Mathematical interaction in different social settings

February 23, 2009 / Reidar Mosvold / Leave a comment

Marcus Nührenbörger and Heinz Steinbring have written an article called Forms of mathematical interaction in different social settings: examples from students’, teachers’ and teacher–students’ communication about mathematics. The article was published on Friday in Journal of Mathematics Teacher Education. This article is related to teachers’ reflection and the construction of mathematical knowledge. Here is the abstract:

The study presented in this article investigates forms of mathematical interaction in different social settings. One major interest is to better understand mathematics teachers’ joint professional discourse while observing and analysing young students mathematical interaction followed by teacher’s intervention. The teachers’ joint professional discourse is about a combined learning and talking between two students before an intervention by their teacher (setting 1) and then it is about the students learning together with the teacher during their mathematical work (setting 2). The joint professional teachers’ discourse constitutes setting 3. This combination of social settings 1 and 2 is taken as an opportunity for mathematics teachers’ professionalisation process when interpreting the students’ mathematical interactions in a more and more professional and sensible way. The epistemological analysis of mathematical sign-systems in communication and interaction in these three settings gives evidence of different types of mathematical talk, which are explained depending on the according social setting. Whereas the interaction between students or between teachers is affected by phases of a process-oriented and investigated talk, the interaction between students and teachers is mainly closed and structured by the ideas of the teacher and by the expectations of the students.

Teachers’ reflective thinking skills

February 23, 2009 / Reidar Mosvold / Leave a comment

Amanda Jansen and Sandy M. Spitzer have written an article entitled Prospective middle school mathematics teachers’ reflective thinking skills: descriptions of their students’ thinking and interpretations of their teaching. The article was published online in Journal of Mathematics Teacher Education on Friday. Jansen and Spitzer takes the belief “that mathematics teacher educators should foster reflective thinking among prospective teachers” as point of departure, and they ask how teacher educators can help students prepare for this. In their article, which I think is very interesting by the way, they present Lesson study as an approach that can be used in order to learn from practice. Their study is also described as a “modified lesson study experience”.

Here is the article abstract:

In this study, we examined prospective middle school mathematics teachers’ reflective thinking skills to understand how they learned from their own teaching practice when engaging in a modified lesson study experience. Our goal was to identify variations among prospective teachers’ descriptions of students’ thinking and frequency of their interpretations about how teaching affected their students’ learning. Thirty-three participants responded to open-ended questionnaires or interviews that elicited reflections on their own teaching practice. Prospective teachers used two forms of nuance when describing their students’ thinking: (1) identifying students’ specific mathematical understandings rather than general claims and (2) differentiating between individual students’ thinking rather than characterizing students as a collective group. Participants who described their students’ thinking with nuance were more likely to interpret their teaching by posing multiple hypotheses with regard to how their instruction affected their students’ learning. Implications for supporting continued growth in reflective thinking skills are discussed in relation to these results.

Anniversary!!!

February 20, 2009 / Reidar Mosvold / Leave a comment

I can hardly believe that it is only a little more than a year since I started this blog! It has been a great learning experience for me, and hopefully for someone else as well. I just found out that I have actually reached my 400^th post, which is quite an anniversary! So, happy 400 🙂

IJMEST, volume 40, issue 2, 2009

February 20, 2009 / Reidar Mosvold / Leave a comment

International Journal of Mathematical Education in Science and Technology has just released issue 2 of 2009. Here is a list of the original articles included in the issue:


	Mathematics textbooks and their potential role in supporting misconceptions 173 – 181 Authors: Ann Kajander; Miroslav Lovric DOI: 10.1080/00207390701691558
	Using components of mathematical ability for initial development and identification of mathematically promising students 183 – 199 Authors: T. Vilkomir; J. O’Donoghue DOI: 10.1080/00207390802276200
	Conceptual and procedural performance of undergraduate students in integration 201 – 211 Author: Nevin Mahir DOI: 10.1080/00207390802213591
	Mathematically gifted and talented learners: theory and practice 213 – 228 Authors: Valsa Koshy; Paul Ernest; Ron Casey DOI: 10.1080/00207390802566907
	An investigation of the mathematical literacy of first year third-level students in the Republic of Ireland 229 – 246 Authors: Sinead Breen; Joan Cleary; Ann O’Shea DOI: 10.1080/00207390802566915
	Developing science and math integrated activities for middle school students 247 – 257 Authors: Sonya Ellouise Sherrod; Jerry Dwyer; Ratna Narayan DOI: 10.1080/00207390802566923
	Modelling and inverse-modelling: experiences with O.D.E. linear systems in engineering courses 259 – 268 Author: Victor Martinez-Luaces DOI: 10.1080/00207390802276291

Exemplary mathematics lessons

February 20, 2009 / Reidar Mosvold / Leave a comment

What can we learn from exemplary math lessons? This is a question asked by Ngai-Ying Wong in the article: Exemplary mathematics lessons: what lessons we can learn from them? The article was published in ZDM two days ago. Sadly it does not include an abstract, but the free preview looks interesting!

