1. RTI Institute: Math Module for Elementary Schools Carroll County Schools Sharon Rinks, Psy.D. Lisa Sirian, Ph.D. Michelle Avila Bolling, Ed.S., NCSP Carroll County Schools

3. Agenda Round Robin problem solving for RTI Evidence-based RTI practices in math Universal screening Intervention Intervention fidelity Progress monitoring Establishing goals challenge activity Math case studies Discuss application activity

4. Round Robin Problem Solving for RTI Challenges 1. Who will do the interventions? 2. How do we do the interventions and still do all of the curriculum? 3. How can we make time for meetings? 4. How can we increase buy in from teachers? 5. How can we increase buy in from administration? 6. How do we train everyone? 7. What about progress monitoring– who can do it & when? 8. What types of support do we need from the district? 9. How can we increase skills with documentation? 10. How do we figure out the logistics of universal screening? 11. How do we transition from SST to Tiers 1-3?

5. Exploring Evidence-Based RTI Practices for Math

7. Math Research Math intervention has received little attention as compared to reading research Dyscalculia- poor skills in numerical calculating Deficits in fluency with basic math skills and conceptual understanding in math exist pk-12 in the US (Perie, Grigg & Dion, 2005) For students who have both math and reading problems (as opposed to those with just math problems) these deficits are likely to endure into later grades (Jordan & Hanich, 2003)

8. Math Research The number of children with math difficulties exceeds the 5-8% that would be LD in math (Fuchs & Fuchs, 2005) Persistence, motivation and concentration are associated with good math performance (Vaughn, 2008) Students with low math scored poorly on Sustained attention Planning and organization during work Accepting responsibility (Badian & Ghublikian, 1983)

9. Math Research There are major inconsistencies in math standards across the nation “Despite years of research, no single method of mathematics instruction has been proven to be significantly better than others.” (Vaughn & Bos, 2009) Goal setting with students and allowing them to progress monitor and chart their own performance has proven effective at increasing math skills and motivation for even very young students (Fuchs, Bahr and Rieth, 1989)

10. Factors that Influence Math Ability Psychological Factors Cognitive ability, distractibility, etc. Educational Factors Quality and amount of prior experience and intervention Personality Factors Persistence, self-concept, attitude toward math Neuropsychological Patterns Perception, neurological trauma (Kosc, 1981)

11. Factors that Interfere with Math Ability Perceptual Skills Spatial, distance, size, sequencing Perseveration Trouble shifting from one task to another Impacts multi-step and applied problem solving Language Too much jargon can create confusion Reasoning Abstract thinking Reprogramming of faulty reasoning Memory Symbolism Difficulty Cannot interpret symbols (Ginsburg, 1997)

12. The National Math Panel (2008) Streamlined a well-defined set of standards for pk-8 Avoid approaches that revisit topics year after year without bringing them to closure 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 Students should develop immediate recall of arithmetic facts to free the “working memory” for solving more complex problems More algebra courses at Grade 8 www.ed.gov/MathPanel

13. The National Math Panel (2008) Student effort is important! “Much of the public’s ‘resignation’ about mathematics education is based on the erroneous idea that success comes from inherent talent or ability in mathematics, not effort. A focus on the importance of effort in mathematics learning will improve outcomes. If children believe that their efforts to learn make them ‘smarter,’ they show greater persistence in mathematics learning.”

14. The National Math Panel (2008) Effective Instruction Matters Formative assessments can improve student learning in mathematics Instructional practice should be informed by high-quality research, when available, and by the best professional judgment and experience The belief that children of particular ages cannot learn certain content because they are “too young” or “not ready” has consistently been shown to be false Explicit instruction for students who struggle with math is effective in increasing student learning Mathematically gifted students should be allowed to accelerate their learning

15. Math Components National Council of Teachers of Mathematics (NCTM, 2000) gives 2 categories of math skills Mathematical reasoning Problem solving Communications Reasoning Connections Mathematical content Estimation Number sense Geometry and spatial sense Measurement Statistics and probability Fractions and decimals Patterns and relationships

16. Math Components As comprehension is to reading, problem solving is to math! Pre-requisites to problem solving Number sense Basic math principles Basic facts rules

