Online resources in mathematics

Laetitia Bueno-Ravel and Ghislaine Gueudet have written an article that was recently published in International Journal of Computers for Mathematical Learning. The article provides some interesting perspectives on issues that should be relevant to most mathematics teachers: Online Resources in Mathematics, Teachers’ Geneses and Didactical Techniques. The examples provided in their article is related to a particular electronic resource called (in French) "Mathenpoche" (or "Maths in the pocket"). Here is the abstract of their article:

The study we present here concerns the consequences of integrating online resources into the teaching of mathematics. We focus on the interaction between teachers and specific online resources they draw on: e-exercise bases. We propose a theoretical approach to study the associated phenomena, combining instrumental and anthropological perspectives. For given didactical tasks, we observe teachers’ instrumental geneses, and the didactical techniques they develop. We exemplify our approach with the analysis of a case study of trigonometry in grade 9.

Supervision of mathematics student teachers

Maria Lorelei Fernandez and Evrim Erbilgin have written an article about Examining the supervision of mathematics student teachers through analysis of conference communications. The article was published online in Educational Studies in Mathematics on Tuesday. Here is the abstract of their article:

Student teaching is often a capstone experience in the preparation of mathematics teachers. Thus, it is essential to better understand key aspects of the experience. We conducted a qualitative study of post-lesson conferences led by supervisors (classroom cooperating teachers and a university supervisor) working with mathematics student teachers. Analysis of conference communications revealed differences in the types and content of communications in conferences led by the cooperating teachers and by the university supervisor. Cooperating teachers tended toward evaluative supervision that lacked a focus on the mathematics of the lessons while the university supervisor tended toward educative supervision, guiding student teachers to reflect on and learn from their own classroom experiences including the mathematics of their lessons. Differences are discussed, and suggestions concerning the supervision of student teachers are made along with recommendations for further research.

Mathematics classrooms with immigrant students

Núria Gorgorió and Guida de Abreu have written an article that was published in Educational Studies in Mathematics on Tuesday. The article is entitled Social representations as mediators of practice in mathematics classrooms with immigrant students. Here is a copy of their abstract:

This article suggests that a critical perspective of the notion of social representations can offer useful insights into understanding practices of teaching and learning in mathematics classrooms with immigrant students. Drawing on literature using social representations, previous empirical studies are revisited to examine three specific questions: what are the dominant social representations that permeate the mathematics classroom with immigrant students? What impact do these social representations have on classroom practices? What are the spaces for changing these practices through becoming reflective and critically aware of these representations? These questions are addressed mostly in relation to teachers’ representations, though the article also draws on data from research with students and parents to illustrate the diversity of representations and to argue for a critical and reflective perspective.

IJSME, Vol 7, Number 2

International Journal of Science and Mathematics Education has just released their second issue this year, the April issue (!). The issue contains 9 interesting articles:

• Language and Student Performance in Junior Secondary Science Examinations: The Case of Second Language Learners in Botswana, by Robert B. Prophet and Nandkishor B. Badede
• The system of coordinates as an obstacle in understanding the concept of dimension, by Constantine Skordoulis, Theodore Vitsas, Vassilis Dafermos and Eugenia Koleza
• Misconceptions of Turkish Pre-Service Teachers about Force and Motion, by Sule Bayraktar
• Variable Relationships among Different Science Learners in Elementary Science-Methods Courses, by Robert E. Bleicher
• Efficacy of Two Different Instructional Methods Involving Complex Ecological Content, by Christoph Randler and Franz X. Bogner
• Correlations Among Five Demographic Variables and the Performance of Selected Jamaican 11th-graders on Some Numerical Problems on Energy, by Nicholas Emepue and Kola Soyibo
• From "exploring the middle zone" to "constructing a bridge": Experimenting in the Spiral Bianshi mathematics curriculum, by Ngai-Ying Wong, Chi-Chung Lam, XuHua Sun and Anna Mei Yan Chan
• Number Sense Strategies Used by Pre-Service Teachers in Taiwan, by Der-Ching Yang, Robert E. Reys and Barbara J. Reys
• Listen to the silence: The left-behind phenomenon as seen through classroom videos and teachers' reflections, by Hagar Gal, Fou-Lai Lin and Jia-Ming Ying
  

Transition between different coordinate systems

Mariana Montiel, Biguel R. Wilhelmi, Draga Vidakovic and Iwan Elstak have written an article called Using the onto-semiotic approach to identify and analyze mathematical meaning when transiting between different coordinate systems in a multivariate context. The article was published online in Educational Studies in Mathematics on Saturday. Here is the abstract of their article:

The main objective of this paper is to apply the onto-semiotic approach to analyze the mathematical concept of different coordinate systems, as well as some situations and university students’ actions related to these coordinate systems. The identification of objects that emerge from the mathematical activity and a first intent to describe an epistemic network that relates to this activity were carried out. Multivariate calculus students’ responses to questions involving single and multivariate functions in polar, cylindrical, and spherical coordinates were used to classify semiotic functions that relate the different mathematical objects.

