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.

Fringe Types and KOS Systematics: Examining the Limits of the Population Perspective of Knowledge Organization Systems

We find ourselves, after the close of the twentieth century, looking back at a mass of responses to the knowledge organization problem. Many institutions, such as the Dewey Decimal Classification (Furner, 2007), have grown up to address it. Increasingly, many diverse discourses are appropriating the problem and crafting a wide variety of responses. This includes many artistic interpretations of the act and products of knowledge organization. These surface as responses to the expressive power or limits of the Library and Information Studies institutions (e.g., DDC) and their often primarily utilitarian gaze.One way to make sense of this diversity is to approach the study from a descriptive stance, inventorying the population of types of KOS. This population perspective approaches the phenomenon of types and boundaries of Knowledge Organization Systems (KOS) as one that develops out of particular discourses, for particular purposes. For example, both DDC and Martianus Capella, a 5th Century encyclopedist, are KOS in this worldview. Both are part of the population of KOS. Approaching the study of KOS from the population perspective allows the researcher a systematic look at the diversity emergent at the constellation of different factors of design and implementation. However, it is not enough to render a model of core types, but we have to also consider the borders of KOS. Fringe types of KOS inform research, specifically to the basic principles of design and implementation used by others outside of the scholarly and professional discourse of Library and Information Studies.Four examples of fringe types of KOS are presented in this paper. Applying a rubric developed in previous papers, our aim here is to show how the conceptual anatomy of these fringe types relates to more established KOS, thereby laying bare the definitions of domain, purpose, structure, and practice. Fringe types, like Beghtol’s examples (2003), are drawn from areas outside of Library and Information Studies proper, and reflect the reinvention of structures to fit particular purposes in particular domains. The four fringe types discussed in this paper are (1) Roland Barthes’ text S/Z which “indexes” a text of an essay with particular “codes” that are meant to expose the literary rhythm of the work; (2) Mary Daly’s Wickedary, a reference work crafted for radical liberation theology – and specifically designed to remove patriarchy from the language used by what the author calls “wild women”; (3) Luigi Serafini’s Codex Seraphinianus a work of book art that plays on the trope of universal encyclopedia and back-of- the book index; and (4) Martinaus Capella – and his Marriage of Mercury and Philology, a fifth century encyclopedia. We compared these using previous analytic taxonomies (Wright, 2008; Tennis, 2006; Tudhope, 2006, Soergel, 2001, Hodge, 2000).