Asymmetrical awnings : a way to increase daylight in buildings without increasing the overheating

Different shapes of asymmetric awnings for east and west windows are investigated mathematically as well as by measurement in a model. A box with 90 cm side and a 30x30 cm window was placed outdoor in overcast weather and the daylight factor was measured at the bottom of the box when the window was unshaded or equipped with different awnings. The average daylight factor in the box decreased from 4.6% for the unshaded window to 1.0% when a full awning was used. With “the best” asymmetrical awning, the average daylight factor was 80% larger than with the full awing. Using Dutch climate, calculation of the energy from direct radiation transmitted through the window during the cooling season showed that this was decreased from 100% as an annual mean for the unshaded window down 22% with a full awing. With “the best” asymmetrical awning, 26% of the energy was transmitted. Calculation of the indoor temperature in a hypothetical row house in Netherlands show that the use of either normal or asymmetrical awnings considerable decrease the indoor temperature during the hot season. Therefore the use of asymmetrical awnings for east or west faced windows considerable can increase the daylight in buildings, with almost no change in overheating, compared to if traditional awnings are used.

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.