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Title: Best Practices in Classroom Math Interventions (Elementary) Jim Wright www.interventioncentral.org


1
Best Practices in Classroom Math Interventions
(Elementary) Jim Wright www.interventioncentral.o
rg
2
Workshop PPTs and handout available at
http//www.interventioncentral.org/rtimath
3
Workshop Agenda RTI Challenges
4
Core Instruction Tier 1 Intervention Focus of
Inquiry What are the indicators of high-quality
core instruction and classroom (Tier 1)
intervention for math?
5


Tier I of an RTI model involves quality core
instruction in general education and benchmark
assessments to screen students and monitor
progress in learning. p. 9


It is no accident that high-quality intervention
is listed first in the RTI model, because
success in tiers 2 and 3 is quite predicated on
an effective tier 1. p. 65
Source Burns, M. K., Gibbons, K. A. (2008).
Implementing response-to-intervention in
elementary and secondary schools. Routledge New
York.
6
Common Core State Standards Initiative http//www.
corestandards.org/ View the set of Common Core
Standards for English Language Arts (including
writing) and mathematics being adopted by states
across America.
7
Common Core Standards, Curriculum, and Programs
How Do They Interrelate?
School Curriculum. Outlines a uniform sequence
shared across instructors for attaining the
Common Core Standards instructional goals.
Scope-and-sequence charts bring greater detail to
the general curriculum. Curriculum mapping
ensures uniformity of practice across classrooms,
eliminates instructional gaps and redundancy
across grade levels.
8
An RTI Challenge Limited Research to Support
Evidence-Based Math Interventions
  • in contrast to reading, core math programs
    that are supported by research, or that have been
    constructed according to clear research-based
    principles, are not easy to identify. Not only
    have exemplary core programs not been identified,
    but also there are no tools available that we
    know of that will help schools analyze core math
    programs to determine their alignment with clear
    research-based principles. p. 459

Source Clarke, B., Baker, S., Chard, D.
(2008). Best practices in mathematics assessment
and intervention with elementary students. In A.
Thomas J. Grimes (Eds.), Best practices in
school psychology V (pp. 453-463).
9
National Mathematics Advisory Panel Report 13
March 2008
10
Math Advisory Panel Report at http//www.ed.gov/
mathpanel
11
2008 National Math Advisory Panel Report
Recommendations
  • The areas to be studied in mathematics from
    pre-kindergarten through eighth grade should be
    streamlined and a well-defined set of the most
    important topics should be emphasized in the
    early grades. Any approach that revisits topics
    year after year without bringing them to closure
    should be avoided.
  • Proficiency with whole numbers, fractions, and
    certain aspects of geometry and measurement are
    the foundations for algebra. Of these, knowledge
    of fractions is the most important foundational
    skill not developed among American students.
  • Conceptual understanding, computational and
    procedural fluency, and problem solving skills
    are equally important and mutually reinforce each
    other. Debates regarding the relative importance
    of each of these components of mathematics are
    misguided.
  • Students should develop immediate recall of
    arithmetic facts to free the working memory for
    solving more complex problems.

Source National Math Panel Fact Sheet. (March
2008). Retrieved on March 14, 2008, from
http//www.ed.gov/about/bdscomm/list/mathpanel/rep
ort/final-factsheet.html
12
The Elements of Mathematical Proficiency What
the Experts Say
13
Five Strands of Mathematical Proficiency
  1. Understanding Comprehending mathematical
    concepts, operations, and relations--knowing what
    mathematical symbols, diagrams, and procedures
    mean.
  2. Computing Carrying out mathematical procedures,
    such as adding, subtracting, multiplying, and
    dividing numbers flexibly, accurately,
    efficiently, and appropriately.
  3. Applying Being able to formulate problems
    mathematically and to devise strategies for
    solving them using concepts and procedures
    appropriately.

Source National Research Council. (2002).
Helping children learn mathematics. Mathematics
Learning Study Committee, J. Kilpatrick J.
Swafford, Editors, Center for Education, Division
of Behavioral and Social Sciences and Education.
Washington, DC National Academy Press.
14
Five Strands of Mathematical Proficiency (Cont.)
  1. Reasoning Using logic to explain and justify a
    solution to a problem or to extend from something
    known to something less known.
  2. Engaging Seeing mathematics as sensible, useful,
    and doableif you work at itand being willing to
    do the work.

Source National Research Council. (2002).
Helping children learn mathematics. Mathematics
Learning Study Committee, J. Kilpatrick J.
Swafford, Editors, Center for Education, Division
of Behavioral and Social Sciences and Education.
Washington, DC National Academy Press.
15
Five Strands of Mathematical Proficiency (NRC,
2002)
  • Table Activity Evaluate Your Schools Math
    Proficiency
  • As a group, review the National Research Council
    Strands of Math Proficiency.
  • Which strand do you feel that your school /
    curriculum does the best job of helping students
    to attain proficiency?
  • Which strand do you feel that your school /
    curriculum should put the greatest effort to
    figure out how to help students to attain
    proficiency?
  • Be prepared to share your results.
  • Understanding Comprehending mathematical
    concepts, operations, and relations--knowing what
    mathematical symbols, diagrams, and procedures
    mean.
  • Computing Carrying out mathematical procedures,
    such as adding, subtracting, multiplying, and
    dividing numbers flexibly, accurately,
    efficiently, and appropriately.
  • Applying Being able to formulate problems
    mathematically and to devise strategies for
    solving them using concepts and procedures
    appropriately.
  • Reasoning Using logic to explain and justify a
    solution to a problem or to extend from something
    known to something less known.
  • Engaging Seeing mathematics as sensible, useful,
    and doableif you work at itand being willing to
    do the work.

16
What Works Clearinghouse Practice Guide
Assisting Students Struggling with Mathematics
Response to Intervention (RtI) for Elementary and
Middle Schools http//ies.ed.gov/ncee/wwc/ This
publication provides 8 recommendations for
effective core instruction in mathematics for K-8.
17
Assisting Students Struggling with Mathematics
RtI for Elementary Middle Schools 8
Recommendations
  • Recommendation 1. Screen all students to identify
    those at risk for potential mathematics
    difficulties and provide interventions to
    students identified as at risk
  • Recommendation 2. Instructional materials for
    students receiving interventions should focus
    intensely on in-depth treatment of whole numbers
    in kindergarten through grade 5 and on rational
    numbers in grades 4 through 8.

