Adapting Curriculum

Math Games for AdolescentsJulia Shaftel Lisa Pass Shawn Schnabel

Carlos, a high school sophomore,missed several days of school eachmonth and became more involved ingang activity as the school year pro-gressed. He had been moved to an alter-native high school but was in danger ofbeing expelled because of his repeatedabsences and because he did not com-ply with rules. His mother, who wasworried about his academic achieve-ment and prospects for high schoolgraduation, brought him to our univer-sity training center for academic tutor-ing.

Carlos was a warm and friendly ado-lescent who developed a close relation-ship with his tutor as his academic skillsimproved. However, he did not seem tofully realize the consequences of hisactions. The tutor, a graduate student inpsychology, became concerned aboutCarlos' choice of friends and activities,both at school and during his free time.She talked with Carlos about his expec-tations and discovered that he believedhe would be able to support himselfcomfortably with the kind of job that hecould find as a high school dropout.Because she wanted to help him under-stand the financial difficulties that drop-ping out would cause, she developed agame called That's Life—Money GameAbout Real-Life Expenses (see box,"What Does the Literature Say AboutMathematical Games?"). Figure 1includes the rules for this game, as wellas a depiction of the game board.

Carlos and his tutor played this gamemany times during their tutoring andcounseling sessions and refined it to cre-ate a realistic picture of life after highschool. When Carlos landed on a squarethat represented financial difficulty, hewas often surprised to learn that anevent might really happen. When he

counted the money that he had at theend of a game, or when he ran out ofmoney during a game, he began to real-ize that supporting himself might not beas easy as he had thought.

That's Life and Shopping 5|»reeThat's Life is loosely based on theMonopoly™ board game but incorpo-rates financial events that young adultsoften face. A teacher can adapt thegame in several ways. For example,expenses such as income, rent, or trans-portation can reflect typical costs in agiven locality. Students can use check-book registers or play money to keeptrack of income and expenses.

The second game. Shopping Spree.uses a game board that is somewhatsimilar to that used in the Clue''" game.Players must complete their shoppinglist by making purchases at differentstores shown on the board and return-ing home. They move through the boardto get from store to store. While shop-ping, students develop strategies andsolve math problems. Figure 2 includesthe rules for this game and shows thegame board.

Students can play these games inmany different ways. Two or more play-ers can play either That's Life orShopping Spree in a classroom orresource room setting. Students can playthe games in pairs or in teams. In addi-tion, a student can play either That'sLife or Shopping Spree alone.

The teacher can ask students todesign and create their own gameboards, which can include local shopsand banks. And, of course, the teachercan control the level of mathematicaldifficulty by varying prices and expens-es in That's Life or by changing theproblems required for purchases inShopping Spree. These basic formats

enable teachers and students to cus-tomize the games to meet their owninstructional objectives and needs.

Using Games in the Clcusroom:Some CautionsGames are only one type of classroomactivity. To maintain their motivationalvalue, the teacher should not overusethem. As with any classroom activity,teachers should monitor and evaluatethe effectiveness of games as part of theinstructional curriculum (Blum &Yocom, 1996).

Other factors that teachers shouldconsider include the following:

• Teachers should watch for excessivecompetition and overstimulation.

• Before students play games such asThat's Life and Shopping Spree with-out direct teacher involvement, theirmastery of the content should be at ahigh level—in fact, it should approach100 %, unless students can obtainprompt teacher assistance whenneeded (Brophy & Good, 1986).

• Teachers should consider the com-plexity of the rules and the mathe-matical concepts necessary for suc-cessful play, any physical require-ments, and the social skills needed forinteraction, so that every player has achance to win (Blum & Yocom, 1996).

Finai ThougiitsProponents of mathematical games(Blum & Yocom, 1996; de la Cruz, Cage,& Lian, 2000; Holton, Ahmed, Williams& Hill, 2001; Quinn, Koca, & Weening,1992) have enumerated many benefitsin instructional settings. Games andsimulations can:

• Increase student motivation and par-ticipation in practice and reviewactivities.

• Provide immediate feedback.

TEACHING EXCEPTIONAL CHILDREN • JAN/FEB 2005 • 25

Whut Does Hw Utemhire Say About Maftienuriical Games?

Such experts as Dewey, Erikson, and Piaget [Holton et al..2001) have emphasized the importance of piay in learning.Educational games and simulations motivate and engagelearners and provide opportunities for students to practiceacquired skills (Blum & Yocom, 1996; Kafai, Franke, Ching, &Shih, 1998). Mathematical simulations allow for creativity andexperimentation in developing strategies to reach a goal andrequire metacognitive skills to maintain focus on the goalwhile playing the game (Holton et al.).

