Search results for "matemaattinen ajattelu"
showing 7 items of 27 documents
Tietokonevallankumous ja ohjelmoinnillinen ajattelu peruskoulussa : havaintoja mikro- ja makrotasoilta
2022
Väitöskirjassa tutkitaan ”ohjelmoinnilliseksi ajatteluksi” lanseeratun tieto- ja taitokokonaisuuden oppimista, opettamista ja arviointia perusopetuksessa. Tämän erityisesti ohjelmoinnin kautta opittavan osaamiskokonaisuuden tuloa koulumaailmaan on kiihdyttänyt ennen kaikkea tietokoneiden ja tietokoneohjelmien kasvanut läsnäolo eri elämänalueilla. Ohjelmoinnillinen ajattelu on kuitenkin ollut jokseenkin hajanaisesti ymmärretty aihepiiri kasvatusalalla, mistä kielii muun muassa sen varsin suppea jalansija peruskoulumme opetussuunnitelmassa. Väitöstutkimuksessa selkeytettiinkin ohjelmoinnillisen ajattelun kasvatustavoitteita määrittelemällä aihealueen opetuksen perusprinsiipit. Tutkimuksen kes…
Adapting Formal Logic for Everyday Mathematics
2022
Although logic is considered central to mathematics and computer science, there is evidence that teaching logic has not been a great success. We identify three issues where what is typically taught conflicts with what is needed by those who are supposed to apply logic. First, what is taught about the notion of implication often disagrees with human intuition. We argue that in some cases human intuition is wrong, and in some others teaching is to blame. Second, the formal concepts of logical consequence, logical equivalence and tautology are not the similar concepts that everyday mathematicians and computer scientists need. The difference is small enough to go unnoticed but big enough to cau…
Automated Checking of Flexible Mathematical Reasoning in the Case of Systems of (In)Equations and the Absolute Value Operator
2021
We present an approach and a tool for automatically providing feedback on solutions that involve complicated reasoning patterns. Currently the tool supports linear systems of equations and inequations that may also contain the absolute value operator and a restricted form of rational functions. This suffices for designing problems that are laborious to solve with standard mechanical procedures, but much easier using short-cuts that students may find by creative thinking. Earlier research has found that struggling with important mathematics promotes conceptual development. Our goal is to encourage students to such struggling. A crucial feature is to give them great freedom to choose the path…
The development of Early Mathematical Skills – A Theoretical Framework for a Holistic Model
2019
This article presents a theoretical framework for a holistic model of the development of early mathematical skills in early childhood education. The first aim of this study was to conduct a comprehensive international review of the literature to explore early mathematical skills categories. The literature review yielded three early mathematical skills categories, namely (1) numerical skills, (2) spatial thinking skills and (3) mathematical thinking and reasoning skills. Previous studies have shown that several mathematical skills develop gradually and simultaneously in early ages and that these skills areas are interconnected in mathematical skills learning. Accordingly, the second aim of t…
Kielentämisen näkökulmia kuudennen luokan oppilaiden matematiikan sanallisten tehtävien ratkaisuihin
2022
Artikkelissa tarkastellaan kuudennen luokan lopussa oppilaiden tuottamia ratkaisuja kahteen sanalliseen ongelmanratkaisutehtävään. Tutkimuksen toteutti matemaattiseen ajatteluun ja sen kielentämiseen perehtynyt opettaja. Tutkimukseen osallistui 35 kuudennen luokan oppilasta. Tutkimusaineistona olivat oppilaiden kirjalliset ratkaisut kahteen sanalliseen ongelmanratkaisutehtävään. Oppilaat kuvasivat kielentämisen keinoin omaa matemaattista ajatteluaan sekä tehtävien tuottamisessa että ratkaisuprossien avaamisessa. Tuloksista on nähtävissä, että oppilailla oli taitoja kielentää monipuolisesti matemaattista ajatteluaan. Matematiikan opetuksessa olisikin hyvä ohjata oppilaita ilmaisemaan matemaa…
Computational thinking and acting: An approach for primary school competency development
2020
Computational Thinking has become an important concept for almost all age groups. It describes the purposeful utilization of Information and Communication Technologies for solving problems. The approach of Computational Thinking and Acting combines the computational thinking approach with physical computing, including physical activities to explore real-world problems and tangible outcomes. In this paper, we present a competency framework, design principles, and a sample learning scenario for Computational Thinking and Acting. The evaluation has shown that the approach can be integrated across subjects and is promising for both teachers and pupils. peerReviewed
Mathematical thinking and understanding in learning of mathematics
2022
The concept “mathematical thinking” can be found in several studies of mathematics education, in national curricula or in media during the decades all over the world. We searched words “mathematical thinking” from the database of international scientific articles, and we found 456 707 mentions at first time. These are the main reasons why we have chosen “mathematical thinking” as the central concept of the Special Issue. The other interesting question from our point of view is how a student can express his/her mathematical thinking? By answering this question, we have made simple model for the teacher education purposes, and we call it “languaging” (of mathematical thinking). The articles o…