Author: Reidar Mosvold

Do you use math in your everyday life?

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I am thrilled to see that the post I made yesterday about Sarah Clark’s article in The Spectrum, and Deb Peterson’s comments in her blog at About.com, actually resulted in Deb finding out about my work. She has followed this up with another nice post about the issue. Be sure to check out the last part of the title of her post 🙂

I am not sure that I would totally agree that I have actually proven Sarah right, though. My study was a qualitative study of a small sample of teachers, and I don’t think it can be generalized like that. What I do think is interesting with the results of my work is that even these skilled teachers, who were actually chosen in order to provide good examples on how teachers connect mathematics with everyday life, did not do this so much!

There was another teacher in my study, called Harry, who also made a lot of connections with everyday life in his teaching, though. I wrote an article with some examples from his teaching for the Norma 05 conference (Mosvold, 2007). You can find a pre-print of this article here. (See full reference below!)

References:
Mosvold, R. (2007). Teaching “Mathematics in everyday life”. In C. Bergsten et al. (Eds.): Relating Practice and Research in Mathematics Education. Proceedings of Norma 05, Fourth Nordic Conference on Mathematics Education, 389-399, Trondheim: Tapir Academic Press.

Algebra: Use it or lose it?

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Yesterday, there was an interesting article in The Spectrum. The title of the article is “Algebra: Use it or lose it?“, and the claim that is put forth by author Sarah Clark was that algebra teachers all over the world are lying when they tell students that algebra is important because they’ll use it in their daily life.

Clark (32) describes herself as a non-traditional student:

(…) who hasn’t taken an algebra class in 15 years. If, for the past 15 years, I had been using algebra in my everyday life, I would be blowing through my algebra homework with ease, thinking, “Hey! I just did this yesterday while I was washing laundry,” or, “I’m so glad I’ve known this all along. I’d never be able to drive anywhere without it!” or “Wow! I just used this formula last week to calculate the ratio of jazz to classical music on my iPod.

Apparently, this is not what she has experienced. On the contrary, she has never experienced using algebra in her daily life, and she now finds herself uncapable of doing it. She also proposes an algebra revolution, where we should share the truth with every student who is struggling with algebra: these skills will not be crucial for you in adult life.

There are lots of things to comment on these statements, for sure. And lots of people did comment on it already (so be sure to read the comments below the article as well!). Deb Peterson at About.com made an interesting (external) comment to the article, that might be worth reading.

Myself, I think all these claims about how mathematics is/can be useful in your everyday life is a mixed bag. I think Clark’s article illustrates a common issue as well: when teachers claim that mathematics is useful in everyday life, it might be their own everyday life they think of rather than their students’. (Lots of people have written about the connections with everyday life, and if you are interested, you might want to take a look at my own PhD thesis: Mathematics in everyday life: a study of beliefs and actions.)

Four-digit numbers which are squared sums

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Heather Coughlin and Brian Jue have written an article called Four-digit numbers which are squared sums. The article was recently published online in International Journal of Mathematical Education in Science and Technology. Here is the article abstract:

There is a very natural way to divide a four-digit number into 2 two-digit numbers. Applying an algorithm to this pair of numbers, determine how often the original four-digit number reappears.

Diagrams in problem solving

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Marilena Pantziara, Athanasios Gagatsis and Iliada Elia have written an article entitled Using diagrams as tools for the solution of non-routine mathematical problems. The article has recently been published online in Educational Studies in Mathematics. Here is the abstract of their article:

The Mathematics education community has long recognized the importance of diagrams in the solution of mathematical problems. Particularly, it is stated that diagrams facilitate the solution of mathematical problems because they represent problems’ structure and information (Novick & Hurley, 2001; Diezmann, 2005). Novick and Hurley were the first to introduce three well-defined types of diagrams, that is, network, hierarchy, and matrix, which represent different problematic situations. In the present study, we investigated the effects of these types of diagrams in non-routine mathematical problem solving by contrasting students’ abilities to solve problems with and without the presence of diagrams. Structural equation modeling affirmed the existence of two first-order factors indicating the differential effects of the problems’ representation, i.e., text with diagrams and without diagrams, and a second-order factor representing general non-routine problem solving ability in mathematics. Implicative analysis showed the influence of the presence of diagrams in the problems’ hierarchical ordering. Furthermore, results provided support for other studies (e.g. Diezman & English, 2001) which documented some students’ difficulties to use diagrams efficiently for the solution of problems. We discuss the findings and provide suggestions for the efficient use of diagrams in the problem solving situation.

