assessment article reflection

Data-Based Individualization

Using Data-Based Individualization to Intensify Mathematics Intervention for Students With Disabilities Sarah R. Powell and Pamela M. Stecker

Riverview Middle School serves students in Grades 5 through 8. Molly, a sixth grader at the school, receives special education services on the basis of a specific Learning disability in mathematics. Molly's special education teacher, Mr. Drummond. works with Molly five days a week, but Molly is demonstrating minimal progress with the current intervention. Mr. Drummond is especially concerned about Molly's understanding of fractions because of the emphasis on fractions with new standards and standardized assessments at the school. Mr. Drummond does not want to ignore all of the intervention work already conducted with Molly, so he decides to use principles for intensifying instruction as well as Molly's progress monitoring data to try to better meet her individual needs and to inform his decision making about whether these intervention changes are working as desired for Molly.

Data-based individualization (DBI) is a continuous process connecting assessment and intervention (see Fuchs, Fuchs, & Vaughn, this issue). DBI provides teachers like Mr. Drummond with an evidence-based method for

individualizing interventions for students who do not demonstrate adequate response. Assessment data gathered through flie use of progress monitoring help teachers analyze and determine ways to modify components of intervention. After teachers make instructional modiflcations, they continue to use progress monitoring data to determine whether these adaptations are acceptable or whether subsequent adaptations must be made. Consequently, DBI is an iterative process that involves (a) adapting instruction using principles of intensive intervention and evidence-based practices and (b) implementing these adaptations consistently and regularly. Progress monitoring probes used to evaluate the success of each intervention should be technically sound and conducted at least weekly. At periodic intervals (depending upon the frequency of data collection and the length of the intervention), a progress check helps teachers compare individual student progress to goal expectations. In addition, teachers

may use informal diagnostic assessment, such as analyzing student responses on the probes and following up with an interview while the student works selected problems, to gain insight about student strengths and weaknesses. This process is repeated, as the teacher continues to build a more effective instructional program for a particular student across time.

The National Center on Intensive Intervention (NCII; www.intensiveinter vention.org) has identifled the

TEACHING EXCEPTIONAL CHILDREN | MARCH/APRIL 2014 31

principles of and processes for intensive intervention (Fuchs et al., 2008: Vaughn, Wanzek, Murray, & Roberts, 2012):

• smaller steps, • precise language, • repeat language, • student explains, • modeling, • manipulatives, • worked examples, • repeated practice, • error correction, • fading support, • fluency, and • move on.

In this article, we illustrate how Mr. Drummond uses DBI to strengthen Molly's skills by intensifying her instruction within the multitiered system of support in place at Riverview Middle School. Mr. Drummond's approach to applying the principles of intensive intervention also illustrates how tracking student progress informs instructional decisions about the effectiveness of intervention adaptations.

Implementing DBI

When Molly started at Riverview Middle at the beginning of fifth grade, her general education teacher, recognizing that Molly was struggling, paid closer attention to Molly's work and tried to provide additional assistance to Molly and two of her classmates who also were performing below standards. Molly's teacher monitored their mathematics performance using computation progress monitoring probes. Figure 1 provides sample items from a fifth- grade probe that reflects the computational skills outlined by the Common Core State Standards (CCSS; National Governors Association Center for Best Practices & Council of Chief State School Officers, 2010) and matches the curriculum used in Molly's school.

At this stage (Tier 1), Molly's teacher was following the system of support used at Riverview Middle School: weekly progress monitoring

of students who did not meet the beginning benchmark for fifth grade. After 8 weeks of monitoring and instruction, Molly continued to demonstrate inadequate growth and an inadequate end level, so she was included in small-group tutoring in mathematics (Tier 2).

