AC : STEPWISE METHOD FOR DEAF AND HARD-OF-HEARING STEM STUDENTS IN SOLVING WORD PROBLEMS

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1 AC : STEPWISE METHOD FOR DEAF AND HARD-OF-HEARING STEM STUDENTS IN SOLVING WORD PROBLEMS Gary Behm, Rchester Institute f Technlgy Gary Behm is a Senir Prject Assciate and Directr f the NTID Center n Access Technlgy Innvatin Labratry and a Visiting Lecturer at NTID. He is a deaf engineer at IBM wh received his BS frm RIT and his MS frm Lehigh University. He currently serves as a laned executive at NTID/RIT wrking in the Center n Access Technlgy and the department f Engineering Studies. At IBM, he is a delivery prject manager in the Rapid Applicatin Develpment Engineering System. Behm has six patents and has presented ver 20 scientific and technical papers at varius prfessinal cnferences. Jeanne Behm, Rchester Institute f Technlgy Jeanne Behm is a visiting ASL instructr at Rchester Institute f Technlgy / Natinal Technical Institute fr the Deaf. She has been invlved in hme educatin fr abut 20 years. ASL educatin in cntinuing educatin, cmmunity cllege, and the Deaf cmmunity has been her passinate invlvement. She received her B.S. frm RIT then wrked fr IBM Crpratin fr several years prir t hme educatin. Sctt Bellinger, Rchester Institute f Technlgy (COE) Sctt Bellinger is an assistant prfessr in the Autmatin Technlgies prgram at The Natinal Technical Institute fr the Deaf (NTID). Sctt served as the Directr f Manufacturing Technlgies at RIT's Center fr Integrated Manufacturing Studies (CIMS) befre jining NTID. He has mre than twenty years f experience in develping manufacturing systems with a specialty in factry autmatin. He served as Applicatins Engineer, Prpsals Engineer, Prject Manager and Applicatin Engineering Manager at Hansfrd Assembly & Test Systems (NY); Directr f Applicatins Engineering at Wes-tech Autmatin Systems (IL); and Vice-president f Engineering at Cx Autmatin (IL). Sctt has received an MS in Manufacturing Management and Leadership frm RIT in 1997 and a BS in Electrical Engineering and Cmputer Science frm the University f Illinis-Chicag in Jseph Stanislw, Rchester Institute f Technlgy Jseph Stanislw is a faculty in the Infrmatin and Cmputing Studies Department at the Rchester Institute f Technlgy / Natinal Technical Institute fr the Deaf. Je has been teaching and tutring cmputer and infrmatin technlgy t AOS/AAS/AS/BS students fr ver 9 years. He has a Bachelr s degree in Electrical Engineering Technlgy frm the Rchester Institute f Technlgy and a Master f Science in Cmputer Science frm Stevens Institute f Technlgy. Befre jining the NTID faculty he wrked fr several cmpanies as an electrical engineer, a physical designer, and a cmputer prgrammer fr ver 20 years. American Sciety fr Engineering Educatin, 2010 Page

2 StepWise Methd fr Deaf and Hard-f-Hearing STEM Students in Slving Wrd Prblems Abstract At Natinal Technical Institute fr the Deaf (NTID), a large percentage f the deaf / hard f hearing (d/hh) students enrlled in cllege level studies are challenged by their English and mathematical skills. 1 Because f these tw critical skills areas, they struggle t master the interpretatin f a wrd prblem r written instructinal manuals t a prblem in rder t derive a crrect slutin. The StepWise prcedural methd was develped as a general step-by-step guideline fr students t fllw in slving a scientific, technlgical, engineering, r mathematical prblem r the instructins f a wrd prblem. The gal was t help d/hh STEM students fcus n their English, mathematical and critical thinking skills while they srt thrugh wrd prblems. Based n several bservatins, sme d/hh students wh benefit frm this methd appear t have increased cmprehensin f the steps necessary t slve a wrd prblem. If the resulting answer des nt match the expected answer, StepWise allws students t red the prcess. This StepWise methd was develped and implemented during the winter f 2009 when the students struggled in an engineering curse with physics and math emphases. This methd will be tested in ther engineering and infrmatin technlgy curses. In sme prgramming curses, this methd is available t students wh develp sftware and web applicatins. Other applicatins are under investigatin. Results fr students wh utilized the StepWise methd will be presented and discussed. While the preliminary findings lk prmising, mre wrk needs t be addressed. The gal f this paper is t share the preliminary findings and t cllect feedback frm the instructrs at the cnference. Backgrund At NTID, a large percentage f the deaf / hard f hearing (d/hh) students enrlled in cllege level studies are challenged by their insufficiently develped English and mathematical skills. Because f a weakness in these tw critical skills areas, they struggle t understand wrd prblems and instructin manuals, which make it very difficult fr them t find crrect slutins. It has been well dcumented that the majrity f the deaf ppulatin has sme degree f reading and writing challenges. The rt f the prblem is a lack f cmmunicatin, especially during the early years. In ur sciety, hearing peple acquire their first language frm what is spken arund them, chiefly frm their parents and frm ther children. English as a spken language is very rich, and with ur technlgies, peple gather infrmatin thrugh varius audi mediums. Even cnsidering syntax, spken language usually has its wn set f grammatical patterns that may be quite different frm written language. Being deaf, especially at birth, affrds a persn very limited ways t acquire the language thrugh hearing and speaking. Page

