Author: Reidar Mosvold

Mathematics Teaching in the Middle School, April 2008

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The April issue of Mathematics Teaching in the Middle School has arrived, and it presents the following articles:

By Way of Introduction: Developing Mathematical Understanding through Representations

Developing Mathematical Understanding through Multiple Representations by Preety N. Tripathi (free preview article)
Promoting Mathematics Accessibility through Multiple Representations Jigsaws by Wendy Pelletier Cleaves

Oranges, Posters, Ribbons, and Lemonade: Concrete Computational Strategies for Dividing Fractions by Christopher M. Kribs-Zaleta

Student Representations at the Center: Promoting Classroom Equity by Kara Louise Imm, Despina A. Stylianou and Nabin Chae
Analyzing Students’ Use of Graphic Representations: Determining Misconceptions and Error Patterns for Instruction by Amy Scheuermann and Delinda van Garderen

Developing Meaning for Algebraic Symbols: Possibilities and Pitfalls by John K. Lannin, Brian E. Townsend, Nathan Armer, Savanna Green and Jessica Schneider

Sense-able Combinatorics: Students’ Use of Personal Representations by Lynn D. Tarlow

The Role of Representations in Fraction Addition and Subtraction by Kathleen Cramer, Terry Wyberg and Seth Leavitt

After the Math Panel

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A little less than a month ago, the National Mathematics Advisory Panel published their final report on the future of mathematics education in the U.S. The report has raised much discussion in the U.S., and today I came across an interesting blog called After the Math Panel. In this blog, an educator and mom gives us her opinions and analyses of the report. The blog contains some interesting and readable summaries of the report, and I think it is worth reading!

From static to dynamic mathematics

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Educational Studies in Mathematics recently published an article called: “From static to dynamic mathematics: historical and representational perspectives“. The article is written by Luis Moreno-Armella, Stephen J. Hegedus and James J. Kaput. The point of departure for this article is the issue of new digital technologies, their capacities, issues concerning design and use of them, etc. They build upon one of Kaput’s works on notations and representations, in order to:

(…) present new theoretical perspectives on the design and use of digital technologies, especially dynamic mathematics software and “classroom networks.”

In the article they present some interesting perspectives on the historical development on media, from static to dynamic, and they discuss some dynamical perspectives related to variation and geometry (dynamic geometry, like Cabri, Geometer’s Sketchpad, etc.). Here is the abstract of this interesting article:

The nature of mathematical reference fields has substantially evolved with the advent of new types of digital technologies enabling students greater access to understanding the use and application of mathematical ideas and procedures. We analyze the evolution of symbolic thinking over time, from static notations to dynamic inscriptions in new technologies. We conclude with new perspectives on Kaput’s theory of notations and representations as mediators of constructive processes.

Awards and medals

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According to the Math Forum, the following people have been given awards in our field recently:

  • Anna Sfard has received the Hans Freudenthal Medal for 2007 (see this post for more information)
  • Jeremy Kilpatrick has received the Felix Klein Medal for 2007 (see this post for more information)

Both news were posted at the request of Mogens Niss, who is Chair of the ICMI Awards Committee. The posts linked above give a nice overview of the research efforts of these two distinguished scholars.

Aztec math

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Both National Geographic and Scientific American published articles about Aztec mathematics yesterday. The article in National Geographic focused on a specialized arithmetic that Aztec mathematicians developed to measure tracts of taxable land. In this arithmetic they used symbols like hearts, hands and arrows, which probably had a relation to the human body. The article refers to a study that was reported in this week’s issue of Science. Science covers the topic in a news story as well as the research article. The Scientific American article also focus on the hearts and arrows, and they also refer to another article (in Science) about the Aztec number system. So, for those interested in Aztec mathematics in particular, and history of mathematics in general, there are lots of interesting and up to date articles to read here!

Implementing Kaput’s research programme

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Celia Hoyles and Richard Noss recently published an article called “Next steps in implementing Kaput’s research programme” in Educational Studies in Mathematics. These two distinguished professors have written a multitude of books and articles together in the past, so you might have come across something written by “Hoyles and Noss” before. In this particular article, they explore and discuss some key ideas from Jim Kaput and connect them to their own research. Here is the abstract of the article:

We explore some key constructs and research themes initiated by Jim
Kaput, and attempt to illuminate them further with reference to our own
research. These ‘design principles’ focus on the evolution of digital
representations since the early 1990s, and we attempt to take forward
our collective understanding of the cognitive and cultural affordances
they offer. There are two main organising ideas for the paper. The
first centres around Kaput’s notion of outsourcing of processing power,
and explores the implications of this for mathematical learning. We
argue that a key component for design is to create visible, transparent
views of outsourcing, a transparency without which there may be as many
pitfalls as opportunities for mathematical learning. The second
organising idea is Kaput’s notion of communication and the importance
of designing for communication in ways that recognise the mutual
influence of tools for communication and for mathematical expression.

Testing, testing and comparing test results…

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In 2003 (in the U.S.), the National Assessment of Educational Progress (NAEP) administered assessments in reading and mathematics for grades 4 and 8. Representative samples of students were made from about 100 public schools in each state. A research report called “Comparison Between NAEP and State Mathematics Assessment Results: 2003” now focus on the question whether these results are comparable to the results published by individual state testing programs. The entire report is available online (only!), and can be downloaded in PDF format (Vol I and II).

The introduction contains some interesting historical remarks about achievement testing in the U.S., and this might be interesting to non-Americans (like myself).

IJMEST, vol. 39, issue 3

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International Journal of Mathematical Education in Science and Technology has published their third issue (of 8) this year. In the table of contents, we find the following original articles:

285 – 292
Authors: K. Renee Fister; Maeve L. McCarthy
DOI: 10.1080/00207390701690303
293 – 299
Author: Betty McDonald
DOI: 10.1080/00207390701688141
301 – 311
Author: Stan Lipovetsky
DOI: 10.1080/00207390701639532
313 – 324
Authors: Modestina Modestou; Iliada Elia; Athanasios Gagatsis; Giorgos Spanoudis
DOI: 10.1080/00207390701691541
325 – 340
Authors: Juana-Maria Vivo; Manuel Franco
DOI: 10.1080/00207390701691566
341 – 356
Author: I. S. Jones
DOI: 10.1080/00207390701734523
357 – 363
Author: Jesper Rydén
DOI: 10.1080/00207390701639508

Excellent math blog

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There are many academic journals in our field, and there are many articles to read if you want to keep up. On some occasions though, a couple of days might pass by without any new publications from the major journals. On instances like that, you might want to take a look at some of the mathematics related blogs on the internet. One of my favorites is Wild About Math! by Sol Lederman. This blog presents several interesting articles about mathematics and how to learn “to get wild about Math“, and a regular feature of the blog is the “Monday Math Madness contest” (Sol loves mathematical problems and puzzles). You can also find a list of links to other web pages with mathematical problems and puzzles.