At Tier 2, Molly also participated in 18 weeks of a standardized, small- group tutoring program. Riverview Middle uses this intervention platform for all fifih-grade students targeted as needing additional assistance in mathematics. The emphasis of this supplementary program is building fluency with multiplication and division facts and computational algorithms. Students also focus on fraction and decimal concepts. Molly's Tier 2 tutor administered computation progress monitoring probes on a

Assessment data gathered through the use of progress monitoring help teachers analyze and determine ways to modify components of

intervention.

weekly basis. Despite 18 weeks of intensive tutoring, Molly still failed to demonstrate an adequate slope or an adequate end-level performance, so she was referred for a special education evaluation. (Although many schools complete three or four tiers of intervention before special education referral, Riverview Middle uses a three-tier model with the third tier as special education.) During the evaluation process, other factors, such as an intellectual disability and emotional/behavioral disorder, were ruled out as contributing to Molly's difficulty with mathematics. In addition to administering a standardized, norm-referenced assessment in mathematics, the progress monitoring data collected during the first two tiers helped to corroborate Molly's learning disability in the area of mathematics, and the school developed an

individualized education program (IEP) for Molly in the area of mathematics. The school year, however, was at its end by this point in time, so IEP implementation began at the beginning of Molly's sixth-grade year.

Planning

Setting Molly's goal. Following the summer break, Molly entered sixth grade, and Mr. Drummond began to implement interventions to respond to Molly's mathematics difficulties. He reviewed the work conducted for Molly's IEP development and consulted the NCII website. Because Molly's performance had been so weak during the fifih grade, the IEP team decided that Molly's computational goal should focus on fifth-grade content and standards and recommended that fifth-grade progress monitoring probes continue to he used to track Molly's progress toward meeting her annual goal. Molly's present level of performance in computation on fifth- grade probes was included in the IEP: Given 25 computational problems sampled randomly from the fifth-grade curriculum, Molly currently writes 12 digits correct in answers in 6 minutes.

Afier consulting normative data about typical growth on the probes, the team decided that a growth rate of 0.9 digits correct per week would be an appropriately ambitious rate of improvement for Molly to help close in the widening gap between her performance and that of her peers. With 36 weeks to the end of the school year, the team multiplied the growth rate of 0.9 digits per week by 36 weeks to yield an improvement of approximately 32 digits; Molly's IEP computational goal read: Given 25 computational problems sampled randomly from the fifth-grade curriculum, Molly will write 44 digits correct in answers in 6 minutes by the end of the school year.

Diagnosing Molly's performance. Based on his work with Molly and her performance on computation progress monitoring probes, Mr. Drummond knows that Molly does well with whole-number computation. After

32 COUNCIL FOR EXCEPTIONAL CHILDREN

Figure 1 . Sample Fifth-Grade Computation Progress Monitoring Probe

9.14 -1- 33.26

4

'̂ 4 5

.08 )9.44

4.6 )37.72

3 4

3.3 + 6.14

4.35 X .96

^x7 = 4

5 + 3 = 6 4

4598 -1- 7006

82.04 - 7.99

7 7

36 )7488

10605 - 929

9 3

6 8

7 _ 2 = 8 5

560 X 27

5 6

6 x 2 = 7 5

12.77 - .96

.56 X 7

8 - 2 = 9 9

consulting the CCSS and reading about the importance of understanding fractions for later mathematics competence (Bailey, Hoard, Nugent, & Geary, 2012), Mr. Drummood focuses on Molly's skill with fractions. Examining Molly's performance on the fifth-grade probes, he had noticed that, although Molly got some digits correct in the answers, she missed parts of all 13 fractions items represented on the measure as well as six of eight problems involving decimals.

Establishing instructional objectives. Mr. Drummond refers to the CCSS, the progress monitoring probes, and Molly's performance to determine the critical content for instruction. He groups Molly's instructional objectives as they related to (a) adding and subtracting fractions with like and unlike denominators, [b) multiplying fractions by fractions and whole numbers, (c) dividing fractions by whole numbers and dividing whole numbers by fractions, and [d) performing all four operations with decimals.

Making an assessment plan. Because Molly's IEP requires regular progress monitoring using probes at the flfth-grade level, Mr. Drummond administers probes for 6 minutes on the last day of school each week. He grades Molly's performance while Molly watches, and then helps Molly graph her own score. Mr. Drummond also decides to periodically check Molly's progress [every 3-4 weeks) on sixth-grade probes to see how she performs on grade-level content and to check whether Molly is able to generalize her new skills to more difflcult problems. He decides to implement intensive intervention for 9 weeks before determining whether the intervention is helping Molly to stay on track toward meeting her IEP goal.

