Digital Tools in Matriculation Exams
Explore the role of digital tools, including CAS calculators, in Finnish matriculation exams. Learn how these tools are used, the impact on problem-solving, and the importance of manual analysis in mathematical activities.
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Presentation Transcript
GUIDINGQUESTIONS WHATIS MATH? IS IT, USEONECASCOMMAND? WHATIS MATHEMATICALACTIVITY?
THE FINNISH MATRICULATION FINNISH MATRICULATION EXAMINATION EXAMINATION national exam taken at the end of secondary education to qualify for entry into university. In practice, the test also constitutes the high school's final exam(s) universities accept students based on the entrance exam points, the matriculation exam points, a combined score of these two, and possibly other merits Exams twice a year
IN 90S GRAPHICALCALCULATORS, NO CAS. IN 2012? CAS CALCULATORS DIGITAL EXAMSIN 2019 2020 HANDHELDCALCULATORSWERE ALLOWEDLASTTIME NOW A-PART, 4 PROBLEMS, NO CAS B-PART, 6 PROBLEMS, CAS STUDENTSUSEEXAMENVIROMENT FROMTHEBEGINOF UPPERSECONDARYSCHOOL Iltasanomat 15.4.2013 Top gradein examwith 200 calculator brains arenotneeded
Tool GNOME GNOME KCalc KCalc SpeedCrunch SpeedCrunch Texas Instruments TI Texas Instruments TI- -Nspire CAS* CAS* wxMaxima* wxMaxima* Casio ClassPad Manager* Casio ClassPad Manager* GeoGebra 5* ja Classic* GeoGebra 5* ja Classic* Python Python Libre Libreoffice office calculator calculator calculator Nspire CAS CAS CAS CAS
THEROLEOF DIGITALTOOLSIN EXAMS Theroleis evaluatedin eachproblem. If CAS is used, it shouldbeableto beseenfromthe answer. Calculatorcanbeusedin routine taskssuchas simplifyingexpressions, solvingequations, derivatingand integrat ngfunctions In problemswereanalysingis needed(prove), the answerfromcalculatoris notenought, other argumentis reguired.
CHECKINGOF MATRICULATIONEXAMS Teachers makeprelimanarychecking Afterexams, nationalgraders (40-50 person) Meetand decidefinalguidelinesfor points Make thefinalchecking
PROBLEMS, WERETOOLSHELP IN SOLUTION Lower Lowerlevel level Upper Upper level level S23 5, 6, 8, 9, 11, 12 6, 9 K23 5, 6, 8, 9, 10, 12, 13 5, 6, 7 s22 5, 6, 9, 10, 11, 13 5, 8, 9?
TOOLS ARE MORE USEFULL IN LOWER LEVEL MATH THAN IN HIGHER LEVEL MATH IN HIGHER LEVEL, 1-3/13 PROBLEMS, STUDENTS ANSWER 10 A BIG CHANGE IN HIGHER LEVEL MATH PROBLEM TYPES. USE OF TOOLS IS NOT THE ONLY REASON. IN SOME PROBLEMS, EASY QUESTION WITH TOOLS + HARDER QUESTION, TOOLS NOT USEFULL LAST PROBLEMS, CALCULATION WITH TOOLS CAN BE HARD/ IMPOSSIBLE HOW TO WRITE ANSWER, WHEN USING TOOLS? THE ROLE OF ARGUMENTATION. HOW TO TEACH IT?
JUSTIFYFOLLOWINGINEQUALITIES, (NO USEOF CAS)
Useof tools: wasteof time.
THENSOME EXAMPLESOF QUESTIONSWERETOOLSWEREUSEFULL QUESTION5 IS THEFIRSTONECAS IS ALLOWED, SOMAYBETHEEASIESTQUESTIONTO SOLVE
CALCULATE RULEUSING10 AND 100 SUBINTERVALS. WITHTRAPEDZOID 12/12, command shown& it hasall neededdetails. Samekindof commandfor 100 subintervalsofc. Notmanypoints
5. RighttrianglesABC and DEF intersectas shownin thepicture, AB = DF = 4 and BC = FE =3. Lentghof BF is 1. Find the area of overlap of two triangles.
S20 T5, POINTS, GG SCHEME Figurewithrightlengths Thecornersof pentagonareselected Approximationof thearea Theexactarea Explainedwhathavebeendoneorcommandsshown, cornerswithintersect (explainedorcommandshown), pentagondonewithpolygoncommand (explainedorcommandshown) 2 3 (2) 2 3
FEWEXAMPLESOF QUESTIONS, FOR WHICHADDITIONAL EXPLANATIONWASREQUIRED
5, K19. BASEOF THEBUILDING. 1. DEFINE THEEQUATIONSOF THEPARABOLAS2. CALCULATETHEAREA. Differentwayswereallowed, fitting thefunction, sliders Wasrequired, that studentsverifies thatthefunctionis a rightone: -pointsoruseof snippingtool
+ bx c + 7. K19. GIVEAN EXAMPLEOF A POLYNOMIAL FOR WHICHEQUATION SOLUTIONS. PROVIDEAN EXPLANATION. 2 ax HASEXATLYTHREE 2 bx c ax + + = 4 6/12 p
10.2 K19. DEFINEONEX FOR WHICH n 3 2 = tan( ) x = 0 n USING SOLVE6/9 POINTS 3 POINTS, STUDENTSHOWSWHYTHESERIESCONVERSE.
WHYTO USETOOLSIN MATH? GOALSARENOTCLEAR. THEROLEOF TOOL& THEROLEOF EXPLANATION LIMITSOF CAS WHENYOUCANTRUSTTHERESULT? WHATCANBESEENFROMTHEGRAPH? CHANGEIN QUESTIONS/GRADING, MANYPARALLELPROCESSES. SOME PROBLEMSAREMORE COMPETITIONMATH THANWHATWEHAVEIN TEXTBOOKS, PROBLEMSTHAT ONLYFEWSTUDENTSIN FINLANDCANSOLVE IN HIGHERLEVELMATH, PROBLEMSWHICHCANBESOLVEDEASILYWITHGEOGEBRA, AREAVOIDED MATHEMATICAL FLEXIBILITY: MATH PROBLEMS CAN BE APPROACHED IN MANY DIFFERENT WAYS, BUTHARDTO GETALLPOINTS. (SOLVINGEQUATION, UNIQUESOLUTION)
Matriculationexamsin swedish https://svenska.yle.fi/abimix/matematik Thankyou