18
Assisting Students Struggling with Mathematics
RtI for Elementary Middle Schools 8
Recommendations (Cont.)
  • Recommendation 3. Instruction during the
    intervention should be explicit and systematic.
    This includes providing models of proficient
    problem solving, verbalization of thought
    processes, guided practice, corrective feedback,
    and frequent cumulative review
  • Recommendation 4. Interventions should include
    instruction on solving word problems that is
    based on common underlying structures.

19
Assisting Students Struggling with Mathematics
RtI for Elementary Middle Schools 8
Recommendations (Cont.)
  • Recommendation 5. Intervention materials should
    include opportunities for students to work with
    visual representations of mathematical ideas and
    interventionists should be proficient in the use
    of visual representations of mathematical ideas
  • Recommendation 6. Interventions at all grade
    levels should devote about 10 minutes in each
    session to building fluent retrieval of basic
    arithmetic facts

20
Assisting Students Struggling with Mathematics
RtI for Elementary Middle Schools 8
Recommendations (Cont.)
  • Recommendation 7. Monitor the progress of
    students receiving supplemental instruction and
    other students who are at risk
  • Recommendation 8. Include motivational strategies
    in tier 2 and tier 3 interventions.

21
How Do We Reach Low-Performing Math Students?
Instructional Recommendations
  • Important elements of math instruction for
    low-performing students
  • Providing teachers and students with data on
    student performance
  • Using peers as tutors or instructional guides
  • Providing clear, specific feedback to parents on
    their childrens mathematics success
  • Using principles of explicit instruction in
    teaching math concepts and procedures. p. 51

Source Baker, S., Gersten, R., Lee, D.
(2002).A synthesis of empirical research on
teaching mathematics to low-achieving students.
The Elementary School Journal, 103(1), 51-73..
22
Activity How Do We Reach Low-Performing
Students? p.5
  • Review the handout on p. 5 of your packet and
    consider each of the elements found to benefit
    low-performing math students.
  • For each element, brainstorm ways that you could
    promote this idea in your math classroom.

23
(No Transcript)
24
Three General Levels of Math Skill Development
(Kroesbergen Van Luit, 2003)
  • As students move from lower to higher grades,
    they move through levels of acquisition of math
    skills, to include
  • Number sense
  • Basic math operations (i.e., addition,
    subtraction, multiplication, division)
  • Problem-solving skills The solution of both
    verbal and nonverbal problems through the
    application of previously acquired information
    (Kroesbergen Van Luit, 2003, p. 98)

Source Kroesbergen, E., Van Luit, J. E. H.
(2003). Mathematics interventions for children
with special educational needs. Remedial and
Special Education, 24, 97-114..
25
Math Challenge The student can not yet reliably
access an internal number-line of numbers 1-10.
What Does the Research Say?...
26
What is Number Sense? (Clarke Shinn, 2004)
  • the ability to understand the meaning of
    numbers and define different relationships among
    numbers. Children with number sense can
    recognize the relative size of numbers, use
    referents for measuring objects and events, and
    think and work with numbers in a flexible manner
    that treats numbers as a sensible system. p. 236

Source Clarke, B., Shinn, M. (2004). A
preliminary investigation into the identification
and development of early mathematics
curriculum-based measurement. School Psychology
Review, 33, 234248.
27
What Are Stages of Number Sense? (Berch, 2005,
p. 336)
  1. Innate Number Sense. Children appear to possess
    hard-wired ability (or neurological foundation
    structures) in number sense. Childrens innate
    capabilities appear also to be to represent
    general amounts, not specific quantities. This
    innate number sense seems to be characterized by
    skills at estimation (approximate numerical
    judgments) and a counting system that can be
    described loosely as 1, 2, 3, 4, a lot.
  2. Acquired Number Sense. Young students learn
    through indirect and direct instruction to count
    specific objects beyond four and to internalize a
    number line as a mental representation of those
    precise number values.

Source Berch, D. B. (2005). Making sense of
number sense Implications for children with
mathematical disabilities. Journal of Learning
Disabilities, 38, 333-339...
28
The Basic Number Line is as Familiar as a
Well-Known Place to People Who Have Mastered
Arithmetic Combinations
29
Internal Number-Line
  • As students internalize the number-Line, they
    are better able to perform mental arithmetic
    (the manipulation of numbers and math operations
    in their head).

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
16 17 18 19 20 21 22 23 24 25 26 27 28 29
30
Math Challenge The student can not yet reliably
access an internal number-line of numbers 1-10.
  • Solution Use this strategy
  • Building Number Sense Through a Counting Board
    Game (Supplemental Packet)

31
Building Number Sense Through a Counting Board
Game
  • DESCRIPTION The student plays a number-based
    board game to build skills related to 'number
    sense', including number identification,
    counting, estimation skills, and ability to
    visualize and access specific number values using
    an internal number-line (Siegler, 2009).

Source Siegler, R. S. (2009). Improving the
numerical understanding of children from
low-income families. Child Development
Perspectives, 3(2), 118-124.
32
Building Number Sense Through a Counting Board
Game
  • MATERIALS
  • Great Number Line Race! form
  • Spinner divided into two equal regions marked "1"
    and "2" respectively. (NOTE If a spinner is not
    available, the interventionist can purchase a
    small blank wooden block from a crafts store and
    mark three of the sides of the block with the
    number "1" and three sides with the number "2".)

Source Siegler, R. S. (2009). Improving the
numerical understanding of children from
low-income families. Child Development
Perspectives, 3(2), 118-124.
33
Source Siegler, R. S. (2009). Improving the
numerical understanding of children from
low-income families. Child Development
Perspectives, 3(2), 118-124.
34
Building Number Sense Through a Counting Board
Game
  • INTERVENTION STEPS A counting-board game
    session lasts 12 to 15 minutes, with each game
    within the session lasting 2-4 minutes. Here are
    the steps
  • Introduce the Rules of the Game. The student is
    told that he or she will attempt to beat another
    player (either another student or the
    interventionist). The student is then given a
    penny or other small object to serve as a game
    piece. The student is told that players takes
    turns spinning the spinner (or, alternatively,
    tossing the block) to learn how many spaces they
    can move on the Great Number Line Race! board.
  • Each player then advances the game piece, moving
    it forward through the numbered boxes of the
    game-board to match the number "1" or "2"
    selected in the spin or block toss.

