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The current issue of American Educator includes a very interesting article about mathematics teaching in the elementary grades. The article is entitled What's Sophisticated about Elementary Mathematics? Plenty—That's Why Elementary Schools Need Math Teachers , and it is written by Hung-Hsi Wu, who is professor emeritus of mathematics at UC Berkeley. I should probably say a lot more about him, because his list of merits is impressive, but I will leave it to you to find out more . It appears to be a rather common impression that teaching elementary mathematics is ... well, rather elementary. I mean, the mathematics is quite simple, so how hard can it be? In this article, Wu provides a very nice introduction to how challenging it can actually be. In the introductory part of the article, he claims: "The fact is, there's a lot more to teaching math than teaching how to do calculations." In the article, he provides examples of how hard it can actually be to teach some...

Yeping li, Jianyue Zhang and Tingting Ma have written an article entitled Approaches and practices in developing school mathematics textbooks in China . This article was published online in ZDM a couple of days ago. This article gives a very interesting overview of how Chinese textbooks are developed, but it also provides nice insights into how mathematics teaching has developed (or is developing) in China. Here is the abstract of this article: In this study, we aim to examine and discuss approaches and practices in developing mathematics textbooks in China, with a special focus on the development of secondary school mathematics textbook in the context of recent school mathematics reform. Textbook development in China has its own history. This study reveals some common practices and approaches developed and used in selecting, presenting and organizing content in mathematics textbooks over the years. With the recent curriculum reform taking place in China, we also discuss some new deve...

Michela Maschietto and Luc Trouche have written an article called Mathematics learning and tools from theoretical, historical and practical points of view: the productive notion of mathematics laboratories . The article was published online in ZDM on Monday. Although they start with a glimpse from a babylonian clay tablet, their main focus is on the development of tools and use of tools in the last century. In the main part of their article, they have a strong focus on the so-called mathematics laboratories. Here is the abstract of their article: In our research work, we have looked at the way in which artefacts become, for teachers as well as for students, instruments of their mathematical activity. The issues related to the use of tools and technologies in mathematical education are now widely considered. A look to history highlights the different ways in which the same questions have been studied at different times and in different places. This suggests that the contribution of art...

A new issue of International Journal of Science and Mathematics Education has been published, Volume 7, Number 5, October 2009 . The issue contains nine articles, several of which are related to mathematics education: CREATING OPTIMAL MATHEMATICS LEARNING ENVIRONMENTS: COMBINING ARGUMENTATION AND WRITING TO ENHANCE ACHIEVEMENT , by Dionne I. Cross APPROACHES TO TEACHING MATHEMATICS IN LOWER-ACHIEVING CLASSES , by Ruhama Even and Tova Kvatinsky ANALYSIS OF THE LEARNING EXPECTATIONS RELATED TO GRADE 1–8 MEASUREMENT IN SOME COUNTRIES , by Jung Chih Chen, Barbara J. Reys and Robert E. Reys EPISTEMOLOGICAL OBSTACLES IN COMING TO UNDERSTAND THE LIMIT OF A FUNCTION AT UNDERGRADUATE LEVEL: A CASE FROM THE NATIONAL UNIVERSITY OF LESOTHO , by Eunice Kolitsoe Moru

Aiso Heinze, Franziska Marschick and Frank Lipowsky have written an article that was published in the recent issue of ZDM . The article is entitled Addition and subtraction of three-digit numbers: adaptive strategy use and the influence of instruction in German third grade . Here is the abstract of their article: Empirical findings show that many students do not achieve the level of a flexible and adaptive use of arithmetic computation strategies during the primary school years. Accordingly, educators suggest a reform-based instruction to improve students’ learning opportunities. In a study with 245 German third graders learning by textbooks with different instructional approaches, we investigate accuracy and adaptivity of students’ strategy use when adding and subtracting three-digit numbers. The findings indicate that students often choose efficient strategies provided they know any appropriate strategies for a given problem. The proportion of appropriate and efficient strategies st...

Aiso Heinze, Jon R. Star and Lieven Verschaffel have written an article entitled Flexible and adaptive use of strategies and representations in mathematics education . The article was published in ZDM , Volume 41, Number 5 on Wednesday. Here is the abstract of their article: The flexible and adaptive use of strategies and representations is part of a cognitive variability, which enables individuals to solve problems quickly and accurately. The development of these abilities is not simply based on growing experience; instead, we can assume that their acquisition is based on complex cognitive processes. How these processes can be described and how these can be fostered through instructional environments are research questions, which are yet to be answered satisfactorily. This special issue on flexible and adaptive use of strategies and representations in mathematics education encompasses contributions of several authors working in this particular field. They present recent research on f...

