Classwide Instruction Individual Instruction Models for selecting interventions Supporting MATH skills

Models 1. Won’t Do or Can’t Do Can’t do reasons: Accuracy, Fluency, Too hard

2. Powerful Effective teaching

Solving standard word problems ComputationTool Skills Math Vocabulary Conversation 3. Morningside Big 5 Math Targets Generic Problem solving

Tool skills Reading numbers quickly –1-9 digit numbers Writing numbers quickly and legibly –1-9 digit numbers Copying and taking dictation Place value Quickly identifying, explaining, manipulating Math facts fluency –Number family method –E.g., = 5x9 = 45, 9x5= 45, 45~9 + 5, 45~5 + 9 Number sense of number relationships

Computation Working with number combinations Addition, subtraction, Multiplication and division Whole numbers, fractions, decimals, & simple percentage calculations “Mental” arithmetic Direct and explicit instruction of algorithms

Solving standard work problems Typical story problems involving quantities Between 20 to 70 word lengths Students learn to –Write an algebraic equation with one unknown –Determine the unknown by manipulating the equation and doing arithmetic Direct instruction for 10 types of word problems Fluency building

How To…. 1)Select students for intervention using screening data 1) Identify Can’t do problems 2) Conduct math level of assessment. 3) Set up progress monitoring. 4) Plan for implementation. Who will do what and when.

CBM- To identify who Screen early for struggling students (K-1) –Number Identification –Quantity Discrimination –Missing Number On going Screening for basic skills (1-6) –Computation Screen for Solving and Predict end of year test (2-6) –Concepts and Applications Fuchs Manual: tegory&id=10&Itemid=56

Concepts and Applications –18–25 problems –year-long. –Timed –Score: total number of correct blanks GradeTime limit 28 minutes 3-46 minutes 5-67 minutes

Early Skills 3. orally identify the missing number 3 4 __ 6 2. orally identify the larger number orally identify the number ( 0 thru100). 13

Why CBM? To identify level for Intervention Common computation errors: 1. Inadequate tool skills and mastery of facts 2. Ineffective strategy (error in steps in procedure) but sound facts 3. Inadequate facts but effective strategies

Single CBM Tools skills Tool Skill Single probes CorrectErrors Reading numbers Writing numbers Place value Add facts Subtract facts Multiply facts Division facts ACCURACY PROBLEM SLOW AND MANY ERRORS FLUENCY PROBLEM SLOW AND FEW ERRORS To assess TOOL Skills

GradeProbeMaximum scoreBenchmark KindergartenData not yet available FirstComputation3020 digits FirstData not yet available SecondComputation4520 digits SecondConcepts and Applications3220 blanks ThirdComputation4530 digits ThirdConcepts and Applications4730 blanks FourthComputation7040 digits FourthConcepts and Applications4230 blanks FifthComputation8030 digits FifthConcepts and Applications3215 blanks SixthComputation10535 digits SixthConcepts and Applications3515 blanks Using End-of-Year Benchmarks

How to…Tool skills Class-wide Math Intervention

Classwide monitoring of skill acquisition

After classwide instruction

Tool Skill Flashcard Intervention 15 Min per Day Model, Guided Practice, Independent Timed Practice with delayed error correction

STEP 1: GET READY Get out flashcards and a regular pencil and a colored pen. Move to math partner seating. MATH FLASHCARD PARTNERS Demonstration Math 1: Flashcards Tear to make 6 flashcards. Write answers on back. Your partner is someone sitting next to you.