Source Siegler, R. S. (2009). Improving the
numerical understanding of children from
low-income families. Child Development
Perspectives, 3(2), 118-124.
35
Building Number Sense Through a Counting Board
Game
  • INTERVENTION STEPS A counting-board game
    session lasts 12 to 15 minutes, with each game
    within the session lasting 2-4 minutes. Here are
    the steps
  • Introduce the Rules of the Game (cont.). When
    advancing the game piece, the player must call
    out the number of each numbered box as he or she
    passes over it. For example, if the player has a
    game piece on box 7 and spins a "2", that player
    advances the game piece two spaces, while calling
    out "8" and "9" (the names of the numbered boxes
    that the game piece moves across during that
    turn).

Source Siegler, R. S. (2009). Improving the
numerical understanding of children from
low-income families. Child Development
Perspectives, 3(2), 118-124.
36
Building Number Sense Through a Counting Board
Game
  • INTERVENTION STEPS A counting-board game
    session lasts 12 to 15 minutes, with each game
    within the session lasting 2-4 minutes. Here are
    the steps
  • Record Game Outcomes. At the conclusion of each
    game, the interventionist records the winner
    using the form found on the Great Number Line
    Race! form. The session continues with additional
    games being played for a total of 12-15 minutes.
  • Continue the Intervention Up to an Hour of
    Cumulative Play. The counting-board game
    continues until the student has accrued a total
    of at least one hour of play across multiple
    days. (The amount of cumulative play can be
    calculated by adding up the daily time spent in
    the game as recorded on the Great Number Line
    Race! form.)

Source Siegler, R. S. (2009). Improving the
numerical understanding of children from
low-income families. Child Development
Perspectives, 3(2), 118-124.
37
Source Siegler, R. S. (2009). Improving the
numerical understanding of children from
low-income families. Child Development
Perspectives, 3(2), 118-124.
38
Math Challenge The student has not yet acquired
math facts.
What Does the Research Say?...
39
Math Skills Importance of Fluency in Basic Math
Operations
  • A key step in math education is to learn the
    four basic mathematical operations (i.e.,
    addition, subtraction, multiplication, and
    division). Knowledge of these operations and a
    capacity to perform mental arithmetic play an
    important role in the development of childrens
    later math skills. Most children with math
    learning difficulties are unable to master the
    four basic operations before leaving elementary
    school and, thus, need special attention to
    acquire the skills. A category of interventions
    is therefore aimed at the acquisition and
    automatization of basic math skills.

Source Kroesbergen, E., Van Luit, J. E. H.
(2003). Mathematics interventions for children
with special educational needs. Remedial and
Special Education, 24, 97-114.
40
Big Ideas The Four Stages of Learning Can Be
Summed Up in the Instructional Hierarchy
(Supplemental Packet) (Haring et al., 1978)
  • Student learning can be thought of as a
    multi-stage process. The universal stages of
    learning include
  • Acquisition The student is just acquiring the
    skill.
  • Fluency The student can perform the skill but
    must make that skill automatic.
  • Generalization The student must perform the
    skill across situations or settings.
  • Adaptation The student confronts novel task
    demands that require that the student adapt a
    current skill to meet new requirements.

Source Haring, N.G., Lovitt, T.C., Eaton, M.D.,
Hansen, C.L. (1978). The fourth R Research in
the classroom. Columbus, OH Charles E. Merrill
Publishing Co.
41
Math Shortcuts Cognitive Energy- and Time-Savers
  • Recently, some researchershave argued that
    children can derive answers quickly and with
    minimal cognitive effort by employing calculation
    principles or shortcuts, such as using a known
    number combination to derive an answer (2 2
    4, so 2 3 5), relations among operations (6
    4 10, so 10 -4 6) and so forth. This
    approach to instruction is consonant with
    recommendations by the National Research Council
    (2001). Instruction along these lines may be much
    more productive than rote drill without linkage
    to counting strategy use. p. 301

Source Gersten, R., Jordan, N. C., Flojo, J.
R. (2005). Early identification and interventions
for students with mathematics difficulties.
Journal of Learning Disabilities, 38, 293-304.
42
Students Who Understand Mathematical Concepts
Can Discover Their Own Shortcuts
  • Students who learn with understanding have less
    to learn because they see common patterns in
    superficially different situations. If they
    understand the general principle that the order
    in which two numbers are multiplied doesnt
    matter3 x 5 is the same as 5 x 3, for
    examplethey have about half as many number
    facts to learn. p. 10

Source National Research Council. (2002).
Helping children learn mathematics. Mathematics
Learning Study Committee, J. Kilpatrick J.
Swafford, Editors, Center for Education, Division
of Behavioral and Social Sciences and Education.
Washington, DC National Academy Press.
43
Math Short-Cuts Addition (Supplemental Packet)
  • The order of the numbers in an addition problem
    does not affect the answer.
  • When zero is added to the original number, the
    answer is the original number.
  • When 1 is added to the original number, the
    answer is the next larger number.

Source Miller, S.P., Strawser, S., Mercer,
C.D. (1996). Promoting strategic math performance
among students with learning disabilities. LD
Forum, 21(2), 34-40.
44
Math Short-Cuts Subtraction (Supplemental Packet)
  • When zero is subtracted from the original number,
    the answer is the original number.
  • When 1 is subtracted from the original number,
    the answer is the next smaller number.
  • When the original number has the same number
    subtracted from it, the answer is zero.

Source Miller, S.P., Strawser, S., Mercer,
C.D. (1996). Promoting strategic math performance
among students with learning disabilities. LD
Forum, 21(2), 34-40.
45
Math Short-Cuts Multiplication (Supplemental
Packet)
  • When a number is multiplied by zero, the answer
    is zero.
  • When a number is multiplied by 1, the answer is
    the original number.
  • When a number is multiplied by 2, the answer is
    equal to the number being added to itself.
  • The order of the numbers in a multiplication
    problem does not affect the answer.

Source Miller, S.P., Strawser, S., Mercer,
C.D. (1996). Promoting strategic math performance
among students with learning disabilities. LD
Forum, 21(2), 34-40.
46
Math Short-Cuts Division (Supplemental Packet)
  • When zero is divided by any number, the answer is
    zero.
  • When a number is divided by 1, the answer is the
    original number.
  • When a number is divided by itself, the answer is
    1.

Source Miller, S.P., Strawser, S., Mercer,
C.D. (1996). Promoting strategic math performance
among students with learning disabilities. LD
Forum, 21(2), 34-40.
47
Math Challenge The student has not yet acquired
math facts.
  • Solution Use these strategies
  • Strategic Number Counting Instruction
    (Supplemental Packet)
  • Incremental Rehearsal
  • Cover-Copy-Compare
  • Peer Tutoring in Math Computation with
    Constant Time Delay

48
Strategic Number Counting Instruction
  • DESCRIPTION The student is taught explicit
    number counting strategies for basic addition and
    subtraction. Those skills are then practiced with
    a tutor (adapted from Fuchs et al., 2009).

