58 SPRING 2004 • VOL. 27, NO. 2

b y R e b e c c a L . P i e r c e a n d C h e r y l l M . A d a m s

TI

ER

ED

LE

SS

T h e m o v e m e n t t o w a r d i n c l u s i o n h a s i m p a c t e d c l a s s r o o m s b y

requiring teachers to respond to a broader range of academic needs. How can

we possibly reach all the students in our classrooms when they are acad-

emically diverse, have special needs, are ESL learners, or have some

combination of any or all of these factors? An answer to this

question lies in differentiating instruction. Wo rking in

the Burris Laboratory School, an inclusion school

using a re s o u rce consultation model to

s e rve the needs of all its students, we

h a ve found that using tiere d

lessons is a viable method

for differe n t i a t i n g

i n s t ru c t i o n .

GIFTED CHILD TODAY 59

What is Differentiation?

Although differentiated instructionis not a new idea, the differentiationm ovement has recently taken centerstage as a means of meeting the needs ofall students in the classroom. It is anorganized, yet flexible way of proactivelyadjusting teaching and learning to meetstudents where they are and help all stu-dents achieve maximum growth as learn-ers (Tomlinson, 1999). Instruction maybe differentiated in content/input,process/sense-making, or product/out-put according to the students’ readiness,interest, or learning style. By content, wemean the material that is being pre-sented. Process activities help studentspractice or make sense out of the con-tent, while product refers to the outcomeof the lesson or unit, such as a test, pro-ject, or paper. Readiness refers to priorknowledge and a student’s current skilland proficiency with the material pre-sented in the lesson. A student’s interestmay be assessed with an interest inven-tory for the particular topic being stud-

ied or by an individual conversationwith the student. Many teachers use thetheory of multiple intelligences to char-a c t e r i ze learning styles (Armstro n g ,1994; Gardner, 1993; Martin, 1996).

Essential elements for successful dif-ferentiation include specific classroommanagement techniques addressing thespecial needs of a differentiated class-room, planned use of anchoring activi-ties, and flexible use of time, space, andstudent groups. In a differentiated class-room, the management plan mustinclude rules for working in a variety ofconfigurations. You can only work withone group or individual at a time.Therefore, we have developed two criti-cal rules that thwart chaos and preservesanity. The first is “Use six-inch voices,”meaning that students should modulatetheir speaking level so that their voicescan only be heard six inches away. Thesecond rule is “Ask three before me.” Ifstudents need assistance completing atask or come to a stumbling block in alesson and you are not available, theyshould find three other students to ask

before they may interrupt you. If theirthree peers cannot answer the question,the student has permission to interruptyou. Adding the caveat that the studentshould also bring along the three stu-dents who were asked will nearly elimi-nate the chance that you will bei n t e r rupted except in extreme cases.Anchoring or “sponge” activities are pro-vided for students to use when they arewaiting for you to assist them beforethey can go any further or at the begin-ning of the class period to get themready to work. A wide variety of materi-als and resources can serve as anchoringactivities (see our Web site at http://w w w. b s u . e d u / t e a c h e r s / s e rv i c e s / c t r / j a v-its/Instruction/anchoring.htm for a list-ing of books that have great activities foranchoring). Flexible grouping arrange-ments such as pairs, triads, or quads, aswell as whole-group and small-groupinstruction, create opportunities to meetindividual needs. A flexible use of timeallows lessons to proceed to their naturalconclusion, rather than being carried outin set blocks of time. The desks or tables

SO

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W a y

t o D i f f e r e n t i a t e

M a t h e m a t i c s

I n s t r u c t i o n

60 SPRING 2004 • VOL. 27, NO. 2

should be arranged in such a way as tofacilitate group work, as well as whole-class groupings that encourage sharingof ideas.

A variety of instructional strategies,including compacting, learning con-tracts, cubing, and tiered lessons, can beused to differentiate instruction (for adiscussion of these and other strategies,see Gre g o ry & Chapman, 2002;He a c ox, 2002; Sm u t n e y, Wa l k e r, &Me c k s t roth, 1997; Tomlinson, 1999;Winebrenner, 1992). It makes sense toalert your administration and the par-ents that you will be trying some newstrategies in the classroom in case thereare questions.