Preparing to implement DBI and making instructional adaptations. After consulting resources on the NCII website, Mr. Drummond chooses three principles to incorporate when adapting instruction during the first phase of Molly's intervention to make it more intensive [see Eigure 2) :

• Smaller steps: Mr. Drummond plans to use a task analysis to break specific fraction problems into smaller steps.

• Modeling: Mr. Drummond reads more about modeling from the teacher's perspective and how to engage the student in active involvement.

• Manipulatives: A conference with one of the mathematics teachers at Riverview Middle helps Mr. Drummond to learn more about appropriate manipulatives for teaching fractions.

Intensive Intervention A

Considering Molly's weak performance and the importance of understanding and using fractions for future mathematics success, Mr. Drummond determines that the focus of Molly's intervention adaptation should include addition, subtraction, multiplication, and division of fractions. Considering sequence of skills, Mr. Drummond decides to focus on comparing fractions before working on addition and subtraction of fractions. He also thinks it is best to work on addition and subtraction before moving onto multiplication and division.

DBI. Using the principle of smaller steps, Mr. Drummond teaches Molly to

Figure 2 . Molly's Intensive Intervention

iv e

it io

In t

In te

assm

L sas

Smaller steps

Modeling

Manipulatives

nt ei

er v

IMPLEMEHTED PHINCIPUES

(all from A) J

Repeated practice |

Error correction |

Precise language |

V .S

l»PLE»iNri!DPI>l»aplES

(all from A and B)

'S g | | ¡ Worked examples

nt e

er v <

Student expia ns

Fading support

TEACHING EXCEPTIONAL CHILDREN | MARCH/APRIL 2014 33

flrst check to see if the denominators are the same when comparing fractions. If denominators are alike, Molly can compare the numerators to determine which fraction is greater. If the denominators are not the same, Mr, Drummond teaches Molly how to flnd the least common denominator (LCD), Mr, Drummond breaks this process into even smaller steps so Molly knows what to do. Learning how to calculate the LCD of two fractions will help Molly with addition and subtraction of fractions, so Mr, Drummond believes this time is well spent.

The second principle Mr, Drummond incorporates in Molly's intensive intervention is modeling, Mr, Drummond exphcitly models how to flnd the LCD by saying:

First, let's find the multiples of 4. Whaf s 4 times 1? (4) Whaf s 4 times 21 (8) Whaf s 4 times 3? (12) Whaf s 4 times 4? (16). Multiples are the answer to multiplication problems with the same number. So, to find the multiples, think of the number times 1, times 2, times 3, times 4, and keep going. What are the multiples of 4? Lefs say them together: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40. Thaf s enough multiples for now!

The third principle Mr. Drummond incorporates in Molly's instruction is using manipulatives, Mr. Drummond usually uses fraction circles to help students understand fractions. Because Molly has not been performing well with fractions, Mr, Drummond decides to use other fraction manipulatives, such as fraction bars and two-color counters (see Figure 3), Fraction bars allow Molly to identify

Figure 3 . Comparing Fractions With Fraction Bars and Two-Color Counters

Figure 4 . Molly's Computation Scores, Intensive Intervention Phase A

Compare 3/5 to 1/2 with fraction bars. Which is greater?

Compare 3/5 to 1 /2 with two-color counters. Which Is greater?

9 11 13 15 17 19 21 23 25 27 29 31 33 35 Weeks of Instruction

Note: The blue diamonds are Molly's scores. The black line over the blue diamonds is Molly's trend line. The green dot is Molly's end-of-year goal. The green line is Molly's goal line.

which of two fractions is longer (i,e., the greater fraction), and fhe two-color counters help her identify the LCD, Molly can change the denominator easily with the two-color counters by adding or subtracting counters.

Progress check. After 9 weeks of instruction, Mr. Drummond evaluates Molly's progress monitoring graph to determine whether the intervention has kept Molly on track toward her IEP goal (see Figure 4), Although

last three progress monitoring probes Mr. Drummond reahzes that the only fraction problems Molly answers correctly are addition or subtraction with like denominators.

Intensive Intervention B. Mr, Drummond decides to continue instruction in fractions with unlike denominators using the principles of intensive intervention from Intensive Intervention Phase A (i.e., smaller steps, modeling, manipulatives).

