Browsing by Author "Svanteson Wester, Jenny"

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Hur kan dubbelt så långt bli fyra gånger större?
(2014) Svanteson Wester, Jenny; Institutionen för didaktik och pedagogisk profession, Göteborgs universitet/Department of Pedagogical, Curricular and Professional Studies, University of Gothenburg
Previous research has shown that a large majority of 12- to 16-year old students have a tendency to improperly apply the linear model when solving non-linear problems about the relation between lengths and area of enlarged and reduced plane geometric figures (De Bock et al., 1998). A major deficiency associated with the passage from one-dimensional to two-dimensional units is linked to ‘the illusion of linearity’, an explicit belief in a linear relation between lengths and areas of similarly enlarged or reduced figures. The main aim of this study was to investigate whether it could contribute to students’ deeper understanding of scaling of two-dimensional geometric figures when they were given the opportunity to simultaneously discern aspects related to linear and quadratical scaling. A Learning Study approach was adopted to improve instruction and the students’ learning outcomes. The interest was to, based on a perspective of Variation Theory, study how mathematical content was treated regarding the offered aspects of the object of learning and to what extent the instruction was powerful in helping the students to overcome the “illusion of linearity” and develop their understanding of the object of learning. In total 46 students and three teachers participated. The results of the study describe in what way the differences in treatment of the content handled in the classroom affect the students’ learning. The analysis is based on the videotaped lessons, the transcription of the conversations between the teacher and the students, and the students’ results at pre and post-tests. The major qualitative difference in student learning is to what extent the students managed to discern the differences in change of length and area in the same figure simultaneously when scaling two-dimensional geometric figures. The results show how the students’ learning outcome increased during the third cycle, which suggests that the handling of the content in this cycle was more powerful. The activities that took place during the third cycle was more intentionally systematic, both regarding in what order the critical aspects were highlighted, and how the relationship between them was explicitly problematized in several occasions. Another interesting finding is that the teachers encouraged the students to communicate about the content and by doing so the teachers and students were given an opportunity to jointly enact patterns of variation where students’ misconceptions, or way of looking at the content, could be, not only visualized, but also problematized and the critical aspects could explicitly be discerned. The students also got the opportunity to more explicitly express what they had discerned and were able to justify their answers more distinctly.
Teaching and learning mathematics with integrated small-group discussions. A learning study about scaling geometric figures
(2022-11-09) Svanteson Wester, Jenny
The aim of this thesis is to contribute to a deeper understanding of the relationship between teaching and student learning in mathematics when small-group discussions are used in teaching. This thesis focuses on student learning of specific subject matter when small group discussions are used in whole-class teaching. The data analysed was generated in a learning study about enlarging and reducing two- dimensional geometric figures in Grade 8. The learning study involved four cycles, and five classes and three teachers participated. The data consist of 10 video- recorded lessons and 33 video-recorded small-group discussions. Variation theory was the theoretical framework used to analyse the data. Results show that the use of small-group discussions as a planned and integrated part of whole class teaching can contribute to widening the space of learning and increase students’ opportunities to learn what was intended during the lesson. In the study it was found that the small-group discussions solely did not provide sufficient opportunities for students to learn what was intended. Instead, lessons with pre- planned tasks for small-group discussion integrated in whole-class discussions, seems to provide more powerful learning opportunities in relation to what was intended to be compared to lessons with a less systematic use of small-group discussions. In the small-group discussions different ways of experiencing the object of learning were made possible to explore and in the subsequent whole- class discussions those different ways of experiencing were further explored. The results show that teachers benefit from listening to small-group discussions and when students report on such discussions. It was shown that teachers’ insights about the students’ ways of experiencing the object of learning were vital for enacting whole-class teaching with small-group discussions in a powerful way. The teachers changed their teaching in response to what they noticed about what could be critical for student learning about the object of learning. The result of this study suggests that it is not a matter of whether small-group discussions should be used or not, but how small-group discussions can be used during whole class teaching to support student learning of an intended object of learning in mathematics for the whole class.