Changing practice, changing minds

I like the title of a new article written by Jeanne Tunks and Kirk Weller, especially the first part of it! Here is the entire title: Changing practice, changing minds, from arithmetical to algebraic thinking: an application of the concerns-based adoption model (CBAM). This article was published online in Educational Studies in Mathematics on Saturday, and it discusses the results of a yearlong innovation program called "Teacher Quality Grant". And, just to avoid any misunderstandings: it is not only the title of the article I find interesting. The article itself is very interesting, and the program described also appears to be quite interesting. Here is the abstract of the article:

This study examines the process of change among grade 4 teachers (students aged 9–10 years) who participated in a yearlong Teacher Quality Grant innovation program. The concerns-based adoption model (CBAM), which informed the design and implementation of the program, was used to examine the process of change. Two questions guided the investigation: (1) How did teachers’ concerns about and levels of use of the innovation evolve during the course of the project? (2) What changes in teachers’ perceptions and practices arose as a result of the innovation? Results showed that several of the teachers’ concerns evolved from self/task toward impact. With continued support, several participants achieved routine levels of use, which they sustained beyond the project.

ESM, March 2009

Educational Studies in Mathematics - one of the most important journals within our field - has just released their Volume 70, Number 2/March, 2009. This is a special issue with a focus on Gestures and Multimodality in the Construction of Mathematical Meaning. It contains 10 interesting articles:

10 Articles

	Article Introduction: beyond words L. Radford, L. Edwards and F. Arzarello PDF (94.8 KB)HTML	91-95
	Article Gestures as semiotic resources in the mathematics classroom Ferdinando Arzarello, Domingo Paola, Ornella Robutti and Cristina Sabena PDF (319.4 KB)HTMLSupplemental HTML	97-109
	Article Why do gestures matter? Sensuous cognition and the palpability of mathematical meanings Luis Radford PDF (344.8 KB)HTML	111-126
	Article Gestures and conceptual integration in mathematical talk Laurie D. Edwards PDF (312.8 KB)HTMLSupplemental HTML	127-141
	Article Working with artefacts: gestures, drawings and speech in the construction of the mathematical meaning of the visual pyramid Michela Maschietto and Maria G. Bartolini Bussi PDF (403.1 KB)HTML	143-157
	Article Mathematical imagination and embodied cognition Ricardo Nemirovsky and Francesca Ferrara PDF (329.6 KB)HTML	159-174
	Article Bodily experience and mathematical conceptions: from classical views to a phenomenological reconceptualization Wolff-Michael Roth and Jennifer S. Thom PDF (364.0 KB)HTML	175-189
	Article What’s all the fuss about gestures? A commentary Anna Sfard PDF (169.3 KB)HTML	191-200
	Article Embodied multi-modal communication from the perspective of activity theory Julian Williams PDF (171.2 KB)HTML	201-210
	Article Building intellectual infrastructure to expose and understand ever-increasing complexity James Kaput PDF (84.2 KB)HTML	211-215

Geometric and algebraic approaches

Iliada Elia, Athanasios Gagatsis, Areti Panaoura, Theodosis Zachariades and Fotini Zoulinaki have written an article entitled Geometric and algebraic approaches in the concept of "limit" and the impact of the "didactic contract". The article was published in International Journal of Science and Mathematics Education on Friday. Here is a copy of their article abstract:

The present study explores students’ abilities in conversions between geometric and algebraic representations, in problem- solving situations involving the concept of “limit” and the interrelation of these abilities with students’ constructed understanding of this concept. An attempt is also made to examine the impact of the “didactic contract” on students’ performance through the processes they employ in tackling specific tasks on the concept of limit. Data were collected from 222 12th-grade high school students in Greece. The results indicated that students who had constructed a conceptual understanding of limit were the ones most probable to accomplish the conversions of limits from the algebraic to the geometric representations and the reverse. The findings revealed the compartmentalized way of students’ thinking in non-routine problems by means of their performance in simpler conversion tasks. Students who did not perform under the conditions of the didactic contract were found to be more consistent in their responses for various conversion tasks and complex problems on limits, compared to students who, as a consequence of the didactic contract, used only algorithmic processes.

Ethiopian students in Israel

Tiruwork Mulat and Abraham Arcavi have written an article about Success in mathematics within a challenged minority: the case of students of Ethiopian origin in Israel (SEO). The article was published on Friday in Educational Studies in Mathematics. Here is an abstract of their article:

Many studies have reported on the economical, social, and educational difficulties encountered by Ethiopian Jews since their immigration to Israel. Furthermore, the overall academic underachievement and poor representation of students of Ethiopian origin (SEO) in the advanced mathematics and science classes were highlighted and described. Yet, studies focusing on differential achievements within SEO and on students who succeed against all odds are scarce. In this study, we explored success stories of five SEO studying in a pre-academic program at a prestigious technological university in Israel. Our goal was to understand how these students frame and interpret their success in mathematics and to identify elements perceived as fostering their mathematics and academic trajectories. Using qualitative methodology, we identified perceived personal motivational variables, effective learning and coping strategies, and students’ immediate environment as key elements contributing to achieving and maintaining success. We discuss possible theoretical contributions and practical implications of the findings.

Mathematical interaction in different social settings

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

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!!!

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

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

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

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

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

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

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

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