Although Molly's performance is improving very gradually ... Mr. Drummond recognizes that,

at this slow rate of improvement, Molly is not likely to meet her year-end goal and that it is time

to make another intervention adaptation.

Molly's performance is improving very gradually, the trend of her current progress is much less steep than her goal line, Mr. Drummond recognizes that, at this slow rate of improvement, Molly is not likely to meet her year-end goal and that it is time to make another intervention adaptation to try to increase Molly's rate of improvement. Although Molly is performing fairly well on whole- number computation problems, hy conducting an error analysis of Molly's

while incorporating three additional principles to further intensify instruction: providing repeated practice, correcting errors, and using precise language.

DBI. With repeated practice, Mr, Drummond provides multiple addition and subtraction problems for Molly to practice on a daily basis. He switches between addition and subtraction, so Molly learns to be aware of the operator signs (i.e., -i-, -) and

34 COUNCIL FOR EXCEPTIONAL CHILDREN

Figure 5. iVIelly's Computation Scores, Intensive intervention Piiase B

13 15 17 19 21 23 Weeks of Instruction

25 27 29 31 33 35

Note; The blue diamonds are Molly's scores. The black vertical line denotes the shift from Phase A to Phase B. The black hne over the blue diamonds is Molly's trend line during Phase B. The green dot is Molly's end-of-year goal. The green hne is Molly's goal line.

what the signs mean. By incorporating both operator signs, Molly also practices discriminating among problem types.

In an effort to improve Molly's self-esteem about mathematics, Mr. Drummond had shied away from correcting all of Molly's errors during Phase A. He realizes now that he may have been doing her a disservice, as one of the guiding principles of intensive intervention is to correct errors. In Intensive Intervention Phase B, when Molly makes an error, Mr. Drummond says, "Let's look at this part again." Then, he and Molly work through the mistakes with Mr. Drummond asking questions to guide Molly's thinking. Sometimes Mr. Drummond models how to do a part of a problem (e.g., finding the LCD, changing a mixed fraction into an improper fraction), and then asks Molly to solve a similar problem.

Mr. Drummond generates a hst of important vocabulary words related to fractions—numerator, denominator, LCD, multiple, like, and unlike—and then takes time to provide Molly with precise definitions of each term (e.g.. The numerator is the number of parts of the whole). Mr. Drummond also reviews the way he explains the steps of adding and subtracting fractions, and tries to make his teaching steps more direct and his language precise.

Progress check. Mr. Drummond continues to monitor Molly's progress using fifth-grade computation probes. After the intervention's 9-week second phase, the number of Molly's correct digits and the overall trend of her improvement have increased (see Figure 5). Mr. Drummond is pleased and recognizes that intensifying instruction seems to be helping Molly. Because the trend of Molly's current progress, however, is still not as steep as it needs to be for Molly to reach her year-end goal, Mr. Drummond decides to implement another round of intervention adaptations. He conducts an error analysis on Molly's last three computation probes to better understand where she is struggling, and realizes that although Molly is solving most addition and subtraction fraction problems correctly, she is not able to correctly answer any multiplication and division problems.

Intensive Intervention C

Molly's data have convinced Mr. Drummond that using the principles of intensive intervention has helped Molly be more successful with her mathematics. In addition, Mr. Drummond thinks that incorporating these principles has made him more conscious of the details of instructional design and of

his own decision making during instructional delivery; his instructional skills are improving along with Molly's performance. Because Molly still is not proficient with the fraction problems on the probes, Mr. Drummond decides to incorporate three more principles for intensive intervention: using worked examples, asking the student to explain, and fading support.

DBI. Mr. Drummond begins Intensive Intervention Phase C by continuing to reinforce addition and subtraction of fractions, but he also introduces muhiplication of fractions. With multiplication, Mr. Drummond starts off using worked examples. With a worked example, the answer is already provided; the idea is to engage the student in a conversation about how the work was completed. Worked examples help Molly understand procedures and concepts as she works on developing knowledge of the steps involved in solving a specific type of problem. Molly often refers back to the worked example while she is working new problems to compare her steps against those shown in the worked example.

As Molly gains proficiency, Mr. Drummond removes

the worked examples and Molly does more problems on her own.