17. Prerequisites to Problem Solving 5 components to Number Sense Well-understood number meanings ( 3 = ● ● ●) Awareness of multiple relationships among numbers (6 = ● ● ● ● ● ● or or ) Recognition of the relative magnitude of number (5 is bigger than 3) Knowledge of the effects of operations in numbers (+ makes a number bigger) Knowledge that numbers measure things in the real world (Van de Walle, 1998) ● ● ● ● ● ●

18. Prerequisites to Problem Solving Countingskills typically develop in progression Counting all (3 + 2 = … 1,2,3,4,5) Counting on (2 + 3 = … 2…3,4,5) Count on from larger addend (2 + 3 = 3…4,5) Memory (2 + 3 = 5) (Garnett, 1992)

19. Prerequisites to Problem Solving Place value- a number’s position helps you understand its value Expanded notation- 520 = 5 100s + 2 10s Commutative property- number order doesn’t affect result in + and x Associative property- grouping of numbers doesn’t affect result in + and x Distributive property- numbers can be redistributed (5+4) x 7 = (7x5) + (7x4) Equivalence- what’s on one side of = is equal in quantity to the other side of = (Harniss, Carnine, Silbert, Dixon, 2002)

20. Top Ten Recommended General Core Instructional Practices (Vaughn & Bos, 2009) 1. Use data to make decisions about instruction and progress. 2. Involve peers in working together. 3. Inform parents about progress & success. 4. Use instructional routines that focus on cognitive behavioral techniques. 5. Use instructional design features to help students differentiate problem types. 6. Teach to mastery, then move on.

21. Top Ten Recommended General Core Instructional Practices (Vaughn & Bos, 2009) 7. Establish realistic goals for progress with students. 8. Monitor progress weekly through graphing or visual display. Involve students. 9. Provide evidence that hard work and effort yield good outcomes. 10. Use computer-assisted instruction as an instructional supplement.

22. Universal Screening Mathematics

23. Universal Screening in Math Comprehensive Math Assessment Group administered Grades 2-8 Based on NCTM critical elements Math-Level Indicator: A Quick Group Math Placement Test Group Administered Grades 4-12 30 min administration time Based on NCTM standards

24. Universal Screening in Math Aimsweb – Math Uses CBM in: Oral Counting Number Identification Quantity Discrimination Missing Number Basic Skill areas Grades 1-8 for universal screening 40 alternate forms $5/student complete (reading, language arts and math computation) www.aimsweb.com

25. AIMSweb Sample Probe– Computation

26. AIMSweb Sample Probe–Basic Mult & Div Facts

27. Benchmarks for Math- Correct Digits GradeFallWinterSpring Mean ROI 1 51115.3 21022.3 3152428.4 4334452.5 5303847.5 6283634.2 7303635.1 8334037.1 IMPORTANT NOTE: THESE NORMS ARE ALL FOR 2 MINUTES grades 1-3 and 4 MINUTES grades 4+-- From AIMSweb, 2007

28. Universal Screening in Math Star Math Concepts addressed Computation Application Concepts Grades 1-12 Unlimited forms available Computer administered www.renlearn.com

29. STAR Math – Two Stage Assessment

30. STAR Math- Growth Report

31. STAR Math- Progress Monitoring Report Monitor WHOLE CLASS Progress

32. STAR Math- Can help identify intervention & PM target

33. Universal Screening in Math Yearly Progress Pro Grades 1 - 8 13 forms per grade Custom assessment/problem set creation capability Instructional, guided, and practice exercises correlated to each skill Audio available for assessments and exercises in grades 1 and 2 Data Management System Automated recommendations and assignments that support instructional focus Reporting tools that generate reports by skill, student, class, district, and student demographics

34. Yearly Progress Pro Sample Test Item

35. Yearly Progress Pro- Instructional Component Item

36. Yearly Progress Pro- Individual Class Reports

37. Universal Screening with CBM Curriculum Based Measurement Everything we have talked about is a collection of CBM Probes Your school can assemble your own collection of CBM probes that will be free! There are over 40 sample probes on this CD and more available on the internet You need three sets of probes per grade level that all assess a sample of the year long curriculum for that grade level