The tenets of differentiated instru c-tion support both the Equity Pr i n c i p l eand the Teaching Principle of thePrinciples and St a n d a rds for SchoolMathematics (National Council ofTeachers of Mathematics, 2000). Theseprinciples direct us to select and adapt

content and curricula to meet the inter-ests, abilities, and learning styles of ourstudents; to re c o g n i ze our students’d i versity; and to encourage them toreach their full potential in mathemat-i c s .

What is a Tiered Lesson?

Tomlinson (1999) described tiere dlessons as “the meat and potatoes of dif-f e rentiated instruction.” A tiered lesson isa differentiation strategy that addresses ap a rticular standard, key concept, andgeneralization, but allows several path-ways for students to arrive at an under-standing of these components based ontheir interests, readiness, or learning pro-files. A lesson tiered by readiness leve limplies that the teacher has a goodunderstanding of the students’ abilityl e vels with respect to the lesson and hasdesigned the tiers to meet those needs.

Think of a we d d i n gcake with tiers ofva rying sizes. Ma n yexamples of lessonst i e red in re a d i n e s sh a ve three tiers:b e l ow grade level, atgrade level, anda b ove grade leve l .T h e re is no rule thatstates there may onlybe three tiers, how-e ve r. The number oftiers we use willdepend on the rangeof ability levels inyour own classro o msince you are form-ing tiers based onyour assessment ofyour students’ abili-ties to handle thematerial particular tot h i s lesson. St u d e n t sa re re g rouped the

next time you use tier-ing as a strategy. Hence, the idea of flex-ible, rather than static, groups ise s s e n t i a l .

No matter how you choose to dif-ferentiate the lesson—readiness, interest,or learning profile—the number ofgroups per tier will vary, as will the num-ber of students per tier. You are not look-ing to form groups of equal size. Whenyou form groups based on the readinessneeds of individual students, Tier I mayhave two groups of three students, TierII five groups of four students, and TierIII may have one group of two students.When the lesson is tiered by interest orlearning profile, the same guidelinesapply for forming groups: Different tiersmay have varying numbers of students.Even when students are already homoge-neously grouped in classes by ability,there is still variance in their ability lev-els that must be addressed.

To take a closer look at the anatomyof a tiered lesson, we have included a

Tiered Lessons

F i rs t - g ra de te a c he r Ma r t ha Ken d r i c k re a ds f r om E a t i n g F r a c t i o n s to Ti e r I I s t ude n t s

GIFTED CHILD TODAY 61

mathematics lesson (see Figure 1) thatwas developed as part of the Ja v i t sGrant, Project GATE, a federally fundedp a rtnership between the In d i a n a p o l i sPublic Schools and Ball State University,both in Indiana. When developing atiered lesson, we have found the eightsteps described below useful.

1. First, identify the grade level and sub-ject for which you will write the lesson. Inthis case, the grade level is first and thesubject is mathematics.

2. Second, identify the standard(national, state, district, etc.) you are tar-geting. A common mistake for those just

beginning to tier is to develop threegreat activities and then try to force-fitthem into a tiered lesson. Start with thestandard first. If you don’t know whereyou are going, how will you know if youget there? The author of this lesson hasselected the Content Standard “Numberand Op e r a t i o n s” of the Na t i o n a l

Subject: Mathematics

Grade: First

Standard: Numbers and Operations

Key Concept: Students understand and represent commonly used fractions such as 1/4 and 1/2.

Generalization: Students will be able to illustrate how fractions represent part of a whole.

Background: Fractions (halves/thirds) have been introduced and illustrated by the students with pictures.Materials: Paper circles, squares, rectangles, triangles

Tier I: Using paper circles (pizza) and squares (sandwich), students in pairs determine how to share the foodequally and illustrate by folding the paper. Have two pairs determine how they can share equally withfour people. They can cut the parts and stack them to see if they match. Have the quad repeat theprocess for sharing a Reese’s Peanut Butter Cup equally with three people.