3 Educatrs have struggled t find new ways t teach deaf students reading and writing. There is extensive research addressing these challenges. In a nutshell, the sner thse deaf children develp persnal cmmunicatin with family and cmmunity, the better the pprtunity fr the children t acquire the language with reading and writing skills. Cmmunicatin is the tie that binds children t parents and t sciety and that prvides fr scial and academic educatin. There is n aspect f educating deaf learners-frm infancy t adulthd-that des nt depend n r benefit frm clear and accessible cmmunicatin. 2 The mst cmmn apprach is t prvide deaf children an early interventin with listening devices such as cchlear implants and t start speech training at a very early age. Anther methd that has been prven t be successful is t teach deaf children sign language when they have nrmal visin. The challenge is fr parents and family t learn sign language. It is nt pssible t learn sign language in a shrt perid f time. The family culd start learning as sn as they find ut that the baby is deaf r hard f hearing but it will require effrt. There is nthing new abut these appraches and unfrtunately, they have nt always prven t be very successful. Even tday, a large percentage f the deaf cmmunity has reading cmprehensin and writing deficits and this has nt changed much ver the past 30 years. 3 When deaf r hard f hearing students arrive at cllege, they have high expectatins f themselves fr cmpleting bachelr s and graduate degrees. 4 The research led by Cuculick and Kelly has shwn thrugh statistical analysis that nly abut 17% f incming deaf students at NTID, 2001 and 2002 had the requisite reading and language skills t enter a baccalaureate prgram in their first year. Als, with the same data, it indicated that at NTID it takes lnger fr the deaf students t cmplete Assciate f Occupatinal Studies (AOS), Assciated f Applied Science (AAS), r Bachelr f Science (BS) degrees. Because f challenges with reading cmprehensin and writing skills, deaf peple face ther challenges in learning mathematics wrd prblem slving. Many NTID STEM students have t start with entry-level mathematics as a pre-requisite befre they can begin their majr in technical r engineering prgrams. The findings frm ne surce f educatinal research shw that regardless f instructinal settings, deaf students are nt being sufficiently engaged in a cgnitively challenging wrd prblem situatin. 5 A Structured Apprach The StepWise prcedural methd was develped as a general step-by-step guideline fr students t fllw in slving a scientific, technlgical, engineering, r mathematical wrd based prblem. The gal was t help d/hh STEM students use their English, mathematical and critical thinking skills while they srt thrugh wrd prblems. Based n numerus bservatins sme d/hh students wh benefit frm this methd can cmprehend and d what is necessary t slve a wrd prblem. If the resulting answer des nt match the expected answer, the StepWise methd allws students t crrect their mistakes and red the prcess until an acceptable answer is achieved. Page

