http://isc.sagepub.com/Intervention in School and Clinic

http://isc.sagepub.com/content/42/4/198The online version of this article can be found at:

 DOI: 10.1177/10534512070420040201

2007 42: 198Intervention in School and ClinicAllison J. Fahsl

Mathematics Accommodations for All Students  

Published by:

  Hammill Institute on Disabilities

and

http://www.sagepublications.com

can be found at:Intervention in School and ClinicAdditional services and information for    

  http://isc.sagepub.com/cgi/alertsEmail Alerts:

 

http://isc.sagepub.com/subscriptionsSubscriptions:  

http://www.sagepub.com/journalsReprints.navReprints:  

http://www.sagepub.com/journalsPermissions.navPermissions:  

What is This? 

- Mar 1, 2007Version of Record >>

at UNIV TORONTO on November 22, 2014isc.sagepub.comDownloaded from at UNIV TORONTO on November 22, 2014isc.sagepub.comDownloaded from

198 INTERVENTION IN SCHOOL AND CLINIC VOL. 42, NO. 4, MARCH 2007 (PP. 198–203)

Mathematics Accommodations for All Students

ALLISON J. FAHSL

This article presents some simple mathematics ac-

commodations that general education teachers can

implement without extensive preparation time.

The accommodations are appropriate for all stu-

dents in the classroom regardless of whether they

have identified disabilities. The accommodations

are intended as supplemental or supportive strate-

gies used in conjunction with regular planning

and instruction for students who need minimal or

intermittent instructional adaptations.

Students with exceptionalities are being includedin general education classrooms at an increasingrate. For example, in 2002, according to theU.S. Department of Education (2004), 48.2%of students with disabilities were educated for

the majority of the day in general education classrooms.However, many teachers have expressed concern abouttheir ability to effectively educate students with specialneeds due to lack of knowledge, training, and experience,as well as the additional preparation and collaborationtime involved (Burstein, Sears, Wilcoxen, Cabello, &Spagna, 2004; Pivik, McComas, & LaFlamme, 2002;Tapasak & Walther-Thomas, 1999). Teachers also worryabout accommodating these students—those who are atrisk and require remediation but are not classified as hav-ing a disability—while simultaneously providing appro-priate instruction for the rest of the students in the class.It has been reported that 5% to 10% of elementaryschool students without identified disabilities have trou-ble with mathematics (Kroesbergen & Van Luit, 2003);for example, children may have persistent and specificdeficits in some areas of mathematics while excelling inothers (Geary, 1999).

Students who struggle with math, as well as studentswith disabilities, have needs that can often be addressedthrough using simple accommodations that require littleor no extra teacher preparation time. Everyone in theclass has the opportunity to take advantage of the strate-gies used. The mathematics accommodations presentedin this article can be easily and immediately implementedwithout extensive preparation time. The intent is not tohave students rely on accommodations but to providesome suggestions and strategies that are beneficial whenand if students need them. The accommodations andsuggestions are not meant to be used instead of more in-depth planning and specific instruction but are intendedas a supplement for students who need minimal or inter-mittent instructional adaptations.

at UNIV TORONTO on November 22, 2014isc.sagepub.comDownloaded from

VOL. 42, NO. 4, MARCH 2007 199

Organization

Some students’ problems stem more from difficulties withorganization rather than content. For these students,teaching them how to organize their work more effi-ciently can be very beneficial. Many students with orga-nizational problems benefit from something as simple asan alternative to standard lined paper. If possible, allowstudents to use graph paper for all mathematical work.This enables the students to keep the columns alignedand reduce computational errors. It also reinforces neat-ness and organization for students without organizationalproblems. Graph paper can easily be enlarged for stu-dents who have fine motor-skill problems, visual deficits,or simply poor handwriting. It is also possible to cus-tomize graph paper to format certain types of problems,such as only supplying the number of squares needed fora specific problem or adding a square above a columnthat requires regrouping (Bley & Thornton, 2001). Thismethod provides procedural guidelines as well as an or-ganizational structure and can gradually be faded out as astudent internalizes the procedure (see Figure 1). If graphpaper is not available, students can use regular wide-ruledpaper turned sideways, so the lines are vertical instead ofhorizontal, to provide at least some column alignment (seeFigure 2). This strategy can be used as a standard proce-dure with all students, regardless of necessity.