To reinforce Molly's understanding of addition and subtraction with like and unlike denominators, Mr. Drummond asks Molly to explain or to instruct him on how to solve specific problems. By getting Molly to talk about her fractions work, Mr. Drummond is able to check for (a) understanding of concepts,

(b) correct use of vocabulary, and (c) understanding of procedures. Molly is a little hesitant at the beginning to talk aloud about her mathematics work, so Mr. Drummond first models how he would talk about solving a problem, and then Molly gives it a try. Mr. Drummond also uses this strategy when asking Molly to make corrections; having Molly explain to him how she

TEACHING EXCEPTIONAL CHILDREN | MARCH/APRIL 2014 35

Figure 6 . Molly's Computation Scores, Intensive Intervention C

13 15 17 19 21 23 Weeks of instruction

25 27 29 31 33 35

Note: The blue diamonds are Molly's scores. The black vertical line denotes the shifts between phases. The black line over the blue diamonds Is Molly's trend line during Phase B. The green dot is Molly's end-of-year goal. The green line is Molly's goal line.

Figure 7 . Principles of Intensive intervention and DBI

Principles

?

en si

In t

c

ti o

'v en A

In te

l

Implen^nttd Principles

PROGRISSCHECIC.

Smaller Steps

Precise language

JRepeat language

Student explains

[Modeling

>

«

o

>UJ V1

Implemented Principles

(all/some from A)

1 [Manipulatives

PROGRESS CHECK...

Worked examples

I Repeated practice^

I Error correction

[Fading support

¡Fluency

[ Move on

LS

U te

n si

l i o r

e rv

e n

t

u Impleinented Principles

(all/some from A, B)

PROGRESS CHECK...

n te

n si

ve

o

1Û Implemented Principles

(all/some from A, B,C)|

PROGRESS CHECK...

Note: Visit the National Center on Intensive Intervention website (www.intensiveintervention.org) for information and resources on academic and behavioral progress monitoring, enhancing instruction, and implementing intensive intervention.

worked the missed problem helps her to identify where she made mistakes.

Finally, Mr. Drummond realizes Molly needs to be able to complete mathematics problems on her own in her general education classroom or at home: He decides to begin fading support during instruction. Mr. Drummond decides to do less modeling and give Molly more independent practice on items where she is showing accuracy. When Molly appears to require support on a particular problem type, Mr. Drummond provides prompts while asking her to talk through the steps. As Molly gains proflciency, Mr. Drummond removes the worked examples and Molly does more problems on her own. In this way, Mr. Drummond fades support based on Molly's performance on speciflc types of problems. Mr. Drummond continues to incorporate the principles for intensifying intervention when he introduces new topics (e.g., introducflon to division of fractions), but he fades support systematically in areas where Molly is doing well. In this way, Molly is able to develop independence in mathematical problem solving.

Progress check. After 9 weeks of implementing these additional principles for intensifying instruction, Mr. Drummond reviews Molly's progress (see Figure 6). Molly has acquired so much skill that the trend of her progress is now steeper than the goal line. Although Molly has not yet reached her actual goal, she is on track toward meeflng (and actually exceeding) her goal by the end of the year. Mr. Drummond will meet with the IEP team to discuss the possibility of raising Molly's goal; trying to accelerate Molly's progress even more will help to narrow the gap between Molly's performance and that of her peers. Because Molly has not met her goal yet for fifth-grade problems and because he has seen only slight improvement on his monthly checks on sixth-grade probes, Mr. Drummond thinks It is premature to change the goal and progress monitoring to reflect sixth-grade standards. He anticipates, however, that Molly will be able to transition to more difflcult material

36 COUNCIL FOR EXCEPTIONAL CHILDREN

during the following year and may show even faster rates of improvement in the future, especially if he continues to use principles of DBI to monitor Molly's growth and to adapt instructional interventions to better meet her needs.

