A proposed esp reading syllabus for the second year students of mathematics department at ha noi pedagogical univesity number 2

tM4 MW M nfli m m M INISTRY OF EDUCATION AND TRAINING H A N O I U N IV ER SITY BUI THI HUONG GIANG A PROPOSED ESP READING SYLLABUS FOR TH E SECOND - YEAR STUDENTS OF M ATH E M ATIC S DEPARTM ENT A T H AN O I PED AG O G ICAL UNIVERSITY NUMBER S U B M IT T E D IN P A R T IA L F U L F IL L M E N T O F R E Q U IR E M E N T S O F T H E D E G R E E O F M A S T E R IN T E S O L Hanoi Jan u ary 2009 S T A T E M E N T O F A U T H O R S H IP I hereby certify that the m inor thesis entitled “A Proposed ESP Reading Syllabus fo r the Second-Year Students o f Mathematics Department at Hanoi Pedagogical University N um ber 2”, submitted in partial fulfillment o f the requirements for the degree o f M aster o f Arts in TESOL, is the result o f my work, except where otherwise acknowledged, and that this minor thesis or any part o f the same has not been submitted for a higher degree to any other university o r institution The research reported in this thesis was approved by Hanoi University Signed: Dated: TA B L E O F C O N TEN TS S T A T E M E N T O F A U T H O R S H I P I T A B L E O F C O N T E N T S II A C K N O W L E D G E M E N T S V A B S T R A C T VI L I S T O F A B B R E V I A T I O N S VII L I S T O F C H A R T S A N D T A B L E S V III C H A P T E R O N E : I N T R O D U C T I O N .I 1.1 R a t i o n a l e f o r t h e S t u d y 1.4 SCOPE OF THE STUDY 1.3 A i m s o f t h e S t u d y 1.4 S i g n i f i c a n c e o f t h e S t u d y 1.5 ORGANIZATION OF THE STUDY C H A P T E R T W O : L I T E R A T U R E R E V I E W 2.1 R e a d i n g T h e o r i e s / / D efinitions about R eading 2.1.2 The P rocess o f R ea d in g 2.1.3 R eading Sub- S k ills 2.2 AN OVERVIEW OF E S P 10 2.2.1 D efinitions about ESP 10 2.2.2 Types o f E S P / / 2.2.5 R eading in E S P 12 2.3 N e e d s A n a l y s i s 13 2.3.1 Types o f needs .13 2.3.2 Instrum ents to Collect D ata f o r a N eeds A n a lysis 18 2.4 SYLLABUSES 18 ! D efinitions o f Syllabus 18 2.4.2 Types o f S ylla b u ses 19 R e a d i n g M a t e r i a l s .21 A uthentic R eading M aterials 21 2.5.2 M aterials A d a p ta tio n 22 2.6 T e s t i n g in E S P 23 2.7 P r e v i o u s S t u d i e s in t h e F i e l d 24 C H A P T E R T H R E E : M E T H O D O L O G Y 26 R e s e a r c h Q u e s t i o n s 26 D a t a C o l l e c t io n I n s t r u m e n t s 26 D ocum ents A nalysis 26 3.2.2 Interview s f o r the Teachers o f M athem atics a n d the Teachers o f E n g lish 27 3.2.3 Q uestionnaire f o r the M athem atics U ndergraduates 28 3.3 S u b j e c t s o f t h e S t u d y 29 3 S u bjects o f th e In terview s 29 3.3.2 S u bjects o f the Q uestionnaire 30 3.4 D a t a C o l l e c t io n P r o c e d u r e s 30 C H A P T E R F O U R : P R E L IM IN A R Y R E S U L T S , D A T A A N A L Y S IS A N D R E S E A R C H F I N D I N G S 32 P r e l im in a r y R e s u l t s a n d D a t a A n a l y s is 32 1 P r e l im in a r y R e s u l t s o f t h e D o c u m e n t s A n a l y s is 32 / 1.1 F L D 's D ocum ented Curriculum A nalysis 32 4.J 1.2 A u th en tic Texts A n a lysis 33 4.1.1.3 L atest G E Exam ination Scores A nalysis 33 P r e l im in a r y R e s u l t s o f t h e I n t e r v ie w s f o r T e a c h e r s o f M a t h e m a t ic s 35 4.1.2.1 R eading T echnical D ocum ents 35 4.1.2.2 Types o f R eading M aterials 35 4.1.2.3 Text T yp es 36 4.1.2.4 N ecessary R eading Skills/ Strategies f o r Technical D ocum ents 36 4.1.2.5 Students *D ifficulties in Reading Technical D ocum ents .36 4.1.2.6 S u g g ested T o p ic s 37 l P r e l im in a r y R e s u l t s fr o m t h e In t e r v ie w s f o r T e a c h e r s o f E n g l is h 37 4.1.3.1 O bjectives o f th e ESP Reading C o u rse 37 4.1.3.2 S u b R eading Skills fo r the S ylla b u s .37 4.1.3.3 G ram m ar Item s f o r the Syllabus 38 4.1.3 E xercises f o r th e Syllabus 39 4.L3.5 S u g g ested R eading M aterials 39 1.4 P r e l im in a r y R e s u l t s o f t h e Q u e s t io n n a ir e 39 4.1.4.1 S tu d e n ts ' b a ck g ro u n d 39 1.4.2 M athem atics Undergraduates ' A ttitudes a n d E xpectations tow ards the ESP Course 40 4.1.4.3 M athem atics U ndergraduates' Purposes