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.

Biolinguistics or Physicolinguistics? Is The Third Factor Helpful Or Harmful In Explaining Language?

Noam Chomsky (2005) proposed that a ‘third factor’, consisting of general principles and natural laws, may explain core properties of language in a principled manner, minimizing the need for either genetic endowment or experience. But the focus on third-factor patterns in much recent bio-linguistic work is misguided for several reasons: First, ‘the’ third factor is a vague and disparate collection of unrelated components, useless as an analytical tool. Second, the vagueness of the third factor, together with the desire for principled explanations, too often leads to sweeping claims, such as syntax “coming for free, directly from physics”, that are unwarranted without a case-by-case causal analysis. Third, attention is diverted away from a proper causal analysis of language as a biological feature. The point with biolinguistics is to acknowledge the language faculty as a biological feature. The best way forward towards an understanding of language is to take the biology connection seriously, instead of dabbling with physics.

How to make active interactions in Japanese as a second language.

This paper analyzes Japanese language classes at Dalarna University in Sweden that are held through a web conferencing system. It discusses how students’ learning and language acquisition can be supported by making better use of the available features of using a web conferencing system for language lessons. Of particular interest is the existence of an “information gap” among students, created because of the limits posed by distance communication. Students who take Japanese courses at Dalarna University usually access classes from their home, which are located all over Sweden or even abroad. This fact can be utilized in language classes because the “information gap” can lead to interactions that are essential for language learning. In order to make use of this natural “information gap” and turn it into an opportunity for communication, our classes used a teaching method called “personalization” [Kawaguchi, 2004].  “Personalization” aims to persuade students to express their own ideas, opinions, feelings and preferences. The present analysis suggests that “personalization” in web-based language classes is a surprisingly effective teaching method. By making students explain about things at home (why they have them, what they use them for, or why they are important), students become motivated to express themselves in Japanese. This makes communication meaningful and enhances students’ interest in improving their vocabulary. Furthermore, by knowing each other, it becomes easier to create a ”supportive classroom environment” [Nuibe, 2001] in which students feel able to express themselves. The analysis suggests that that web-based education can be seen not simply as a supplement to traditional face-to face classroom education, but as a unique and effective educational platform in itself.