4 After studying incrrect student answers t multiple wrd prblems, several patterns emerged. Students struggled with selecting the crrect frmula t use and als in applying them after selectin. Specific mistakes included: Selecting wrng frmula Using mixed units, i.e.: Secnds/minutes/hurs English/metric Inches/feet/miles/kilmeters Using cnversin factrs upside dwn (60 sec/min vs. min/60 sec) Using wrng data type when prgramming, i.e.: Integer/real/text string Cnstants/variables Unable t slve if several steps are required (tw unknwns) Algebraic mistakes Inability t estimate if answer is reasnable Basic magnitude errrs Incrrect units errrs (i.e., ft 2 fr vlume, ft/min 2 fr speed, etc.) In rder t assist students in aviding these mistakes, a structured, step-by-step prcedure was created fr appraching and slving wrd prblems. With this rdered prcess we seek t: Help students in selecting the crrect frmula t use Prvide ways t select the best sequence rder fr slving multi-answer prblems Prvide specific steps t fllw Remind students t unify units Imprve estimatin skills and reasnableness checking With these gals in mind, the StepWise methd was develped. The StepWise apprach will nw be shwn and a specific example will be demnstrated. StepWise Methd 1. List the desired gal fr the prblem (the unknwn r what is being asked fr) including units. If there is mre than ne questin, list all f the unknwns. 2. List all knwn and unknwn values (numeric value) 3. Lk at pssible frmulae fr slving prblem 4. Pick a frmula that has ne gal symbl (unknwn) while all ther symbls are knwn 5. If units d nt match (bth feet and inches OR English and metric OR minutes and secnds, etc.) cnvert values s that all are the same and match the gal 6. Simplify by eliminating any knwn zer values and, using algebra, rearrange frmula (symbls nly) s that the single unknwn is islated n the left side f equatin 7. Insert knwn values fr symbls including units 8. Slve using algebra, carefully preserving all units 9. Check result by substituting the result int the riginal frmula 10. If the answer is wrng r nt reasnable, r units in the answer d nt match expected values, red steps 4-9 Repeat steps 4-9 fr next part f the questin (if needed) Page

5 A specific illustratin fllws: A car is traveling at 60 mph. The brakes are applied unifrmly and the car cmes t a stp in 15 secnds. A) What is the acceleratin rate in feet/sec 2? B) Hw many feet did it take t stp? Step 1) List the desired gal fr the prblem (the unknwn r what is being asked fr) including units; If there are mre than ne questin, list all f the unknwns Example A) Acceleratin (a) =? ft/sec 2 B) Stpping distance (s) =? ft 2) List all Knwn and Unknwn values Knwn Time t = 15 sec Initial Velcity v 0 = 60 mph Final Velcity v = 0 mph Unknwn 3) Lk at pssible frmulae fr slving prblem 4) Pick a frmula that has ne gal symbl (unknwn) and all ther symbls knwn 5) If units d nt match (bth feet and inches OR English and metric OR minutes and secnds, etc.) cnvert values s that all are the same and match the gal units 6) Simplify by eliminating any knwn zer values and, using algebra, simplify and rearrange frmula (symbls nly) s that unknwn is islated n the left side f equatin 7) Insert knwn values fr symbls INCLUDING UNITS 8) Slve using algebra, carefully preserving all units 9) Check result by substituting the result int the riginal frmula 10) If the check fails r the answer is nt reasnable r units in the answer d nt match expected values, red step 4-9 Answer t part A) Acceleratin = ft/sec 2 Distance s =? ft Acceleratin a =? ft/sec 2 s = v 0 t + ½ at 2 v = v 0 + at v 2 = v as (frm Newtn s laws f unifrmly accelerated mtin) s = v 0 t + ½ at 2 tw unknwns (skip) v 2 = v as tw unknwns (skip) v = v 0 + at nly ne unknwn (OK) 60 mph (des nt match feet r secnds) 60 miles/hr x 5280 ft/mile x 1 hr/ 3600 sec v 0 = 88 ft/sec v = v 0 + at (v = 0 s substitute) 0 = v 0 + at at = - v 0 a = (-v 0 )/t (unknwn islated n left) a = (-88ft/sec)/15sec a = (-88ft/sec)/15sec a = ft/sec 2 NOTE: a is negative because deceleratin instead f acceleratin v = v 0 + at 0 = 88ft/sec ft/sec 2 * 15 sec 0 = 88ft/sec - 88 ft/sec 0 = 0 checks (Ok) Checking units a =? ft/sec 2 a = ft/sec 2 (Ok) Page