o f R ea d in g 41 1.4.4 M athem atics U ndergraduates' R eading A ctivities in G E le s s o n s 42 4.1.4.5 M athem atics U ndergraduates' Strategies o f D ealing with N ew V ocabulary 43 4.1.4.6 M athem atics U ndergraduates' D ifficulties in R eading G E Texts 44 4.1.4.7 M athem atics U ndergraduates' P references f o r Reading E xe rcises 45 1.4.8 M athem atics U ndergraduates' P references f o r Teacher s A ctivities 46 / M athem atics U ndergraduates' Preferences f o r Types o f Technical M a teria ls 47 4.1.4.10 M athem atics Undergraduates ’ Preferences f o r Text - T yp es 48 4.1.4.11 M athem atics U ndergraduates' Preferences f o r T opics 49 4.2 R e s e a r c h F i n d i n g s 50 The Learning N eeds f o r the M athem atics U ndergraduates 50 4.2.2, The Target N eeds f o r the M athem atics U ndergraduates 52 C H A P T E R F I V E : T H E P R O P O S E D S Y L L A B U S , S U G G E S T I O N S A N D C O N C L U S I O N S 54 5.1 THE PROPOSED SYLLABUS 54 5.1.1 The Time F ram e 54 5.1.2 A im s a n d O bjectives o f the ESP R eading C o u rse .54 1.3 The C ontents o f the Syllabus .55 5.2 S u g g e s t i o n s 65 5.2.1 M aterial A daptation 65 5.2.2 Suggestions f o r a Sam ple Unit 66 5.2.3 Suggestions f o r C ourse Assessm ent a n d T estin g 66 5.3 C o n c l u s i o n s 67 R E F E R E N C E S .70 A P P E N D I X E S 73 A P P E N D I X 73 A P P E N D I X 79 A P P E N D I X A 82 A P P E N D I X B 87 A P P E N D I X 93 A P P E N D I X 94 A P P E N D I X 97 A P P E N D I X 99 A P P E N D I X 100 iv ACKNOW LEDGEM ENTS I am greatly indebted to my supervisor Mrs Doan Thi Minh Nguyet, M.A, for her precious guidance Her generous support and encouragement gave me motivation and self-confidence to com plete this thesis My profound thanks also go to Mrs Nguyen Thai Ha, M.A, Vice Dean o f Postgraduate Departm ent for her extremely valuable help, useful comments and suggestions during my time studying at the Department, and especially during the study period My special thanks also go to the leader and my colleagues at Hanoi Pedagogical University N um ber for their support and encouragement I would like to thank my students for their enthusiasm and helpfulness during the process o f collecting data Finally, I would like to convey my deepest gratitude to my family for their love, care and support to help m e finish this study v A BSTR A C T The study A Proposed ESP Reading Syllabus f o r the Second-Year Students o f M athematics Department at Hanoi Pedagogical University Num ber 2” was carried out in order to meet the students' needs o f reading mathematic materials in English The study would also meet the requirements o f an ESP syllabus o f Foreign Language Department at Hanoi Pedagogical University N um ber as well as curriculum requirements o f M inistry o f Education and Training The overall aim o f the study was to propose an applicable syllabus for the second-year students at Hanoi pedagogical University Number 2.on the basis o f the learning needs as well as the target needs o f the M athematics undergraduates The study started with the review o f the literature related to the field o f the study including the theories o f reading, English for specific purposes, syllabuses, testing and the previous studies Next, an investigation on the learning needs and target needs o f the students o f M athem atics was done, and then a compile o f the learning needs and the target needs to identify the contents and skills that m ust be included in the syllabus In order to investigate students’ learning needs and target needs, the author sought for the data from sets o f documents, teachers o f M athematics, teachers o f English and 90 M athem atics undergraduate students The students provided information about their learning English and their learning needs The teachers o f M athematics, teachers o f English and the sets o f documents, which consist o f the docum ented curriculum o f Foreign Language Department at Hanoi Pedagogical University N um ber 2, the selected authentic texts and the latest examination scores provided the data about the students’ level before the course and the target needs The analysis o f the learning needs and target needs help