Source Fuchs, L. S., Powell, S. R., Seethaler,
P. M., Cirino, P. T., Fletcher, J. M., Fuchs, D.,
Hamlett, C. L. (2009). The effects of strategic
counting instruction, with and without deliberate
practice, on number combination skill among
students with mathematics difficulties. Learning
and Individual Differences 20(2), 89-100.
49
Strategic Number Counting Instruction
  • MATERIALS
  • Number-line (attached)
  • Number combination (math fact) flash cards for
    basic addition and subtraction
  • Strategic Number Counting Instruction Score Sheet

Source Fuchs, L. S., Powell, S. R., Seethaler,
P. M., Cirino, P. T., Fletcher, J. M., Fuchs, D.,
Hamlett, C. L. (2009). The effects of strategic
counting instruction, with and without deliberate
practice, on number combination skill among
students with mathematics difficulties. Learning
and Individual Differences 20(2), 89-100.
50
Strategic Number Counting Instruction
  • PREPARATION The tutor trains the student to use
    these two counting strategies for addition and
    subtraction
  • ADDITION The student is given a copy of the
    number-line. When presented with a two-addend
    addition problem, the student is taught to start
    with the larger of the two addends and to 'count
    up' by the amount of the smaller addend to arrive
    at the answer to the problem. E..g., 3 5 ___

Source Fuchs, L. S., Powell, S. R., Seethaler,
P. M., Cirino, P. T., Fletcher, J. M., Fuchs, D.,
Hamlett, C. L. (2009). The effects of strategic
counting instruction, with and without deliberate
practice, on number combination skill among
students with mathematics difficulties. Learning
and Individual Differences 20(2), 89-100.
51
Strategic Number Counting Instruction
  • PREPARATION The tutor trains the student to use
    these two counting strategies for addition and
    subtraction
  • SUBTRACTION With access to a number-line, the
    student is taught to refer to the first number
    appearing in the subtraction problem (the
    minuend) as 'the number you start with' and to
    refer to the number appearing after the minus
    (subtrahend) as 'the minus number'. The student
    starts at the minus number on the number-line and
    counts up to the starting number while keeping a
    running tally of numbers counted up on his or her
    fingers. The final tally of digits separating the
    minus number and starting number is the answer to
    the subtraction problem. E..g., 6 2 ___

Source Fuchs, L. S., Powell, S. R., Seethaler,
P. M., Cirino, P. T., Fletcher, J. M., Fuchs, D.,
Hamlett, C. L. (2009). The effects of strategic
counting instruction, with and without deliberate
practice, on number combination skill among
students with mathematics difficulties. Learning
and Individual Differences 20(2), 89-100.
52
Strategic Number Counting Instruction
  • INTERVENTION STEPS For each tutoring session,
    the tutor follows these steps
  • Create Flashcards. The tutor creates addition
    and/or subtraction flashcards of problems that
    the student is to practice. Each flashcard
    displays the numerals and operation sign that
    make up the problem but leaves the answer blank.

Source Fuchs, L. S., Powell, S. R., Seethaler,
P. M., Cirino, P. T., Fletcher, J. M., Fuchs, D.,
Hamlett, C. L. (2009). The effects of strategic
counting instruction, with and without deliberate
practice, on number combination skill among
students with mathematics difficulties. Learning
and Individual Differences 20(2), 89-100.
53
Strategic Number Counting Instruction
  • INTERVENTION STEPS For each tutoring session,
    the tutor follows these steps
  • Review Count-Up Strategies. At the opening of the
    session, the tutor asks the student to name the
    two methods for answering a math fact. The
    correct student response is 'Know it or count
    up.' The tutor next has the student describe how
    to count up an addition problem and how to count
    up a subtraction problem. Then the tutor gives
    the student two sample addition problems and two
    subtraction problems and directs the student to
    solve each, using the appropriate count-up
    strategy.

Source Fuchs, L. S., Powell, S. R., Seethaler,
P. M., Cirino, P. T., Fletcher, J. M., Fuchs, D.,
Hamlett, C. L. (2009). The effects of strategic
counting instruction, with and without deliberate
practice, on number combination skill among
students with mathematics difficulties. Learning
and Individual Differences 20(2), 89-100.
54
Strategic Number Counting Instruction
  • INTERVENTION STEPS For each tutoring session,
    the tutor follows these steps
  • Complete Flashcard Warm-Up. The tutor reviews
    addition/subtraction flashcards with the student
    for three minutes. Before beginning, the tutor
    reminds the student that, when shown a flashcard,
    the student should try to 'pull the answer from
    your head'but that if the student does not know
    the answer, he or she should use the appropriate
    count-up strategy. The tutor then reviews the
    flashcards with the student. Whenever the student
    makes an error, the tutor directs the student to
    use the correct count-up strategy to solve. NOTE
    If the student cycles through all cards in the
    stack before the three-minute period has elapsed,
    the tutor shuffles the cards and begins again. At
    the end of the three minutes, the tutor counts up
    the number of cards reviewed and records the
    total correct responses and errors.

Source Fuchs, L. S., Powell, S. R., Seethaler,
P. M., Cirino, P. T., Fletcher, J. M., Fuchs, D.,
Hamlett, C. L. (2009). The effects of strategic
counting instruction, with and without deliberate
practice, on number combination skill among
students with mathematics difficulties. Learning
and Individual Differences 20(2), 89-100.
55
Strategic Number Counting Instruction
  • INTERVENTION STEPS For each tutoring session,
    the tutor follows these steps
  • Repeat Flashcard Review. The tutor shuffles the
    math-fact flashcards, encourages the student to
    try to beat his or her previous score, and again
    reviews the flashcards with the student for three
    minutes. As before, whenever the student makes an
    error, the tutor directs the student to use the
    appropriate count-up strategy. Also, if the
    student completes all cards in the stack with
    time remaining, the tutor shuffles the stack and
    continues presenting cards until the time is
    elapsed. At the end of the three minutes, the
    tutor once again counts up the number of cards
    reviewed and records the total correct responses
    and errors.

