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.

PANA V : Evaluation of a Literacy Project

PANA V Evaluation of a Literacy ProjectSUMMARY AND CONCLUSIONSThis evaluation set out to explore the impact of the literacy work carried out through PANA V. It focussed on clarifying effects such as empowerment and poverty reduction in relation to the civil society. Two specific objectives were to evaluate the methodological approach and the didactic materials and to evaluate the sustainability of the project.Although the focus of the evaluation has been PANA V, the project has been evaluated in its context, as one in a series of five projects located in Rwanda ten years after the war and genocide. The conclusion will consider future plans in this field.The evaluator has striven to create a holistic picture of the effects of the project, although the given time for the evaluation was short. Only three weeks were spent in the field study and only ten days in the actual field. Although there were some organisational and logistic problems, as is common when carrying out a study like this in a poor country, many literacy sites were visited and quite many participators were interviewed. The overall impression from the study is overwhelmingly positive. So many people commit themselves in this task of teaching Rwandans reading, writing and numeracy. Despite harsh conditions learners strive to learn and group leaders devote themselves to the task. Many leaders on different levels try their very best to manage their difficult and demanding task. The main objective was to explore the impact of the project on poverty reduction, particularly on empowerment and strategies for everyday life. Women were to be regarded particularly. From the results it is clear that the project has a strong, positive impact both on poverty reduction and empowerment of marginalised groups. Among those who have benefited from the alphabetisation are mainly women. Unfortunately, when it comes to leaders in PANA, who may also be said to have benefited from the project, only a small minority is women. This is something that is recommended that it be reconsidered inside the organisation. As a majority of the targeted learners are women, and as the economic and social situation of women in Rwanda is generally weak, this is a question that I recommend the Pentesostal church and ADEPR to look particularly into. With many women being single breadwinners of their households, it is important that also women get access to positions that may bring benefits of different kind.It is also clear that the project has positive effects for the civil society. In the present situation in Rwanda, during the process of reconciliation and rapid progress, basic education for the poor majority is a democratic issue. In a country with a plethora of internet-cafés in the capital and a small minority that use cars and mobile-telephones to communicate nation-wide, it is of outmost importance that the majority acquires basic education, of which literacy is a central part. To strengthen the civil society in Rwanda literacy is important. One central issue is then that Rwanda develops toward becoming a country where literacy is used for the benefit of the citizens and it is a democratic issue that all citizens get an opportunity to participate. Crucial for this is that strong efforts are put into primary schools nation-wide. Literacy projects for adults, like PANA, may only complement these efforts, but they constitute important and necessary complements. Other relevant ways to promote literacy are campaigns in Radio and TV and through cultural events such as festivals, music and theatre. News papers, magazines and books are natural parts of such campaigns as well as adult education. As stated under the results not much can be said about the didactics in this evaluation. On the whole the methodology and the materials fill their function well and receive a high reputation. As people learn to read and write under very simple conditions, obviously the approach is appropriate. A few suggestions may be given from the study:•Focus groups leaders’ attention on clearness, that they show very clearly what is to be read. Good structuring is probably of great importance for many learners.•Make clear what is tested in the tests and consider the possibility to use a holistic test that would be more congruent with the methodology. The possibility to use only one grade, pass, would enable a more practical test, such as reading a short, relevant text, writing something relevant and solving practical mathematic problems. Avoid tests that demand school knowledge.•Avoid using methaphors such as “fight against illiteracy” and connections between illiteracy/literacy and darkness/light. It is not true that illiteracy causes bad things and that literacy only brings good. •Be prepared that it may be more difficult in the future to achieve the goals as it may be the case that the early learners where the ones who achieved easily. The goal of “literacy in six month” in PANA will probably hold only for some learners but also those who do not manage in six months need literacy skills.A third objective was to secure sustainability. As for sustainability of the project in itself, and of the literacy process, the main conclusion is that there is a good potential. The commitment and devotedness among many involved in PANA proves good. One weakness is individual leaders in ADEPR who do not see this as an important task for the Pentecostal church in Rwanda. Other weaknesses are the unwillingness to mention explicitly the wish, for example among group leaders, to get some kind of incentive and the fear of loosing believers by cooperation with other organisations. A higher degree of transparency in this issue would probably solve some irritations and tensions.As for the sustainability of the literacy skills much may be done to improve. The acquired skills seem to be comparably relevant. The level achieved, and the level tested, may be defined as basic literacy skills, consisting of basic reading, writing and numeracy skills. However, these skills are very restricted and there is a high risk that the skills will decline, which means that there is a high risk that people will forget how to read and write because of lack of exercising. From these conclusions a few suggestions for future development will be given.

Behaviour of Surface Defects in Wire Rod Rolling

Defects are often present in rolled products, such as wire rod. The markets demand for wire rod without any defects has increased. In the final wire rod products, defects originating from the steel making, casting, pre-rolling of billets and during the wire rod rolling can appear. In this work, artificial V-shaped longitudinal surface cracks has been analysed experimentally and by means of FEM. The results indicate that the experiments and FEM calculations show the same tendency except in two cases, where instability due to a fairly “round” false round bars disturbed the experiment. FE studies in combination with practical experiments are necessary in order to understand the behaviour of the material flows in the groove and to explain whether the crack will open up as a V-shape or if it will be closed as an I-shape.