38. Sampling performance on yearlong curriculum for each CBM Avoids need to specify a skills hierarchy Avoids single skill tests Automatically assesses maintenance/generalization Permits standardized procedures for sampling the curriculum, with known reliability and validity SO THAT: CBM scores relate well to performance on highstakes tests

39. Positive and negatives of assembling your own set of CBM probes Positives You get to make them yourselves FREE Curriculum specific No copyright problems Negatives You have to make them yourselves You have to create your own norms Need a way to manage the grade level and class level data

40. Universal Screening of Number Sense “Whether a student’s understanding of a number and of its use and meaning are flexible and fully developed.” (Vaughn & Bos, 2009) Several counting measures can be used as universal screeners of number sense (appropriate for the lower grades) Count to 20 Count by 3 and 6 Count by 2, 5, and 10 (Clarke & Shinn, 2004)

41. Universal Screening of Number Sense Number identification (0-20) Given mixed probe of random #s to 20 Number writing (1-20) Numbers randomly presented orally Quantity discrimination Given probe with sets of paired numbers students indicates either larger or smaller #s Missing Number Fill in the blank in a string of numbers Computation Two-minute computation probes appropriate to grade level

42. Setting Goals Challenge Activity Pair up and do the math!

43. Jenny’s Reading Subtract baseline from benchmark to get amount of gain needed 150-80=70 Count number of weeks until benchmark= 33 Divide amount of gain needed by number of weeks to get weekly rate of improvement (ROI) 70/33=2.1 Multiply ROI by number of weeks for intervention implementation 2.1 x 7=14.7 Add this to the baseline 80 + 14.7= 94.7 By 10/31 Sarah should be reading 94.7 words correct per minute on oral reading fluency.

44. Susan’s Writing Subtract baseline from benchmark to get amount of gain needed 40-6=34 Count number of weeks until benchmark= 17 Divide amount of gain needed by number of weeks to get weekly rate of improvement (ROI) 34/17=2 Multiply ROI by number of weeks for intervention implementation 2 x 6=12 Add this to the baseline 6 + 12= 18 By 10/2 Susan should be writing 18 correct word sequences.

45. April’s Reading Subtract baseline from benchmark to get amount of gain needed 30-12=18 Count number of weeks until benchmark= 24 Divide amount of gain needed by number of weeks to get weekly rate of improvement (ROI) 18/24=.75 Multiply ROI by number of weeks for intervention implementation.75 x 6=4.5 Add this to the baseline 12 + 4.5= 16.5 By 1/9 April should be making 16.5 correct replacements on maze probes.

46. Sabrina’s Math Concepts subtract baseline from benchmark to get amount of gain needed 15-5=10 Count number of weeks until benchmark= 33 Divide amount of gain needed by number of weeks to get weekly rate of improvement (ROI) 10/33=.30 Multiply ROI by number of weeks for intervention implementation.3 x 9= 2.7 Add this to the baseline 5 + 2.7= 7.7 By 11/6 Sabrina should be scoring 7.7 correct problems on math concepts probes.

47. Sydney’s Computation Skills subtract baseline from benchmark to get amount of gain needed 20-5=15 Count number of weeks until benchmark= 34 Divide amount of gain needed by number of weeks to get weekly rate of improvement (ROI) 15/33=.44 Multiply ROI by number of weeks for intervention implementation.44 x 7= 3.08 Add this to the baseline 5 + 3.08= 8.08 By 10/13 Sydney should be scoring 8.08 correct problems on math computation probes.

48. Interventions

49. Number Sense Strategies STAR for Number Writing Activities to Increase Pre-Number Skills Kinesthetic Activities to Increase Counting Skills The Number Game Fill the Chutes Find and Press More or Less More, Less, and Same Sets Patterned Set Recognition with Dot Plates Patterned Set Recognition with Dominoes Patterns and Functions

50. The Number Game Improves number i.d. skills of preschoolers Counting and 1:1 correspondence are prerequisites Students take turns spinning a spinner and moving on the board Player says the name of each number as he moves past it (can ask for help) Land on a yellow square… follow arrow forward or back as indicated First person to the end wins

51. The Number Game: 0 to 10

52. More, Less, & Same Sets The first player to go chooses from the pile an object card that contains a certain number of objects He places the card above 3 cards in a row that say “more”, “less”, & “same” Using counters, he then makes 3 collections of counters: a set that is more, one that is less, and one that is the same as the selected object card The next player takes her turn