A new and interesting article has been published in Early Childhood Education Journal : How Do Parents Support Preschoolers’ Numeracy Learning Experiences at Home? The article is written by Sheri-Lynn Skwarchuk. Abstract This study described the kinds of early numeracy experiences that parents provide for their preschoolers, and determined the extent to which parental experiences and involvement in home activities enhanced preschoolers’ numeracy knowledge. Twenty-five parents completed a home activity questionnaire, a 2-week diary study, and a videotaped play session where they were asked to draw out numerical content. Preschoolers’ numeracy scores were predicted by: (1) parental reports of positive personal experiences with mathematics and (2) involvement in activities with complex (versus basic) numeracy goals. Parents felt that most activities had important or essential mathematical value, but focused on number sense goals. Finally, parents who reportedly spent more time on numerac...

New article in Educational Studies in Mathematics , written by Raimo Kaasila, Erkki Pehkonen and Anu Hellinen: Finnish pre-service teachers’ and upper secondary students’ understanding of division and reasoning strategies used Abstract In this paper, we focus on Finnish pre-service elementary teachers’ ( N  = 269) and upper secondary students’ ( N  = 1,434) understanding of division. In the questionnaire, we used the following non-standard division problem: “We know that 498:6 = 83. How could you conclude from this relationship (without using long-division algorithm) what 491:6 = ? is?” This problem especially measures conceptual understanding, adaptive reasoning, and procedural fluency. Based on the results, we can conclude that division seems not to be fully understood: 45% of the pre-service teachers and 37% of upper secondary students were able to produce complete or mainly correct solutions. The reasoning strategies used by these two groups did not differ very much. We identified...

David S. Bolden, Tony V. Harries and Douglas P. Newton have written an article entitled Pre-service primary teachers' conceptions of creativity in mathematics . This article was recently published online in Educational Studies in Mathematics . The issues concerning creativity that are raised in this article are interesting. I also find it interesting to observe how the authors make use of concepts like "beliefs" and "conceptions". As far as I can tell, they don't make a distinction between these concepts, and they also talk about teachers "views" without making a clear distinction between this concept in relation to the two former. Although attempts have been made in the past by researchers to define and distinguish between these concepts, I think we still have a challenge here! Here is the abstract of their article: Teachers in the UK and elsewhere are now expected to foster creativity in young children (NACCCE, 1999; Ofsted, 2003; DfES, 2003; DfE...

Murat Bursal has written an article about Turkish preservice elementary teachers' self-efficacy beliefs regarding mathematics and science teaching . This article was published online in International Journal of Science and Mathematics Education on Thursday. A key finding is that the preservice teachers in this study had "adequate" self-efficacy beliefs when they graduated. These findings are linked with a recent reform in Turkish teacher education. Here is the abstract of the article: This study investigated Turkish preservice, elementary teachers’ personal mathematics teaching efficacy (PMTE), and science teaching efficacy (PSTE) beliefs at the end of their teacher education program. A majority of the participants believed they were well prepared to teach both elementary mathematics and science, but their PSTE scores were significantly lower than their PMTE scores. However, a significant correlation was found between the PMTE and PSTE scores. No significant gender effec...

Three new articles have been published online in ZDM lately. One of these articles is entitled The role of fluency in a mathematics item with an embedded graphic: interpreting a pie chart , and it is written by Carmel Mary Diezmann and Tom Lowrie. Here is the abstract of their article: The purpose of this study was to identify the pedagogical knowledge relevant to the successful completion of a pie chart item. This purpose was achieved through the identification of the essential fluencies that 12–13-year-olds required for the successful solution of a pie chart item. Fluency relates to ease of solution and is particularly important in mathematics because it impacts on performance. Although the majority of students were successful on this multiple choice item, there was considerable divergence in the strategies they employed. Approximately two-thirds of the students employed efficient multiplicative strategies, which recognised and capitalised on the pie chart as a proportional represen...

Kemal Altiparmak and Ece Özdogan have written an article that was recently published online in International Journal of Mathematical Education in Science and Technology . The article is entitled A study on the teaching of the concept of negative numbers . Here is the abstract of their article. This study mainly aims to develop an effective strategy to overcome the known difficulties in teaching negative numbers. Another aim is to measure the success of this teaching strategy among a group of elementary level pupils in Idotzmir, Turkey. Learning negative concepts are supported by computer animations. The academic achievement test developed by the researchers was administered to 150 sixth-grade pupils at the beginning of and following the learning period. The teaching strategy was applied to the experiment group (n = 75) as stated above, while the traditional teaching model most frequently used in Turkey was applied to the control group (n = 75). At the end of the study, a significant di...