Many students have difficulty transcribing problemsfrom the board or text onto their own paper in an orga-nized manner. For example, they fail to line up the columnscorrectly, or they put the number of the problem tooclose to the mathematics problem and include it in theircalculations. Again, the use of graph or vertically linedpaper may help, but it may be necessary to instruct stu-dents on how to efficiently set up their math papers. Forexample, teaching them to skip a square between thenumber of the problem and the mathematics problem,line up numbers in the correct columns (color codingplace values may help with this) and how much space toleave between each problem. These simple instructions

can eliminate or reduce the number of errors due to lackof proper organization.

Highlighting

Highlighting in various colors can also benefit studentsin multiple ways. For example, when students are com-puting a long multiplication problem, they often forgetto place the zero down first when multiplying the tens(this is a common problem for all students). By high-lighting the placeholder (or correct box on the graphpaper), the student is given a visual reminder to write downthe zero (see Figure 3). Along the same lines, studentsoften forget to regroup when necessary or they write theregrouped number in the wrong column. Again, simplyhighlighting the appropriate spot can assist students withthis problem. If students are capable, they can eventuallydo the highlighting themselves (see Figure 4).

Another challenge for many students is to solve agroup of problems with mixed operations (e.g., someproblems require addition and some subtraction). It isquite common for students to make the mistake of com-pleting all assigned problems using the same operation(e.g., adding all or subtracting all). If this is known beforestudents begin, they can either circle the signs on prob-

Figure 1. Customized formats for graph paper can assist students with organizational problems.

Figure 2. Vertical use of standard lined paper can assist withcolumn alignment.

at UNIV TORONTO on November 22, 2014isc.sagepub.comDownloaded from

200 INTERVENTION IN SCHOOL AND CLINIC

lems with the same operation or highlight all the sub-traction signs in one color and the addition signs in an-other (see Figure 5). This provides a visual cue to changecomputational operations. This strategy can also be usedfor students who have trouble remembering directions.The directions on an assignment can be highlighted as areminder for students of what needs to be done. If morethan one step is required, the steps can be highlighted indifferent colors or outlined in different ways to empha-size the multiple processes (see Figure 6).

Fact Charts

Due to memory and processing problems, many studentswith and without disabilities have a difficult time remem-bering math facts. They are often required to memorizeall the facts before they can move on to more complexskills. As long as the concept is fully understood (i.e., the

student understands the concept of multiplication andcan demonstrate it to you), there is no reason to preventstudents from progressing to more complex skills whilestill working on fact memorization (e.g., 2 digit × 1 digit).

To assist them with these more complex skills, stu-dents can use a fact chart. To prevent dependency on thechart and unnecessarily using it for facts they have al-ready memorized, mastered facts can be blackened outwith a permanent marker. Assess each student to deter-mine which facts he or she knows and does not know.This can be done by quickly going through a set of flash-cards or administering a timed test. Paraprofessionalsand parent volunteers can help with this activity.

Now provide the student with a multiplicationchart. First, highlight the factors to eliminate confusionand provide a visual reminder of where to begin whenlooking for the answer to a fact problem. Then, take apermanent marker and blacken out the facts the studentknows automatically (see Figure 7). If the answers canstill be seen after they are blackened out, run the sheetthrough a copy machine. As the student continues tomemorize and master more facts, continue to blackenthem out. In this manner, the student is receiving thesupport he or she needs and can focus on more complextasks but is still held accountable for the facts alreadymemorized.