Source Fuchs, L. S., Powell, S. R., Seethaler,
P. M., Cirino, P. T., Fletcher, J. M., Fuchs, D.,
Hamlett, C. L. (2009). The effects of strategic
counting instruction, with and without deliberate
practice, on number combination skill among
students with mathematics difficulties. Learning
and Individual Differences 20(2), 89-100.
56
Strategic Number Counting Instruction
  • INTERVENTION STEPS For each tutoring session,
    the tutor follows these steps
  • Provide Performance Feedback. The tutor gives the
    student feedback about whether (and by how much)
    the student's performance on the second flashcard
    trial exceeded the first. The tutor also provides
    praise if the student beat the previous score or
    encouragement if the student failed to beat the
    previous score.

Source Fuchs, L. S., Powell, S. R., Seethaler,
P. M., Cirino, P. T., Fletcher, J. M., Fuchs, D.,
Hamlett, C. L. (2009). The effects of strategic
counting instruction, with and without deliberate
practice, on number combination skill among
students with mathematics difficulties. Learning
and Individual Differences 20(2), 89-100.
57
Strategic Number Counting Instruction Score Sheet
58
Acquisition Stage Math Review Incremental
Rehearsal of Math Facts
Step 1 The tutor writes down on a series of
index cards the math facts that the student needs
to learn. The problems are written without the
answers.
59
Math Review Incremental Rehearsal of Math Facts
KNOWN Facts
UNKNOWN Facts
Step 2 The tutor reviews the math fact cards
with the student. Any card that the student can
answer within 2 seconds is sorted into the
KNOWN pile. Any card that the student cannot
answer within two secondsor answers
incorrectlyis sorted into the UNKNOWN pile.
60
Math Review Incremental Rehearsal of Math Facts
61
Math Review Incremental Rehearsal of Math Facts
62
Cover-Copy-Compare Math Computational
Fluency-Building Intervention
  • The student is given sheet with correctly
    completed math problems in left column and index
    card. For each problem, the student
  • studies the model
  • covers the model with index card
  • copies the problem from memory
  • solves the problem
  • uncovers the correctly completed model to check
    answer

Source Skinner, C.H., Turco, T.L., Beatty, K.L.,
Rasavage, C. (1989). Cover, copy, and compare
A method for increasing multiplication
performance. School Psychology Review, 18,
412-420.
63
Cover-Copy-Compare Math Computational
Fluency-Building Intervention
  • Here is one way to create CCC math worksheets,
    using the math worksheet generator on
    www.interventioncentral.org
  • From any math operations page, select the
    computation target.
  • Then click the Cover-Copy-Compare button. A
    scaffolded version of the CCC worksheet will be
    created that provides the student with both a
    completed model and a partially completed model.

Source Skinner, C.H., Turco, T.L., Beatty, K.L.,
Rasavage, C. (1989). Cover, copy, and compare
A method for increasing multiplication
performance. School Psychology Review, 18,
412-420.
64
Cover-Copy-Compare Math Computational
Fluency-Building Intervention
  • Here is another way to create CCC math
    worksheets, using the math worksheet generator on
    www.interventioncentral.org
  • From any math operations page, select a
    computation skill for the CCC worksheet.
  • Next, set the Number of Columns setting to 1.
  • Then set the Number of Rows setting to the
    number of CCC problems that you would like the
    student to complete.
  • Click the Single-Skill Computation Probe
    button.
  • Print off only the answer keyand use it as your
    students CCC worksheet.

Source Skinner, C.H., Turco, T.L., Beatty, K.L.,
Rasavage, C. (1989). Cover, copy, and compare
A method for increasing multiplication
performance. School Psychology Review, 18,
412-420.
65
Peer Tutoring in Math Computation with Constant
Time Delay pp. 20-26
66
Peer Tutoring in Math Computation with Constant
Time Delay
  • DESCRIPTION This intervention employs students
    as reciprocal peer tutors to target acquisition
    of basic math facts (math computation) using
    constant time delay (Menesses Gresham, 2009
    Telecsan, Slaton, Stevens, 1999). Each
    tutoring session is brief and includes its own
    progress-monitoring component--making this a
    convenient and time-efficient math intervention
    for busy classrooms.

67
Peer Tutoring in Math Computation with Constant
Time Delay
  • MATERIALS
  • Student Packet A work folder is created for each
    tutor pair. The folder contains
  • 10 math fact cards with equations written on the
    front and correct answer appearing on the back.
    NOTE The set of cards is replenished and updated
    regularly as tutoring pairs master their math
    facts.
  • Progress-monitoring form for each student.
  • Pencils.

68
Peer Tutoring in Math Computation with Constant
Time Delay
  • PREPARATION To prepare for the tutoring program,
    the teacher selects students to participate and
    trains them to serve as tutors.
  • Select Student Participants. Students being
    considered for the reciprocal peer tutor program
    should at minimum meet these criteria (Telecsan,
    Slaton, Stevens, 1999, Menesses Gresham,
    2009)
  • Is able and willing to follow directions
  • Shows generally appropriate classroom behavior
  • Can attend to a lesson or learning activity for
    at least 20 minutes.

69
Peer Tutoring in Math Computation with Constant
Time Delay
  • Select Student Participants (Cont.). Students
    being considered for the reciprocal peer tutor
    program should at minimum meet these criteria
    (Telecsan, Slaton, Stevens, 1999, Menesses
    Gresham, 2009)
  • Is able to name all numbers from 0 to 18 (if
    tutoring in addition or subtraction math facts)
    and name all numbers from 0 to 81 (if tutoring in
    multiplication or division math facts).
  • Can correctly read aloud a sampling of 10
    math-facts (equation plus answer) that will be
    used in the tutoring sessions. (NOTE The student
    does not need to have memorized or otherwise
    mastered these math facts to participatejust be
    able to read them aloud from cards without
    errors).
  • To document a deficit in math computation When
    given a two-minute math computation probe to
    complete independently, computes fewer than 20
    correct digits (Grades 1-3) or fewer than 40
    correct digits (Grades 4 and up) (Deno Mirkin,
    1977).

70
Peer Tutoring in Math Computation Teacher
Nomination Form
71
Peer Tutoring in Math Computation with Constant
Time Delay
  • Tutoring Activity. Each tutoring session last
    for 3 minutes. The tutor
  • Presents Cards. The tutor presents each card to
    the tutee for 3 seconds.
  • Provides Tutor Feedback. When the tutee responds
    correctly The tutor acknowledges the correct
    answer and presents the next card. When the
    tutee does not respond within 3 seconds or
    responds incorrectly The tutor states the
    correct answer and has the tutee repeat the
    correct answer. The tutor then presents the next
    card.
  • Provides Praise. The tutor praises the tutee
    immediately following correct answers.
  • Shuffles Cards. When the tutor and tutee have
    reviewed all of the math-fact carts, the tutor
    shuffles them before again presenting cards.