to develop the final ESP reading syllabus for the secondyear students o f M athematics Department at Hanoi Pedagogical University number The study concluded with a proposal o f an ESP reading syllabus and some suggestions for ESP reading material design, teaching methodology, assessm ent and testing vi L IST O F A B BR EV IA TIO N S ESP English for Specific Purposes EAP English for Academic Purposes EBE English for Business and Economics ELT English Language Teaching EOP English for Occupational Purposes ESS English for Social Studies EST English for Science and Technology FLD Foreign Language Department GE General English HPUN Hanoi Pedagogical University N um ber MD M athem atics Department vii LIST O F C H A R T S AND T A B L E S Table 4.1: M athem atics undergraduates' latest GE exam ination scores Table 4.2: M athem atics undergraduates sub-parts exam ination results Chart 1: M athem atics undergraduates’ attitudes towards the ESP course Table 4.3: S tudents’ background Table 4.4: M athem atics undergraduates' expectations tow ards the ESP course Table 4.5: M athem atics undergraduates' reading purposes Table 4.6: M athem atics undergraduates’ current practice o f reading skills Table 4.7: M athem atics undergraduates' frequency o f using strategies to deal with new vocabulary Table 4.8: M athem atics undergraduates' difficulties when reading G E texts Table 4.9: M athem atics undergraduates' preferences for exercises Table 4.10: M athem atics undergraduates’ preferences for teacher’s activities Table 4.11: M athem atics undergraduates’ preferences for types o f technical reading materials Table 4.12: M athem atics undergraduates’ preferences for text-types Table 4.13: M athem atics undergraduates’ preferences for topics b B ài b o c ù a c c ấ n p h ẩ m c B ài b o trê n m n g d C c n g h iên u e.C c b ả n b áo c o f C c d a n g k h c (g h i r õ ) 10.B ạn th íc h đ ọ c lo i v ă n b n c h u y ê n n g n h n o sa u đ â y ? M ứ c đ ộ th íc h n h th ế n ? Mức độ Loại vân Thích Khơng thích Binh thường Khơng thlch lăm a N guyên bàn (độ kh ó , văn p h ong, chù đề, cấu trúc) v iết ch o n g i x ứ đọc b V ăn v iết c h o người học tiếng A nh, b ản xứ c D ang khác (ghi r õ ) 11 N h n g c h ủ đ ề n o d i đ â y b n m u ố n h ọ c tro n g k h ó a h ọ c tiế n g A n h c h u y ê n n g n h s ấ p tó i? (H ã y đ n h d ấ u v o m ú c đ ộ th íc h c ủ a b n ) _ Phân ngành C h ủ đ ề lự a ch ọn cho khóa h ọc S ố tư n h iê n P h é p tín h số h ọ c Số học S ố n g u y ê n tố v h ợ p số P h â n số T ỷ s ố v tỷ lệ S ố â m v số d n g P h é p tín h v i đ n th ứ c v đ a th ứ c Đ i số P h n g trìn h v b ấ t p h n g trìn h S ố m ũ 10 S ố h ữ u tỷ v số p h ứ c 91 M ứ c đ ộ th íc T h lc h B in h th n g K hơng th íc h la m H o n tồn k h n g th íc h 11 Lơ g a rít 12 Đ n g th ẳn g , tia v điểm 13 G ó c tro n g h ìn h trịn H ình h ọc 14 D iện tích cảu hình tro n g m ặt phẳng 15 R a an v đô 16 H ệ số th ự c v số phức 17 D ãy số v ch u ỗ i số G iải tích 18 H àm c ủ a m ộ t số biến 19 H ọ p củ a m ộ t số dạng vi p h ân 20 T ín h liên tục 92 A P P E N D IX INTERVIEW CHECKLIST FOR TEACHERS OF MATHEMATICS Do your stu d en ts need to read technical d o cu m en ts in English? A Y es □ B N o □ W hat types o f re a d in g m aterials you ask them to read? A T echnical b o oks B A rticles on w eb s C A rticles on p rin ted papers D R eports E R esearch Please give y our c o m m e n ts/ su g g estio n s ab o u t o th er d o cu m en ts ( if any) Do yo u o ften g iv e y o u r stu d en ts the follow ing types o f tex ts? A A uthentic texts B N on-auth en tic te x ts P lease g iv e y o u r c o m m e n ts/ su g g estio n s ab o u t o th er types o f te x ts ( if an y ) W hat fo llo w in g read in g ta sk s/ strateg ies can be useful fo r y o u r stu d en ts to read technical d o cu m en ts? A R eading for g en eral ideas B L ooking for sp ecific inform ation C R eading for d etails D G uessing m e an in g o f u n fam iliar lexical item s E R eading to u n d e rsta n d th e w rite rs’ p o in ts o f view s W hat y o u th in k are th e m ain d ifficu lties th at y our students m ay m eets when reading technical d o c u m e n ts in E n g lish ? A T echnical w o rd s B N on-technical w o rd s C G ram m atical stru