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 Basic Facts Module 2

2. Basic Structure of PPt • Lecture(slides 3-16) • How the D&C Process works with Basic Facts • Application(slide 17-18) • Some error patterns associated with Basic Facts • Homework - (See Course Calendar).

3. Lecture • The Diagnosing and Correcting Process • How does D&C Process work with basic facts? • What is a basic fact? • Definition • Examples and Non-examples • What is mastery of basic facts?

4. The D&C Process

5. The Four D&C Processes: Diagnose • There are five diagnosing steps: • Give a pre-test 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.

6. About the Pre-test • Give a pre-test and make sure student provides all of his/her work. • For whole numbers and for basic facts use one of May’s diagnostic tests as your pre-test. • Allow only 10 minutes to complete this test. • For fractions, decimals, geometry, measurement, time, or money use a worksheet, a chapter test, or a unit test as your pre-test. • Can use up to 15 problems and no less than 5. • Allow one minute for each problem on test.

7. About Analyzing Errors • Work each problem on the pretest and compare student’s work (step by step) and answer to your work (step by step) and answer. • For any problem that is wrong, ask yourself: • What exactly is student doing to get this work (step by step) and this answer?

8. About the Pre-diagnosis • Ask yourself: • Are the errors due to problems with… • basic facts, • the algorithm, or • both the basic facts and the algorithm? • If basic facts, which facts might need work? • If the algorithm, which step(s) in the algorithm and which mathematical concepts might need work?

9. About the Interview • The interview has four goals: • To establish a relationship with the student • See this hyperlink for required questions to use in this interview (Read the entire reading titled Interview Questions. Ppay close attention to the questions in red. These are the required questions for your interview). • To either verify or modify the pre-diagnosis • Say to student: Here is a problem. Show me how you would solve this problem and talk out loud so I can hear what you’re thinking. • To get insight about problems you were unable to pre-diagnose • Say to student: Here is a problem. Show me how you would solve this problem and talk out loud so I can hear what you’re thinking. • If basic facts is a pre-diagnosis, to find out which basic facts need work • Prior to interview, create a set of flash cards for all basic facts within the designated operation. • Jumble all cards so that they are out of order. • During the interview, flash each card one at a time (Remember: Do not flash cards in order. You need them to be jumbled – out of order). • As you flash each card, count to 3 in your mind. • Based on student’s answer to card, place the card in one of three piles: • Pile one: Facts the student knows WITHIN 3 seconds • Pile two: Facts the student does not know. • Pile three: Facts the student knows AFTER 3 seconds • Repeat the process of flashing a card, counting to 3, and placing cards in one of three piles until all of the flash cards in the designated operation have been shown to the student. • After the interview, use the piles to complete the Basic Facts’ Cardthat can be found under Instructional Resources in Module 2 • Make sure your completed Basic Facts’ Card has a legend/key for any symbols you used to show each pile.

10. About the Final Diagnosis • Based on my understanding of the pre-test and the interview, these errors are due to problems with… • basic facts, • the algorithm, or • both basic facts and the algorithm? • If basic facts, these are the facts that need work (refer to the results of a completed Basic Facts’ Card). • If the algorithm, these steps in the algorithm and these mathematical concepts need work (refer to the results of the appropriate diagnosing checklist).

11. The Four D&C Processes: Correct • For Basic Facts, there are three correction steps that must be followed. • Teach the meaning of the operation (addition, subtraction, multiplication, or division). • You will need to provide evidence that you have taught this correction step to your field assignment student. See this hyperlink for how evidence of this correction step needs to look. • Please note the request on this evidence: “Draw me a picture that shows what x means.” • Teach and practice at least one number strategy for each basic fact that needs work. • You will need to provide evidence that you have taught this correction step to your field assignment student. See this hyperlink for how evidence of this correction step needs to look. • Number strategies are a more efficient way of counting than counting each and every item in all sets (Van de Walle, 2004). • Notice what is required: List of basic facts being worked on and name of strategy used. • Choose between Plan A or Plan Bwhen you turn in your work. Do not use both plans. • Goal of this step: Get student to provide… • A correct response to fact(s) • A justification of answer (stating or demonstrating how they got answer using the strategy you taught) • Work of automaticity of all basic facts. • You will need to provide evidence that you have taught this correction step to your field assignment student. See this hyperlink for how evidence of this correction step needs to look. • Any activity or game that helps students achieve a ≤ 3 second response is appropriate. • You will simply need to briefly explain the activity or game you used and emphasize a focus on TIME.. • Some common examples include: any competition situation (Around the World, relays, etc), rhymes, songs, repetitive writing of facts, repetitive oral response situations, and speed tests. • GOAL of this step: Get an accurate answer within 3 seconds.

12. The Four D&C Processes: Evaluate • Give a post-test and make sure that student provides all of his/her work. • 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?

13. 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 mastered a sufficient number of basic facts. • If ≥85%, this student is on his/her way to mastery. • Continue to work on number strategies and on automaticity in classroom through learning centers whenever students finished assigned tasks earlier than peers and through drill time (15-20 minutes of every math lesson). • Aside from these learning opportunities, move on to work with more needy students or on other mathematical topics in mathematics curriculum.

14. Basic Facts • For addition, basic facts refer to combinations where both addends are less than 10. • 8 + 7 = 15 • For multiplication, basic facts refer to combinations where both factors are less than 10. • 8 x 7 = 56 • Subtraction and division facts correspond to addition and multiplication facts. • Thus, our basic facts for subtraction and for division come from the inverse operations of addition and multiplication.

15. Are these basic facts? • 16 ÷ 4 => Why or Why not? • 13 - 2 => Why or Why not? • 4 x 6 => Why or Why not? • 7 + 9 => Why or Why not? • 10 + 3 => Why or Why not? • 81 ÷ 9 => Why or Why not? • 20 – 10 => Why or Why not?

16. More about Basic Facts • “Mastery of basic facts means that a child can give a quick response (in less than 3 seconds) without resorting to non-efficient means, such as counting” (Van de Walle, 2001, p. 128). • Addition and subtraction facts usually begin in first grade (fact families). • Multiplication and division facts usually begin in third grade (multiplication tables). • However, mastery of these may not be achieved by eighth grade.

17. Application: Error Patterns • Let’s apply what we’ve learned today about the D&C Process to some error patterns: • Mary Elizabeth – See Instructional Materials. • Leah – See Instructional Materials. • Donna – See Ashlock: Chapter 2.

18. 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: • Which problems are wrong? • What exactly is this student doing to get each problem wrong (i.e., skills and/or steps for solving problem)? • What mathematical misunderstandings might cause a student to make this error? • Given my diagnosis, … • Which corrections 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?