Tier II: Using paper circles (pizza) and squares (sandwich), have students in triads determine how to share thefood equally and illustrate by folding the paper. Have two triads determine how they can share equallywith six people. Have the group of six repeat the process for sharing a birthday cake with 12 people.In each case, they can cut the parts and stack to match. Have the group start with half a cake anddivide equally for 3, 6, and 12 people.

Tier III: Using paper rectangles (sandwiches) and triangles (slices of pie), have students in pairs determine howto share the food in three different ways to get two equal parts. Have them illustrate by folding thepaper. Are there other different ways to divide each shape equally? How many ways are there? Havethe pair determine which shapes—circles, squares, rectangles, triangles—are easier to divide evenlyand illustrate why with a particular food of their choice.

Assessment: As the students work, the teacher will circulate among the groups and note the children’s abilities todivide materials into equal parts and to recognize and check for equal parts. Can children explainorally how many equal parts there are and demonstrate how they know the parts are equal? It is at theteacher’s discretion to determine which children need more in-depth questioning to ascertain masteryof the concept.

Figure 1Tiered Lesson in Mathematics: Tiered in Content According to Readiness

62 SPRING 2004 • VOL. 27, NO. 2

Council of Teachers of Mathematics’(2000) Principles and St a n d a rds forSchool Mathematics (pp. 78–88).

3. Third, identify the key concept andgeneralization. The key concept followsfrom the standard. Ask yourself, “Whatbig idea am I targeting?” In this exam-ple, it is to understand and representcommonly used fractions. While thereare many concepts that could be coveredunder the standard chosen, this lessonaddresses only one. The generalizationfollows from the concept chosen. Ask,“What do I want the students to knowat the end of the lesson, regardless oftheir placement in the tiers?” In this les-son, all students will develop their

understanding of fractions as represent-ing parts of a whole.

4. Fo u rth, be sure students have thebackground necessary to be successful in thelesson. What scaffolding is necessary?What must you have already covered orwhat must the student have alre a d ylearned? Are there other skills that mustbe taught first? Before engaging in thislesson, students have been exposed toh a l ves and thirds. Fractions (halve s /thirds) have been introduced to the stu-dents, and they have illustrated themwith pictures. There are several literaturebooks that illustrate fractional part susing food that could be used to intro-duce the lesson.

5. Fifth, deter-mine in which partof the lesson (content,process, product) youwill tier. You maychoose to tier thecontent (what youwant the students tolearn), the pro c e s s(the way studentsmake sense out ofthe content), or thep roduct (the out-come at the end of alesson, lesson set, orunit—often a pro-ject). When begin-ning to tier, wesuggest that yo uonly tier one ofthese three. On c eyou are comfortablewith tiering, yo umight try to tiermore than one partin the same lesson.This lesson is tieredin content.

6. Sixth, deter-mine the type of tier-ing you will do:

readiness, interest, or learning pro f i l e .Readiness is based on the ability levels ofthe students. Giving a pretest is a goodway to assess readiness. Students’ interestin a topic is generally gauged through aninterest survey, while the learning profilemay be determined through va r i o u slearning style inventories. In this lesson,the author chose readiness.

7. Seventh, based on your choices above,determine how many tiers you will needand develop the lesson. When tieringaccording to readiness, you may havethree tiers: below grade level, at gradel e vel, and above grade level. If yo uchoose to tier in interest or learning pro-

Tiered Lessons

Ti e r I I I s t ude nt s wo rk on f o ld i n g t he i r f ra c t i o n p i e c es i n t h i rd s .

GIFTED CHILD TODAY 63

file, you may control the number of tiersby limiting choices or using only a fewdifferent learning styles. For example,tiering on all eight of Gardner’s multipleintelligences in one lesson may not be agood place to start, so choose only a few,such as logical-mathematical intelli-gence, spatial intelligence, and linguisticintelligence. (For further information onmultiple intelligences in an easy-to-understand format, see Wahl, 1997). Forthis lesson, students are placed in one ofthree tiers based on their ability to workwith halves and thirds as assessed by theteacher through observation.

Differentiation means doing some-thing different—qualitatively different.Make sure you keep this in mind whentiering the lessons. Second, be sure thatstudents are doing challenging, respect-ful, and developmentally appro p r i a t ework within each tier. In other words,no group should be given “busywork.”We don’t want one group doing black-line practice sheets and another doing afabulous experiment.

