Knowledge and writing in school mathematics : a communicational approach

This thesis is about young students’ writing in school mathematics and the ways in which this writing is designed, interpreted and understood. Students’ communication can act as a source from which teachers can make inferences regarding students’ mathematical knowledge and understanding. In mathematics education previous research indicates that teachers assume that the process of interpreting and judging students’ writing is unproblematic. The relationship between what students’ write, and what they know or understand, is theoretical as well as empirical. In an era of increased focus on assessment and measurement in education it is necessary for teachers to know more about the relationship between communication and achievement. To add to this knowledge, the thesis has adopted a broad approach, and the thesis consists of four studies. The aim of these studies is to reach a deep understanding of writing in school mathematics. Such an understanding is dependent on examining different aspects of writing. The four studies together examine how the concept of communication is described in authoritative texts, how students’ writing is viewed by teachers and how students make use of different communicational resources in their writing. The results of the four studies indicate that students’ writing is more complex than is acknowledged by teachers and authoritative texts in mathematics education. Results point to a sophistication in students’ approach to the merging of the two functions of writing, writing for oneself and writing for others. Results also suggest that students attend, to various extents, to questions regarding how, what and for whom they are writing in school mathematics. The relationship between writing and achievement is dependent on students’ ability to have their writing reflect their knowledge and on teachers’ thorough knowledge of the different features of writing and their awareness of its complexity. From a communicational perspective the ability to communicate [in writing] in mathematics can and should be distinguished from other mathematical abilities. By acknowledging that mathematical communication integrates mathematical language and natural language, teachers have an opportunity to turn writing in mathematics into an object of learning. This offers teachers the potential to add to their assessment literacy and offers students the potential to develop their communicational ability in order to write in a way that better reflects their mathematical knowledge.

Brytmånens utformning vid trädfällning - Jämförande studier av böjmotstånd och gångjärnseffekt : Designing felling hinge in tree felling - Comparative studies of bending resistance and hinge effect

Vid trädfällning med motorsåg sparar man en så kallad brytmån som skall fungera som ett gång¬järn när trädet fälls. Om brytmånen går av tidigt finns en risk att trädet faller okontrolle¬rat. De rekommendationer som finns säger att brytmånens bredd skall göras proportionell mot trädets diameter. Genom att teoretiskt och praktiskt undersöka vilka krafter brytmånen utsätts för och vad den håller för har det varit möjligt att dra vissa slutsatser om hur en bra brytmån skall se ut. Ett viktigt resultat är att en bred brytmån (över 30-40 mm) är mycket trög att böja och inte fungerar i det avseendet att den går av redan vid små böjningar. Teoretiska be¬räkningar och praktiska försök visar att en relativt smal brytmån håller för belastningen vid rakt motlut även på stora träd. Som ny rekommendationen föreslås att brytmånens bredd inte bör vara mer än 30 mm. Av försöken kan man också dra slutsatsen att frusen ved är stel och brister tidigt, varför svår¬fällda träd inte bör fällas när veden är fryst.A felling hinge is used when felling trees by help of chain saw. If the hinge breaks early in the fall of the tree there is a great risk that the tree will fall without control. Present recommenda¬tions in Sweden say that the thickness of the felling hinge shall be made in proportion to the stem diameter. By use of theoretical and practical examinations of the forces stressing the felling hinge, and the strength of the wood itself, it has been possible to draw conclusions regarding the correct design of a felling hinge. One important result is that a thick felling hinge (over 30-40 mm) is very hard to bend and does not work well as it looses most of its strength already at a small forward bending angel. Theoretical calculations and practical tests show that a relatively narrow felling hinge will manage very well the forces when felling trees with lean opposite to the felling direction even for large trees. Our new recommendation is that the thickness of the felling hinge in normal Swedish conditions should not exceed 30 mm. Through the studies it can also be seen that frozen, brittle wood breaks at small bending angels. For that reason particularly difficult trees not should be felled when the wood is frozen.

The priority of temporal aspects in L2-Swedish prosody : Studies in perception and production

Foreign accent can be everything from hardly detectable to rendering the second language speech unintelligible. It is assumed that certain aspects of a specific target language contribute more to making the foreign accented speech intelligible and listener friendly, than others. The present thesis examines a teaching strategy for Swedish pronunciation in second language education. The teaching strategy “Basic prosody” or BP, gives priority to temporal aspects of Swedish prosody, which means the temporal phonological contrasts word stress and quantity, as well as the durational realizations of these contrasts. BP does not prescribe any specific tonal realizations. This standpoint is based on the great regional variety in realization and distribution of Swedish word accents. The teaching strategy consists virtually of three directives: · Stress the proper word in the sentence. · Stress proper syllables in stressed words and make them longer. · Lengthen the proper segment – vowel or subsequent consonant – in the stressed syllable. These directives reflect the view that all phonological length is stress-induced, and that vowel length and consonant length are equally important as learning goals. BP is examined in the light of existing findings in the field of second language pronunciation and with respect to the phonetic correlates of Swedish stress and quantity. Five studies examine the relation between segment durations and the categorization made by native Swedish listeners. The results indicate that the postvocalic consonant duration contributes to quantity categorization as well as giving the proper duration to stressed syllables. Furthermore, native Swedish speakers are shown to apply the complementary /V: C/ - /VC:/ pattern also when speaking English and German, by lengthening postvocalic consonants. The correctness of the priority is not directly addressed but important aspects of BP are supported by earlier findings as well as the results from the present studies.

'Moving On' and Transitional Bridges : Studies on migration, violence and wellbeing in encounters with Somali-born women and the maternity health care in Sweden

During the latest decade Somali-born women with experiences of long-lasting war followed by migration have increasingly encountered Swedish maternity care, where antenatal care midwives are assigned to ask questions about exposure to violence. The overall aim in this thesis was to gain deeper understanding of Somali-born women’s wellbeing and needs during the parallel transitions of migration to Sweden and childbearing, focusing on maternity healthcare encounters and violence. Data were obtained from medical records (paper I), qualitative interviews with Somali-born women (II, III) and Swedish antenatal care midwives (IV). Descriptive statistics and thematic analysis were used. Compared to pregnancies of Swedish-born women, Somali-born women’s pregnancies demonstrated later booking and less visits to antenatal care, more maternal morbidity but less psychiatric treatment, less medical pain relief during delivery and more emergency caesarean sections and small-for-gestational-age infants (I). Political violence with broken societal structures before migration contributed to up-rootedness, limited healthcare and absent state-based support to women subjected to violence, which reinforced reliance on social networks, own endurance and faith in Somalia (II). After migration, sources of wellbeing were a pragmatic “moving-on” approach including faith and motherhood, combined with social coherence. Lawful rights for women were appreciated but could concurrently risk creating power tensions in partner relationships. Generally, the Somali-born women associated the midwife more with providing medical care than with overall wellbeing or concerns about violence, but new societal resources were parallel incorporated with known resources (III). Midwives strived for woman-centered approaches beyond ethnicity and culture in care encounters, with language, social gaps and divergent views on violence as potential barriers in violence inquiry. Somali-born women’s strength and contentment were highlighted, and ongoing violence seldom encountered according to the midwives experiences (IV). Pragmatism including “moving on” combined with support from family and social networks, indicate capability to cope with violence and migration-related stress. However, this must be balanced against potential unspoken needs at individual level in care encounters.With trustful relationships, optimized interaction and networking with local Somali communities and across professions, the antenatal midwife can have a “bridging-function” in balancing between dual societies and contribute to healthy transitions in the new society.