72
Peer Tutoring in Math Computation with Constant
Time Delay
  • Progress-Monitoring Activity. The tutor concludes
    each 3-minute tutoring session by assessing the
    number of math facts mastered by the tutee. The
    tutor follows this sequence
  • Presents Cards. The tutor presents each card to
    the tutee for 3 seconds.
  • Remains Silent. The tutor does not provide
    performance feedback or praise to the tutee, or
    otherwise talk during the assessment phase.
  • Sorts Cards. Based on the tutees responses, the
    tutor sorts the math-fact cards into correct
    and incorrect piles.
  • Counts Cards and Records Totals. The tutor counts
    the number of cards in the correct and
    incorrect piles and records the totals on the
    tutees progress-monitoring chart.

73
Peer Tutoring in Math Computation with Constant
Time Delay
  • Tutoring Integrity Checks. As the student pairs
    complete the tutoring activities, the supervising
    adult monitors the integrity with which the
    intervention is carried out. At the conclusion of
    the tutoring session, the adult gives feedback to
    the student pairs, praising successful
    implementation and providing corrective feedback
    to students as needed. NOTE Teachers can use
    the attached form Peer Tutoring in Math
    Computation with Constant Time Delay Integrity
    Checklist to conduct integrity checks of the
    intervention and student progress-monitoring
    components of the math peer tutoring.

74
Peer Tutoring in Math Computation Intervention
Integrity Sheet (Part 1 Tutoring Activity)
75
Peer Tutoring in Math Computation Intervention
Integrity Sheet (Part 2 Progress-Monitoring)
76
Peer Tutoring in Math Computation Score Sheet
77
Math Challenge The student has acquired math
computation skills but is not yet fluent.
What Does the Research Say?...
78
Benefits of Automaticity of Arithmetic
Combinations (Gersten, Jordan, Flojo, 2005)
  • There is a strong correlation between poor
    retrieval of arithmetic combinations (math
    facts) and global math delays
  • Automatic recall of arithmetic combinations frees
    up student cognitive capacity to allow for
    understanding of higher-level problem-solving
  • By internalizing numbers as mental constructs,
    students can manipulate those numbers in their
    head, allowing for the intuitive understanding of
    arithmetic properties, such as associative
    property and commutative property

Source Gersten, R., Jordan, N. C., Flojo, J.
R. (2005). Early identification and interventions
for students with mathematics difficulties.
Journal of Learning Disabilities, 38, 293-304.
79
Associative Property
  • within an expression containing two or more of
    the same associative operators in a row, the
    order of operations does not matter as long as
    the sequence of the operands is not changed
  • Example
  • (23)510
  • 2(35)10

Source Associativity. Wikipedia. Retrieved
September 5, 2007, from http//en.wikipedia.org/wi
ki/Associative
80
Commutative Property
  • the ability to change the order of something
    without changing the end result.
  • Example
  • 23510
  • 25310

Source Associativity. Wikipedia. Retrieved
September 5, 2007, from http//en.wikipedia.org/wi
ki/Commutative
81
How much is 3 8? Strategies to Solve
Source Gersten, R., Jordan, N. C., Flojo, J.
R. (2005). Early identification and interventions
for students with mathematics difficulties.
Journal of Learning Disabilities, 38, 293-304.
82
Math Challenge The student has acquired math
computation skills but is not yet fluent.
  • Solution Use these strategies
  • Explicit Time Drills
  • Self-Administered Arithmetic Combination Drills
    With Performance Self-Monitoring Incentives

83
Explicit Time Drills p. 25 Math Computational
Fluency-Building Intervention
  • Explicit time-drills are a method to boost
    students rate of responding on math-fact
    worksheets.
  • The teacher hands out the worksheet. Students
    are told that they will have 3 minutes to work on
    problems on the sheet. The teacher starts the
    stop watch and tells the students to start work.
    At the end of the first minute in the 3-minute
    span, the teacher calls time, stops the
    stopwatch, and tells the students to underline
    the last number written and to put their pencils
    in the air. Then students are told to resume work
    and the teacher restarts the stopwatch. This
    process is repeated at the end of minutes 2 and
    3. At the conclusion of the 3 minutes, the
    teacher collects the student worksheets.

Source Rhymer, K. N., Skinner, C. H., Jackson,
S., McNeill, S., Smith, T., Jackson, B. (2002).
The 1-minute explicit timing intervention The
influence of mathematics problem difficulty.
Journal of Instructional Psychology, 29(4),
305-311.
84
Fluency Stage Math Computation p. 30 Math
Computation Increase Accuracy and
Productivity Rates Via Self-Monitoring and
Performance Feedback
  1. The student is given a math computation worksheet
    of a specific problem type, along with an answer
    key Academic Opportunity to Respond.
  2. The student consults his or her performance chart
    and notes previous performance. The student is
    encouraged to try to beat his or her most
    recent score.
  3. The student is given a pre-selected amount of
    time (e.g., 5 minutes) to complete as many
    problems as possible. The student sets a timer
    and works on the computation sheet until the
    timer rings. Active Student Responding
  4. The student checks his or her work, giving credit
    for each correct digit (digit of correct value
    appearing in the correct place-position in the
    answer). Performance Feedback
  5. The student records the days score of TOTAL
    number of correct digits on his or her personal
    performance chart.
  6. The student receives praise or a reward if he or
    she exceeds the most recently posted number of
    correct digits.

Application of Learn Unit framework from
Heward, W.L. (1996). Three low-tech strategies
for increasing the frequency of active student
response during group instruction. In R. Gardner,
D. M.S ainato, J. O. Cooper, T. E. Heron, W. L.
Heward, J. W. Eshleman, T. A. Grossi (Eds.),
Behavior analysis in education Focus on
measurably superior instruction (pp.283-320).
Pacific Grove, CABrooks/Cole.
85
Self-Monitoring Performance Feedback Examples
of Student Worksheet and Answer Key
Worksheets created using Math Worksheet
Generator. Available online at http//www.interve
ntioncentral.org/htmdocs/tools/mathprobe/addsing.p
hp
86
Self-Monitoring Performance Feedback
87
Student Self-Monitoring of Productivity to
Increase Fluency on Math Computation Worksheets
(Supplemental Packet)
  • DESCRIPTION The student monitors and records
    her or his work production on math computation
    worksheets on a daily basiswith a goal of
    improving overall fluency (Maag, Reid, R.,
    DiGangi, 1993). This intervention can be used
    with a single student, a small group, or an
    entire class.