53. Pattern Recognition with Dominoes Dominoes can be used to teach pattern recognition For a greater variety of patterns, make your own dominoes with posterboard Students can play the standard way by matching up the ends, or with new rules such as “two less than” what is on the end As a speed activity, all dominoes can be spread out to see how long it takes students to play all of them or to play until no more can be played

54. Patterns & Functions A set of cards, each one with a single shape on it, is used to teach how to complete patterns Cards can be made with index cards and markers or pattern blocks can be used Place one shape after another in a line to make a repeating pattern Ask student to tell you the next shape in the pattern, then the next You can also have the student predict the tenth shape in the pattern and so on

55. Arithmetic Skills Strategies Cover, Copy, Compare Incremental Rehearsal Problem Interspersal Self-Monitoring and Performance Feedback Increase Accuracy by Intermixing Easy & Challenging Computation Problems Multiplication Attack Self-Monitoring Arithmetic

56. Arithmetic Skills Strategies continued Subtraction Strategy Addition Fact Families Multiplication Fact Families Money Match Shopping Multiplying Numbers Under 10 by 9 Multi-component Interventions for Math Fluency Folding-In Number Goal Game

57. Money Match A game that helps students learn to count change The object of the game is to be the 1 st player to earn a set amount of change 1 st player rolls a die and takes that amount in pennies from a container of money when 5 pennies accumulate, student trades them for a nickel; 2 nickels are traded for a dime, and so forth All take turns until there is a winner

58. Multiplying Numbers Under 10 By 9 9 x 4 = ___ Spread 10 fingers in front of you, palm down Count fingers from left pinkie to the number you are multiplying by 9 (in this case, the number is 4, so you count to the left index finger) The number of fingers to the left of that finger (3) is the number of 10s (30), and the number of fingers to the right of that finger (6) is the number of ones In this example, the answer is 3 tens and 6 ones, or 36

59. Cover, Copy, Compare Students cover, copy, and compare math problems to improve their math skills Students begin by looking at a sheet of paper with two columns: the left column has the math problem solved and the right column is left blank Students review the first column then cover it up Then, they copy the problem in the blank column from memory When finished, they compare the two columns If they’re different, the students correct the problem This process continues until the worksheet is finished

60. Folding-In Peer tutors work with tutees on fluency in basic math facts by “folding in,” or slowly incorporating, unknown math facts to known ones Preassessment Phase: to find out what they already know and what facts they have not yet mastered, students take a quiz involving computational problems Flash cards of the students’ known and unknown facts are then made

61. Folding-In continued Instructional Phase: Students use peer tutoring to drill each other using the folding-in technique: Each student selects 7 cards from their pile of pre- assessed known facts and 3 cards from their pile of pre-assessed unknown facts They have 20 minutes for peer tutoring: The first teacher presents the 1 st unknown fact to the learner; the learner writes the fact on a piece of paper, says it to himself 3x, then turns paper over The teacher then presents a known fact, followed by the unknown fact, the first known fact, and another known fact The unknown fact is presented sequentially in this fashion until all 7 known facts have been presented and folded-in among the unknown facts

62. Folding-In continued The groups of 8 facts (1 unknown and 7 known) are shuffled. The 2 nd unknown fact is then presented and folded-in among the other 8 facts. This is repeated again for the 3 rd unknown fact. If the student hesitates on a fact, he completes a correction procedure – he is told the correct answer and he writes the fact 3x When all facts have been folded in, the entire group of 10 facts is presented 3x, shuffling each time The final step is a test of the 10 facts that the students have practiced A mark is placed on the unknown fact cards if a student is correct on this trial When an unknown fact attains 3 consecutive marks, it is considered a learned fact The students switch roles of teacher and learner Students graph the number of new facts learned each week

63. Fluency Strategies Boost Fluency Through Explicit Time Drills Explicit Timing Free Time Taped Problems Reciprocal Peer Tutoring Multicomponent Interventions for Math Fluency Folding-In Number Goal Game

