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

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

The D&C Process The Diagnosing and Correcting ProcessDiagnosing and Correcting – 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?

The D&C Process

The Four D&C Processes: DiagnoseDiagnose 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. – Interview student. – Make a final diagnosis of errors.

The Four D&C Processes: CorrectCorrect 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.

The Four D&C Processes: EvaluateEvaluate 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?

The Four D&C Processes: ReflectReflect 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.

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

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.

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.

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.

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.

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.

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?