Notice in this lesson that all threetiers are working on fractions. Studentsin each tier use paper shapes to divide.However, the activities for each tier inthe sample lesson, beginning in Tier Iand moving through Tier III, differ fromconcrete to abstract and from simple tocomplex, to use Tomlinson’s Equalizerword pairs (Tomlinson, 1999).

8. Finally, develop the assessment compo-nent to the lesson. The assessment can beformative, summative, or a combinationof both. You may use some means ofrecording observations of the variousgroups, such as flip cards or sticky notes.You could develop a rubric for each tierbased on the particular product that iscreated. You may give a formal paper-and-pencil test. Whatever it is, chooseyour assessment based on your needsand your lesson design.

In this lesson, the teacher observesthe students as they share their answers

and jots down notes for a formativeassessment of each student. For example,which child is struggling with the con-cept? Which child is moving rapidly andaccurately through the material? Whoseanswers show more thought and insight?Answers to these and other questionswill assist you in determining who needsreteaching and who is ready to gobeyond the material presented. A formalassessment is not used here since thes t a n d a rds emphasize that studentsshould have “informal experiences [withfractions] at this age to help develop afoundation for deeper learning in thehigher grades” (NCTM, 2000, p. 83).

When this lesson was taught, thestudents were engaged during the entirelesson. The lesson was introduced by

reading the book Eating Fra c t i o n s(McMillan, 1991). Students were placedin groups based on their level of readi-ness to interact with the content. Fourstudents did not have a clear under-standing of halves and fourths. Thesestudents needed a more concrete activityand were placed in Tier I. Another 12students could re c o g n i ze halves andthirds and were ready to complete theTier II activity. They were placed in fourtriads. Two students had in-depthknowledge of halves and thirds and wereplaced in Tier III. This pair worked at amore abstract level, and the questionsthey were asked required them to usedifferent critical thinking skills than theother two groups. Tier I and Tier II stu-dents were provided with activities fromthe book Fractions (Watt, 2001) to use as

Ti e r I I s t uden t s d et e rm i n e wa y s t o sha re t he i r “ c a ke” w i t h 12 p eo p le a n d t h e i r “ sa nd w ic h” w i t h 6 p eop l e .

64 SPRING 2004 • VOL. 27, NO. 2

anchoring activities if they finished earlyor were waiting for the teacher’s assis-tance. The anchor for Tier III studentswas Apple Fra c t i o n s ( Pallotta, 2002),which introduced fifths through tenths.

The second sample lesson (seeFigure 2) is tiered in process accordingto learning style. In this case, studentsare grouped heterogeneously based onone of two learning preferences: kines-thetic or visual. The same eight steps fortiering a lesson apply in this case. In thesecond lesson, notice that the activitiesare at relatively the same level of com-plexity. This would be the “layer cake”model as opposed to the “wedding cake”model used when tiering according toreadiness.

Final Thoughts

Time, energy, and patience are

required to learn to differentiate instruc-tion effectively in an academicallydiverse classroom. In addition, you needadministrative and peer support, as wellas professional development ove rextended periods of time; there f o re ,don’t expect to have a differentiatedclassroom by Monday morning. Startsmall: Choose a favorite lesson in yournext unit and differentiate it accordingto the needs of your students. Seek theexpertise of specialists such as specialand gifted education coord i n a t o r s ,media specialists, and others with whomyou can collaborate to improve instruc-tion in the academically diverse class-room.

For more information on tiering,contact the Center for Gifted St u d i e sand Talent De velopment, Ball St a t eUn i versity (BSU) at (800) 842-4251.Two Web sites that provide good exam-ples of tiered lessons are the Center for

Gifted Studies andTalent De velopment atBSU as part of the Ja v i t sGrant, Project GAT E ,and the In d i a n aDe p a rtment of Ed u c a -tion Gifted and Ta l e n t e dUn i t’s Ti e red LessonProject, developed byC h e ryll Adams, Fe l i c i aDi xon, and Re b e c c aPi e rce and funded by theIndiana De p a rtment ofEducation (IDOE). Fo rthe BSU site, go toh t t p : / / w w w. b s u . e d u /t e a c h e r s / s e rv i c e s / c t r / j a v-its and click on theIn s t ruction picket on thewhite gate. For theIDOE site, go toh t t p : / / d o e . s t a t e . i n .u s / e x c e p t i o n a l / g t /t i e re d _ c u r r i c u l u m / we l-come.html.

