Oodatavate vastuste ja arvutialgebra süsteemide vastuste erinevused koolimatemaatika võrrandite puhul

Arvutialgebra süsteemidega saab lahendada erinevat tüüpi matemaatikaülesandeid, sealhulgas koolimatemaatika võrrandeid. Sageli langevad arvutialgebra süsteemide vastused kokku koolikontekstis oodatavate vastustega (koolivastustega), vahel aga mitte. Sellised ootamatud arvutialgebra süsteemide vastused on tihti küll matemaatiliselt korrektsed, aga mõne teise standardi järgi, näiteks kompleksarvude vallas. Arvutialgebra süsteemide vastuste ja koolivastuste erinevuste süstemaatiline ülevaade on kasulik arvutialgebra süsteemide arendamisel ning õppetöö planeerimisel. Käesolev dissertatsioon annab ülevaate arvutialgebra süsteemide vastuste ja koolivastuste erinevustest ning nende põhjustest koolimatemaatika võrrandite puhul. Erinevuste spektrit selgitatakse kahe võimaliku klassifikatsiooni abil. Esimese klassifikatsiooni aluseks on see, kas arvutialgebra süsteemi vastus sisaldab rohkem või vähem lahendeid kui oodatav vastus. Teine klassifikatsioon on sisupõhisem ja toob esile vastuste kuju, täielikkuse, arvuvallast sõltuvuse, harunemise ja automaatse lihtsustamise teemad. Arvuvalla ja harunemisega seotud erinevusi käsitletakse dissertatsioonis põhjalikumalt eraldi peatükkides. Koolivastuste ja arvutialgebra süsteemide vastuste erinevusi saab kasutada õpetamisel ja õppimisel. Käesolev dissertatsioon pakubki välja pedagoogilise lähenemise, mis põhineb arvutialgebra süsteemide vastuste ja õppijate endi vastuste võrdlemisel paaristööna. Lisaks õpetamisele ja õppimisele saab selle formaadiga koguda andmeid õppijate teemamõistmise kohta. Väljapakutud lähenemist kasutati tunnisituatsioonis trigonomeetriliste võrrandite käsitlemisel. Põhjalikumalt analüüsiti, kui adekvaatselt õppijad tuvastasid enda vastuse ja arvutialgebra vastuse ekvivalentsust/mitteekvivalentsust ja korrektsust. Leiti, et isegi kui õppijate lahendus paistab korrektne, võib siiski olla lünki arusaamises.It is possible to solve most mathematical problems, including equations of school mathematics, with the help of Computer Algebra Systems (CAS). The answers offered by CAS (CAS answers) often coincide with the answers that are expected in the school context (school answers), but sometimes not. Such unexpected CAS answers are often correct, but based on different standards, for example in complex domain. A systematic review of the differences between CAS answers and school answers is useful for development of CAS and organizing the teaching process. A review of the differences between CAS answers and school answers and their reasons in case of school mathematics equations is provided in this dissertation. The spectrum of differences is explained by using two possible classifications. A key criterion of the first classification is comparing whether the CAS answer includes a larger or a smaller number of solutions than the expected answer. The other classification is more content-oriented, highlighting the issues of the form, completeness, dependence on the number domain, branching and automatic simplification of answers. The differences caused by number domain and branching are discussed separately in greater depth in separate chapters. The differences between school answers and CAS answers can be used in teaching and learning. This dissertation proposes a pedagogical approach that is based on comparative discussions on students' answers and CAS answers in pairs. In addition to teaching and learning, the format is also suitable for collecting data on students' understandings and misunderstandings. The proposed approach was used in lessons on trigonometric equations. The focus was on analyzing whether students can adequately identify the equivalence/non-equivalence and correctness of their answer and CAS answer. It is found that even if a student's solution looks to be correct, students can have misunderstandings and knowledge gaps

