Math Error Analysis Worksheet by stt79717

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									Supporting MATH skills
            Models
  for selecting interventions


    Classwide
    Instruction




     Individual
    Instruction
             Models
         1. Won’t Do or Can’t Do




Can’t do reasons:
 Accuracy, Fluency,   Too hard
2. Powerful Effective teaching
3. Morningside Big 5 Math Targets

 Tool Skills   Computation            Math Vocabulary
                                       Conversation




                   Solving standard
                    word problems



                   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=blogca
     tegory&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
                  1. orally identify the
        13
                     number ( 0 thru100).


                    2. orally identify the
    3        7         larger number


                    3. orally identify the
3   4 __ 6            missing number
               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
                  To assess TOOL Skills
                 Single CBM Tools skills

Tool Skill         Correct   Errors
Single probes                         ACCURACY PROBLEM
Reading numbers                       SLOW AND MANY ERRORS
Writing numbers
Place value
                                      FLUENCY PROBLEM
Add facts
                                      SLOW AND FEW ERRORS
Subtract facts
Multiply facts
Division facts
                 Using End-of-Year
                    Benchmarks
    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
    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
      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 1: GET READY

Get out flashcards and a regular pencil 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
          Demonstration Math 2 Practice Test




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.


             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        8
x   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        5
x   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        4
x   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        2
x   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        9
x   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        9
x   3    x   5    x   3    x   1    x   3    x   3    x   3
    9        15       6        3        6        0        27
                                               RECORD
                                          Demonstration MATH 3
                                         50

                                         45
Number of digits correct per 2 minutes
                                         40

                                         35

                                         30
                                                                                                    Score
                                         25
                                                                                                    Errors
                                         20

                                         15

                                         10

                                         5

                                         0
                                              1   2   3   4   5   6   7   8   9 10 11 12 13 14 15

                                                                  Practice day
MATH FLASHCARD     PARTNERS
          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.
      To assess if knows strategies
       even with inadequate facts

    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
1)              2)              3)              4)            5)
        21             125             26              92            215
      + 43            +721            + 5             +18           +495



6)              7)              8)              9)            10)
        54             367             51               40           932
       -12            -121            -22             - 11          -167




11)             12)             13)             14)           15)
       34               12             67               523           37
      x 2             x 24            x 2              x 5          x 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     Yes
Multiply 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
            Fuchs Math: 17 Scripted Topics

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

                                                                    30
   How to…Computation
Class-wide Math Intervention




Teacher first reviews steps and write SKILL STEPS on board.
1)              2)            3)           4)            5)
          21           125           26           92            215
        + 43          +721          + 5          +18           +495



6)              7)            8)           9)            10)
         54            367           51            40           932
        -12           -121          -22          - 11          -167




11)             12)           13)          14)           15)
         34             12           67            523           37
        x 2           x 24          x 2           x 5          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


                                           Tens Ones
1. Look at the ones column.                  53
                                           - 38
2. Is top number is smaller than bottom?           53
   YES                                            -38
   So need to make top bigger.
                                                        4
3. Burrow a 10 from the tens column.                    53
Cross out the top number in tens column.               -38
Subtract 1 from top number  5 – 1 = 4
Write the number on top.                                     4
4. Add the 10 to the one column.                             5 14
10 + 4 = 14                                                 -38
Write in the 1 next to the top number.                              4
5. Subtracted ones column correctly.                                    1
                                                                  54
   (14 – 8= 6)                                                   -38
                                                                   6        4
6. Subtracted tens column correctly.                                         5 4
   ( 4 - 3 = 1)                                                             -3 8
                                                                              16
          MATH COMPUTATION COACHES

             Demonstration Math 4
             Your partner is someone sitting next to you.



   STEP 1: GET READY

   Move to math partner seating with folder, regular
pencil 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
             Demonstration MATH 5 : Practice test




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.
MATH COMPUTATION COACHES
          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.
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:
  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
                KEEP IT SIMPLE
PROBLEM    Tools skills   Computation             Problem Solving
Accurate   Peer tutor     1. Mini skill step
           flashcard      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

								
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