The March issue of International Journal of Early Years Education contains several articles that are related to mathematics education:

• Elizabeth Dunphy has written an article called Early childhood mathematics teaching: challenges, difficulties and priorities of teachers of young children in primary schools in Ireland. Abstract: Issues of pedagogy are critical in all aspects of early childhood education. Early childhood mathematics is no exception. There is now a great deal of guidance available to teachers in terms of high-quality early childhood mathematics teaching. Consequently, the characteristics of high-quality early childhood mathematics education are clearly identifiable. Issues such as building on young children’s prior-to-school knowledge; engaging children in general mathematical processes; and assessing and documenting children’s learning are some of the key aspects of high-quality early childhood mathematics education. The extent to which teachers of four- and five-year-old children in primary schools in Ireland incorporate current pedagogical guidance in early childhood mathematics education was explored in 2007 in a nationally representative questionnaire survey of teachers of four- and five-year-old children attending primary schools. This paper presents some of the findings of the study in relation to teachers’ self-reported challenges, difficulties and priorities in teaching early childhood mathematics. Implications are drawn for professional development, curriculum guidance and educational policy.
• Sally Howell and Coral Kemp have written an article called A participatory approach to the identification of measures of number sense in children prior to school entry. Abstract: The research reported in this paper used a modified Delphi procedure in an attempt to establish a consensus on tasks proposed to assess components of number sense identified as essential for early mathematics success by a broad range of academics with expertise in the area of early mathematics. Tasks included as measures of these components were based on assessment tasks developed by early mathematics researchers. Eighteen questionnaires were returned by academics from Australia, the UK, New Zealand, The Netherlands and the USA, all with published work in the areas of early mathematics and/or number sense. Both the proposed components and tasks in the questionnaires were limited to the number domain. The study revealed considerable agreement with a number of the proposed tasks and thus provided a way forward for the development of an early number sense assessment to be trialled with young children prior to their first year of formal schooling. 
• A third article, entitled Numeracy-related exchanges in joint storybook reading and play, was written by Maureen Vandermaas-Peeler, Jackie Nelson, Charity Bumpass annd Bianca Sassine. Abstract: Studies of the processes by which parents encourage early numerical development in the context of parent-child interactions during routine, culturally relevant activities at home are scarce. The present study was designed to investigate spontaneous exchanges related to numeracy during parent-child interactions in reading and play activities at home. Thirty-seven families with a four-year-old child (13 low-income) were observed. Two types of numeracy interactions were of interest: socio-cultural numeracy exchanges, explaining the use and value of money or numbers in routine activities such as shopping or cooking, and mathematical exchanges, including counting, quantity or size comparisons. Results indicated that high-income parents engaged in more mathematical exchanges during both reading and play than did low-income parents, though there were no differences in the initiation of socio-cultural numeracy exchanges. The focus of parental guidance related to numeracy was conceptual and embedded in the activity context, with few dyads focusing on counting or numbers per se. The findings suggest the importance of parent education efforts that incorporate numeracy-related discourse in the context of daily routines to augment young children’s numeracy development.

Robyn Pierce, Lynda Ball and Kaye Stacey have written an article called Is it worth using CAS  for symbolic algebra manipulation in the middle secondary years? Some teachers’ views. The article was published online in International Journal of Science and Mathematics Education on Thursday. Here is the abstract of their article:

The use of Computer Algebra Systems (CAS) in years 9 and 10 classrooms as a tool to support learning or in preparation for senior secondary mathematics is controversial. This paper presents an analysis of the positive and negative aspects of using CAS identified in the literature related to these year levels, along with the perceptions of 12 experienced secondary teachers who were working with years 9 and 10 students. The literature review shows that CAS is valued for calculation and manipulation capabilities, the option of alternative representations, the opportunity for systematic exploration and for prompting rich discussion. However, the technical overhead, initial workload for the teacher and unresolved questions about the perceived relative contribution of machine and by-hand work to learning currently pose obstacles to teaching with CAS in the middle secondary years. The teachers who contributed data to this study perceived that using CAS in their teaching is, on balance, worth the effort. However, they believed that CAS is of most benefit to their high ability students and may present an obstacle to their low ability students’ learning of mathematics.

Catherine C. Lewis, Rebecca R. Perry and Jacqueline Hurd have written an interesting article called Improving mathematics instruction through lesson study: a theoretical model and North American case. The article was published online in Journal of Mathematics Teacher Education on Monday. Here is the abstract of their article:

This article presents a theoretical model of lesson study, an approach to instructional improvement that originated in Japan. The theoretical model includes four lesson study features (investigation, planning, research lesson, and reflection) and three pathways through which lesson study improves instruction: changes in teachers’ knowledge and beliefs; changes in professional community; and changes in teaching–learning resources. The model thus suggests that development of teachers’ knowledge and professional community (not just improved lesson plans) are instructional improvement mechanisms within lesson study. The theoretical model is used to examine the “auditable trail” of data from a North American lesson study case, yielding evidence that the lesson study work affected each of the three pathways. We argue that the case provides an “existence proof” of the potential effectiveness of lesson study outside Japan. Limitations of the case are discussed, including (1) the nature of data available from the “auditable trail” and (2) generalizability to other lesson study efforts.