Laptops for Students

Research Project in EstoniaThe aim of the current research was to study: 1) The type of activities students administered on laptops, frequency and duration of these activities; 2) Changes in students’ learning styles, learning preferences, learning methods, communication, attitudes towards school and using ICT, learning outcomes, missing classes and extracurricular activities; 3) Changes in laptop –based classroom and homework assignments given by teacher; 4) Changes in teachers’ teaching methods, teaching styles, communication with students and parents and attitude towards application of ICT in studies; 5) Changes in parents’ attitudes towards application of ICT in studies, towards school and teachers; 6) Advantages and problems of using laptops from the perspective of students, parents, teachers as well as school administrators.http://www.innovatsioonikeskus.ee/sites/default/files/tekstifailid/Sylearvuti_opilastele_raportENG_2009.pd

Sülearvuti õpilastele

Tiigrihüppe Sihtasutuse uurimuse lõppraport.Käesoleva uurimuse eesmärgiks oli selgitada, missugused on: 1) õpilaste tegevused sülearvutitega ja nende tegevuste sagedus ja kestvus; 2) muutused õpilaste õppimisstiilis, õppimiseelistustes, õppimismeetodites, suhtluses, suhtumises IKT kasutamisse ja kooli, õpitulemustes, puudumistes ning koolivälistes tegevustes; 3) muutused õpetaja poolt antud õppeülesannetes ja –tegevustes klassis ning koduste tööde jaoks, kus on vajalik sülearvuti kasutamine; 4) muutused õpetaja õpetamismeetodites, õpetamisstiilis, suhtluses õpilaste ja lapsevanematega ning suhtumises IKT rakendamisse õppetöös; 5) muutused lapsevanemate suhtumises IKT rakendamisse õppetöös, kooli ja õpetajatesse; 6) sülearvutite kasutamise eelised ja probleemid nii õpilaste, lapsevanemate, õpetajate kui ka koolijuhtide poolt vaadatuna.http://www.innovatsioonikeskus.ee/sites/default/files/tekstifailid/Sylearvuti_opilastele_raportEST_2009.pd

Why do students choose to study Information and Communications Technology?

Abstract It is a worldwide problem that although many students are highly interested in Information and Communications Technology (ICT), they do not study it at the higher education level, or if they do then many of them eventually dropout. We studied the reasons student candidates choose to study ICT, in order to gather data that can be used for improving future ICT recruitment and retention. During the admissions procedure to three higher education institutions in Estonia, 1,464 student candidates were asked what reasons influenced them to apply to Informatics or Information Technology. On average, 2.6 candidates competed per available position at the institutions. Qualitative content analysis was used to code the candidates' open-ended answers and resulted inductively in 14 distinguishable categories. The most frequent reasons for studying ICT were general interest in ICT, previous experience in the field, need for personal professional development, and importance of the field in the future. Interestingly, only a few candidates expressed as a reason the importance of high salaries. Chi-square analysis showed that candidates were accepted with higher probability if they found ICT to be suitable for them, or expressed good opportunities in the labour market. These results are useful for planning effective admission procedures to recruit ICT students

Troubleshooters for Tasks of Introductory Programming MOOCs

Learning programming has become more and more popular and organizing introductory massive open online courses (MOOCs) on programming can be one way to bring this education to the masses. While programming MOOCs usually use automated assessment to give feedback on the submitted code, the lack of understanding of certain aspects of the tasks and feedback given by the automated assessment system can be one persistent problem for many participants. This paper introduces troubleshooters, which are help systems, structured like decision trees, for giving hints and examples of certain aspects of the course tasks. The goal of this paper is to give an overview of usability (benefits and dangers) of, and the participants’ feedback on, using troubleshooters. Troubleshooters have been used from the year 2016 in two different programming MOOCs for adults in Estonia. These MOOCs are characterized by high completion rates (50–70%), which is unusual for MOOCs. Data is gathered from the learning analytics integrated into the troubleshooters’ environment, letters from the participants, questionnaires, and tasks conducted through the courses. As it was not compulsory to use troubleshooters, the results indicate that only 19.8% of the users did not use troubleshooters at all and 10% of the participants did not find troubleshooters helpful at all. The main difference that appeared is that the number of questions asked from the organizers about the programming tasks during the courses via helpdesk declined about 29%