A review of tbe research on instructional games and simu-lations from 1963 to 1991 showed that games are more likelyto have beneficial effects when they focus on precisely definedcontent or when they require drill and practice, such as inmathematics (Randel, Morris, Wetzel, & Whitehill, 1992). Thisreview also indicated that students show more interest ingames than in traditional classroom instruction and thatgames result in improved content retention over time, possi-bly because of the opportunity for greater student participa-tion. Mathematics games improved on-task behavior andachievement in arithmetic for students with mild intellectualdisabilities (Beattie & Algozzine, 1982).

When students and teachers developed their own mathgames, they engaged in reflective inquiry about the mathe-

matical content and about ways to represent that contentwithin the game. At the highest level of sophistication, bothstudents and teachers attained seamless integration of thecontent with the motivational aspects of the game (Kafai etai., 1998), as exemplified by the two games presented in thisarticle. Results of that study suggest that it is advisable toinvolve students in analyzing, adapting, or modifying games,either commercial games or those in this article, for their ownneeds before playing.

Mathematical games allow the learner many opportunitiesto reinforce current knowledge and to try out strategies ortechniques without fear of getting the "wrong" answer. Theyoften encourage students to use trial-and-error strategies.Games can provide an environment for experiencing incorrectsolutions not as mistakes but as steps in connecting pieces ofmathematical knowledge (Holton et al., 2001; Quinn et al.,1992). With reference to money games and simulations,Hopkins and Dorsey (1992) state that mathematical learningis optimized when it is tied to real-life experiences and thatsimulations develop metacognitive skills for analyzing andorganizing data, checking responses, justifying solutions toproblems, and applying mathematical knowledge to dailyactivities.

• Increase opportunities to respond.• Use a variety of manipulatives in

problem-solving.• Support positive attitudes toward

mathematics.

• Encourage connections among differ-ent areas of mathematics.

• Allow students to try new strategies.• Stimulate logical reasoning.

In addition to reinforcing mathemat-ics content knowledge, the use of gamesand simulations also encourages stu-dents to develop such skills as attentionto task; social skills, including takingturns and courtesy; cooperation withothers; leadership skills; and fine motorskills. Games such as That's Life andShopping Spree encourage students toreview mathematical concepts and helpthem better understand their weakness-es and their areas of competence. Inaddition, students benefit from watch-ing others solve problems. These flexi-ble games in familiar formats canenhance students' math skills.

ReferencesBeattie, J., & Algozzine, B. (1982). Improving

basic academic skills of educable mental-ly retarded adolescents. Education and

TYeatment of the Mentally Retarded. 17,255-258.

Blum, H. T, & Yocom, D. J. (19%). A funalternative; Using instructional games tofoster student learning. TEACHINGExceptional Children, 29[1), 60-63.

Brophy, J., & Good, T. L. (1986). Teacherbehavior and student achievement. In M.C, Wittrock (Ed.), Handbook of researchon teaching (pp. 328-375). New York:MacMillan.

de la Cruz, R. E., Cage, C. E., & Lian. M-G.J.I (2000). Let's play mancala and sung-ka! TEACHING Exceptional Children,32(3), 38-42.

Holton, D., Ahmed, A., Williams, H., & Hili,C. (2001). On the importance of mathe-matical play. International Journal ofMathematical Education in Science andTechnology, 32, 401-415.

Hopkins, M. A., & Dorsey, C. M. (1992).Math is eveiywhere—If only we couldfind it! Preventing School Failure, 37, 10-13.

Kafai. Y. B., Franke, M. L., Ching, C. C, &Shih, J. C. (1998). Game design as aninteractive learning environment for fos-tering students' and teachers' mathemati-cal inquiry. International Journal ofComputers for Mathematical Learning, 3,149-184.

Quimi, A. L., Koca, R. M., Jr., & Weening, F.[1992). Developing mathematical reason-ing using attribute games. MathematicsTeacher. 92, 768-775.

Randel, J. M., Morris, B. A., Wetzel, C. D,, &Whitehill, B. V. (1992). The effectivenessof games for educational purposes: Areview of recent research. Simulation &Gaming, 23. lb\-276.

Julia Shaftel ( CEC Chaptei #665), Director,Center for Psychoeducational Services,University of Kansas, Lawrence. Lisa Pass,School Psychologist. Athens City Schools,Athens. Alabama. Shawn Schnabel, SchoolPsychologist, Haysville School District,Haysville, Kansas.

Address correspondence to Julia Shaftel,University of Kansas. School of Education,1122 W. Campus Road, Room 130, Lawrence,KS 66045 (e-mail: jshaftel@ku.edu).

TEACHING Exceptional Children, Vol 37, No.3, pp. 25-30.