Source Maag, J. W., Reid, R., DiGangi, S. A.
(1993). Differential effects of self-monitoring
attention, accuracy, and productivity. Journal of
Applied Behavior Analysis, 26, 329-344.
88
Student Self-Monitoring of Productivity to
Increase Fluency on Math Computation Worksheets
  • MATERIALS
  • Student self-monitoring audio prompt Tape /
    audio file with random tones or dial-style
    kitchen timer
  • Math computation worksheets containing problems
    targeted for increased fluency
  • Student Speed Check! recording form

Source Maag, J. W., Reid, R., DiGangi, S. A.
(1993). Differential effects of self-monitoring
attention, accuracy, and productivity. Journal of
Applied Behavior Analysis, 26, 329-344.
89
Student Speed Check! Form
Source Maag, J. W., Reid, R., DiGangi, S. A.
(1993). Differential effects of self-monitoring
attention, accuracy, and productivity. Journal of
Applied Behavior Analysis, 26, 329-344.
90
Student Self-Monitoring of Productivity to
Increase Fluency on Math Computation Worksheets
  • Preparation To prepare for the intervention the
    teacher
  • Decides on the Length and Frequency of Each
    Self-Monitoring Period. The instructor decides on
    the length of session and frequency of the
    student's self-monitoring intervention. NOTE One
    good rule of thumb is to set aside at least 10
    minutes per day for this or other interventions
    to promote fluent student retrieval of math facts
    (Gersten et al., 2009).

Source Maag, J. W., Reid, R., DiGangi, S. A.
(1993). Differential effects of self-monitoring
attention, accuracy, and productivity. Journal of
Applied Behavior Analysis, 26, 329-344.
91
Student Self-Monitoring of Productivity to
Increase Fluency on Math Computation Worksheets
  • Preparation To prepare for the intervention the
    teacher
  • Selects a Math Computation Skill Target. The
    instructor chooses one or more problem types that
    are to appear in intervention worksheets. For
    example, a teacher may select two math
    computation problem-types for a student
    Additiondouble-digit plus double-digit with
    regrouping and Subtractiondouble-digit plus
    double-digit with no regrouping.

Source Maag, J. W., Reid, R., DiGangi, S. A.
(1993). Differential effects of self-monitoring
attention, accuracy, and productivity. Journal of
Applied Behavior Analysis, 26, 329-344.
92
Student Self-Monitoring of Productivity to
Increase Fluency on Math Computation Worksheets
  • Preparation To prepare for the intervention the
    teacher
  • Creates Math Computation Worksheets. When the
    teacher has chosen the problem types, he or she
    makes up sufficient equivalent worksheets (with
    the same number of problems and the same mix of
    problem-types) to be used across the intervention
    days. Each worksheet should have enough problems
    to keep the student busy for the length of time
    set aside for a self-monitoring intervention
    session.

Source Maag, J. W., Reid, R., DiGangi, S. A.
(1993). Differential effects of self-monitoring
attention, accuracy, and productivity. Journal of
Applied Behavior Analysis, 26, 329-344.
93
Student Self-Monitoring of Productivity to
Increase Fluency on Math Computation Worksheets
  • Preparation To prepare for the intervention the
    teacher
  • Determines How Many Audio Prompts the Student
    Will Receive. This intervention relies on student
    self-monitoring triggered by audio prompts.
    Therefore, the teacher must decide on a fixed
    number of audio prompts the student is to receive
    per session. NOTE On the attached Student Speed
    Check! form, space is provided for the student to
    record productivity for up to five audio prompts
    per session.

Source Maag, J. W., Reid, R., DiGangi, S. A.
(1993). Differential effects of self-monitoring
attention, accuracy, and productivity. Journal of
Applied Behavior Analysis, 26, 329-344.
94
Student Self-Monitoring of Productivity to
Increase Fluency on Math Computation Worksheets
  • Preparation To prepare for the intervention the
    teacher
  • Selects a Method to Generate Random Audio
    Prompts. Next, the teacher must decide on how to
    generate the audio prompts (tones) that drive
    this intervention. There are two possible
    choices (A) The teacher can develop a tape or
    audio file that has several random tones spread
    across the time-span of the intervention session,
    with the number of tones equaling the fixed
    number of audio prompts selected for the
    intervention. For example, the instructor may
    develop a 10-minute tape with five tones randomly
    sounding at 2 minutes, 3 minutes, 5 minutes, 7
    minutes, and 10 minutes.

Source Maag, J. W., Reid, R., DiGangi, S. A.
(1993). Differential effects of self-monitoring
attention, accuracy, and productivity. Journal of
Applied Behavior Analysis, 26, 329-344.
95
Student Self-Monitoring of Productivity to
Increase Fluency on Math Computation Worksheets
  • Preparation To prepare for the intervention the
    teacher
  • (B) The instructor may purchase a dial-type
    kitchen timer. During the intervention period,
    the instructor turns the dial to a randomly
    selected number of minutes. When the timer
    expires and chimes as a student audio prompt, the
    teacher resets the timer to another random number
    of minutes and repeats this process until the
    intervention period is over.

Source Maag, J. W., Reid, R., DiGangi, S. A.
(1993). Differential effects of self-monitoring
attention, accuracy, and productivity. Journal of
Applied Behavior Analysis, 26, 329-344.
96
Student Self-Monitoring of Productivity to
Increase Fluency on Math Computation Worksheets
  • INTERVENTION STEPS Sessions of the productivity
    self-monitoring intervention for math computation
    include these steps
  • Student Set a Session Computation Goal. The
    student looks up the total number of problems
    completed on his or her most recent timed
    worksheet and writes that figure into the 'Score
    to Beat' section of the current day's Student
    Speed Check! form.

Source Maag, J. W., Reid, R., DiGangi, S. A.
(1993). Differential effects of self-monitoring
attention, accuracy, and productivity. Journal of
Applied Behavior Analysis, 26, 329-344.
97
Student Self-Monitoring of Productivity to
Increase Fluency on Math Computation Worksheets
  • INTERVENTION STEPS Sessions of the productivity
    self-monitoring intervention for math computation
    include these steps
  • Teacher Set the Timer or Start the Tape. The
    teacher directs the student to begin working on
    the worksheet and either starts the tape with
    tones spaced at random intervals or sets a
    kitchen timer. If using a timer, the teacher
    randomly sets the timer randomly to a specific
    number of minutes. When the timer expires and
    chimes as a student audio prompt, the teacher
    resets the timer to another random number of
    minutes and repeats this process until the
    intervention period is over.

