Ac tive Co lla b o ra tive L e a rning a nd F a c ulty De ve lo - PowerPoint PPT Presentation

Ac tive Co lla b o ra tive L e a rning a nd F a c ulty De ve lo pme nt in the Re de sig n o f I ntro duc to ry Ma the ma tic s Co urse Mic he lle Gua n a nd Ve sna K ilib a rda I U No rthwe st Ja nua ry 19 th , 2019 Jo int Ma the ma tic s Me e ting s, Ba ltimo re , MD

Why is Our Re de sig n I mpo rta nt?  Introductory courses enroll twice as many students as all other mathematics courses combined [CBMS, 2000].  Intro math courses have the greatest impact on strengthening students' quantitative and logical reasoning abilities [CUPM, 2004].  What are difficulties in Intro Math Courses?  Low proficiency in symbol manipulation  Perception that mathematics eludes mastery  Lack of engagement and effective practice [Levi at al, 2016]

I U No rthwe st – re g io na l, urb a n, c o mmute r unive rsity with 40% mino rity stude nt po pula tio n  Re de sig n Co urse s – Ga te wa y c o urse s (20-40 stude nts) sing – 9-11 se c tio ns pe r M100 Mathe matic s for L ibe r al Ar ts and Nur se me ste r two inte rve ntio ns in 2016 a nd two in 2017(instruc to rs vo lunte e re d), F A2018 – a ll 9 se c tio ns a – 5 se c tio ns, M117 Inte r me diate Alge br 2 with inte rve ntio ns (two o f the a utho rs)

Our Multifa c e te d Appro a c h  PIGS - Study Ac tive Co lla b o ra tive L e a rning  Pursue Gra nt Writing – Pro vide Re so urc e s fo r F a c ulty De ve lo pme nt a nd I nvo lve me nt in Co urse Re de sig n  Ma the ma tic s Pla c e me nt Pe e r Co a c hing  Ca re fully Ca lib ra te d Pla c e me nt E xa ms  E xplo re me a ning ful pro b le ms in g ro ups, te st c o nje c ture s, find so lutio ns, a nd e xpla in re sults.  Co mmo n Midte rm a nd F ina l E xa ms  Atte nda nc e a nd Ho me wo rk  Asso c ia te F a c ulty Wo rksho p

De finitio n o f Ac tive Co lla b o ra tive L e a rning - I nstruc tio na l me tho d tha t e ng a g e s stude nts in the le a rning pro c e ss – a c tivitie s intro duc e d into the c la ssro o m with va rying inte nsitie s (10% to 100% o f c la ss time ) - Re q uire s stude nts to do me a ning ful le a rning a c tivitie s a nd think a b o ut wha t the y a re do ing - I nstruc to r pro vide s fo rma tive a sse ssme nt - I nq uiry-b a se d le a rning (I BL ) – c lo se ly re la te d – e mpha size s individua l kno wle dg e c o nstruc tio n suppo rte d b y pe e r inte ra c tio ns: e xplo ring , te sting c o nje c ture s, de ve lo ping pro o fs a nd so lutio ns, e xpla ining

Ac tive le arning inc re ase s stude nt pe rfo rmanc e in sc ie nc e , e ng ine e ring , and mathe matic s [ F re e ma n e t a l, 2014]  Me ta -a na lysis o f 225 studie s  E xa mina tio n sc o re s o r fa ilure ra te s whe n c o mpa ring stude nt pe rfo rma nc e in unde rg ra dua te ST E M c o urse s unde r T ra ditio na l L e c turing ve rsus ve rsa Ac tive L e a rning .

Re sults  Ave ra g e e xa mina tio n sc o re s impro ve d b y a b o ut 6% in a c tive le a rning se c tio ns  Stude nts in c la sse s with tra ditio na l le c turing we re 1.5 time s mo re like ly to fa il tha n we re stude nts in c la sse s with a c tive le a rning .  He te ro g e ne ity a na lyse s indic a te d tha t b o th re sults ho ld a c ro ss the ST E M disc ipline s

F urthe r F inding s  Ac tive le a rning inc re a se s sc o re s o n c o nc e pt inve nto rie s mo re tha n o n c o urse e xa mina tio ns  Ac tive le a rning ha s a g re a te r impa c t o n stude nt ma ste ry o f hig he r- ve rsus lo we r-le ve l c o g nitive skills [Ha uko o s GD, Pe nic k JE (1983), Ma rtin e t a l (2007), Co rdra y e t a l (2009), Je nse n JL , L a wso n A (2011)]  Ac tive le a rning a ppe a rs e ffe c tive a c ro ss a ll c la ss size s— although the greatest effects are in small (n ≤ 50) classes.