64. A large square card with a number on it is placed in the center Each student draws 6 small squares from a facedown pile & turns them over Taking turns, each student tries to combine 2 or more of her squares to make a sum equal to the center card if the number is 13 and a player has squares 2, 3, 5, 5, 5, and 8, she could combine 5 & 8 to make 13 she could also combine 3, 5, & 5 to make 13 Each solution is worth 1 point Or, points can be awarded for the number of parts used – combining 5 and 8 would yield 2 points; 3, 5, and 5 would yield 3 points Students then draw new cards, so that they have 6, until all of the small squares have been used. Play can continue using different center cards The student with the most points wins the game

65. Multicomponent Intervention for Math Fluency (Rhymer, Dittmer, Skinner and Jackson, 2000) Math facts CBM probes are administered to establish classroom baseline & obtain each student’s baseline rate of problems cpm Racetrack is shown to help explain automaticity Peer tutoring strategy is explained and modeled Entire class practices peer tutoring For 2 minutes, tutor presents flashcards (generated by A+ Math Flashcard Creator for free!) and tutee answers Correct → goes on a green circle Incorrect → goes on a red circle; tutee is told it’s incorrect & given correct answer; tutee writes problem & answer 3x on scratch paper before next flashcard is presented

66. Multicomponent Intervention for Math Fluency (Rhymer, Dittmer, Skinner and Jackson, 2000) Students exchange roles Each is tutored, then clock is set for 1 minute while each completes problems on their assessment sheets They exchange papers & score them using the red pens & answer key; or, scoring is completed in whole group by calling out answers Assessment sheets are collected to verify scoring accuracy & compute class average Each session begins by handing out previous assessments & giving the pairs few minutes to go over; students can graph own progress in their math folders Class progress is recorded on race track; class effort is praised Group contingencies/rewards for progress are given Students remain partnered for a week at a x

67. Free Time Increases the accuracy and completion rates of math class work with a group-oriented free-time contingency Assess students’ current level of math performance by calculating percent-correct scores on daily math drill sheets or weekly quizzes and/or administering Curriculum-Based Math Probes Calculate the average percent correct rate for the class – this score is used in the intervention procedures Students are told they will earn free time if the class correctly completes a specified average number of problems during each work session Set the free-time period from 5 to 15 minutes, depending on the length of the entire math period Using the class average percent correct rate you calculated, select a criterion for assignment completion that is 5% higher

68. Problem-Solving Strategies Using Question-Answer Relationships (QARs) to Interpret Math Graphics Structured Organizers Let Me Do It! Self-Monitoring Multi-Step Problems Intervention Based on PASS Theory SOLVE IT! for Secondary Grades SOLVE IT! for Primary Grades Structured Organizers FAST DRAW for Basic Math FAST DRAW for Algebra

69. Math Reasoning Strategies Let Me Do It! Self-Monitoring Multi-Step Problems Hands-On Equations Math Mnemonic Strategies: these are NOT interventions unless taught to mastery through Cognitive Strategy Instruction

70. General Steps in Teaching Cognitive Strategy Instruction 1. Teach any needed pre-requisite skills (based on pretest results) and activate prior knowledge 2. Describe the strategy to students with the help of a prompt or cue 3. Teach the cognitive strategy using small steps 4. Model the strategy using think-alouds 5. Students verbally rehearse the strategy and memorize it using a checklist 6. Support the strategy by having students do guided practice with corrective feedback as necessary 7. Students independently practice the strategy 8. Promote generalization, self-monitoring, and gaining mastery

71. Math Mnemonic Strategies ADD: Positive Integers ASSOC: the Associative Property COMAS: the Commutative Property DIST: the Distributive Property DRAW for Algebra DRAW for Basic Math FAST DRAW for Algebra FAST DRAW for Basic Math ORDER ROOT-IT SPIES Please Excuse My Dear Aunt Sally

72. FAST DRAW for Basic Math F – Find what you are solving for A – Ask yourself, "What information is given?" S – Set up the equation. T – Tie down the equation. Solve the problem if you can, or draw pictures to solve it using DRAW.

73. FAST DRAW for Basic Math continued D – Discover the sign. Find and circle the sign Say the name of the sign aloud. R – Read the problem. Say the problem aloud. A – Answer the problem or draw. Be sure to double-check your answer. W – Write the answer.