c tu re s D A ppropriate re a d in g sk ills E T he scope o f k n o w le d g e th a t th e m aterials m ention W hat topics o f m a jo r areas sh o u ld be included in th e E S P tex tb o o k ? a T o p ics for A lg eb b T o p ics for A rith m etic c T o p ics for G eo m etry d T o p ics for A n aly sis 93 A P P E N D IX IN T E R V IE W C H E C K L IS T FO R T E A C H E R S O F EN G LISH What you think the objectives o f the ESP course fo r Mathematics students should be? / A T o help stu d en ts co n so lid ate gram m ar and structures B To provid e students w ith tech n ical vocabulary C T o im pro v e the stu d en ts’ read in g skills D T o im pro v e read in g skill and o th e r sk ills as well Which o f the following reading skills you think are necessary fo r the ESP reading syllabus? - R ecognizin g th e scrip t o f a language (d iscrim inating the g raphem es, follow ing graphem e seq u en cin g , u n d erstan d in g punctuation) - D educing the m ean in g and use o f unfam iliar lexical item s, th ro u g h understanding w ord form atio n or contextual clues - U nderstand in g ex p licitly stated inform ation; - U nderstan d in g in fo rm atio n in th e te x t, n ot ex p licitly stated, th ro u g h m aking inferences o r u n d erstan d in g fig u rativ e language; - U nderstan d in g co n cep tu al m ean in g , especially, q uantity and am o u n t, definiteness and indefiniten ess, co m p ariso n , degree; - U nderstand in g th e co m m u n icativ e v alu e (function) o f sentences and u tterances (w ith explicitly in d icato rs; w ith o u t ex p licitly indicators); - U nderstan d in g relatio n s w ith in th e sentence esp ecially elem en ts o f sentence m odificatio n stru ctu re (pre /p o st m odification), negation, m o d al auxiliaries; - E xpandin g salien t/ relev an t p o in ts in to sum m ary o f th e w h o le te x t, a specific idea/ topic in the text; - S kim m ing to ob tain the g ist o f th e text; - S canning to lo cate sp ecifically req u ired inform ation ; - U nderstan d in g co h esio n b etw een p arts o f a tex t th rough g ram m atical and lexical cohesion devices (rep etitio n , syn o n y m y , hyponym y, ); - D educing th e te x t th ro u g h rejectin g redundant o r irrelevant in fo rm atio n and items, especially (o m issio n o f clo sed - sy stem item s ) - R ecognizin g d isco u rse m a rk e rs fo r introducing, dev elo p in g , co n clu d in g an idea, transition to an o th er idea - D istinguish in g th e m ain id ea from su p p o rtin g details; - B asic reference sk ill o f u n d erstan d in g an d use o f headings, tab les o f contents; - P lanning and o rg an iz in g in fo rm atio n in ex pository language (esp presentation o f reports, ex p o u n d in g an arg u m en t, evalu atio n o f evidence), u sin g rhetorical functions, especially defin itio n , classificatio n , descrip tio n o f properties, d escrip tio n o f process or description o f ch an g e o f state; 94 - T ran sco d in g in fo rm atio n presented in diagram m atic d isp lay o r to diagram m atic display, th ro u g h in terp retatio n o r co m p letio n o f diagram s, ta b les o r graphs Which o f the following grammar structures you think are necessary for your students to understand English specialist materials? - R elative clau ses - Present tense - Past tense - Future tense - P articiples - G erund - C om parativ es - Infinitive - S uperlatives - Past p articip les - M odal verbs at p resen t - M odal v erb s in th e past - L inking verbs - Word formation - Passive voice - Conditionals - Conjunctions - Reported speech Which o f the following exercises you think are necessary fo r the ESP reading syllabus? - C o m p reh en sio n q u estio n s - M ultiple choice - T ru e/ F alse - T ran slatio n p c tic e - W ord- fo rm atio n - G ap- Filling - O rganizin g in fo rm atio n in th e text - Identifyin g facts from o p in io n s - C om pleting p arag rap h s w ith in fo rm atio n from diagram s - S entence tran sfo rm atio n - S entence b u ild in g 95 - S um m arizing - N ote- taking W h ic h o f th e fo llo w in g m a teria ls y o u th in k th e E S P s tu d e n ts s h o u ld learn? A B ooks B A rticles on papers C A rticles on w eb s D R esearch