6 Repeat steps 4-9 fr part B) f the questin. Step 4b) Pick a frmula that has the gal symbl (unknwn) and all ther symbls knwn 5b) If units d nt match (bth feet and inches OR English and metric OR minutes and secnds, etc.) cnvert values s that all are the same and match the gal units 6b) Simplify by eliminating any knwn zer values and, using algebra, rearrange frmula (symbls nly) s that unknwn is islated n the left side f equatin 7b) Insert knwn values fr symbls INCLUDING UNITS 8b) Slve using algebra, carefully preserving all units 9b) Check result by substituting the result int the riginal frmula 10b) If the answer is nt reasnable r units in the answer d nt match expected values, red step 4-9 Example s = v 0 t + ½ at 2 nly ne unknwn (OK) v = v 0 + at all knwn nw s ignre v 2 = v as nly ne unknwn (OK) Either 1 st r 3 rd will wrk. I chse 3 rd Frm previus step 5 v 0 = 60 mph = 88 ft/sec v 2 = v as 0 = v as 2 2as = -v 0 s = (-v 2 0 )/2a s = (-v 2 0 )/2a s = (-88 ft/sec) 2 /(2 * ft/sec 2 ) s = (-7744ft 2 /sec 2 )/(-11.7 ft/sec 2 ) s = 660 ft v 2 = v as 0 = (88ft/sec) 2 + 2*(-5.87ft/sec 2 )*660 ft 0 = (7744ft 2 /sec 2 ) - (7744ft 2 /sec 2 ) 0 = 0 checks (Ok) s =? ft s = 660 ft (Ok) Answer t part B) Stpping distance = 660 ft Fr any wrd prblem, students will need t have memrized, be given, r knw hw t find all f the frmulae needed t slve the prblem. Just listing the knwn and unknwn values (step 2) can help students get a better big picture view f the prblem. Step 4 is smething many students struggle with n their wn. By cmparing the list f knwn and unknwn values with the ptential frmulae, and lking fr a frmula with nly ne unknwn, the selectin prcess becmes clear. Unifying units in step 5 can be supprted by in-class and hmewrk activities specifically fcused n cnversins frm metric t/frm English, and in making sure all units f a specific dimensin are the same. Fr the previus example, speed was given in miles per hur but the desired answer fr acceleratin was in feet per secnd 2 s bth distance (miles t feet) and time (hurs t secnds) cnversins were needed befre slving the prblem. Fr step 8 it is best t emphasize the imprtance f including units when applying algebra because arriving at an answer with incrrect units is usually an indicatin that either a wrng cnversin factr was used r an errr in algebra has ccurred. Students ften ignre units and just use numbers thus masking cmmn mistakes. Anther step ften mitted is simply substituting the answer back int the riginal frmula t see if the equatin is true. Page

7 Findings Befre develping the StepWise prcess, the authrs used examples and illustratins frm textbks and supplementary materials such as Schaum s Outline Series: Thery and Prblems f Engineering Mechanics including fully slved prblems. Students cntinued t struggle with wrd prblems. After develpment f wrksheets utlining the StepWise methd, the authrs made cmparisns in tw different curses: Digital Lgic, and Industrial Electrnics, students using the StepWise wrksheets scred 14% higher than thse withut n quiz wrd questins. The results lk prmising. One challenge encuntered in this study was lcating enugh d/hh students t frm tw grups t make meaningful cmparisns. A mre lngitudinal study will imprve the accuracy and usefulness f the results. In the spring quarter, the evaluatin will be applied in several different curses such as System Trubleshting, Prgramming, PC Hardware / Sftware, Cmputer Cncepts and Mechanical Devices and Systems curses. The gal f this paper is t share the methdlgy and t cllect feedback frm instructrs at the cnference. Bibligraphy 1 Rnald R. Kelly, Harry G. Lang, Keith Musley, Stacey M. Davis,2006 Deaf Cllege Students' Cmprehensin f Relatinal Language in Arithmetic Cmpare Prblems 2 Marschark, Lang, & Albertini, 2002 Bk: Educating Deaf Students: Frm Research t Practice 3 Dwaliby, Lang, 1999 Adjunct Aids in Instructinal Prse: A Multimedia Study With Deaf Cllege Students 4 Cuculick, & Kelly, 2003 Relating Deaf Students' Reading and Language Scres at Cllege Entry t Their Degree Cmpletin Rates 5 Kelly, Lang, & Pagliar, 2003 Mathematics Wrd Prblem Slving fr Deaf Students: A Survey f Practices in Grades 6-12 Page