Information Age Publishing is about to publish a " Festschrift in honor of Paul Ernest's 65th Birthday ". This is a volume in the monograph series of The Montana Mathematics Enthusiast , and it is edited by Bharath Sriraman and Simon Goodchild. Paul Ernest has a big name in the community of mathematics education researchers, and his main field of interest is within the area of philosophy of mathematics and philosophy of mathematics education. Here is a copy of the publisher's description of the book: Paul Ernest’s name is synonymous with social constructivism as a philosophy of mathematics. His contributions to mathematics education have occurred at a very fundamental level and to a extent shaped theory development in this field. His research addresses fundamental questions about the nature of mathematics and how it relates to teaching, learning and society. For the last three decades Paul has been a prolific scholar who has published in a wide array of topics such ...

Angela Heine and colleagues have written an article called: What the eyes already 'know': using eye movement measurement to tap into children's implicit numerical magnitude representations . The article has recently been published in Infant and Child Development . The authors make interesting links between eye movements and childrens understanding of numbers. Here is the abstract of their article: To date, a number of studies have demonstrated the existence of mismatches between children's implicit and explicit knowledge at certain points in development that become manifest by their gestures and gaze orientation in different problem solving contexts. Stimulated by this research, we used eye movement measurement to investigate the development of basic knowledge about numerical magnitude in primary school children. Sixty-six children from grades one to three (i.e. 6-9 years) were presented with two parallel versions of a number line estimation task of which one was rest...

Kyeong Hah Roh has written an article entitled An empirical study of students’ understanding of a logical structure in the definition of limit via the ε-strip activity . This article was published online in Educational Studies in Mathematics last Thursday. Here is the abstract of the article: This study explored students’ understanding of a logical structure in defining the limit of a sequence, focusing on the relationship between ε and N. The subjects of this study were college students who had already encountered the concept of limit but did not have any experience with rigorous proofs using the ε–N definition. This study suggested two statements, each of which is written by using a relationship between ε and N, similar to the ε–N definition. By analyzing the students’ responses to the validity of the statements as definitions of the limit of a sequence, students’ understanding of such a relationship was classified into five major categories. This paper discusses some essential comp...

Atara Shriki has written an interesting article called Working like real mathematicians: developing prospective teachers’ awareness of mathematical creativity through generating new concepts . This article was recently published online in Educational Studies in Mathematics . The author reports from a study related to a methods course, where a strong focus is on creativity in mathematics. The article has a particular focus on prospective teachers' awarenes of creativity in mathematics. Here is the abstract of Shriki's article. This paper describes the experience of a group of 17 prospective mathematics teachers who were engaged in a series of activities aimed at developing their awareness of creativity in mathematics. This experience was initiated on the basis of ideas proposed by the participants regarding ways creativity of school students might be developed. Over a period of 6 weeks, they were engaged in inventing geometrical concepts and in the examination of their propertie...

Paulus Gerdes has written an article called Exploration of technologies, emerging from African cultural practices, in mathematics (teacher) education . This article was recently published online in ZDM . In this article, Gerdes provides an interesting overview of how the cultural practices of African mathematics (teacher) education has developed, and he makes a seemingly (to me) impossible connection between traditional basket weaving and exploration of technologies. Here is the abstract of the article: The study at teacher education institutions in Africa of mathematical ideas, from African history and cultures, may broaden the horizon of (future) mathematics teachers and increase their socio-cultural self-confidence and awareness. Exploring educationally mathematical ideas embedded in, and derived from, technologies of various African cultural practices may contribute to bridge the gap between ‘home’ and ‘school’ culture. Examples of the study and exploration of these technologies an...

A new book, entitled Theories of Mathematics Education , is about to be published by Springer (due October 2009). One of the editors, Bharath Sriraman (also editor of The Montana Mathematics Enthusiast) has been kind enough to give me permission to post the book cover and the table of contents here on my blog. Thanks, Bharath! Looking at the table of contents is enough to make me believe that this is definitely going to be an important book, and it will make an impact on our field of research! If you won't take my word for it, please take the time to read through the table of contents yourself: Theories of Mathematics Education - TOC I especially like the way it is built up, with introductions and commentaries to all the parts of the book. This will give the reader a feeling of how the field has evolved, and how it is still in a process of evolving. The publisher has given the following description of the book: This inaugural book in the n...