Conclusion

Many schools are using multitiered systems of support for students with mathematics disabilities (Gersten et a l , 2009), so it is necessary for teachers to understand how to use DBI to create instructional programs that benefit individual students. As highlighted in this special issue of TEAGHING Exceptional Ghildren, DBI is an iterative process that teachers can use to create intervention adaptations and to determine whether these adaptations are appropriate or need to be changed. Many students like Molly are expected not only to meet IEP goals but also to perform well on standardized assessments aligned with the CCSS; teachers therefore need to be able to individualize instruction to help students meet or exceed individual and district goals (Jitendra, 2012; Powell, Fuchs, & Fuchs, 2013). Figure 7 provides a structure to support educators like Mr. Drummond in identifying a process for intensifying interventions, to more closely respond to students' instructional needs.

References

Bailey, D. H., Hoard, M. K., Nugent, L., & Geary, D. C. (2012). Competence with fractions predicts gains in mathematics achievement. Journal of Experimental Child Psychology, 113,

447-455. http://dx.doi.Org/10.1016/j/ jeep.2012.06.004

Fuchs, L. S., Fuchs, D., Powell, S. R., Seethaler, P. M., Cirino, P. S., & Fletcher, J. M. (2008). Intensive intervention for students with mathematics disabilities: Seven principles of effective practice. Learning Disability Quarterly, 31, 79-92.

Gersten, R., Beckmann, S., Clarke, B., Foegen, A., Marsh, L., Star, J. R., & Witzel, B. (2009). Assisting students struggling with mathematics: Response

to intervention (Rtl) for elementary

and middle schools (NCEE 2009-4060). Washington, DC: Institute of Education Sciences, U.S. Department of Education.

Jitendra, A. K. (2012). Understanding and accessing standards-based mathematics for students with mathematics difficulties. Learning Disability Quarterly, 36, 5-8. http://dx.doi .org/10.1177/0731948712455337

National Governors Association Center for Best Practices & Council of Chief State School Officers. (2010). Common core state standards for mathematics.

Washington, DC: Author.

Powell, S. R., Fuchs, L. S., & Fuchs, D. (2013). Reaching the mountaintop: Addressing the Common Core State Standards in mathematics for students with mathematics difficulties. Learning Disabilities Research and Practice, 28,

38-48. http://dx.doi.org/10.1111/ ldrp.12001

Vaughn, S., Wanzek, J., Murray, C. S., & Roberts, G. (2012). Intensive interventions for students straggling in

reading and mathematics: A practice

guide. Portsmouth, NH: RMC Research Corporation, Center on Instruction.

Sarah R. Powell (Texas CEC), Assistant Professor of Special Education,

University of Texas at Austin, Austin, Texas;

Pamela M. Stecker (South Carolina CEC), Professor of Special Education, Clemson

University, South Carolina.

Address correspondence regarding this

article to Sarah R. Powell, 1 University

Station, D5300, Austin, TX 78712

(e-mail: srpowell®austin,utexas.edu).

This work was supported in part by the

National Center on Intensive Intervention

(Grant No. H326Q110005), which was

awarded to the American Institutes for

Research by the Office of Special Education

Programs, U.S. Department of Education

(Celia Rosenquist, QSEP Project Officer),

The views expressed herein do not

necessarily represent the positions or

polices of the U.S. Department of

Education. No official endorsement by the

U,S, Department of Education of any

product, commodity, service, or enterprise

mentioned in this publication is intended

or should be inferred.

TEACHING Exceptional Children, Vol. 46, No, 4,pp, 31-37,

Copyright 2014 The Author(s),

Teachers change lives. Ĵife'U change

yours. Meredith Colleges coeducational Master of Education and Master of Arts in Teaching programs develop highly qualified special education teachers—and our strong reputation in teacher education is recognized nationally.

Learn more today at

meredith.edu/graduate/education

MEREDITH ^ - C o L L E G E

Graduate Programs

Meredith's John E. Weems Graduate School admits qualified students without regard to race, creed, gender, sexual orientation, age or disahility. ¡3-074

GET YOUR EDITION OF THE NASCO SPECIAL EDUCATION CATALOG. • Sensory Products • Assistive Technology

• Language, Communication, & Reading

• Basic Math, Money & Time • Life Skills

• Arts & Cratts • Resources

•Therapy Supplies • And More!

1-80Û-558-9595 Shep ealine

S3

TEACHING EXCEPTIONAL CHILDREN | MARCH/APRIL 2014 37

Copyright of Teaching Exceptional Children is the property of Council for Exceptional Children and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use.