ATM • Conference 2008 - Keele University
tags: conference, education, mathematics, research
A researcher's attempt to follow his field
Education Week has an interesting article about the uncertainties about the skills that are needed to be a successful mathematics teacher. The point of departure for the article is the recent report by the National Mathematics Advisory Panel in the U.S. The report has several suggestions about the curriculum, cognition, instruction, etc. When it comes to the skills that are needed to become a good mathematics teacher, though, the answers were fewer:
A new article has been published online at Educational Studies in Mathematics. The article is entitled: "The role of scaling up research in designing for and evaluating robustness", and it is written by J. Roschelle, D. Tatar, N. Shechtman and J. Knudsen. Here is the abstract of the article:
The full title of this new ZDM article is: "When, how, and why prove theorems? A methodology for studying the perspective of geometry", and it is written by P. Herbst and T. Miyakawa.
Every theorem has a proof, but not every theorem presented in schools (not only in the U.S., although this is the focus of the article). Why is that? Here is the abstract of the article, which truly raises some important questions:
Megan E. Staples wrote an article called: "Promoting student collaboration in a detracked, heterogeneous secondary mathematics classroom". The article was published online in Journal of Mathematics Teacher Education on Wednesday. Here is the abstract of the article:
The final program of the Norma 08 conference has arrived (download as pdf). I am not going to repeat the entire program here, but I will point at the plenary lectures that will be presented at the conference:
The April issue of Journal of Mathematics Teacher Education has been published. The following articles are enclosed:
In the U.S., the National Mathematics Advisory Panel (on request from the President himself) has delivered a report to the President and the U.S. Secretary of Education. This final report was delivered on March 13, and is freely available for anyone to download (pdf or Word document). I know this is old news already, but I will still present some of the highlights from the report here. Be also aware that there will be a live video webcast of a discussion of the key findings and principle messages in the report. The webcast will be held tomorrow, Thursday March 26, 10-11.30 a.m. Eastern Time. This discussion will be lead by Larry R. Faulkner (Chair of the Panel) and Raymond Simon (U.S. Deputy Secretary of Education).
A key element of the report is a set of "Principal Messages" for mathematics education. This set of messages consists of six main elements (quoted from pp. xiii-xiv):
The April issue of Mathematics Teacher has arrived, and it contains the following three articles:
Linda Pilkey-Jarvis and Orrin H. Pilkey have written an article in Public Administration Review about the use of mathematical models in environmental decision making. Mathematical models are used extensively in the context of environmental issues and natural resources, and when these methods were first used, they were thought to represent a bridge to a better and more foreseeable future. There has also been much controversy in this respect, and the authors pose the question whether the optimism about the use of these models were ever realistic. In this article, they review the two main types of such models: quantitative and qualitative.
Yesterday, NCME (National Council on Measurement in Education) started their annual meeting. NCME's mission is among other things to "Advance the science of measurement in the field of education", so the focus is not on mathematics education solely. There are, however several presentations that deal with mathematics in the program. Here are the ones that I could find:
Yesterday, the 2008 annual meeting of AERA started. Although this is not only a mathematics education conference, it has a lot of interesting presentations for our field as well. A brief search through the searchable program gave 353 hits on individual presentations with the word "math" in the title. There are also several paper sessions with themes related to mathematics education. Today, for instance, there is a session entitled "Addressing Mathematics Education in Special Education", which has the following participants:
Beyond Either/Or: Enhancing the Computation and Problem-Solving Skills of Low-Achieving Adolescents
*Brian A. Bottge (University of Kentucky), Jorge Enrique Rueda-Sarmiento (University of Wisconsin - Madison), Ana C. Stephens (University of Wisconsin - Madison)Calculators, Friend or Foe? Calculators as Assessment Accommodations for Students With Disabilities
*Emily C. Bouck (Purdue University)Interventions to Enhance Math Problem Solving and Number Combinations Fluency for Third-Grade Students With Math Difficulties: A Field-Based Randomized Control Trial
*Lynn S. Fuchs (Vanderbilt University), *Sarah Rannells Powell (Vanderbilt University), *Pamela M. Seethaler (Vanderbilt University), *Rebecca O'Rand Zumeta (Vanderbilt University), Douglas Fuchs (Vanderbilt University)The Effects of Conceptual Model-Based Instruction on Solving Word-Problems With Various Contexts: “Transfer in Pieces”
*Yanping Xin (Purdue University), *Dake Zhang (Perdue University)The Effects of Two Manipulative Devices on Hundreds Place-Value Instruction
*Amy Scheuermann (Bowling Green State Univeristy)
Ferdinando Arzarello, Marianna Bosch, Josep Gascón and Cristina Sabena have written an article called "The ostensive dimension through the lenses of two didactical approaches", that has recently been published (online first) in ZDM. Here is the abstract.
This article by Gila Hanna and Ed Barbeau was published online two days ago in ZDM. The article examines a main idea from an article by Yehuda Rav in Philosophia Mathematica, that it is “proofs rather than theorems that are the bearers of mathematical knowledge”. An interesting theme of an article, with strong implications. Here is the entire abstract:
The aim of this dissertation is to describe and analyze how discourse as a theoretical and didactical concept can help in advancing knowledge about the teaching of mathematics in school. The dissertation has been written within a socio-cultural perspective where active participation and support from artefacts and mediation are viewed as important contributions to the development of understanding. Discourse analysis was used as a theoretical point of departure to grasp language use, knowledge construction and mathematical content in the teaching practises. The collection of empirical data was made up of video and audio tape recordings of the interaction of teachers and pupils in mathematics classrooms when they deal with problem-solving tasks, as well as discussions between student teachers as they engage in planning a teaching situation in mathematics. Discourse analysis was used as a tool to shed light upon how pupils learn and develop understanding of mathematics.
