rti institute: math module for elementary schools carroll county schools sharon rinks, psy.d. lisa...

RTI Institute: Math Module for Elementary Schools Carroll County Schools

Sharon Rinks, Psy.D. Lisa Sirian, Ph.D.

Michelle Avila Bolling, Ed.S., NCSPCarroll County Schools

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

Round Robin Problem Solving for RTI

Challenges1. 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?

Exploring Evidence-Based RTI Practices for Math

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)

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)

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)

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)

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)

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


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.”


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

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

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

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)

● ● ●

● ● ●

● ●

● ● ● ●


Counting skills 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)


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)

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.

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.

Universal Screening

Mathematics

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


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

AIMSwebSample Probe– Computation

AIMSwebSample Probe–Basic Mult & Div Facts

Benchmarks for Math- Correct Digits

Grade Fall Winter Spring Mean ROI

1 5 11 15 .3

2 10 22 22 .3

3 15 24 28 .4

4 33 44 52 .5

5 30 38 47 .5

6 28 36 34 .2

7 30 36 35 .1

8 33 40 37 .1

IMPORTANT NOTE: THESE NORMS ARE ALL FOR 2 MINUTES grades 1-3 and 4 MINUTES grades 4+ -- From AIMSweb, 2007


Star Math Concepts addressed

Computation Application Concepts

Grades 1-12 Unlimited forms available Computer administered www.renlearn.com

STAR Math – Two Stage Assessment

STAR Math- Growth Report

STAR Math- Progress Monitoring Report Monitor WHOLE CLASS Progress

STAR Math- Can help identify intervention & PM target


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

Yearly Progress ProSample Test Item

Yearly Progress Pro- Instructional Component Item

Yearly Progress Pro-Individual Class Reports

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

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

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

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)

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

Setting Goals Challenge Activity

Pair up and do the math!

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.

Susan’s Writing



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.

April’s Reading



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.

Sabrina’s Math Concepts

subtract baseline from benchmark to get amount of gain needed 15-5=10


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.

Sydney’s Computation Skills

subtract baseline from benchmark to get amount of gain needed 20-5=15


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.

Interventions

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

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

The Number Game: 0 to 10

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

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

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

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

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

Money Match

A game that helps students learn to count change

The object of the game is to be the 1st player to earn a set amount of change

1st 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

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

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

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

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 1st 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

Folding-In continued

The groups of 8 facts (1 unknown and 7 known) are shuffled. The 2nd unknown fact is then presented and folded-in among the other 8 facts. This is repeated again for the 3rd 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

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

Number Goal Game 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

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

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

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

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

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

General Steps in Teaching Cognitive Strategy Instruction1. Teach any needed pre-requisite skills (based on

pretest results) and activate prior knowledge2. Describe the strategy to students with the help of a

prompt or cue3. Teach the cognitive strategy using small steps 4. Model the strategy using think-alouds5. Students verbally rehearse the strategy and

memorize it using a checklist6. Support the strategy by having students do guided

practice with corrective feedback as necessary7. Students independently practice the strategy8. Promote generalization, self-monitoring, and gaining

mastery

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

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.

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.

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

Please Excuse My Dear Aunt Sally

Equation to Solve: 23 + (4 x 5) – 14 ÷ 2 = _____

Parentheses: 23 + ____ – 14 ÷ 2 = _____ Exponents: __ + ____ – 14 ÷ 2 = _____ Mult / Div: __ + ____ – ______ = _____ Add / Subtract: _________________ = _____ Answer: ___________

Intervention Fidelity

Intervention Fidelity

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?)

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)

Characteristics that Influence Fidelity

Characteristics Characteristics 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)

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

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

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

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

Intervention Fidelity Checklist

Progress Monitoring

Math

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

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/revision of interventions

Analyze scores in relation to classroom/district performance

Commercial Products – Math PM Tools with Rigor

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

MBSP: Monitoring Basic Skills Progress: Sample Computation Probe

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.

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


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???

PASeries MathematicsSample Item


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

PASeries Algebra ISample Item

Star MATH – PM graph for individual student

Yearly Progress Pro – Tracks Toward Mastery

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)

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

Place students in a Math Curriculum-Based Measurement Task

Kindergarten – 1st 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

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

Number Identification

84 items Requires the student to orally identify

numbers between 0-100 Can be used as screening tools or progress

monitoring

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

Sample Number Identification: Student

The actual Number Identification student copy

is 3 pages long.

Sample Number Identification: Administrator

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

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

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

Sample Quantity Discrimination: Student

The actual Quantity Discrimination student copy is 3 pages long.

Sample Quantity Discrimination: Administrator

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

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

Sample Missing Number: Student

CBM Computation

Administer to group 25 computational

problems CBM probes remain

similar in content from test to test

Time limits:

Grade Time limit

1 2 minutes

2 2 minutes

3 3 minutes

4 3 minutes

5 5 minutes

6 6 minutes

Sample 6th Grade Computation Probe

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.

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

Scoring Different Operations

Scoring Division with Remainders

Scoring Decimals & Fractions

How many digits did Samantha get correct?

Computation 5 Answers

A.

11/35

B.

2.397

C.

73,615

D.

1

E.

18,600

F.

5 10/11

G.

17,424

H.

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

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

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

Grade Time limit Number of blanks

2 8 minutes 18 blanks




6 7 minutes 24 or 25 blanks

Sample CBM Concepts and Application Probe

Sample CBM Concepts and Application Probe (continued)

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

How many blanks did Quinten answer correctly?

End of Year Benchmarks CBM Progress Monitoring

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.

Team Work: Case StudyEvaluate 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.

Adequate Response to Intervention?

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