Calculators

Calculators can be wonderful tools if used appropriately.Some students may need instruction in how to accuratelyuse a calculator. It is helpful for all students and theteacher to have the same calculator. That way, studentscan follow directions easier, and the teacher can modelappropriate skills more effectively. For younger studentsor those working on less complex skills, a more simplisticcalculator is better. It is less confusing, and the chance ofpressing the wrong key is less likely. Set guidelines forstudent use to prevent dependency and inappropriate useof calculators. For example, calculators are great for self-checking work. Solving complex problems is often a timeconsuming and cumbersome process for some students.It is discouraging to finish a long assignment and find outyou have to recalculate the problems all over again in an-other way to check your work (e.g., making studentscheck division with multiplication). A simple solution isto allow students to check their work with a calculator. Besure to require that they complete all work before check-ing so students are not using the calculator to find the an-swer instead of checking it. In some instances, it may alsobe appropriate to allow students to use calculators towork through complex problems. For example, whileworking on a long multiplication problem, the calculatorcan be used if a fact chart is unavailable or inappropriate.

Figure 3. Highlight the placeholder as a reminder for studentsto write down the zero during long multiplication.

Figure 4. Highlight the placeholder as a reminder for studentsto regroup.

at UNIV TORONTO on November 22, 2014isc.sagepub.comDownloaded from

VOL. 42, NO. 4, MARCH 2007 201

Manipulatives

Numerous studies have shown that students learn math-ematics better when manipulatives are used (Funkhouser,1995; Marsh & Cooke, 1996; Peterson, Mercer, &O’Shea, 1988). Mathematics is an exceptionally appro-priate subject for the use of hands-on activities. Man-ipulatives do not have to be expensive, store-boughtproducts. Many household or classroom items suffice.For example, paperclips, bingo chips, and stickers caneasily be used as counters. Strips of paper can be foldedand cut to use for fraction instruction. Students them-selves can even act as manipulatives during class or groupactivities. Providing concrete and semiconcrete represen-tations will help students who do not learn as wellthrough just an auditory style or who have difficulty withabstract concepts. Computer software and Web sites alsoprovide visual and interactive representations of mathconcepts and can be very beneficial.

Time Management

For students who have self-management problems, atimer can help keep them on task. Timers may be set for

the whole class or for individual students. A time limitcan be set to help students stay on task and give them anidea of how long each problem should take. This helpsstudents manage their time more effectively on assign-

Figure 5. Highlight or circle operational changes as a visual reminder to students.

Figure 6. Highlight or outline directions in different ways to remind students of multiplesteps.

Figure 7. Blacken out memorized facts to eliminate unneces-sary use.

at UNIV TORONTO on November 22, 2014isc.sagepub.comDownloaded from

202 INTERVENTION IN SCHOOL AND CLINIC

ments. It may also be beneficial to give reminders orwarnings as to when a transition is coming. This allowsstudents time to plan for the change and finish up withtheir current project. Agendas of daily activities visuallydisplayed in the room also provide a guide for studentswho need structure and self-monitoring practice.

Class Presentations

Lesson presentations are more effective if multiple learn-ing styles are incorporated. The use of visual aids andhands-on activities, whenever possible, will assist stu-dents who learn best through visual and tactile methods.Placing students with attention problems near theteacher can help monitor behavior. Students with audi-tory and visual deficits also need to be near the front ofthe room or near the teacher. The teacher circulatingthrough the room during lessons can effectively reducethe number of off-task behaviors. Further, grouping stu-dents to complement each other’s strengths and weak-nesses can be beneficial. It is recommended that eachstudent be given a job within the group to ensure activeparticipation by all group members. Finally, it may behelpful to provide partial outlines or notes for studentswho have trouble with fine-motor skills, attention prob-lems, or processing difficulties (see Figure 8). With partof the information provided, they are able to focus moreon processing the information and less on worrying aboutgetting everything down. This also helps them followalong with the lecture or activity more effectively.

Assignments

Sometimes it is necessary to modify assignments to meetthe needs of all students in the class. A common method

is to reduce the number of problems given. However, forsome students, it may not be necessary to reduce the totalnumber of problems but to simply reduce the number ofproblems on a page. For example, if 10 homework prob-lems are assigned, put 5 problems on one page and 5 onanother. This helps the child stay focused and feel lessoverwhelmed by the number of problems assigned.

Similarly, many reproducible worksheets include a lotof pictures and details to increase interest and motiva-tion. This may be distracting for someone with an atten-tion or visual perception problem. Reducing the amountof visual stimuli on a page can help students focus moreon the problems instead of extraneous graphics (seeFigure 9). If students have trouble following or readingdirections, completing a sample problem on the pageprovides them with a reference when working indepen-dently.