STEP 2: GUIDED PEER PRACTICE for 3 minutes Partner 1 SAYS flashcard ANSWERS. Partner 2 SHOWS FLASHCARDS for 3 seconds. SAY answer if no answer or mistake. Trade jobs when timer rings Do new job for another 3 minutes

STEP 3: GET READY Turn passed out practice paper over. Write name on back. STEP 4: 2 minute TIMED INDEPENDENT PRACTICE At “GO!” turn paper over and write answers. Hold paper in the air when timer rings. Demonstration Math 2 Practice Test

STEP 5: GRADE and CORRECT ERRORS Mark answers right or wrong with colored pen using overhead answer key. Write correct answers to missed problems. Answers on overhead

ANSWER KEY x3x2x3x6x3x3x x3x6x3x7x3x3x x3x2x3x7x3x3x x3x0x3x3x3x3x x3x2x3x6x3x3x x3x5x3x8x3x3x x3x5x3x1x3x3x

RECORD Demonstration MATH 3

STEP 1: GET READY Get out flashcards and a regular and a colored pen. Move to math partner seating. STEP 2: GUIDED PEER PRACTICE for 3 minutes Partner 1 SAYS flashcard ANSWERS. Partner 2 SHOWS FLASHCARDS for 3 seconds. SAY answer if no answer or mistake. Trade jobs when timer rings Do new job for another 3 minutes STEP 3: GET READY Turn passed out practice paper over. Write name on back. STEP 4: 2 minute TIMED INDEPENDENT PRACTICE At “GO!” turn paper over and write answers. Hold paper in the air when timer rings. STEP 5: GRADE and CORRECT ERRORS Mark answers right or wrong with colored pen using overhead answer key. Write correct answers to missed problems. STEP 6: RECORD Write score on progress graph. Pass paper to teacher. MATH FLASHCARD PARTNERS

Computation Error Analysis Test strategies with “easy” facts to target gaps Fluency: Time 2 to 5 minutes and mark last problem Accuracy: Allow to finish untimed To assess if knows strategies even with inadequate facts

1) ) ) ) ) ) ) ) ) ) ) 34 x 2 12) 12 x 24 13) 67 x 2 14) 523 x 5 15) 37 x 25 (other similar probes with decimal, fractions, rounding, place value)

SKILLTEST #JOHNTIMJANETINA ADDITION Addition Score > 20 digits per minute? YesNo Yes Add two columns no regrouping1  Add three columns no regrouping2  Add one column regrouping3   Add two columns regrouping4   Add three columns regrouping5   SUBTRACTION Subtract > 20 digits per minute? YesNoYesNo Subtract two columns no regrouping6   Subtract three columns no regrouping7   Subtract two columns with regrouping8   Subtract three columns with regrouping and zero9   Subtract three columns with regrouping10 MULTIPLICATION Multiplication > 20 digits per minute? YesNo Yes Multiply one digit no regrouping11   Multiply two digits no regrouping12   Multiply one digit with regrouping13, 14   Multiply two digits with regrouping15

Sample computation Sequence

30 Fuchs Math: 17 Scripted Topics Identifying and writing numbers to 99 Identifying more, less, and equal with objects Sequencing numbers Using, and = symbols Skip counting by 10s, 5s, and 2s Understanding place value (introduction) Identifying operations Place value (0-50) Writing number sentences (story problems) Place value (0-99) Addition facts (sums to 18) Subtraction facts (minuends to 18) Review of addition and subtraction facts Place value review 2-digit addition (no regrouping) 2-digit subtraction (no regrouping) Missing addends

How to…Computation Class-wide Math Intervention Teacher first reviews steps and write SKILL STEPS on board.

1) ) ) ) ) ) ) ) ) ) ) 34 x 2 12) 12 x 24 13) 67 x 2 14) 523 x 5 15) 37 x 25 To subtract two numbers that require regrouping need to know: 1)check ones place (place value) 2)know top number should be bigger 3)know how to take a 10 from tens place to ones place 4)Subtraction facts

MATH COMPUTATION STEP BY STEP COACHES 1. Look at the ones column Is top number is smaller than bottom? YES So need to make top bigger Burrow a 10 from the tens column. Cross out the top number in tens column. Subtract 1 from top number  5 – 1 = 4 Write the number on top Add the 10 to the one column = 14 Write in the 1 next to the top number Subtracted ones column correctly. (14 – 8= 6) Subtracted tens column correctly. ( = 1) Tens Ones

STEP 1: GET READY Move to math partner seating with folder, regular pencil and a colored pen Write name on passed out worksheet. MATH COMPUTATION COACHES Demonstration Math 4 Your partner is someone sitting next to you.

