Abstract
Herein authors disclose the results of prof. Jonas Matulionis young mathematicians contest task’s statistic analysis. Research sums 160 tasks (one task contains 5 exercises) from past nine years, solutions by more than 3 thousand students. This analysis is done by examining exercises suitability for the contest according to few criterions: difficulty, resolution, correlation coefficient with task. Also, exercises were divided into types (algorithmic exercise, half algorithmic exercise and heuristic exercise) and topic (textual exercise; equations, equation systems; inequalities,function features and graphs; elements of number theory; plane geometry; stereometry; arithmetical and algebraical transforms). Description statistic’s methods and cluster analysis was used to summarize material. The analysis exposes that exercises prepared for prof. Jonas Matulionis contest stand out with excellent or very good resolution, reasonable difficulty, relevant correlation coefficient with task. Cluster analysis results indicate that all types of exercises are alike with their correlation coefficient, similar with their difficulty. However, algebraically and arithmetical transform exercises types separates in their correlation coefficient with whole task, it is higher here.
Highlights
Moksleiviu skaicius119 300 499 324 604 599 475 453 uždaviniai klasterizuojami [1,3]. Duomenu apibendrinimui naudojama programa SAS
J. Matulionis young mathematicians contest tasks Herein authors disclose the results of prof
Matulionis young mathematicians contest tasks authors disclose the results of prof
Summary
119 300 499 324 604 599 475 453 uždaviniai klasterizuojami [1,3]. Duomenu apibendrinimui naudojama programa SAS. Taip pat konkurso uždaviniai suskirstomi pagal skiriama už uždavini tašku skaiciu, bei salyginai suskirstyti pagal tematika, ir pagal mastymo tipa. Taciau taip skirstyti konkursinius uždavinius pasirodelabai sunku, todel buvo pasirinktos tokios temos: tekstiniai uždaviniai; lygtys ir lygciu sistemos; nelygybes; funkciju savybes ir grafikai; skaiciu teorijos elementai; planimetrija; stereometrija; aritmetiniai ir algebriniai pertvarkiai. Jei uždavinys buvo lengvas ir ji beveik vienodai sekmingai išsprendeir stipresnieji, ir silpnesnieji dalyviai, tai jo skiriamoji geba maža. Panaši skiriamoji geba gali buti ir labai sunkaus uždavinio, kurio beveik niekas neišsprende. Pritaikius klasterines analizes metodus, uždaviniai pagal skiriamaja geba buvo suskirstyti i klasterius. Suskirstytu pagal mastymo tipa, skaiciaus pasiskirstymas klasteriuose taip pat nesiskiria (1 pav.). Apibendrindami galime teigti, kad šiam konkursui parengtu uždaviniu skiriamoji geba labai gera, ji nepriklauso nuo uždavinio tipo ar tematikos. Klasterines analizes rezultatai rodo, kad visu tipu ir tematikos uždaviniai moksleiviams beveik vienodai sunkus (3 pav.).
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