Assessments

It may also be necessary to consider alternative ways toassess students or provide accommodations during test-ing. Students can be assessed by teacher observation dur-ing task completion. Teachers can simply watch thestudent complete the task to determine if the skill or con-cept is understood. Another method is to ask the studentfor an oral explanation or answer instead of requiring apaper/pencil response. These methods can be combined,and the student can give an oral account of his or herprocedures while performing the task.

If paper/pencil assignments are necessary, considerallowing students to use a calculator or fact chart (if notassessing fact knowledge). This allows students to focuson the more complex facets of the problem instead ofworrying about fact errors. If the type of problem

Figure 8. Provide partial outlines for students with fine-motor, attention, or processing deficits.

at UNIV TORONTO on November 22, 2014isc.sagepub.comDownloaded from

VOL. 42, NO. 4, MARCH 2007 203

changes throughout the test, allow students to highlightthe operation (as described previously) before beginningthe test. This provides a visual reminder to be aware ofthe operation indicated. It may also help to highlight di-rections throughout the test. If students are accustomedto using graph paper, allow them to do so on the test.This will help minimize careless errors due to organiza-tional problems. All of these methods can provide anaccurate account of student understanding while address-ing a variety of student problems.

Conclusion

It is not easy to meet the needs of all students in a class-room. Many teachers who have students with special needsfeel they were inadequately trained to instruct these stu-dents. The suggestions provided here represent only asmall sample of the possible accommodations that can bemade to help meet the needs of all the students in theclassroom. They are simple to incorporate and requirelittle additional planning time. In most instances, the ac-commodations can be implemented for the whole classand will help all students more fully comprehend theconcepts and skills being taught.

ABOUT THE AUTHOR

Allison J. Fahsl, PhD, is an assistant professor of special edu-cation at Southern Illinois University Edwardsville. Her cur-

rent interests include mathematics instruction, collaboration,and learning disabilities. Address: Allison J. Fahsl, SouthernIllinois University Edwardsville, Department of Special Ed-ucation and Communication Disorders, Campus Box 1147,Edwardsville, IL 62026; e-mail: afahsl@siue.edu

REFERENCES

Bley, N. S., & Thornton, C. A. (2001). Teaching mathematics to studentswith learning disabilities (4th ed.). Austin, TX: PRO-ED.

Burstein, N., Sears, S., Wilcoxen, A., Cabello, B., & Spagna, M. (2004).Moving toward inclusive practices. Remedial and Special Education,25(2), 104–116.

Funkhouser, C. (1995). Developing number sense and basic computa-tional skills in students with special needs. School Science and Mathe-matics, 95, 236–239.

Geary, D. C. (1999). Mathematical disabilities: What we know and don’tknow. Retrieved September 20, 2004, from http://www.LDonline.com

Kroesbergen, E. H., & Van Luit, J. (2003). Mathematics interventionsfor children with special educational needs. Remedial and Special Ed-ucation, 24(2), 97–115.

Marsh, L. G., & Cooke, N. L. (1996). The effects of using manipula-tives in teaching math problem solving to students with learningdisabilities. Learning Disabilities Research & Practice, 11, 58–65

Peterson, S. K., Mercer, C. D., & O’Shea, L. (1988). Teaching learningdisabled students place value using the concrete to abstract se-quence. Learning Disabilities Research, 4, 52–56.

Pivik, J., McComas, J., & LaFlamme, M. (2002). Barriers and facilita-tors to inclusive education. Exceptional Children, 69(1), 97–107.

Tapasak, R. C., & Walther-Thomas, C. S. (1999). Evaluation of a first-year inclusion program. Remedial and Special Education, 20, 216–225.

U.S. Department of Education. (2004). Twenty-sixth annual report toCongress on the implementation of the Individuals with Disabilities Act.Washington, DC: U.S. Government Printing Office.

Figure 9. Reduce the amount of visual stimuli on the page.

at UNIV TORONTO on November 22, 2014isc.sagepub.comDownloaded from