Using history as a goal

Uffe Thomas Jankvist has written an article called An empirical study of using history as a ‘goal’. The article was published online in Educational Studies in Mathematics two days ago. Here is the abstract of his article:

This article discusses an empirical study on the use of history as a goal. A historical module is designed and implemented in a Danish upper secondary class in order to study the students’ capabilities at engaging in meta-issue discussions and reflections on mathematics and its history. Based on videos of the implementation, students’ hand-in essay assignments, questionnaires, and follow-up interviews, the conditions, sense, and extent to which the students are able to perform such discussions and reflections are analyzed using a described theoretical framework.

January issue of Science & Education

The January issue of Science & Education has been published. One of the articles contained in the issue is of relevance to mathematics education: A Pilot Study of a Cultural-Historical Approach to Teaching Geometry. The article is written by Stuart Rowlands from the University of Plymouth. Here is the abstract of his article:

There appears to be a widespread assumption that deductive geometry is inappropriate for most learners and that they are incapable of engaging with the abstract and rule-governed intellectual processes that became the world’s first fully developed and comprehensive formalised system of thought. This article discusses a curriculum initiative that aims to ‘bring to life’ the major transformative (primary) events in the history of Greek geometry, aims to encourage a meta-discourse that can develop a reflective consciousness and aims to provide an opportunity for the induction into the formalities of proof and to engage with the abstract. The results of a pilot study to see whether 14–15 year old ‘mixed ability’ and 15–16 year old ‘gifted and talented’ students can be meaningfully engaged with two such transformative events are discussed.

BSHM Bulletin, Issue 2, 2009

The British Society for the HIstory of Mathematics has published issue 2 of their bulletin this year. This issue contains four interesting articles:

Hands-on mathematics

The May issue of Science & Education contains an interesting article that is related to mathematics education. The article is written by Youjun Wang, and it is entitled: Hands-on mathematics: two cases from ancient Chinese mathematics. Here is the abstract of Wang’s article:

In modern mathematical teaching, it has become increasingly emphasized that mathematical knowledge should be taught by problem-solving, hands-on activities, and interactive learning experiences. Comparing the ideas of modern mathematical education with the development of ancient Chinese mathematics, we find that the history of mathematics in ancient China is an abundant resource for materials to demonstrate mathematics by hands-on manipulation. In this article I shall present two cases that embody this idea of a hands-on approach in ancient Chinese mathematics, at the same time offering an opportunity to show how to utilize materials from the history of Chinese math in modern mathematical education.

BSHM Bulletin

Journal of the British Society for the History of Mathematics has published issue 1 of 2009. The issue contains several articles that might be of interest, if you are interested in the history of mathematics. Here is a list of the feature articles in this issue of the BSHM Bulletin:

Using history in mathematics education

Uffe Thomas Jankvist has written an article about using history in mathematics education. The article was published in Educational Studies in Mathematics last week, and it is entitled: A categorization of the “whys” and “hows” of using history in mathematics education. Here is the abstract of his article:

This is a theoretical article proposing a way of organizing and structuring the discussion of why and how to use the history of mathematics in the teaching and learning of mathematics, as well as the interrelations between the arguments for using history and the approaches to doing so. The way of going about this is to propose two sets of categories in which to place the arguments for using history (the “whys”) and the different approaches to doing this (the “hows”). The arguments for using history are divided into two categories; history as a tool and history as a goal. The ways of using history are placed into three categories of approaches: the illumination, the modules, and the history-based approaches. This categorization, along with a discussion of the motivation for using history being one concerned with either the inner issues (in-issues) or the metaperspective issues (meta-issues) of mathematics, provides a means of ordering the discussion of “whys” and “hows.”

Reading tips: Branford (1908)

Many great books have been written, and an increasing number are becoming part of the public domain. One of them, which I would like to point your attention to, is a classical book written by Benchara Branford in 1908! The title of the book is: “A Study of Mathematical Education, including The Teaching of Arithmetic”. Besides being an important book in the history of mathematics education, it also provides a nice insight into the teaching of mathematics as it was 100 years ago!

Personally, I think his very direct connection between the historical development of mathematics and the child’s development of mathematical thinking (often referred to as “the genetic approach” in mathematics education) is interesting.

A Study of Mathematical Education

If you want to read the book in fullscreen format, click here. For download (pdf), click here.

A brief history of mathematics (book)

For those of you who haven’t already discover it, here is a tip for Christmas: Scribd! You can find lots of interesting books and papers here, and some are true gems. Here is one of them: A brief history of mathematics, by Karl Fink. This official translation was published in 1900, and therefore is in the public domain. You can read the book in its entirety here:

A brief history of mathematics

If you want to read the book in fullscreen, you can go here. To download the book as pdf, click on this link.

A cultural-historical approach to teaching geometry

Stuart Rowlands has recently written an article called A Pilot Study of a Cultural-Historical Approach to Teaching Geometry, which was published in Science & Education on Wednesday. Here is the abstract of the article:

There appears to be a widespread assumption that deductive geometry is inappropriate for most learners and that they are incapable of engaging with the abstract and rule-governed intellectual processes that became the world’s first fully developed and comprehensive formalised system of thought. This article discusses a curriculum initiative that aims to ‘bring to life’ the major transformative (primary) events in the history of Greek geometry, aims to encourage a meta-discourse that can develop a reflective consciousness and aims to provide an opportunity for the induction into the formalities of proof and to engage with the abstract. The results of a pilot study to see whether 14–15 year old ‘mixed ability’ and 15–16 year old ‘gifted and talented’ students can be meaningfully engaged with two such transformative events are discussed.