this slide) • Which problems absolutely needed to be included in the interview process? Why? • Given my diagnosis, … • Which correction steps should apply? • Which specific correction strategies should I use? • Generally speaking, how might my chosen correction strategy look at each phase of the correction process?