74. Please Excuse My Dear Aunt Sally This mnemonic strategy is designed to help students remember computational order P – Parentheses E – Exponents M – Multiplication D – Division A – Addition S – Subtraction

75. Please Excuse My Dear Aunt Sally Equation to Solve: 2 3 + (4 x 5) – 14 ÷ 2 = _____ Parentheses: 2 3 + ____ – 14 ÷ 2 = _____ Exponents: __ + ____ – 14 ÷ 2 = _____ Mult / Div: __ + ____ – ______ = _____ Add / Subtract: _________________ = _____ Answer: ___________

76. Intervention Fidelity

77. Also known as intervention integrity, treatment integrity, or intervention follow- through “The degree to which an intervention program is implemented as planned ” (Gresham et al., 2003) When interventions are implemented with fidelity, you can have greater confidence that the data really show whether or not the student is benefiting from the intervention Multifaceted – includes both content (how much?) and the process (how well?)

78. 5 Components of Intervention Fidelity Adherence – extent to which the steps and procedures of the intervention are followed as designed Quality of delivery – includes skill level, decision-making, and judgment by the person implementing the intervention Program differentiation – degree to which the intervention is different than and distinct from existing (e.g., Tier 1) practices Exposure – number, length, frequency, and duration of the intervention sessions Participant responsiveness – how well the student and the person implementing are engaged with the intervention (acceptability) (Dane & Schneider, 1998)

79. Characteristics that Influence Fidelity CharacteristicsCharacteristics that Facilitate Fidelity Characteristics that Discourage Fidelity Intervention - Acceptability - Rate of change produced -Complexity -Multiple resources -Time required Person Implementing Intervention -Level of training/education -Motivation -Resistance -Diversity of students worked with -Familiarity with other interventions that address same problem Student-Motivation -Cooperation -Difficult behavior -Severity or duration of problem (Perepletchikova & Kazdin, 2005)

80. Intervention Review Team (IRT) SST requests consultation by IRT May include administrators, curriculum specialists, instructional facilitators, psychologists, and other members of the RTI team Reviews Tier 3 interventions before a child can be referred to Tier 4 Completes bottom of Tier 3 Intervention Strategies form If intervention fidelity is not sufficient, appropriate steps should be taken and the intervention may be tried for an additional period If fidelity is sufficient but intervention strategies have not shown adequate progress toward goal, the student may be referred to Tier 4

81. Intervention Fidelity: Methods of Measurement Independent Observer IRT member(s) Drop by the classroom occasionally when intervention is occurring Uses a checklist (or intervention strategy write-up) that defines the essential components of the intervention Records whether each step is implemented and how long and how often the intervention occurs Most objective method, but also the most time- consuming

82. Intervention Fidelity: Methods of Measurement Teacher Self-Report Teachers rate their own adherence to an intervention Periodically review the steps of the intervention and rate whether each has been successfully carried out Should evaluate more frequently (e.g., every 1-3 days) when just beginning the intervention to ensure it is implemented properly, then reduce frequency (e.g., weekly) Less likely to skip important steps when using a prompt, but more subjective

83. Intervention Fidelity: Methods of Measurement Review of Permanent Products IRT member(s) Review materials created for intervention, staff training materials, schedule of implementation, progress monitoring data Complete Intervention Fidelity Checklist Objective and easy to implement, but may not fully reflect what is happening in the classroom

84. Intervention Fidelity Checklist

88. Progress Monitoring Math

89. Important things to remember about Progress Monitoring (PM) Remember that progress monitoring is designed to: Estimate rates of improvement Determine efficacy of instructional methods allowing for the creation of more effective, individualized instructional programs for problem learners It is not meant to: Assess every skill associated with math performance Be diagnostic

90. Traditional Assessments v. Progress Monitoring Traditional assessments: Lengthy Not administered on regular basis Do not provide immediate feedback Student is compared to national average Progress monitoring: Brief Conducted on a regular basis Assists with implementation/revisi on of interventions Analyze scores in relation to classroom/district performance

91. Commercial Products – Math PM Tools with Rigor

92. Available Tools for Purchase MBSP: Monitoring Basic Skills Progress: Basic Math Kit – Second Edition Kit Cost- $76 (blackline masters)/ Additional Manual- $25 Individual or group administered Computation Set of 30 reproducible tests for each grade level; Each test contains 25 Basic problems Grade 1 – Addition and subtraction Grade 2 – More complex addition and subtraction Grade 3 – Addition, subtraction, multiplication, and division Grade 4 and Grade 5 – Fractions and decimals with addition and subtraction Grade 6 – Fractions and decimals with multiplication and division www.Proedinc.com

