Kindergarten mathematics with ‘Pepe the Rabbit’

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Chrysanthi Skoumpourdi has written an article that was published in the last issue of European Early Childhood Education Research Journal. The article is entitled Kindergarten mathematics with ‘Pepe the Rabbit’: how kindergartners use auxiliary means to solve problems. Here is the abstract of the article:

The aim of this paper is to investigate the role that auxiliary means (manipulatives such as cubes and representations such as number line) play for kindergartners in working out mathematical tasks. Our assumption was that manipulatives such as cubes would be used by kindergartners easily and successfully whereas the number line would be used by kindergartners rarely and usually unsuccessfully. Through analysis of the 20 children’s (5-years-old) answers which concerned the number sequence as well as simple addition and subtraction problems it appears that although the children mostly used cubes they did not always use them systematically or successfully. The effective use of the number line was limited to defining the number sequence. 

Pre-service teachers’ mathematics anxiety

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Mathematics is a troublesome subject for many pupils, but even more disturbing is the fact that several pre-service teachers have math anxiety. Mehmet Bekdemir discusses whether or not pre-service teachers’ math anxiety relates to their own negative experiences as students. Bekdemir points to teacher behavior as a major factor, and he claims that teacher education programs “should be designed and implemented so as to prevent student anxiety from becoming a barrier to mathematics achievement and a cycle of anxiety”. The title of Bekdemir’s article is The pre-service teachers’ mathematics anxiety related to depth of negative experiences in mathematics classroom while they were students, and it was published online in Educational Studies in Mathematics a couple of days ago. Here is the abstract of the article:

One of the aims of this study is to examine whether the worst experiences and most troublesome mathematics classroom experience affect mathematics anxiety in pre-service elementary teachers. Another goal is to find out how the causes of their anxiety relate to these negative experiences. The participants were 167 senior elementary pre-service teachers. Three different instruments were used to collect data; Mathematics Anxiety Rating Scale, Worst Experience and Most Troublesome Mathematics Classroom Experience Reflection Test, and Interview Protocol. The findings show that many pre-service teachers have mathematics anxiety and that the worst experience and the most troublesome mathematics classroom experience have a direct influence on mathematics anxiety in pre-service teachers. Also, the majority of instances of participants’ mathematics anxiety are caused by the teachers, their behavior or teaching approaches in their past.

Educational Studies in Mathematics, September issue

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The September issue (Volume 75, Number 1) of Educational Studies in Mathematics has been published. This issue contains 6 interesting articles:

Being interested in affective issues, and beliefs in particular, I found the article by Charalambous and Philippou very interesting. They make a very interesting point by discussing the relationship between teachers’ concerns and efficacy beliefs. Although their study was made in a Cypriot context, their discussions and arguments are of general interest. Here is the abstract of their article:

This study brings together two lines of research on teachers’ affective responses toward mathematics curriculum reforms: their concerns and their efficacy beliefs. Using structural equation modeling to analyze data on 151 elementary mathematics teachers’ concerns and efficacy beliefs 5 years into a mandated curriculum reform on problem solving, the study provides empirical support to a model integrating teachers’ concerns and efficacy beliefs. This model suggests that teachers’ concerns of preceding stages inform their concerns of succeeding stages; that teachers’ efficacy beliefs about using the reform affect their task and impact concerns and are, in turn, informed by their self concerns; and that efficacy beliefs about employing pre-reform instructional approaches influence all types of teacher concerns. A qualitative analysis of data from 53 teacher logs provided additional insights into teachers’ concerns about the reform. We discuss the policy and methodological implications of these findings and offer directions for future studies.

Truth and the renewal of knowledge

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Tony Brown has written an article called “Truth and the renewal of knowledge: the case of mathematics education“. This article was recently published online in Educational Studies in Mathematics. Here is the abstract of the article:

Mathematics education research must enable adjustment to new conditions. Yet such research is often conducted within familiar conceptualisations of teaching, of learning and of mathematics. It may be necessary to express ourselves in new ways if we are to change our practices successfully, and potential changes can be understood in many alternative, sometimes conflicting, ways. The paper argues that our entrapment in specific pedagogic forms of mathematical knowledge and the styles of teaching that go with them can constrain students’ engagement with processes of cultural renewal and changes in the ways in which mathematics may be framed for new purposes, but there are some mathematical truths that survive the changing circumstances that require us to update our understandings of teaching and learning the subject. In meeting this challenge, Radford encountered a difficulty in framing notions of mathematical objectivity and truth commensurate with a cultural–historical perspective. Following Badiou, this paper distinguishes between objectivity, which is seen necessarily as a product of culturally generated knowledge, and truth, as glimpsed beyond the on-going attempt to fit a new language that never finally settles. Through this route, it is shown how Badiou’s differentiation of knowledge and truth enables us to conjure more futuristic conceptions of mathematics education.

