Search results for "ajattelu"
showing 10 items of 236 documents
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…
Kasvatustieteen opiskelijoiden argumentaatiotaitojen harjoittelu suullisesti ja sähköpostitse: miten perustelut oikeutettiin?
2001
Käytännöllistä tietoa vai teoriaa? : käyttöteoria opiskelijan kehittymisen apuna
2005
Transitions through the dynamics of adaptive cycles : Evolution of the Finnish agrifood system
2023
CONTEXT The escalating sustainability problems of the current agrifood regime call for a radical, systemic transformation. Such a transformation implies a move into a new stability domain, defined by a new set of systemic attractors. These transformations can be conceptualised as regime shifts. OBJECTIVE In this study, we explored the history of the Finnish agrifood system in order to learn from the past transformations of the system and to inform the current attempts to steer its development in a more sustainable direction. METHODS We conducted a qualitative analysis on literature discussing the history of the Finnish agrifood system by utilising the concept of the adaptive cycle, which ca…
Ryhmäajattelu opiskelijaryhmän tapana vältellä ristiriitoja
2015
Tutkimuksessa tarkastellaan opiskelijaryhmän työskentelyä ryhmän kirjoittamien pöy-täkirjojen sekä tutkijoiden omien kokemusten pohjalta. Huomiota kiinnitetään erityisesti ryhmän tiedostamattomaan puoleen, pyrkimyksenä löytää merkityksiä ryhmän toiminnalle ja tätä kautta selityksiä, miksi ryhmän on ollut vaikea toimia perustehtävänsä mukaisesti. Tutkimus keskittyy tarkastelemaan ryhmän toimintaa psykodynaamisen ryhmäajatteluteorian pohjalta. Tutkimuskohteena on Jyväskylän yliopiston opettajankoulutuslaitoksessa vuonna 2009 aloittanut integraatioryhmä, johon myös tutkijat itse ovat kuuluneet. Aineisto koostuu integraatioryhmän pöytäkirjoista, jotka on kirjoitettu opiskelijoiden kolmen ensimm…
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…
The Dynamic Relationship between Response Processes and Self-Regulation in Critical Thinking Assessments
2021
Our aim was to explore higher education students’ response and self-regulatory processes plus the relationship between these, as evidenced in two types of performance-based critical thinking tasks included in the Collegiate Learning Assessment (CLA+) International instrument. The data collection consisted of 20 cognitive laboratories. The data were analyzed using a qualitative approach. The tasks were found to trigger different response and self-regulatory processes. Overall, the performance task evoked more holistic processes than the selected-response questions, in which students’ processes were more question-oriented. The results also indicated the entanglement of students’ response and …