E R eports 96 A P P E N D IX T H E T O P IC S S U G G E S T E D BY T H E T E A C H E R S O F M A T H E M A T IC S FO R T H E S Y L L A B U S S u b d iv is io n T o p ics can be chosen to include in the syllabus - N atu ral num bers - A rith m etic operations - D ivisibility - P rim e and co m p o site num bers A rithm etic - F ractions - D ecim al and co m m o n fractions - R o u n d in g o ff - A p p ro x im ate num bers - M ean - R atio and proportion - N eg ativ e and p o sitiv e num bers - O p eratio n s w ith neg ativ e and positive num bers - O p eratio n s w ith m onom ials and polynom ials - E q u atio n s A lgebra - E x p o n en ts - Irrational num bers - C o m p lex num bers - H ig h er d eg ree o f equations - In equalities - L o g arith m s - S traig h t line, ray line and points - S im ilarities o f plane figures - A n g les in a circle G eom etry - A reas o f plane figures - P ro jectio n s - C ylinders - The Cone - T h e Sphere - Solid angles 97 - R ad ian s and degrees - T rig o n o m etric function from an angle - G rap h ical so lu tio n o f equations and inequalities - T h e real and com plex num ber system s - B asic topology - N u m erical sequences and series A nalysis - C ontinuity - D ifferen tiatio n - T h e R iem an n - Stieltjes Integral - S eq u en ces and series o f functions - S om e sp ecial functions - F u n ctio n s o f several variables - In teg ratio n o f d ifferential form s 98 APPENDIX S U G G E S T E D S O U R C E S O F T E A C H IN G M A T E R IA L S R ockal'ellar ( 1()X2) C onvex Analysis Princeton l ’n i\c rs ii\ Princeton N e u York I lerstein I N ( I % ) Topics in Algebra Blaisdell Publishing C om pany N ew York M eshane K J ( 1944) Integration Prieeton U niversih Press Princeton N.I Singer l.M T horpe J.A (1 % ) Lecture S o les on Elem entary Topology a m i (¡cam elry Scott I-oresm an and C om pany G lenview III H ardy, G H ( 1950) P ure M athem atics C am bridge lim e r s itv Press N e u York () Flem ing W 11 (1 ) Functions o f Several Variables A ddison-W esley Publishing C om pany Inc R eading M ass M ahnos P R (1950) M easure Theory D Van N ostrand C om pany Inc Princeton NJ S W ebsites: h ttp:/7w w w w orIdfram com / Into:// w w w m at h Ib ru m ,o rcJ 99 A PPE N D IX A SA M PLE LESSON A N IN T R O D U C T IO N T O M A T H E M A T IC S Before You Read D iscuss the fo llo w in g qu estio n s in group H ow im portant d o es m athem atics play in our daily life? W hat are th e m ain branches o f m athem atics? R E A D IN G T he w ord “ m ath em atics” com es from the G reek m athem ata, w h ich m eans “things that are learned ” It m ay seem odd to apply this phrase to a sin g le field o f know ledge, but we should point o u t th at for the ancient G reeks, m ath em atics in clu d ed n ot only the study o f num bers an d space but also astronom y and m usic N o w ad ay s, o f course, w e not think o f astro n o m y and m usic as m athem atical su b jects; y et th e scope o f m athem atics to d a y is b ro ad er than ever M odem m ath em atics is a vast field o f know ledge w ith m an y su b d iv isio n s T here is, first o f all, th e m ath em atics o f num bers, o r quantity T h e b ran ch o f arith m etic deals w ith particular n u m b ers, such as 3, o r 101/2 o r 12.5 W hen w e add, su b tract, m ultiply, or d iv id e such n u m b ers o r get their square roots o r sq u ares, w e a re engaging in arithm etical o p eratio n s Som etim es w e w ish to consider, n o t p articu la r num bers, but relationships th at w ill apply to w hole groups o f num bers W e study su ch relationships in alg eb ra, an o th er b ran ch o f the science o f quantity In alg eb ra, a sy m b o l, such as the letter a o r b , stan d s for an entire class o f num bers For ex am p le, in the form ula: (a+2)2 = a2 + a + , the letter a represents any num ber T h e relationship w h ich is expressed in th e form ula rem ain s th e sam e w hether a stands for 1, o r 5, o r 10, o r an y num ber M athem atics also stu d ies shapes in space, w hich m ay be th o u g h t o f as a w orld o f points, surfaces, an d solids W e study the properties o f d ifferen t sh ap es and the relations betw een th em , and w e learn how to m easure them T