26 • COUNCIL FOR EXCEPTIONAL CHILDREN

Figure 1 . Thot's Ufe: A Game About Real-Life Expenses

That's Life-A Math Game About Real-Life Expenses

PayCollect $850

You can buy acar...if you do,you must pay

$200 each month

Credit CardPaymentPay $50

2 sickdays...when you

pass Pay Day youearn only $765

GroceryShoppingPay $100

If you have a car.Pay Car Insurance

$50

You now have aroommate...

split all monthlybills ia half firoia

on

If you dont havea car pay $25 forbus fare

Heed a Loan?

If you have a car,you can use tiie car as collateraland borrow $500 from the bank.

Jvist pay back $75 each time you get paid.

Cell Phone BillPayment i,-Pay $50 m

If you dont havea car pay $25 forbus fare Entertainment for

the monthPay $100

Rent DnePay $500

ClothesShoppingPay $50

HealthInsurance

Pay $70

Your roommatem.oved out...

start paying fullmonthly bills

Utilities DnePay $100

ObjecriveThat's Life gives students a chance to

apply mathematics and helps them rec-

ognize the costs of hving on their own.

LeaniArs/Context

Learners are students in middle schoolor high school who need practice withmoney concepts and with conceptsrelating to adult life. This game is par-ticularly appropriate for students inresource or consumer math classes.

RationaleThe monthly net pay of $850 reflects a40-hour-long workweek and a wage of$7 per hour, less 25% for taxes. Thenet pay figure assumes that eachmonth consists of exactly 20 workdays.The two-sick'days square lowers themonthly pay to $765 to reflect the

approximate cost of missing 2 days ofwork. The option to purchase a carallows students to determine whetherriding a hus makes more sense finan-cially than incurring the expenses ofowning a car. The only arguments infavor of purchasing a car are that eachcar owner will have some property

Equipment and SetupOne six-sided die and one game piecefor each playerGame board.

Checkbook register for each player;the teacher can create a simple check-book register in the following format:

That's Life Checkbook Register

Date Deposit Wifhdrawal Balance

value at Ihe end of the game and thateach car owner has the option ofobtaining a bank loan.

The teacher or students make a gameboard with 20 squares. The four cornersquares are labeled as follows:

• Payday-collect $850

TEACHING EXCEPTIONAL CHILDREN • JAN/FEB 2005 • 27

Figure I . |Con(inu»d)

• Rent due-pay $500

• Grocery shopping-pay $100

• Utilities due-pay $100

The remaining squares may contain the

following labels, any order:

• If you have a car, pay car insur-

ance-$50

• You have a roommate...split all

monthly bills in half from now on

• If you do not have a car, pay $25 for

bus fare

• Clothes shopping-pay $50

• Health insurance-pay $70

• Your roommate moved out...start

paying full monthly bills

• Entertainment for the month-pay

$100

• If you do not have a car, pay $25 for

bus fare

• Cell phone bill due-pay $50

• Take 2 sick days..,when you pass

Payday, you earn only $765

• Credit card payment due-pay $50

• You can buy a car...if you do, you

must pay $200 each month

The center of the board should contain

the following text:

Need a loan? If you have a car, you can

use the car as collateral and borrow

$500 from the bank. Just pay back $75

each time you get paid.

Playiiig flfce G a m e

1. Each player has a checkbook

register.

2. One trip around the board repre-

sents 1 month.

3. The players start on the square

marked "Payday—collect $850," so

each player enters $850 as a deposit

to start play.

4. Players roll the die to determine

how many squares they should

move. The student then subtracts

the amount owed or adds the

amount deposited to his or her

checkbook register, as indicated on

the square. Each time the student

passes the square marked

"Payday—collect $850," he or she

adds $850 to the checkbook register.

5. The game consists of at least six

rounds, reflecting 6 months.

6. If a player decides to purchase a car,

she or he adds one quarter of the

amount paid toward the car to the

balance (asset: resale value). For

example, if the student has made

three payments [$600), he or she

can add $150 to the checkbook reg-ister as an asset.

7. At the end of the game, a playerwho purchased a car must subtractany remaining loan balance from hisor her checkbook register.

8. The player who has the largest bal-ance in his or her checkbook regis-ter at the end of the game wins.

Modificirtions• The teacher can modify the contents

of the squares to reflect the possiblefuture spending habits of differentstudents and different localities.

• The students can use play moneyinstead of the checkbook register.

• Students can research the costs foritems represented in specific squaresand add information to the game asthey learn it.

• The teacher can vary costs to reflectdifferent levels of mathematical diffi-culty.

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28 • COUNCIL FOR EXCEPTIONAL CHILDREN

Figure S. Shopping Spree

s

Johnson'sDeU

s

CG

ornerroceryStore

sSunburst

Music

•s

Hi• 1

CCarlisle'slothingStore

S

s

CrazyPete's

Electronic

s SodaFountain

s

s

r

s

Beth'sBookstore

••II

s

InternetCafe

•Video

s

s

Vi(Ar

leocade

Jake'iSporti

ObiectiveShopping Spree reviews mathematicalconcepts. Teachers can generate indi-vidual questions based on the contentarea that the class is studying.

