Classwide Instructi on Individual Instructio n Models for selecting interventions Supporting MATH skills
Jan 11, 2016
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., 5 9 45 = 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: http://www.rti4success.org/index.php?option=com_content&task=blogcategory&id=10&Itemid=56
Concepts and Applications
– 18–25 problems– year-long.– Timed– Score: total
number of correct blanks
Grade Time limit
2 8 minutes
3-4 6 minutes
5-6 7 minutes
Early Skills
3. orally identify the missing number3 4 __ 6
2. orally identify the larger number3
7
1. 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
Correct Errors
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
Grade Probe Maximum score
Benchmark
Kindergarten
Data not yet available
First Computation 30 20 digits
First Data not yet available
Second Computation 45 20 digits
Second Concepts and Applications
32 20 blanks
Third Computation 45 30 digits
Third Concepts and Applications
47 30 blanks
Fourth Computation 70 40 digits
Fourth Concepts and Applications
42 30 blanks
Fifth Computation 80 30 digits
Fifth Concepts and Applications
32 15 blanks
Sixth Computation 105 35 digits
Sixth Concepts and Applications
35 15 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 ringsDo 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 2 3 8 3 2 3 8
x 3 x 2 x 3 x 6 x 3 x 3 x 3
6 6 24 18 6 9 24
7 3 9 3 8 5 8x 3 x 6 x 3 x 7 x 3 x 3 x 3
21 18 27 21 24 15 24
2 3 5 3 8 3 5x 3 x 2 x 3 x 7 x 3 x 3 x 3
6 6 15 21 24 9 15
7 3 1 3 0 0 4x 3 x 0 x 3 x 3 x 3 x 3 x 3
21 0 3 9 0 0 12
4 3 3 3 0 3 2x 3 x 2 x 3 x 6 x 3 x 3 x 3
12 6 9 18 0 9 6
6 3 1 3 9 5 9x 3 x 5 x 3 x 8 x 3 x 3 x 3
18 15 3 24 27 15 27
3 3 2 3 2 0 9x 3 x 5 x 3 x 1 x 3 x 3 x 3
9 15 6 3 6 0 27
0
5
10
15
20
25
30
35
40
45
50
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Practice day
Num
ber o
f dig
its c
orre
ct p
er 2
min
utes
Score Errors
RECORDDemonstration 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 ringsDo new job for another 3 minutes
STEP 3: GET READYTurn 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 strategieseven with inadequate facts
1) 21+ 43
2) 125+721
3) 26+ 5
4) 92+18
5) 215+495
6) 54 -12
7) 367-121
8) 51-22
9) 40- 11
10) 932-167
11) 34x 2
12) 12x 24
13) 67x 2
14) 523 x 5
15) 37x 25
•(other similar probes with decimal, fractions, rounding, place value)
SKILL TEST #
JOHN TIM JANE TINA
ADDITION Addition Score > 20 digits per minute?
Yes No No Yes
Add two columns no regrouping 1 Add three columns no regrouping 2 Add one column regrouping 3 Add two columns regrouping 4 Add three columns regrouping 5
SUBTRACTION Subtract > 20 digits per minute? Yes No Yes No
Subtract two columns no regrouping 6 Subtract three columns no regrouping 7 Subtract two columns with regrouping 8 Subtract three columns with regrouping and zero
9
Subtract three columns with regrouping 10
MULTIPLICATION Multiplication > 20 digits per minute? Yes No No YesMultiply one digit no regrouping 11 Multiply two digits no regrouping 12 Multiply one digit with regrouping 13, 14 Multiply two digits with regrouping 15
Sample computation Sequence
3RD GRADE 1. addition and subtraction facts 0-20 flash cards 2. fact families addition and subtraction 0-20 practice set – same as skill 3. 3 digit addition without and with regrouping practice set – same as skill 4. 3 digit subtraction without and with regrouping practice set – same as skill 5. 2 and 3 digit addition and subtraction practice set – same as skill
with and without regrouping 6. multiplication facts 0-9 flash cards 7. division facts 0-9 flash cards 8. fact families multiplication and division 0-9 practice set – same as skill 9. add/subtract fractions with like denominators practice set – same as skill
(3rds, 4ths, 8ths, 10ths, no regrouping) 10. single digit multiplied by double/triple digit practice set – same as skill
without regrouping 11. single digit multiplied by double/triple digit practice set – same as skill
with regrouping
12. single digit divided into double/triple digit practice set – same as skill
without remainders
13. add and subtract decimals to the hundredths practice set – same as skill
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) 21+ 43
2) 125+721
3) 26+ 5
4) 92+18
5) 215+495
6) 54 -12
7) 367-121
8) 51-22
9) 40- 11
10) 932-167
11) 34x 2
12) 12x 24
13) 67x 2
14) 523 x 5
15) 37x 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. 5 3- 3 8
2. Is top number is smaller than bottom? YES So need to make top bigger.
5 3 - 3 8
3. 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.
5 3 - 3 8
4. Add the 10 to the one column. 10 + 4 = 14Write in the 1 next to the top number.
5 4 - 3 8
5. Subtracted ones column correctly. (14 – 8= 6)
5 4 - 3 8 6
6. Subtracted tens column correctly. ( 4 - 3 = 1)
5 4 - 3 8 1 6
4
41
41
4
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 writtenSHOW 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 writtenSHOW how to redo missed or stuck answers.Trade jobs when timer rings
STEP 3: GET READYTurn 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 - CompareSTEP 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:
http://www.interventioncentral.org/htmdocs/tools/mathprobe/addsing.php
Recommended computer fluency building program:
Quarter Mile Math http://www.thequartermile.com/
· Race format to motivate students · > 70,000 problems for K through pre-algebra (K-9th grade)
For Problem solving ideas:
See Interventioncentral.org by Jim Wright
PROBLEM Tools skills Computation Problem Solving
Accurate Peer 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
Fluency Timed trials Time trials with goal setting
KEEP IT SIMPLE