h is sp ace science is called geom etry P lan e geom etry is concerned w ith points, lin es, fig u res in a single plane - a su rface w ith o n ly tw o dim ensions T h e study o f th e th ree-d im en sio n al w orld is called so lid g eom etry T rigonom etry (“trian g le m easu rem en t” ) is an offshoot o f geom etry It is b ased on th e fact th at w hen certain parts o f trian g les are know n, one can d eterm in e the rem ain in g parts and solve m any different problem s A nalytic g eo m etry com bines algebra and geom etry - gen eralized n u m b ers and space relationships It lo cates geom etrical figures in space It ex p lain s circles, ellipses, and o ther figures in te rm s o f algebraic form ulas T he b ran ch o f m ath em atics called calculus is based on th e stu d y o f functions I f the value o f a giv en q u an tity depends on the value w e assig n to a seco n d quantity, w e say th at th e first q u an tity is a function o f the second In integral calcu lu s, w e a re interested in th e lim it o f the d ifferen t values o f a variable function In differen tial calculus, w e d eterm ine th e rate o f ch an g e o f a variable function S tatistics, an o th er b ran ch o f m athem atics, involves the accu m u latio n and tabulation o f data w h ich are ex p ressed in quantities, and the setting up o f general law s w hich are based on such data T h e theory o f probability enables one to calcu late th e chances that certain ev en ts w ill o ccu r - such as the 50 percent chance th at a coin toss will produce 100 heads In th e social sciences, probability can be used to predict the n u m b er o f boys and girls th a t w ill b e born in a particular place at a particular tim e T hese are o n ly a few o f the m any subdivisions o f m athem atics B esides being the m ost ex ten siv e field o f know ledge in its ow n right, it rep resen ts a logical approach that can b e ap p lied to m any different fields It carefully d efin es the ideas that are to be discu ssed an d clearly states the assum ptions th at can b e m ade T h en on the basis o f both the d e fin itio n s and the assum ptions, it forges a chain o f proofs, each link in the chain is as stro n g as any other M athem aticians have d isp lay ed w onderful pow ers o f im agination in d eterm in in g w hat can be proved and in co n stru ctin g ingenious m ethods o f proof (T ext ex tracted fro m The n ew b o o k o f p o p u la r sciences selected by G rothier) C om p reh en sio n q u estion s A nsw er the fo llo w in g qu estio n s referring to the inform ation giv en in th e text D o p eo p le n o w ad ay s think that m athem atics includes as m any su b jects as in the ancient tim e? W h y ? W hat are som e arith m etical operations? W hat d o es a sy m b o l such as the letter a o r b m ean in algebra? W hat m ay p eo p le think o f shapes w hich o ccu r in space? W hat can p eo p le d o w ith trigonom etry? H ow d o es an aly tic geom etry com bine alg eb and geom etry? W hen can w e say th at a quantity is a function o f another? W hat are th e su b d iv isio n s o f calculus? T ru e o r False D ecide i f th e fo llo w in g statem ents are true (T) o r false (F ) acco rd in g to the inform ation given in the text C orrect false statem ents M ath em ata m e an s “th in g s th at are learned” because m ath em atics in clu d ed not only th e study o f n u m b ers an d space b ut also astronom y and m usic for th e an cien t G reeks M o d em m ath em atics stu d ies only num bers o r q uantity and sh ap es in space A nalytic g eo m etry sh o w s th e relationships betw een generalized n u m b ers and space T rig o n o m etry h elp s us to find o ut the unknow n parts o f a trian g le w h en w e are given certain parts o f it 101 C alculus is d iv id ed into integral and differential People can pred ict the n u m b er o f boys and girls that will be b o m in a particular place at a p articu lar tim e w ith the help o f a branch o f m ath em atics called statistics M athem atics is based on definitions and assum ptions to give out a chain o f proofs G ap fd lin g I V ocab ulary review C hoose the ap p ro p riate w ord o r phrase to fill in each gap by referrin g to th e reading d e a ls w