Teachers’ motivation for fractions

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Kristie Jones Newton has written an article that was published in Journal of Mathematics Teacher Education on Wednesday. The article is entitled Instructional practices related to prospective elementary school teachers’ motivation for fractions. Here is Newton’s article abstract:

This study was undertaken in order to better understand prospective elementary school teachers’ motivations for working with fractions before and after taking a course designed to deepen their understanding of mathematics, as well as what instructional practices might be related to any changes detected in their motivations. Eighty-five education students were given a motivation questionnaire at the beginning and end of the semester, and observations were made of the 9 days when fractions were taught. Three levels of teacher data were collected to understand instructional practices. Students’ ratings of the importance and usefulness of fractions (value), self-concept of ability, and anxiety were near the center of the scale at pre-test, with only value in the desired direction. At posttest, value and self-concept of ability increased while anxiety decreased, but these changes differed somewhat by instructor. In particular, reform-oriented practices, such as engaging students in high-level discourse, seemed to be associated with lowered anxiety.

Gem #7: Dewey’s "Democracy and education"

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Yesterday, I mentioned John Dewey in my post about the latest issue of Journal of Curriculum Studies. This gave me an idea, and as a result I figured out that it would have been nice to add a work by Dewey in my gem-series. I know, it is not a famous book of mathematics or mathematics education, but Dewey’s theories have had great influence in educational research in general, and also in research in mathematics education. Therefore, I am happy to present today’s gem: “Democracy and Education”, by John Dewey. As usual, you can read it below, or download the pdf. Happy reading!

John Dewey – Democracy and Education: An Introduction to the Philosophy of Education

Journal of Curriculum Studies

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There are lots of scientific journals related to education out there, and not all of them include articles related to mathematics education (at least not in all issues). Journal of Curriculum Studies is a very interesting journal, and it has now released the first issue of 2009. No articles in this issue are directly related to mathematics education, but there are several interesting articles about teaching and education in general. The issue also includes an essay that was written by John Dewey, and first published in 1922! (If you’re interested in more of Dewey’s writings, you should take a look at this link!)

Gem #6: Napier’s logarithms

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John Napier (1550-1617) John Napier (1550-1617) was a Scottish mathematician. He is most famous for having invented logarithms, and today’s featured book is precisely about that. Napier’s book is entitled “The construction of the wonderful canon of logarithms”, and it is an English translation of the original Latin book. The book is available as Flip Book, or you could download the PDF. You could also start reading it below, without leaving this blog 🙂

Napier’s wonderful world of logarithms

Math Wrath

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Forbes published a nice commentary with a focus on mathematics on Saturday. Here is a taster:

At the tender age of 8, I concluded that, among the varied destinies shimmering before me, being a profound mathematical genius was not one of them. I won’t have a number named after me, like Signor Fibonacci, or propose a problem to perplex the generations, like Monsieur Fermat. Chances are I won’t even get a dinner tip right.

The article is interesting in many ways. Among other things, it includes several thought provoking questions related to mathematics education. For instance: Why do we teach mathematics in the age of the calculator? The article also includes some historical anecdotes that might be of interest to some. In my opinion, it would have been even more interesting to go beyond these anecdotes, but that’s a different story, I guess. (If you want a good resource on the history of mathematics that goes far beyond anecdotes, you should check out MacTutor History of Mathematics Archive!)

Assessing science students’ attitudes

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A new article has recently been published in International Journal of Mathematical Education in Science and Technology. The article is entitled Assessing science students’ attitudes to mathematics: A case study on a modelling project with mathematical software, and it is written by L. L. Lim,  T. -Y. Tso and F. L. Lin. Here is the abstract of their article:

This article reports the attitudes of students towards mathematics after they had participated in an applied mathematical modelling project that was part of an Applied Mathematics course. The students were majoring in Earth Science at the National Taiwan Normal University. Twenty-six students took part in the project. It was the first time a mathematical modelling project had been incorporated into the Applied Mathematics course for such students at this University. This was also the first time the students experienced applied mathematical modelling and used the mathematical software. The main aim of this modelling project was to assess whether the students’ attitudes toward mathematics changed after participating in the project. We used two questionnaires and interviews to assess the students. The results were encouraging especially the attitude of enjoyment. Hence the approach of the modelling project seems to be an effective method for Earth Science students.