November issue of Educational Studies in Mathematics

The November issue of Educational Studies in Mathematics has been published recently, and it contains a number of interesting articles:

Cognitive neuroscience and mathematics learning

A new issue of ZDM – The International Journal on Mathematics Education has been published, and the focus of this theme issue is on cognitive neuroscience and mathematics learning. The issue contains a number of interesting articles:

Guest editors, Elsbeth Stern and Michael Schneider have also written an editorial (A digital road map analogy of the relationship between neuroscience and educational research), and Roland H. Grabner, Daniel Ansari, Bert De Smedt and Minna Hannula have written a Glossary of technical terms in cognitive neuroscience, which are also part of this theme issue. So, if you are interested in the link(s) between neuroscience and mathematics education, this theme issue should be an evident post on your reading list!

Children’s gestures and the embodied knowledge of geometry

Mijung Kim, Wolff-Michael Roth and Jennifer Thom have written an article that was recently published online in International Journal of Science and Mathematics Education. The article is entitled Children’s gestures and the embodied knowledge of geometry. Here is the abstract of their article:

There is mounting research evidence that contests the metaphysical perspective of knowing as mental process detached from the physical world. Yet education, especially in its teaching and learning practices, continues to treat knowledge as something that is necessarily and solely expressed in ideal verbal form. This study is part of a funded project that investigates the role of the body in knowing and learning mathematics. Based on a 3-week (15 1-h lessons) video study of 1-s grade mathematics classroom (N = 24), we identify 4 claims: (a) gestures support children’s thinking and knowing, (b) gestures co-emerge with peers’ gestures in interactive situations, (c) gestures cope with the abstractness of concepts, and (d) children’s bodies exhibit geometrical knowledge. We conclude that children think and learn through their bodies. Our study suggests to educators that conventional images of knowledge as being static and abstract in nature need to be rethought so that it not only takes into account verbal and written languages and text but also recognizes the necessary ways in which children’s knowledge is embodied in and expressed through their bodies.

Making mathematics more mobile

Since personal computers became mainstream, a couple of decades ago, different kinds of computer games and (more or less) educational software have been developed. The proponents of these software and games often claimed that their particular software would revolutionize education. Seymour Papert was one of the true pioneers, and when he invented the Logo programming language, the intention was to improve children’s thinking and problem solving skills. Technology has developed rapidly over the last couple of years, and computers as well as computer games and software have become more and more mobile. Enter MobileMath! This is a computer game which has been developed by the Freudenthal Institute, and it appears to be strongly connected with their ideas concerning Realistic Mathematics Education (RME).

Three colleagues at the Freudenthal Institute – Monica Wijers, Vincent Jonker and Paul Drijvers – have written an article where they discuss how MobileMath can be used with secondary school students. The article is entitled MobileMath: exploring mathematics outside the classroom, and it was recently published online in ZDM – The International Journal of Mathematics Education. Luckily, it is an Open Access article, so it should be available to everyone for free! To sharpen your interest, here is a copy of the article abstract:

Computer games seem to have a potential for engaging students in meaningful learning, inside as well as outside of school. With the growing availability of mobile handheld technology (HHT), a number of location-based games for handheld mobile phones with GPS have been designed for educational use. The exploitation of this potential for engaging students into meaningful learning, however, so far remains unexplored. In an explorative design research, we investigated whether a location-based game with HHT provides opportunities for engaging in mathematical activities through the design of a geometry game called MobileMath. Its usability and opportunities for learning were tested in a pilot on three different secondary schools with 60 12–14-year-old students. Data were gathered by means of participatory observation, online storage of game data, an online survey and interviews with students and teachers. The results suggest that students were highly motivated, and enjoyed playing the game. Students indicated they learned to use the GPS, to read a map and to construct quadrilaterals. The study suggests learning opportunities that MobileMath provides and that need further investigation.

5 interesting articles that almost missed me

Educational Psychology – An International Journal of Experimental Educational Psychology has published a number of articles related to mathematics in their most recent issues. I only recently received the RSS updates in Google Reader, so I have missed some of these articles. Here is a list of some of the most interesting articles that have appeared in the last couple of issues:

The role of pictures in picture books

Iliada Elia, Marja van den Heuvel-Panhuizen and Alexia Georgiou have written an article about The role of pictures in picture books on children’s cognitive engagement with mathematics. This article was published in the last issue of European Early Childhood Education Research Journal. Here is the abstract of their article:

The present study examines the cognitive activity that is evoked in young children when they are read a picture book that is written for the purpose of teaching mathematics. The focus of this study is to explore the effects of pictures on children’s spontaneous mathematical cognitive engagement. The study is based on the assumption that the pictures in a picture book that is aimed at supporting children’s learning of mathematics can have story-related components and mathematics-related components. The story-related components of the pictures contribute to grasp the global story context of the text and the mathematics-related components help to understand the mathematical content of the story. All of the pictures of the book under investigation, Six brave little monkeys in the jungle, have both story-related and mathematics-related components included. The pictures have a representational or an informational function. Four 5-year-old children were read individually the book by one of the authors without any probing. A detailed coding framework was used for analyzing the children’s utterances that provided an in-depth picture of the children’s cognitive activity. The results show that the picture book as a whole has the potential for cognitively engaging children. However, the pictures with a representational function were found to elicit mathematical thinking to a greater extent than the pictures with an informational function. Moreover, this was found for both types of components included in the pictures. Findings are discussed, practical implications for using picture books in kindergarten are drawn and suggestions for further research are made. 

Kindergarten mathematics with ‘Pepe the Rabbit’

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

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

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

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.