ith p ro p e rtie s c o n c e rn e d s u b d iv is io n s a s s ig n a s s u m p tio n s in c lu d e d s ta n d s fo r th o u g h t o f in te rm s o f W e sh o u ld p o in t o ut th at for the ancient G reek, m athem atics not only the stu d y o f n u m b ers and space b ut also astronom y and m usic M odem m ath em atics is a vast field o f know ledge w ith m a n y T he b ran ch o f a rith m e tic particular num bers, such as 3, o r 101/2 o r 12.5 In algebra, a sy m b o l, such as th e letter a o r b , an entire class of num bers W e stu d y t h e .o f different shapes and the relatio n s betw een them , and w e learn h o w to m easu re them P lane g eo m etry i s w ith points, lines, figures in a single plane - a surface w ith o n ly tw o dim ensions It explain s circles, ellip ses, and o th e r f ig u r e s alg eb raic form ulas I f th e v alu e o f a given q u an tity depends on th e value w e to a second q u an tity , w e say th at the first q uantity is a function o f the second M athem atics also stu d ies shapes in space, w hich m ay b e .as a w orld o f points, su rfaces, and solids 10 It care fu lly d efin e s the ideas th at are to be discussed an d clearly states the th at can be made 11 V ocab u la ry in n ew context C hoose an ap p ro p riate w ord o r p h rase given above to fill in each g ap in the follow ing sentences (Y o u m ay have to change th e w ords if necessary) Integral and d ifferen tial calculus a r e o f calculus A nalytic g eo m etry m ay be as a co m b in atio n o f algebra and geom etry S olid g eo m etry i s w ith three-dim ensional figures 102 S ta tis tic s .data M athem atical n o ta tio n sig n s and sym bols an an g le in m athem atics Z T h e sign T h e .o f defin ite integral will be discussed in the next lesson In differen tial g eo m etry , peo p le study p ro p erties o f cu rv es and surfaces and their g eneralizatio n s calculus P ostulates a r e .w ith o u t proof 10 We c a n th is defin itio n to d ifferential calculus G R A M M A T IC A L F O C U S RELATIVE CLAUSE A clause is a d ep en d e n t sen ten ce A relative clau se functions as an adjective It is used to m odify a n o u n in the in d ep en d en t sen ten ce and goes right after th at noun It tells us w hich person o r th in g (o r w h at kind o f perso n o r thing) the sp eak er m eans Exam ple: A m a th em atician is a perso n w ho studies m athem atics “ w ho studies m ath em atics” m athem atician is is a relativ e clau se to tell us w hich perso n a A rithm etic is a branch o f m ath em atics w hich d eals w ith p articular num bers “w hich deals w ith p articu lar n u m b ers” is a relativ e clau se to tell us w hat arith m etic is N ote: “ w h o ” and “ w h ic h ” in rela tiv e clauses are called relativ e pronouns w hich are used to com bine relativ e clau se s w ith the n o uns they m odify W e use “w ho” in a relativ e clau se w h en w e talk a b o u t people W e use “w hich” in a relativ e clau se w hen w e talk ab o u t things o r ideas “T h at” can be u sed to rep lace both “w ho” and “w h ich ” in relative clau ses in m ost cases T hus the ab o v e ex am p les can be w ritten as follow : A m ath em atician is a p erso n th at stu d ies m athem atics A rithm etic is a b ran ch o f m ath em atics that d eals w ith p articu lar num bers R elative p ro n o u n s can b e su b ject p ro n o u n s (th ey are subjects o f relative clau ses) as in the abov e ex am p les R elative p ro n o u n s can also be object p ro n o u n s (they are o b jects o f relative clauses) E xam ples: T h e scientist w h o I am read in g ab o u t w on th e N o b el prize last year M athem atics is o n e o f th e m ain su b jects w h ich all school children have to learn at school 103 F U R T H E R P R A C T IC E R ecogn ition L ist out all the rela tiv e clau se s w hich ap p ear in the reading W R IT IN G C o m b in e the fo llo w in g p airs o f sentences to m ak e co m p lex sen ten ces w ith relative clauses P lane geo m etry is a su b d iv isio n o f g eom etry It is co n cern ed w ith p o in ts, lines, and figures in a sin g le plan e W e use sy m b o ls su ch a s the letter a o r b in algebra T h ey stand fo r an en tire class o f num bers N am is one o f