The results of my studies demonstrate that discussions very often are located in either a mathematical or in an every-day discourse. Furthermore, the results demonstrate how change between every-day and mathematical language often takes place unknowingly. Also the results underline that a specific and precise dialogue can contribute towards teachers’ and pupils’ conscious participation in the learning process. Translated into common vocabulary such as speak, think, write, listen and read teachers and pupils would be able to interact over concepts, signs, words, symbols, situations and phenomena in every-day discourse and its mathematical counterpart. When teachers and pupils become aware of discursive boundary crossing in mathematics an understanding of mathematical phenomena can start to develop. Teachers and pupils can construct a meta-language leading to new knowledge and new learning in mathematics.
Christer Bergsten has wrote an article called "On the influence of theory on research in mathematics education: the case of teaching and learning limits of functions", which was recently published (online first) by ZDM. Here is the abstract of the article:
Regular papers theme B: Education and identity of mathematics teachers
IS THERE ALWAYS TRUTH IN EQUATION? Iiris Attorps and Timo Tossavainen
THE CONSTITUTION OF MATHEMATICS TEACHER IDENTITY Raymond Bjuland
IDENTITY AND GENRE LITERACY IN STUDENT TEACHERS? MATHEMATICAL TEXTS. Hans Jørgen Braathe
TEACHERS' BELIEFS AND KNOWLEDGE ABOUT THE PLACE VALUE SYSTEM Janne Fauskanger and Reidar Mosvold
EXAMINING PROSPECTIVE TEACHERS REASONING OF FUNCTIONS: A FEEDBACK PERSPECTIVE Örjan Hansson
COLLABORATION AND INQUIRY IN MATHEMATICS PRACTICE, Marit Johnsen Høines
Journal of Mathematics Teacher Education (JMTE) recently published an (online first) article by A.J. Stylianides and Deborah L. Ball entitled "Understanding and describing mathematical knowledge for teaching: knowledge about proof for engaging students in the activity of proving". The article has a particular focus on knowledge about proof:
This article is situated in the research domain that investigates what mathematical knowledge is useful for, and usable in, mathematics teaching. Specifically, the article contributes to the issue of understanding and describing what knowledge about proof is likely to be important for teachers to have as they engage students in the activity of proving. We explain that existing research informs the knowledge about the logico-linguistic aspects of proof that teachers might need, and we argue that this knowledge should be complemented by what we call knowledge of situations for proving. This form of knowledge is essential as teachers mobilize proving opportunities for their students in mathematics classrooms. We identify two sub-components of the knowledge of situations for proving: knowledge of different kinds of proving tasks and knowledge of the relationship between proving tasks and proving activity. In order to promote understanding of the former type of knowledge, we develop and illustrate a classification of proving tasks based on two mathematical criteria: (1) the number of cases involved in a task (a single case, multiple but finitely many cases, or infinitely many cases), and (2) the purpose of the task (to verify or to refute statements). In order to promote understanding of the latter type of knowledge, we develop a framework for the relationship between different proving tasks and anticipated proving activity when these tasks are implemented in classrooms, and we exemplify the components of the framework using data from third grade. We also discuss possible directions for future research into teachers’ knowledge about proof (quoted from the abstract).
M. Kaldrimidou, H. Sakonidis and M. Tzekaki have written an article that has recently been published online in ZDM. The article is entitled "Comparative readings of the nature of the mathematical knowledge under construction in the classroom", and it makes an attempt to:
(...) empirically identify the epistemological status of mathematical knowledge interactively constituted in the classroom. To this purpose, three relevant theoretical constructs are employed in order to analyze two lessons provided by two secondary school teachers. The aim of these analyses was to enable a comparative reading of the nature of the mathematical knowledge under construction. The results show that each of these three perspectives allows access to specific features of this knowledge, which do not coincide. Moreover, when considered simultaneously, the three perspectives offer a rather informed view of the status of the knowledge at hand (from the abstract).
International Electronic Journal of Mathematics Education published their first issue this year a while ago (see my post about it). Now, the articles and abstracts are finally available as well! The abstracts are available in plain HTML format, whereas the articles can be freely downloaded in PDF format. I find one of the articles particularly interesting, as it concerns the same area of research as I am involved in myself (teacher thinking and teacher knowledge). The article was written by Donna Kotsopoulos and Susan Lavigne, and it is entitled: Examining “Mathematics For Teaching” Through An Analysis Of Teachers’ Perceptions Of Student “Learning Paths”
I enclose a copy of the abstract here:
The March issue of Mathematics Teacher is out, with several interesting articles:
This study examined conceptions of algebra held by 30 preservice
elementary teachers. In addition to exploring participants’ general
“definitions” of algebra, this study examined, in particular, their
analyses of tasks designed to engage students in relational thinking or
a deep understanding of the equal sign as well as student work on these tasks. Findings from this study suggest that preservice elementary
teachers’ conceptions of algebra as subject matter are rather narrow.
Most preservice teachers equated algebra with the manipulation of
symbols. Very few identified other forms of reasoning – in particular,
relational thinking – with the algebra label. Several participants made comments implying that student strategies that demonstrate traditional
symbol manipulation might be valued more than those that demonstrate
relational thinking, suggesting that what is viewed as algebra is what
will be valued in the classroom. This possibility, along with
implications for mathematics teacher education, will be discussed.