Mo re Re sults  No sta tistic a lly sig nific a nt diffe re nc e in a c tive le a rning ’ s e ffe c t size whe n c o mpa ring  (i) c o urse s fo r ma jo rs ve rsus no n-ma jo rs (Q = 0.045, df = 1, P = 0.883; T a b le S1D), o r  (ii) intro duc to ry ve rsus uppe r-divisio n c o urse s (Q = 0.046, df = 1, P = 0.829; T a b le s S1E a nd S2D).  Ac tive le a rning ha s a dispro po rtio na te ly b e ne fic ia l e ffe c t o n me mb e rs o f mino rity g ro ups in ST E M fie lds [Uri T re isma n (2009)]

Introduction to Mathematical Modeling [Levi at al, 2016]  Majors: education, social and health sciences, arts and humanities  Up to 40 students in class  Objective: translate everyday problems into mathematics language, use math and technology to solve them, communicate solution  Hybrid of different instructional techniques over 4 semesters: face-to- face, online, partially or fully in computer lab; Excel worksheets, homework, Quizzes, Exams in CMS (increasing number of interventions from SP11-FA12) - Communication. - In-class Assignments and Active Learning - a graded graded assignment during each class period

Grades in all sections of Mathematics Modeling Class, Spring 2010-Fall 2012. M=1 : Intervention classes, M=2 : All others [Levi at al, 2016]

Re visio n o f the M100 c la ss a t I U No rthwe st  Ma the ma tic s Pla c e me nt Pe e r Co a c hing  Ca re fully Ca lib ra te d Pla c e me nt E xa ms

Ac tive Co lla b o ra tive L e a rning I n e a c h inte rve ntio n se c tio n, the instruc to r vo lunte e re d to inc o rpo ra te five c o lla b o ra tive a c tivitie s into the ir le c ture s. E a c h a c tivity  c o ve rs o ne to pic / c o nc e pt in the c o urse  is de sig ne d a s a n a pplic a tio n pro b le m  ta ke s a b o ut 15 - 20 minute s  is c o mple te d b y a sma ll g ro up o f stude nts (3 - 4)

Sa mple pro b le ms I ma g ine tha t la st summe r yo u a nd yo ur frie nds de c ide d to run a ka ya k-re nta l b usine ss o n L a ke Mic hig a n. Be c a use the inc o me is g o o d, yo u a re c o ntinuing the ka ya k-re nta l b usine ss until the ka ya k se a so n is o ve r. L e t’ s a ssume tha t whe n yo u sta rte d yo ur b usine ss, yo u c ha rg e d $12 pe r c a no e a nd a ve ra g e d 36 re nta ls a da y. Yo u re a d in Cano e & Kayak Mag azine tha t, fo r e ve ry fifty-c e nt inc re a se in re nta l pric e , the a ve ra g e b usine ss c a n e xpe c t to lo se two re nta ls a da y. Use this info rma tio n to ma ximize yo ur inc o me . Sho uld yo u c ha ng e yo ur re nta l c ha rg e b a se d o n the info rma tio n o b ta ine d? Yo u a re pla ying the Po ke mo n g o in Chic a g o . T he numb e r o f Po ke mo n yo u mig ht se e is inve rse ly pro po rtio na l to the dista nc e b e twe e n yo ur lo c a tio n a nd do wnto wn Chic a g o . Suppo se tha t yo u c a pture 4 Po ke mo n whe n yo u a re 3000 me te rs a wa y fro m do wnto wn Chic a g o . Ho w ma ny Po ke mo n do yo u e xpe c t to c a pture whe n yo u a re 500 me te rs a wa y fro m do wnto wn Chic a g o ?

Canc e r T r e atme nt Pr otoc ol T he de sig n o f the tre a tme nt pro to c o l fo r c a nc e r pa tie nts is ve ry impo rta nt. An inc o rre c t c a lc ula tio n o f a ra te fo r c a nc e r drug , fluo ro ura c il, le a d to a c o mple te o rg a n fa ilure o f a 43-ye a r-o ld c a nc e r pa tie nt tha t wa s b e ing tre a te d in a n a mb ula to ry c linic in July 2006. he following is the a c tua l proble m the me dic a l sta ff fa c e d . Would you be a ble to T de te rmine the ra te c orre c tly ? A do c to r o rde re d F luo ro ura c il (c a nc e r me dic ine ) a t ra te o f 5,250 mg intra ve no us (I V) c o ntinuo us o ve r 4 da ys. T he fluo ro ura c il b a g c o nta ine d so lutio n with c o nc e ntra tio n o f 45.57 mg / mL . De te rmine the infusio n ra te o f I V fo r the pa tie nt. T ha t is, a t wha t ra te (mL / ho ur) the pa tie nt sho uld re c e ive 5,250 mg fluo ro ura c il o ve r 4 da ys?

COUNT ING T E CHNIQUE S Ha rry Po tte r’ s c lo se t c o nta ins 12 numb e re d b ro o ms, o f whic h 8 a re Co me t T wo Sixty’ s (numb e re d 1 - 8) a nd 4 a re Nimb us T wo T ho usa nd’ s (Numb e re d 9-12). Ha rry, Ro n, Ge o rg e a nd F re d wa nt to sne a k o ut fo r a g a me o f Quidditc h in the middle o f the nig ht. T he y do n’ t wa nt to turn o n the lig ht in c a se Sna pe c a tc he s the m. T he y re a c h in the c lo se t a nd pull o ut a sa mple o f 4 b ro o ms. Ho w ma ny diffe re nt wa ys c a n Ha rry a nd his frie nds c ho o se the ir b ro o ms? I de ntify two po ssib le so lutio ns he re : o ne is if we o nly c a re a b o ut whic h fo ur b ro o ms a re pulle d o ut, the o the r is if we ke e p tra c k o f whic h b ro o m Ha rry g e ts, whic h b ro o m Ro n g e ts, a nd so o n. E xpla in why the a nswe rs a re diffe re nt fo r the se two sc e na rio s.