th e b est stu d en ts in o u r class H e w ish es to b eco m e a m athem atician T o som e ex ten t, all o f u s are m athem aticians W e use arith m e tic ev ery d ay in our lives T h ere is a b ran ch o f m ath em atics called calcu lu s It is based on th e study o f functions B ertrand R u ssell w as an im portant th cen tu ry m ath em atician H e w rote th e book: “ P rin cip les o f M ath e m a tic s” W e are stu d y in g m o d e ls o f geom etry T h ese m o d els su g g est th e id eas o f a point, o f a plane, o f a lin e a n d o th e r g eom etric figures W e can co n stru ct a m a g ic ring It is called M o b iu s strip A lb ert E in stein w as b o m in G erm any H e d ev elo p ed th e th eory o f relativity 10 C an to r d ev elo p ed th e th eory o f set T h is th eo ry h as b een ap p lied to v ario u s fields, in clu d in g h ig h e r a lg e b an d statistics T R A N S L A T IO N P R A C T IC E T n sla te th e fo llo w in g p assage into V ietn a m ese M ath em atics as a scien ce, view ed as a w hole, is a co llectio n o f b ran ch e s T h e largest b ran ch is th at w h ic h b u ild s on the o rd in ary w h o le nu m b ers, fractio n s, and irrational n u m b ers, o r w h at, co llectiv ely , is called th e real n u m b e r system A rith m etic, algebra, th e stu d y o f fu n ctio n s, th e calculus in logical o rd er are all d ev elo p m en ts o f the real n u m b e r system T h is p art o f m ath em atics is term ed th e m a th em a tic s o f num ber A second branch is g eo m e try co n sistin g o f sev eral g eom etries M ath em atics c o n ta in s m an y m o re div isio n s E ach b ran ch h as th e sam e logical stru ctu re: it b e g in s w ith certain co n cep ts, such as th e w h o le n u m b ers o r in teg ers in the m ath em atics o f n u m b e r, and such as po in t, lin e and trian g le in g eom etry T h ese co n ce p ts m u st v erify ex p licitly stated ax io m s Som e o f the ax io m s o f th e m ath em atics 104 o f num ber are th e associative, com m utative, and d istributive p ro p erties and the axiom s ab o u t equ alities S om e o f the axiom s o f geom etry a re th a t tw o points determ ine a line, all right angles are equal, etc From the co n cep ts an d axiom s theorem s are d ed uced H ence, from the standpoint o f structure, th e co n ce p ts, axiom s and theorem s are the essential com ponents o f any com partm ent o f m athem atics W e m ust break d o w n m athem atics into separately tau g h t subjects, but this com partm en talizatio n taken as a necessity, m ust be co m p en sated for as m uch as possible S tu d en ts m u st see the interrelationships o f the v ario u s areas and the im portance o f m ath em atics fo r o th er dom ains K now ledge is n ot ad d itiv e b ut an organic w hole, an d m ath em atics is an inseparable part o f th at w h o le T h e full significance o f m ath em atics can b e seen and taught only in te rm s o f its intim ate relationships to o th e r fields o f know ledge I f m athem atics is isolated from other provinces, it lo ses im portance (Text extra c ted fr o m D orozhkina) E xtensive E nglish course fo r M a th em a ticia n s by v.p T ran slate th e fo llo w in g sen ten ces into English H ình học phẳng v hinh học k h ô n g gian dạy trường cấp g ọi hình học clit CĨ sá u p h é p tín h c b ả n tro n g s ố h ọ c : c ộ n g , trừ , n h â n , c h ia , luỹ th a v k h că n N hững ý tư n g c sở v ề vi p hân, tíc h phân đư ợc hai nhà toán h ọ c số n g th ế kỷ 17 Sir Isaac N ew to n c ủ a A nh v B aron G ottfried W ilhelm w on L eib n iz củ a Đ ức phát iriển m ột cách đ ộ c lập với 105 ... C H A R T S AND T A B L E S Table 4.1: M athem atics undergraduates'' latest GE exam ination scores Table 4 .2: M athem atics undergraduates sub-parts exam ination results Chart 1: M athem atics... course and the target needs The analysis o f the learning needs and target needs help to develop the final ESP reading syllabus for the secondyear students o f M athematics Department at Hanoi Pedagogical. .. answers to the following questions: W hat are the language learning needs o f undergraduate students o f M athematics? W hat are the language target needs o f undergraduate students o f M athematics?