Summer updates on the major journals

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The summer holidays  are definitely over, and it is time to provide an update on what has happened in some of the major journals in the field during summer! 

First in line is the Journal of Mathematics Teacher Education. They have released an August issue, and this issue contains five articles:

  • Mathematically based and practically based explanations in the elementary school: teachers’ preferences, by Esther Levenson, Pessia Tsamir and Dina Tirosh
  • Teacher lust: reconstructing the construct for mathematics instruction, by  Andrew M. Tyminski
  • Teachers’ conceptions of representation in middle school mathematics, by Despina A. Stylianou
  • Teachers’ self-representations in teaching mathematics, by O. Chapman
  • The organization of the mathematics preparation and development of teachers: a report from the ICMI Study 15, by Maria Teresa Tatto, Stephen Lerman and, by Jarmila Novotna

Educational Studies in Mathematics does not have an August issue (next issue is the September issue), but the July issue is out, and this  one also contains five interesting articles:

  • What mathematics do teachers with contrasting teaching approaches address in probability lessons? by Ruhama Even and Tova Kvatinsky
  • Drawing space: mathematicians’ kinetic conceptions of eigenvectors, by Nathalie Sinclair and Shiva Gol Tabaghi
  • Focal event, contextualization, and effective communication in the mathematics classroom, by Per Nilsson and Andreas Ryve
  • Zooming in on infinitesimal 1–.9.. in a post-triumvirate era, by Karin Usadi Katz and Mikhail G. Katz
  • Mathematical practices in a technological workplace: the role of tools, by Chrissavgi Triantafillou and Despina Potari

Next in line is Mathematical Thinking and Learning. Their issue 3 (of 4 annual issues) is out, containing two articles and two book reviews:

  • Teaching for Abstraction: A Model, by Paul White and Michael C. Mitchelmore 
  • A Local Instruction Theory for the Development of Number Sense, by Susan D. Nickerson and Ian Whitacre 

NCTM’s Journal for Research in Mathematics Education has also released a July issue, and this issue contains the following articles (along with a book review):

  • RESEARCH COMMENTARY: Toward Clarifying the Meanings of Gender in Mathematics Education Research, by Suzanne Damarin and Diana B. Erchick
  • The Nature of Arguments Provided by College Geometry Students With Access to Technology While Solving Problems, by Karen F. Hollebrands, AnnaMarie Conner and Ryan C. Smith
  • Enacting Proof-Related Tasks in Middle School Mathematics: Challenges and Opportunities, by Kristen N. Bieda
  • One Hundred Years of Elementary School Mathematics in the United States: A Content Analysis and Cognitive Assessment of Textbooks From 1900 to 2000, by David Baker, Hilary Knipe, John Collins, Juan Leon, Eric Cummings, Clancy Blair and David Gamson

Last but not least, The Journal of Mathematical Behavior has released a June issue containing the following articles:

  • Defining as a mathematical activity: A framework for characterizing progress from informal to more formal ways of reasoning, by Michelle Zandieh, Chris Rasmussen
  • A task that elicits reasoning: A dual analysis, by Dina Yankelewitz, Mary Mueller, Carolyn A. Maher
  • Are beliefs believable? An investigation of college students’ epistemological beliefs and behavior in mathematics, by Po-Hung Liu
  • Collegiate mathematics teaching: An unexamined practice, by Natasha M. Speer, John P. Smith III, Aladar Horvath

So, this should give you enough ideas for articles to catch up with before I start giving more updates on all the new articles that continuously get published within the field of mathematics education research 🙂

“Who reads all this stuff, Dad?”