93. MBSP: Monitoring Basic Skills Progress: Sample Computation Probe

94. MBSP: Monitoring Basic Skills Progress: Basic Math Kit – Second Edition Concepts and Applications Grades 2 through 6 Set of 18-25 reproducible tests for each grade level Grade 2 and Grade 3 – 18 problems per test; 24 problems per test. Counting; Number Concepts; Name of Numbers; Measurement; Money; Charts and Graphs; Fractions; Decimals; Applied Computations; and Word problems. Grade 4 – 24 problems per test. Number Concepts; Name of Numbers and Vocabulary; Measurement; Grid Reading; Charts and Graphs; Area and Perimeter; Fractions; Decimals; and Word Problems Grade 5 – 23 problems per test. Numeration; Money; Measurement; Geometry; Charts and Graphs; Fractions and Factors; Decimals; Applied Computation; and Word Problems Grade 6 – 25 problems per test. Numeration; Applied Computation; Measurement; Geometry; Percentages; Charts and Graphs; Word Problems; Ratios and Probability; Proportions; and Variables.

95. MBSP: Monitoring Basic Skills Progress: Sample Concepts & Applications Probe

96. Available Tools for Purchase PASeries Mathematics Paper and pencil or on-line administration For grades 3-8 Screening test for placement Six progress-monitoring tests for each grade Diagnostic tests by strand for targeting instruction Number and Operations Geometry Algebra (patterns and functions) Data analysis and probability Measurement Cost… unknown???

97. PASeries Mathematics Sample Item

98. Available Tools for Purchase PASeries Algebra I For grades 6-12 Six progress-monitoring tests Five diagnostic tests - one in each content strand per grade Foundations of functions Linear Functions, equations and inequalities Nonlinear functions and equations Representing quantitative relationships Applications of algebra

99. PASeries Algebra I Sample Item

100. Star MATH – PM graph for individual student

101. Yearly Progress Pro – Tracks Toward Mastery

102. CBM for Progress Monitoring Extremely effective for Planning intervention efforts Monitoring progress Refining and adjusting intervention efforts (Bryant & Rivera, 1997) When CBM is used More significant gains are made Gains are made at more rapid rates (Vaughn & Bos, 2009)

103. Conducting Curriculum-Based Measurement Step 1: Place students in a math curriculum-based measurement task for progress monitoring Step 2: Identify the level of material for monitoring progress Step 3: Administer and score math curriculum-based measurement probes Number Identification Quantity Discrimination Missing Number Computation Concepts and Applications Step 4: Graph scores and set ambitious goals

104. Place students in a Math Curriculum-Based Measurement Task Kindergarten – 1 st grade Number Identification Quantity Discrimination Missing Number Grades 1-6 Computational Grades 2-6 Concepts and Applications Students in the earlier grades should use the Computation probes until the Concepts and Application probes are appropriate for the grade-level material from the curriculum

105. Identify the Level of Material If student is performing well below grade-level expectations, use lower-grade probe Conclude grade level by: Determining expected grade-level by year’s end Administer CBM test at a grade level lower than grade-appropriate level Avg. score between 10 -15 digits or blanks, use this lower grade-level test Avg. score less than 10 digits or blanks, move down one more grade level or stay at original lower grade level and repeat procedure Avg. score greater than 15 digits of blanks, reconsider grade-appropriate material Progress monitor at established grade level for the entire school year

106. Number Identification 84 items Requires the student to orally identify numbers between 0-100 Can be used as screening tools or progress monitoring

107. Administration and Scoring: Number Identification Administered individually Present the student with student copy of Number Identification test Place administrator copy on clipboard and position so it is not visible to student

108. Sample Number Identification: Student The actual Number Identification student copy is 3 pages long.

109. Sample Number Identification: Administrator

110. Scoring Number Identification Correct: student correctly identified the number Incorrect: student hesitated or struggled with a problem for 3 seconds or gave the wrong answer