STEP 2: GUIDED PEER PRACTICE for 3 minutes Partner 1 WRITES as many answers as possible Partner 2 LOOKS at answers as written SHOW how to redo missed or stuck answers. Trade jobs when timer rings

STEP 3: GET READY Turn passed out practice paper over. Write name on back. STEP 4: 2 minute TIMED INDEPENDENT PRACTICE At “GO!” turn paper over and write answers. Hold paper in the air when timer rings. Demonstration MATH 5 : Practice test

STEP 1: GET READY Move to math partner seating with folder, regular and a colored pen Write name on passed out worksheet. STEP 2: GUIDED PEER PRACTICE for 3 minutes Partner 1 WRITES as many answers as possible Partner 2 LOOKS at answers as written SHOW how to redo missed or stuck answers. Trade jobs when timer rings STEP 3: GET READY Turn passed out practice paper over. Write name on back. STEP 4: 2 minute TIMED INDEPENDENT PRACTICE At “GO!” turn paper over and write answers. Hold paper in the air when timer rings. STEP 5: GRADE and CORRECT ERRORS Mark answers right or wrong with colored pen. Write correct answers to missed problems. STEP 6: RECORD score on progress graph. MATH COMPUTATION COACHES

Computation Coaches Intervention 15 Min per Day Teachers encouraged to –Provide applied practice using mastery-level basic tool skills –Have stronger do it first. That person can then show his or her process on paper if needed. –Make sure students tell how to do it and not just give answer. –Scan papers for high error rates –Do 5-min re-teach for those with high-error rates

Measurement Plan Weekly probe of Intervention skill Weekly probe of Retention of previously mastered computational skills Monthly probe to monitor progress toward year-end computational goals

General Findings Growth rates and trials to criterion varied dramatically across skills Retention probe was strongest predictor of year- end SAT-9 performance Mastery level performance on early skills predicted fewer trials to criterion on future related complex skills Fluency scores higher than “mastery” predicted retention of skill over time (about +20 dc/min) VanDerHeyden, in preparation

Tier 1 Outcome 2 in math

Response Cards Guided practice PREP For each student: a laminate board, a dry erase marker, and paper towel. Train until all students respond to cues : –“Cards write”  write problem and answer –“Cards up”  hold card above head towards teacher –“Cards clean”  wipe clean

Response Cards Small group guided practice After lecture and skill modeling, give 1 problem at a time. Say “Cards write!” Wait sufficient time. Say “Cards up!” Scan students’ answers. –All correct  praise, say “Clean cards!”, and move on. –Two or three wrong  give correct response, instruct the students to check their answers, move on –More than 25% wrong  reteach and ask again. Increase Pace as students learn skill.

Cover - Copy - Compare STEP 1: Give a copy of the answers or another student’s 100% paper. STEP 2: Prompt to do the following 5 steps when working on problems. Look at the solution of the problem. Cover the correct answer. Do the problems on your own paper. Uncover the correct answer. Compare your answer with the correct answer. STEP 3: After 4 problems correct, try 4 problems without procedure. STEP 4: Check work. If incorrect, give help and tell the student to redo the problem 3 times. STEP 5: Have student complete worksheet, grade and chart. Website for cover copy and compare worksheets:

Recommended computer fluency building program: Quarter Mile Math · Race format to motivate students · > 70,000 problems for K through pre- algebra (K-9 th grade) For Problem solving ideas: See Interventioncentral.org by Jim Wright

PROBLEMTools skillsComputationProblem Solving AccuratePeer tutor flashcard 1. Mini skill step lessons PLUS 2. Large group: Peer tutoring or Cover copy Compare Small group: Response cards PLUS 3. Daily fluency test FluencyTimed trialsTime trials with goal setting KEEP IT SIMPLE