The August issue (Volume 7, Number 4) of International Journal of Science and Mathematics Education has been published. This issue contains 9 articles: INVESTIGATING THE EFFECTIVENESS OF AN ANALOGY ACTIVITY IN IMPROVING STUDENTS’ CONCEPTUAL CHANGE FOR SOLUTION CHEMISTRY CONCEPTS , by Muammer Çalik, Alipaşa Ayas and Richard K. Coll INSTRUCTIONAL ACTIVITIES AND GROUP WORK IN THE US INCLUSIVE HIGH SCHOOL CO-TAUGHT SCIENCE CLASS , by Laura J. Moin, Kathleen Magiera and Naomi Zigmond DESIGNING AND EVALUATING RESEARCH-BASED INSTRUCTIONAL SEQUENCES FOR INTRODUCING MAGNETIC FIELDS , by Jenaro Guisasola, Jose Manuel Almudi, Mikel Ceberio and Jose Luis Zubimendi ENGINEERING IN CHILDREN’S FICTION - NOT A GOOD STORY? by Allyson Holbrook, Lisa Panozza and Elena Prieto RELATIONS BETWEEN TEACHING AND RESEARCH IN PHYSICAL GEOGRAPHY AND MATHEMATICS AT RESEARCH-INTENSIVE UNIVERSITIES , by Lene Møller Madsen and Carl Winsløw GEOMETRIC AND ALGEBRAIC APPROACHES IN THE CONCEPT OF “LIMIT” AND THE IMPACT O...

Gwendolyn M. Lloyd has written an article that was recently published online in ZDM . The article is entitled School mathematics curriculum materials for teachers’ learning: future elementary teachers’ interactions with curriculum materials in a mathematics course in the United States . Here is the abstract of her article: This report describes ways that five preservice teachers in the United States viewed and interacted with the rhetorical components (Valverde et al. in According to the book: using TIMSS to investigate the translation of policy into practice through the world of textbooks, Kluwer, 2002) of the innovative school mathematics curriculum materials used in a mathematics course for future elementary teachers. The preservice teachers’ comments reflected general agreement that the innovative curriculum materials contained fewer narrative elements and worked examples, as well as more (and different) exercises and question sets and activity elements, than the mathematics textbo...

A new newsletter has been published from ICMI , and, as usual, it contains lots of interesting information. I would have liked to post the entire newsletter here, but since it is freely available online , I am only going to point to the table of contents: Editorial: Continuing Professional Development and Effective integration of Digital Technologies in Teaching and Learning Mathematics: Two Challenges for ICMI A XXIst century Felix Klein's follow up workshop Deadline Extended: ICMI / ICIAM STUDY EARCOME5: First Announcement Chilean Journal of Statistics (ChJS) Calendar of Events of Interest to the ICMI Community ICMI encounters: Hassler Whitney, Laurence C. Young and Dirk J. Struik: Personal recollections Subscribing to ICMI News You can also check out the archive for a complete listing of previous (and current) newsletters!

Eleanor Chute has written an interesting article about the importance of algebra in school mathematics. It is not a scientific article, but I think it is worth reading even though! (It was published on September 1st in the Pittsburgh Post-Gazette .) The article is part of a series related to school mathematics, and the two previous articles in the series raise interesting questions about early math and fractions . Although algebra to many represents a hurdle, or even the graveyard in their mathematical careers, the article claims that: Algebraic thinking is done even by people who don't realize they're using algebra. After a series of examples, Chute goes on to quote Michele Burgess, who claims that students should not be confronted with algebra for the first time in the Algebra 1 course. This leads me to think about the debate (and research) concerning early algebra, although this is not referred to in this article in particular. If you are interested, I recommend the chapte...

Janet G. Walter and Janelle Hart have written an article about the interesting issue of Understanding the complexities of student motivations in mathematics learning . The article was recently published in The Journal of Mathematical Behavior . Here is the abstract of their article: Student motivation has long been a concern of mathematics educators. However, commonly held distinctions between intrinsic and extrinsic motivations may be insufficient to inform our understandings of student motivations in learning mathematics or to appropriately shape pedagogical decisions. Here, motivation is defined, in general, as an individual's desire, power, and tendency to act in particular ways. We characterize details of motivation in mathematical learning through qualitative analysis of honors calculus students’ extended, collaborative problem solving efforts within a longitudinal research project in learning and teaching. Contextual Motivation Theory emerges as an interpretive means for und...