111. Quantity Discrimination 63 items Requires the student to orally identify the bigger number from a pair of numbers 0 through 20 Can be used as a screening tool or for progress monitoring

112. Administration and Scoring: Quantity Discrimination Administered individually Present the student with student copy of Quantity Discrimination test Place administrator copy on clipboard and position so it is not visible to student

113. Sample Quantity Discrimination: Student The actual Quantity Discrimination student copy is 3 pages long.

114. Sample Quantity Discrimination: Administrator

115. Missing Number 63 item Requires the student to orally identify the missing number is a sequence of four numbers Can be used as a screening tool or for progress monitoring

116. Administration: Missing Number Administered individually Present the student with student copy of the Missing Number test Place administrator copy on clipboard and position it is not visible to student

117. Sample Missing Number: Student

118. CBM Computation Administer to group 25 computational problems CBM probes remain similar in content from test to test Time limits: GradeTime limit 12 minutes 2 33 minutes 4 55 minutes 66 minutes

119. Sample 6 th Grade Computation Probe

120. Administration of Computation Teacher: It’s time to take your weekly math test. As soon as I give you the test, write your first name, your last name, and the date. After you’ve written your name and the date on the test, turn your paper over and put your pencil down so I know you are ready. I want you to do as many problems as you can. Work carefully and do the best you can. Remember, start at the first problem and work left to right. Some problems will be easy for you; others will be harder. When you come to a problem you know you can do, do it right away. When you come to a problem that’s hard for you, skip it, and come back to it later. Go through the entire test doing the easy problems. Then go back and try the harder ones. Remember that you get points for getting part of the problem right. So, after you have done all the easy problems, try the harder problems. Do this even if you think you can’t get the whole problem right. (For appropriate grade levels, say, “Remember to reduce fractions to the lowest terms unless the problem specifies to do something differently. Be sure to write out your remainder if the division problem has one.”) When I say, “Begin,” turn your test over and start to work. Work for the whole test time. You should have enough room to do your work in each block. Write your answers so I can read them. If you finish early, check your answers. When I say, “Stop,” put your pencil down and turn your test face down.

121. Scoring CBM Computation Students score 1pt for each correctly answered digit Correct amount of digits = student’s score Score addition, subtraction, and multiplication: right to left Division: left to right Decimals: begin at decimal point and work outwards Placement of decimal is the most critical aspect Fractions: right to left for all parts evaluate each digit in the whole number part apart from the fractional part evaluate each digit in the numerator separately from the denominator

122. Scoring Different Operations

123. Scoring Division with Remainders

124. Scoring Decimals & Fractions

126. How many digits did Samantha get correct?

127. Computation 5 Answers A. 11/35 B. 2.397 C. 73,615 D.1D.1 E. 18,600 F. 5 10/11 G. 17,424 H.2H.2 I. 35026 J. 17/2 K. 2/3 L. 5 1/3 M. 8.652 N. 8 1/5 O. 74,772 P. 90 R6 Q. 1/4

129. 49

130. Concepts and Applications 18-25 math computation problems Each test is 3 pages long Example: Grade 3: every test includes two problems dealing with charts and graphs and three problems dealing with number concepts Other types of problems remain similarly constant

131. Concepts and Application: Administration Administer to a group of students Present each student with test Establish set amount of time for test Timing is critical to ensure consistency from test to test GradeTime limitNumber of blanks 28 minutes18 blanks 36 minutes24 blanks 46 minutes24 blanks 57 minutes23 blanks 67 minutes24 or 25 blanks

132. Sample CBM Concepts and Application Probe

133. Sample CBM Concepts and Application Probe (continued)

134. Scoring CBM Concepts and Application Students score 1pt for each correctly answered blank Correct amount of blanks = student’s score Scoring: Multiple choice: 1 blank Some questions may contain more than one blank

135. How many blanks did Quinten answer correctly?

136. 10

137. End of Year Benchmarks CBM Progress Monitoring

138. Team Work: Case Study Create an Intervention Plan Look at the individual student data in the case study. Use your CD and team knowledge to complete a Tier 2 intervention plan for the student.

139. Team Work: Case Study Evaluate an Intervention Plan Look at the individual student data in the case study. Use data-based decision making to evaluate the student’s response to Tier 3 intervention.

140. Adequate Response to Intervention?