Source Maag, J. W., Reid, R., DiGangi, S. A.
(1993). Differential effects of self-monitoring
attention, accuracy, and productivity. Journal of
Applied Behavior Analysis, 26, 329-344.
98
Student Self-Monitoring of Productivity to
Increase Fluency on Math Computation Worksheets
  • INTERVENTION STEPS Sessions of the productivity
    self-monitoring intervention for math computation
    include these steps
  • Student At Each Tone, Record Problems
    Completed. Whenever the student hears an audio
    prompt or at the conclusion of the timed
    intervention period, the student pauses to
  • circle the problem that he or she is currently
    working on
  • count up the number of problems completed since
    the previous tone (or in the case of the first
    tone, the number of problems completed since
    starting the worksheet)
  • record the number of completed problems next to
    the appropriate tone interval on the attached
    Student Speed Check! form.

Source Maag, J. W., Reid, R., DiGangi, S. A.
(1993). Differential effects of self-monitoring
attention, accuracy, and productivity. Journal of
Applied Behavior Analysis, 26, 329-344.
99
Student Speed Check! Form
Source Maag, J. W., Reid, R., DiGangi, S. A.
(1993). Differential effects of self-monitoring
attention, accuracy, and productivity. Journal of
Applied Behavior Analysis, 26, 329-344.
100
Student Self-Monitoring of Productivity to
Increase Fluency on Math Computation Worksheets
  • INTERVENTION STEPS Sessions of the productivity
    self-monitoring intervention for math computation
    include these steps
  • Teacher Announce the End of the Intervention
    Period. The teacher announces that the
    intervention period is over and that the student
    should stop working on the worksheet.

Source Maag, J. W., Reid, R., DiGangi, S. A.
(1993). Differential effects of self-monitoring
attention, accuracy, and productivity. Journal of
Applied Behavior Analysis, 26, 329-344.
101
Student Self-Monitoring of Productivity to
Increase Fluency on Math Computation Worksheets
  • INTERVENTION STEPS Sessions of the productivity
    self-monitoring intervention for math computation
    include these steps
  • Student Tally Day's Performance. The student
    adds up the problems completed at the
    tone-intervals to give a productivity total for
    the day. The student then compares the current
    day's figure to that of the previous day to see
    if he or she was able to beat the previous score.
    If YES, the student receives praise from the
    teacher if NO, the student receives
    encouragement from the teacher.

Source Maag, J. W., Reid, R., DiGangi, S. A.
(1993). Differential effects of self-monitoring
attention, accuracy, and productivity. Journal of
Applied Behavior Analysis, 26, 329-344.
102
Student Speed Check! Form
Source Maag, J. W., Reid, R., DiGangi, S. A.
(1993). Differential effects of self-monitoring
attention, accuracy, and productivity. Journal of
Applied Behavior Analysis, 26, 329-344.
103
Math Challenge The student is often
inconsistent in performance on computation or
word problems and may make a variety of
hard-to-predict errors.
What Does the Research Say?...
104
Profile of Students With Significant Math
Difficulties p. 4
  • Spatial organization. The student commits errors
    such as misaligning numbers in columns in a
    multiplication problem or confusing
    directionality in a subtraction problem (and
    subtracting the original numberminuendfrom the
    figure to be subtracted (subtrahend).
  • Visual detail. The student misreads a
    mathematical sign or leaves out a decimal or
    dollar sign in the answer.
  • Procedural errors. The student skips or adds a
    step in a computation sequence. Or the student
    misapplies a learned rule from one arithmetic
    procedure when completing another, different
    arithmetic procedure.
  • Inability to shift psychological set. The
    student does not shift from one operation type
    (e.g., addition) to another (e.g.,
    multiplication) when warranted.
  • Graphomotor. The students poor handwriting can
    cause him or her to misread handwritten numbers,
    leading to errors in computation.
  • Memory. The student fails to remember a specific
    math fact needed to solve a problem. (The student
    may KNOW the math fact but not be able to recall
    it at point of performance.)
  • Judgment and reasoning. The student comes up with
    solutions to problems that are clearly
    unreasonable. However, the student is not able
    adequately to evaluate those responses to gauge
    whether they actually make sense in context.

Source Rourke, B. P. (1993). Arithmetic
disabilities, specific otherwise A
neuropsychological perspective. Journal of
Learning Disabilities, 26, 214-226.
105
Activity Profile of Math Difficulties p. 4
  • Review the profile of students with significant
    math difficulties that appears on p. 4 of your
    handout.
  • For each item in the profile, discuss what
    methods you might use to discover whether a
    particular student experiences this difficulty.
    Jot your ideas in the NOTES column.

106
Math Challenge The student is often
inconsistent in performance on computation or
word problems and may make a variety of
hard-to-predict errors.
  • Solution Use this strategy
  • Increase Student Math Success with Customized
    Math Self- Correction Checklists (Supplemental
    Packet)

107
Increase Student Math Success with Customized
Math Self-Correction Checklists
  • DESCRIPTION The teacher analyzes a particular
    student's pattern of errors commonly made when
    solving a math algorithm (on either computation
    or word problems) and develops a brief error
    self-correction checklist unique to that student.
    The student then uses this checklist to
    self-monitorand when necessary correcthis or
    her performance on math worksheets before turning
    them in.

Sources Dunlap, L. K., Dunlap, G. (1989). A
self-monitoring package for teaching subtraction
with regrouping to students with learning
disabilities. Journal of Applied Behavior
Analysis, 229, 309-314. Uberti, H. Z.,
Mastropieri, M. A., Scruggs, T. E. (2004).
Check it off Individualizing a math algorithm
for students with disabilities via
self-monitoring checklists. Intervention in
School and Clinic, 39(5), 269-275.
108
Increase Student Math Success with Customized
Math Self-Correction Checklists
  • MATERIALS
  • Customized student math error self-correction
    checklist
  • Worksheets or assignments containing math
    problems matched to the error self-correction
    checklist

Sources Dunlap, L. K., Dunlap, G. (1989). A
self-monitoring package for teaching subtraction
with regrouping to students with learning
disabilities. Journal of Applied Behavior
Analysis, 229, 309-314. Uberti, H. Z.,
Mastropieri, M. A., Scruggs, T. E. (2004).
Check it off Individualizing a math algorithm
for students with disabilities via
self-monitoring checklists. In
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