Learning density of numbers in elementary teacher education

Infinity is an important concept in mathematics, which students find difficult to learn. This paper will report Finnish elementary teacher students’ understanding of density at the beginning of their studies and the development of that understanding during a mathematics methods course. The results show that even quite limited teaching can initiate significant improvement. Moreover, students can make progress even if their initial level of performance is low. Yet, only 60 % of elementary education students reach satisfactory content knowledge and pedagogical content knowledge by the end of the course.Peer reviewe

The association between lesson goals and task introduction in problem solving teaching in primary schooling

This study compares six teachers’ learning goals for two problem solving lessons and their 9 to 11 year-old students’ solutions to two open-ended problems. Some of the learning aims were explicitly given before the lesson and some were revealed during the lessons. The pupils worked on the first open problem in primary three and the second problem in the primary four. The problem solving lessons were video-recorded and transcribed, and pupils´ solutions were collated and examined. An additional data source was the teachers´ lesson plans, and the videos taken in the teachers´ meeting sessions. The classification of teachers´ actions was based on the teaching model developed from Polya’s problem solving model (planning, introduction, guidance, feedback). This paper examines the significance of the teachers´ aims of the lessons and the introduction of the two problems, with the focus on the pupils´ justification of the solution for both tasksPeer reviewe

Emotional atmosphere in third-graders’ mathematics classroom – an analysis of pupils’ drawings

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Suomalaisten ja chileläisten alaluokkien opettajien esille tuomia uskomuksia ongelmanratkaisusta

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Emotional atmosphere in mathematics lessons in third graders’ drawings

The aim of this study was based on pupils’ drawings to find out what kind of emotional atmosphere dominates in third graders’ mathematics lessons. Pupils’ (N = 133) drawings were analyzed by looking for content categories related to a holistic evaluation of mathematics lesson. As a summary we can conclude that the emotional atmosphere in the mathematics lessons is positive as a whole even though the differ-rences between the classes are great. Furthermore, it can be said that drawings is a good and many-sided way to collect data about the emotional atmosphere of a class.Peer reviewe

Teachers’ influence on the quality of pupils’ written explanations – Third-graders solving a simplified arithmagon task during a mathematics lesson

The aim of this study is to find out whether there is a connection between teacher’s request and guidance for written explanation and third-graders’ achievements in solving a non-standard problem. Pupils’ task was to solve a simplified arithmagon and to explain their solution. The lessons of seven teachers were recorded and their actions were examined and categorized during a problem-solving lesson. Also pupils’ solutions were checked and classified. The teacher’s behavior seems to have a crucial role in the quality of pupils’ written explanations. The third-graders had difficulties in writing their reasoning for solving the problem.Peer reviewe

Opettajien ja oppilaiden kysymykset ongelmanratkaisutunnilla

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Tunneilmapiiri kolmasluokkalaisten matematiikkapiirroksissa

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Third-graders' problem solving performance and teachers' actions

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Archaea are prominent members of the prokaryotic communities colonizing common forest mushrooms

In this study, the abundance and composition of prokaryotic communities associated with the inner tissue of fruiting bodies of Suillus bovinus, Boletus pinophilus, Cantharellus cibarius, Agaricus arvensis, Lycoperdon perlatum, and Piptoporus betulinus were analyzed using culture-independent methods. Our findings indicate that archaea and bacteria colonize the internal tissues of all investigated specimens and that archaea are prominent members of the prokaryotic community. The ratio of archaeal 16S rRNA gene copy numbers to those of bacteria was >1 in the fruiting bodies of four out of six fungal species included in the study. The largest proportion of archaeal 16S rRNA gene sequences belonged to thaumarchaeotal classes Terrestrial group, Miscellaneous Crenar-chaeotic Group (MCG), and Thermoplasmata. Bacterial communities showed characteristic compositions in each fungal species. Bacterial classes Gammaproteobacteria, Actinobacteria, Bacilli, and Clostridia were prominent among communities in fruiting body tissues. Bacterial populations in each fungal species had different characteristics. The results of this study imply that fruiting body tissues are an important habitat for abundant and diverse populations of archaea and bacteria.Peer reviewe