Leomers/ConlextThis game is targeted particularly forthose students in Grades 5 through 9.The game is designed so that teacherscan modify play for time constraints,number of participants, and questiondifficulty.

RdrionaleThis game is an interactive, motivatingway for students to review differentkinds of math problems. Students mustfollow a randomly generated "ShoppingList" of items by visiting stores aroundtown, "purchasing" items from a list ofdesignated stores by solving teacher-created math problems. The cost ofeach item is determined by the difficul-ty of the math problem that the studentattempts to answer.

Equipment• Three 6-sided dice.• One game piece for each player.

• Calculator for checking answers.• Balance sheets for keeping track of

debit card charges.

• Timer (optional).

The teacher should create a gameboard, as shown in the illustration.The teacher should create the followingthree types of cards:

"Shopping List" cards, each with aname of a different store on theShopping Spree board.Question cards for each store—threedifferent levels of difficulty should bereflected in the value of the ques-tions; the correct answers should beworth $10 for a "Super ShoppingSpree Special" card, $20 for a"Satisfying Saver" card, or $50 for a"Splurge" card, depending on thelevel of difficulty, from hardest to eas-iest.

The teacher can create a simple balance sheet in the following format:

Shopping Spree Debit Card Account

Debit Balance

TEACHING EXCEPTIONAL CHILDREN • JAN/FEB 2005 • 29

Figure 3. (Centlnued)

• Shopping Spree cards: These caninclude "Impulse Buy Cards" thatrequire purchase and "Sale" cardsthat reduce the cost of a purchase.

Playing Mie GiuiteA player shuffles the Shopping Spreecards face down into a pile.

The "Shopping List" cards are shuf-fled and a player deals five cards toeach person or team. The stores listedon these cards become the player's"Shopping List." Each player starts thegame with $500 in their Debit CardAccount. This amount is written on thefirst line under "Balance" on theAccount Balance Sheet.

Each player chooses a game pieceand places it on the square on the gameboard that is the same color as his orher playing piece. Each player rolls onedie. The highest die roll goes first, andplay then moves around the board tothe right.

Player «1 rolls all three dice. He orshe must then use at least two of thedice to form a mathematical question.The player must write down the equa-tion and the answer within 60 secondsof rolhng the dice. If the answer is cor-rect, the player moves that manyspaces vertically, horizontally, or diago-nally, making sure to only land on eachsquare once during a turn. If theanswer is incorrect or the player takesmore than 60 seconds to formulate andsolve the problem, the player's turnends and the next player rolls the dice.

To enter a store, players must landdirectly on the store area, being sure togo through the door, which is markedby a dashed line. If a player lands in astore for which he or she has a"Shopping List" card, he or she choos-es to answer a $10 "Super ShoppingSpree Special," a $20 "SatisfyingSaver," or a $50 "Splurge" question.Easier questions cost the players moremoney, providing motivation forattempting the more difficult questions.The person to that student's right asksthe question from the chosen storeQuestion card and checks the student'sanswer If the player responds correct-ly, he or she keeps the Question card,placing it on top of the corresponding"Shopping List" card. The player (henmarks the amount "paid" for the itembased on the face value of the card inthe Debit column of their balance sheetand records the new Balance in theappropriate column. If he or sheanswers incorrectly, the card goes tothe bottom of the card pile, and thenext player begins his or her turn.

A player who lands on an "S" spacetakes a "Shopping Spree" card. If the"Shopping Spree" card is an "ImpulseBuy" card, players must go directly tothe store indicated and attempt one ofthe Question cards. This is true even ifthe store indicated is not on theplayer's original Shopping List."if the "Shopping Spree" card is a "Sale"card, the player must use the designat-ed discount in the next store he or she

enters. If the player incorrectly an-swers the question, he or she forfeitsthe "Sate" card, and it is returned to thebottom of the "Shopping Spree" cardpile.

Afler purchasing an item from eachrequired store, the student returns tohis or her home square to win. Theplayer who has "purchased" all theitems on their "Shopping List" andreturns home first wins. If time runsout, the player who has made the mostpurchases from their "Shopping List"wins.

flnod IRcinloiis

• Students can make their own gameboards and use local shops andbanks.

• To promote cooperative learning, stu-dents can play in teams of twoagainst another team.

• The teacher can write math ques-tions that are based on skills that thestudents are learning in class, or stu-dents can prepare the questions.

• To adjust the time needed to play thegame, the teacher can increase orreduce the number of stores that stu-dents must visit by designating a dif-ferent number of items on each"Shopping List."

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30 • COUNCIL FOR EXCEPTIONAL CHILDREN