References

Armstrong, T. (1994). Multiple intelli-gences in the classroom. Alexandria,VA: Association for Supervision andCurriculum Development.

Gardner, H. (1993). M ultiple intelli-gences: The theory and practice. NewYork: BasicBooks.

Gre g o ry, G. H., & Chapman, C. (2002).D i f f e rentiated instructional stra t e g i e s :One size doesn’t fit all. T h o u s a n dOakes, CA: Corwin Pre s s .

He a c ox, D. (2002). D i f f e re n t i a t i n ginstruction in the regular classroom.Minneapolis, MN: Free Spirit.

Ma rtin, H. (1996). Multiple intelligencesin the mathematics classro o m. Pa l a t i n e ,IL: IRI/Sk y L i g h t .

McMillan, B. (1991). Eating fractions.New York: Scholastic.

National Council of Teachers ofMathematics (NCTM). (2000).Principles and standards for school

Tiered Lessons

Ti e r I I s t uden t s de te rm i ne how t o sha re a “p i z z a ” a n d a “s an dw ic h” equa l l y w i t h t h re e p eop l e .

GIFTED CHILD TODAY 65

mathematics. Reston, VA: Author.Pallotta, J. (2002). Apple fractions. New

York: Scholastic.Smutney, J., Walker, S., & Meckstroth,

E. (1997). Teaching young giftedc h i l d ren in the regular classro o m .Minneapolis, MN: Free Spirit.

Tomlinson, C. A. (1999). The differenti-ated classroom: Responding to theneeds of all learners. Alexandria, VA:Association for Su p e rvision andCurriculum Development.

Wahl, M. (1997). Math for humans.Langley, WA: LivnLern Press.

Watt, F. ( 2001). Fractions. New York:Scholastic.

Winebrenner, S. (1992). Teaching giftedkids in the regular classroom. Min-neapolis, MN: Free Spirit.

Author Note

Research for this article was supported

under the Javits Act Program (GrantR206A980067) as administered by theOffice of Educational Re s e a rch andIm p rovement, U.S. De p a rtment ofEducation. Grantees undertaking suchprojects are encouraged to express freelytheir professional judgment. This article,therefore, does not necessarily representpositions or policies of the government,and no official endorsement should beinferred.

Subject: Mathematics

Grade: Third

Standard: #5 Geometry and #6 Spatial Sense

Key Concept: Students work with geometric shapes and develop spatial sense.

Generalization: Students identify lines of symmetry of objects.

Background: This would be the fourth or fifth lesson in a unit on geometry where the first few lessons have cov-ered various geometric shapes, as well as slides, flips, turns, congruence, and symmetry.

Tier I: Kinesthetic LearnersPairs of students use brightly colored paper to make several simple origami designs. Provide guidancewhen necessary. When students are finished, have them unfold the figure(s), find any congruent fig-ures, and identify lines of symmetry. Students then share the origami figures and have classmates tryto construct them.

Tier II: Visual LearnersPairs of students work with pictures of items from nature, such as a butterfly, sunflower, rainbow,snowflake, or starfish. Students find any congruent figures and identify lines of symmetry for eachitem. Students color the pictures to help show the lines of symmetry. Students cut out the figures andhave classmates find the lines of symmetry.

Assessment: Use a summative assessment noting students’ abilities to identify the congruent figures and lines ofsymmetry. Have each student reflect in writing about congruent figures and lines of symmetry. Froma list of objects in the classroom, students will select an object and write about whether or not theobject has congruent parts, lines of symmetry, or both and then explain why. The students could alsoinclude a drawing that illustrates the congruent parts, lines of symmetry, or both.

Figure 2Tiered Lesson in Mathematics:

Tiered in Process According to Learning Style

66 SPRING 2004 • VOL. 27, NO. 2

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