Khayyam with Cabri

February 19, 2009 / Reidar Mosvold / Leave a comment

Adnan Baki and Bulent Guven have written an article about the interesting link between Persian mathematician, philosopher, astronomer and poet Omar Khayyam (1048-1122) and the dynamic geometry application Cabri. The article was recently published in Teaching Mathematics and its Applications, and it is entitled Khayyam with Cabri: experiences of pre-service mathematics teachers with Khayyam’s solution of cubic equations in dynamic geometry environment. Here is the abstract of their article:

The study reported in this article deals with the observed actions of Turkish pre-service mathematics teachers in dynamic geometry environment (DGE) as they were learning Khayyam’s method for solving cubic equations formed as x³ + ax = b. Having learned the method, modelled it in DGE and verified the correctness of the solution, students generated their own methods for solving different types of cubic equations such as x³ + ax² = b and x³ + a = bx in the light of Khayyam’s method. With the presented teaching experiment, students realized that Khayyam’s mathematics is different from theirs. We consider that this gave them an opportunity to have an insight about the cultural and social aspects of mathematics. In addition, the teaching experiment showed that dynamic geometry software is an excellent tool for doing mathematics because of their dynamic nature and accurate constructions. And, it can be easily concluded that the history of mathematics is useful resource for enriching mathematics learning environment.

BSHM Bulletin

February 18, 2009 / Reidar Mosvold / Leave a comment

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:

The hunt for the lost cities of Ptolemy, by Daniel Mintz
A puzzle rhyme from 1782, by Kristin Bjarnadottir
International mathematical journals published in Poland between the Wars, by Malgorzata Przenioslo
The contribution of M H A Newman and his mathematicians to the creation of the Manchester ‘Baby’, by David Anderson

Free journal article

February 18, 2009 / Reidar Mosvold / Leave a comment

Springer has decided to make several articles in Early Childhood Education Journal available for free (till March 31, 2009). One of these articles is a very interesting article about mathematics education: Educating the Young Mathematician: The Twentieth Century and Beyond, by Olivia N. Saracho and Bernard Spodek. Here is the abstract of this article:

Educational programs for young children emerged reasonably early in the history of the United States of America. The movements of Child-Centered Education, the Nursery School, the Project Method, Curriculum Reform, and contemporary research have all influenced mathematics in early childhood education. The Froebelian kindergarten and the Montessori Casa die Bambini (Children’s House) included approaches to teaching mathematics. This article reviews the history of mathematics education in relation to the history of early childhood education from the turn of the twentieth century. It also discusses how research in mathematics education attempted to gain its own identity. Throughout history, researchers have identified mathematics issues and addressed them, defining the field, and generating a cadre of mathematics researchers.

Hidden lessons

February 17, 2009 / Reidar Mosvold / Leave a comment

Amy B. Ellis and Paul Grinstead have written an article that was published in The Journal of Mathematical Behavior last week. The article is entitled Hidden lessons: How a focus on slope-like properties of quadratic functions encouraged unexpected generalizations. Here is a copy of their article abstract:

This article presents secondary students’ generalizations about the connections between algebraic and graphical representations of quadratic functions, focusing specifically on the roles of the parameters a, b, and c in the general form of a quadratic function, y = ax² + bx + c. Students’ generalizations about these connections led to a surprising finding: two-thirds of the students interviewed identified the parameter a as the “slope” of the parabola. Analysis of qualitative data from interviews and classroom observations led to the development of three focusing phenomena in the classroom environment that inadvertently supported a focus on slope-like properties of quadratic functions: (a) the use of linear analogies, (b) the rise over run method, and (c) viewing a as dynamic rather than static.

IJMEST, issue 1, 2009

February 17, 2009 / Reidar Mosvold / Leave a comment

Issue 1 of International Journal of Mathematical Education in Science and Technology has been published. The issue contains several articles that I find really interesting! Here is a list of all the articles in this issue:

Original Articles
	Some reasons for change in undergraduate mathematics enrolments 3 – 15 Authors: Derek Holton; Eric Muller; Juha Oikkonen; Oscar Adolfo Sanchez Valenzuela; Ren Zizhao DOI: 10.1080/00207390802597621
	Mathematical sciences in Australia 17 – 26 Authors: Jan Thomas; Michelle Muchatuta; Leigh Wood DOI: 10.1080/00207390802597654
	Recruitment and retention of mathematics students in Canadian universities 27 – 41 Authors: Laura Fenwick-Sehl; Marcella Fioroni; Miroslav Lovric DOI: 10.1080/00207390802568192
	The rise and fall of mathematical enrolments in the French educational system: a case study 43 – 57 Authors: Pierre Arnoux; Daniel Duverney; Derek Holton DOI: 10.1080/00207390802586145
	Status of mathematics teaching and learning in Malaysia 59 – 72 Authors: Hong Kian Sam; Ting Lang Ngiik; Hasbee Hj Usop DOI: 10.1080/00207390802514519
	New numbers in mathematics in South Africa 73 – 86 Authors: Johann Engelbrecht; Ansie Harding DOI: 10.1080/00207390802597738
	Mathematics education in Argentina 87 – 100 Authors: Cristina Varsavsky; Marta Anaya DOI: 10.1080/00207390802514543
	The mathematical needs of secondary teachers: data from three countries 101 – 108 Authors: B. Barton; L. Sheryn DOI: 10.1080/00207390802576807
	Recruitment and retention of students-an integrated and holistic vision of mathematics support 109 – 125 Authors: A. C. Croft; M. C. Harrison; C. L. Robinson DOI: 10.1080/00207390802542395
	Ideas and results in teaching beginning maths students 127 – 138 Author: Juha Oikkonen DOI: 10.1080/00207390802582961
	Systemic integration of evolving technologies in undergraduate mathematics education and its impact on student retention 139 – 155 Authors: Eric Muller; Chantal Buteau; Mihly Klincsik; Ildik Perjsi-Hmori; Csaba Srvri DOI: 10.1080/00207390802551602
	The professional development of graduate mathematics teaching assistants 157 – 172 Authors: Gary Harris; Jason Froman; James Surles DOI: 10.1080/00207390802514493