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A couple of days ago, I shared with you news about the forthcoming issue of The Montana Mathematics Enthusiast. The main editor of this journal, my good friend Professor Bharath Sriraman, has been kind enough to allow me to share the editorial of this next issue with you all here on my blog. In this editorial, he brings up an interesting, important, and thought provoking discussion about scientific publishing. Enjoy reading it!

Great, great and great!

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This winter, I started writing a book review of the recent book “Theories of Mathematics Education – Seeking New Frontiers”, by Bharath Sriraman and Lyn English (Eds.). Unfortunately, I had to let the journal down by telling them that I wasn’t able to finish the review at the time, because of an overall stressful situation. Given this, I have been especially interested to read other reviews that have been made by this book. Most recently, Alan Schoenfeld has written a great review of this book, and the review was published online in ZDM recently. This makes a great review, of a great book, by a great scholar in our field – thus the title “Great, great and great!” What also makes this review great is that it has been published as Open Access, and I am therefore able to share it with all of you directly here in my blog:

Collaborative mathematical problem-solving processes

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In addition to all the journals I subscribe to in Google Reader, I try to keep track of the excellent aggregation of articles related to educational research that my colleague Doug Holton has set up. Going through the latest updates from his shared items, I discovered an interesting article that was published in the journal Learning and Instruction. This particular article is entitled Socially shared metacognition of dyads of pupils in collaborative mathematical problem-solving processes, and it was written by Finish scholars Tuike Iiskala, Marja Vauras, Erno Lehtinen and Pekka Salonen. Here is a copy of the abstract of their article:

This study investigated how metacognition appears as a socially shared phenomenon within collaborative mathematical word-problem solving processes of dyads of high-achieving pupils. Four dyads solved problems of different difficulty levels. The pupils were 10 years old. The problem-solving activities were videotaped and transcribed in terms of verbal and nonverbal behaviours as well as of turns taken in communication (N= 14 675). Episodes of socially shared metacognition were identified and their function and focus analysed. There were significantly more and longer episodes of socially shared metacognition in difficult as compared to moderately difficult and easy problems. Their function was to facilitate or inhibit activities and their focus was on the situation model of the problem or on mathematical operations. Metacognitive experiences were found to trigger socially shared metacognition.

Mathematics education in Brazil

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A while ago, mathematics education in Brazil used to mean Ubiratan D’Ambrosio to many. To me, the combination of mathematics education + Brazil also makes me think about my dear colleague, Professor Maria Luiza Cestari, University of Agder. If this is in any way close to your own level of knowledge about mathematics education in Brazil, you might want to check out the latest issue of ZDM. Some of the articles in this theme issue are related to the Brazilian context by content, and all of the articles are written by Brazilian scholars it seems. If you have no interest in Brazil besides football, you still might be interested in taking a look, because the thirteen articles that this issue includes cover a variety of issues that should be of interest to anyone within the field of mathematics education research. Take a look at the list of contents:

  • Dynamics of change of mathematics education in Brazil and a scenario of current research, by Ubiratan D’Ambrosio and Marcelo C. Borba
  • Mathematics education and democracy, by Adriana Cesar de Mattos and Marcelo Salles Batarce
  • Online distance mathematics education in Brazil: research, practice and policy, by Marcus Vinicius Maltempi and Ana Paula dos Santos Malheiros
  • The encounter of non-indigenous teacher educator and indigenous teacher: the invisibility of the challenges, by Maria do Carmo Santos Domite
  • Trends of the history of mathematics education in Brazil, by Wagner Rodrigues Valente
  • Research on mathematics education, by Maria Aparecida Viggiani Bicudo
  • Brazilian research on modelling in mathematics education, by Jussara de Loiola Araújo
  • Mathematics education and differential inclusion: a study about two Brazilian time–space forms of life, by Gelsa Knijnik and Fernanda Wanderer
  • Adult Education and Ethnomathematics: appropriating results, methods, and principles, by Maria da Conceição Ferreira Reis Fonseca
  • Philosophical reflections prompted by the principles of ethnomathematics, by Rogério Ferreira
  • Mobilizing histories in mathematics teacher education: memories, social practices, and discursive games, by Antonio Miguel and Iran Abreu Mendes
  • Digital technologies and the challenge of constructing an inclusive school mathematics, by Lulu Healy, Ana Paula Jahn and Janete Bolite Frant
  • Modeling empowered by information and communication technologies, by Mónica E. Villarreal, Cristina B. Esteley and María V. Mina