Egan J. Chernoff has written an article about Sample space partitions: An investigative lens. The article has recently been published in The Journal of Mathematical Behavior. Here is the abstract of Chernoff’s article:

In this study subjects are presented with sequences of heads and tails, derived from flipping a fair coin, and asked to consider their chances of occurrence. In this new iteration of the comparative likelihood task, the ratio of heads to tails in all of the sequences is maintained. In order to help situate participants’ responses within conventional probability, this article employs unconventional set descriptions of the sample space organized according to: switches, longest run, and switches and longest run, which are all based upon subjects’ verbal descriptions of the sample space. Results show that normatively incorrect responses to the task are not devoid of correct probabilistic reasoning. The notion of alternative set descriptions is further developed, and the article contends that sample space partitions can act as an investigative lens for research on the comparative likelihood task, and probability education in general.

Luis Radford has written an article called “No! He starts walking backwards!”: interpreting motion graphs and the question of space, place and distance. The article was recently published online in ZDM. Here is the abstract of the article:

This article deals with the interpretation of motion Cartesian graphs by Grade 8 students. Drawing on a sociocultural theoretical framework, it pays attention to the discursive and semiotic process through which the students attempt to make sense of graphs. The students’ interpretative processes are investigated through the theoretical construct of knowledge objectification and the configuration of mathematical signs, gestures, and words they resort to in order to achieve higher levels of conceptualization. Fine-grained video and discourse analyses offer an overview of the manner in which the students’ interpretations evolve into more condensed versions through the effect of what is called in the article “semiotic contractions” and “iconic orchestrations.”

Sarwar J. Abbasi and Kahkashan Iqbal have written an article with a very interesting title: How learning and teaching of mathematics can be made interesting: a study based on statistical analysis. The article was published online recently in International Journal of Mathematical Education in Science and Technology. Here is the abstract of their article:

In this article, we evaluate the true proportion of mathematics educators and teachers at under/post graduate levels in Karachi, Pakistan in making math courses lively to students. We use a random sample of 75 students of engineering and commerce studying in three different universities namely University of Karachi, Usman Institute of Technology (UIT) and Karachi Institute of Economics & Technology (PAF-KIET). A 95% confidence interval based on sample results reveals that the said proportion of math educators is in between 63 and 83%. Furthermore, we investigate with the help of students’ responses how mathematics teachers at under/post graduate levels make their courses interesting-by showing their dedication in their subject, by giving logical reasoning and concrete examples or by making complex mathematical methods accessible to students giving them know-how of mathematical softwares. We find that the second technique is the most dominant and has a very strong impact (positive linear relationship) in achieving the said goal of a math-teacher. The linear correlation coefficient between students’ opinion that math-teachers make their courses interesting and achieving this goal by giving logical reasoning and concrete examples is 0.989. Whereas the technique of using math softwares in attempt to make a math course lively has also a very strong but a cubic relationship and its multiple correlation coefficient is 0.984. Therefore, using technology in math classroom is also helpful in making math learning and teaching interesting but under some conditions that become apparent from our study made on the real data hence obtained.

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Pi-Jen Li and Yeping Li have written an article that was published online in ZDM on Thursday. The article is entitled Searching for good mathematics instruction at primary school level valued in Taiwan. Here is the abstract:

In this article, we aim to provide a glimpse of what is counted as good mathematics instruction from Taiwanese perspectives and of various approaches developed and used for achieving high-quality mathematics instruction. The characteristics of good mathematics instruction from Taiwanese perspectives were first collected and discussed from three types of information sources. Although the number of characteristics of good mathematics instruction may vary from one source to another, they can be generally organized in three phases including lesson design before instruction, classroom instruction during the lesson and activities after lesson. In addition to the general overview of mathematics classroom instruction valued in Taiwan, we also analyzed 92 lessons from six experienced teachers whose instructional practices were generally valued in local schools and counties. We identified and discussed the characteristics of their instructional practices in three themes: features of problems and their uses in classroom instruction, aspects of problem–solution discussion and reporting, and the discussion of solution methods. To identify and promote high-quality mathematics instruction, various approaches have been developed and used in Taiwan including the development and use of new textbooks and teachers’ guides, teaching contests, master teacher training program, and teacher professional development programs.

Yeping Li, Xi Chen and Song An have written an article that was recently published online in ZDM. Their article is entitled Conceptualizing and organizing content for teaching and learning in selected Chinese, Japanese and US mathematics textbooks: the case of fraction division, and here is a copy of the abstract:

In this study, selected Chinese, Japanese and US mathematics textbooks were examined in terms of their ways of conceptualizing and organizing content for the teaching and learning of fraction division. Three Chinese mathematics textbook series, three Japanese textbook series, and four US textbook series were selected and examined to locate the content instruction of fraction division. Textbook organization of fraction division and other content topics were described. Further analyses were then conducted to specify how the content topic of fraction division was conceptualized and introduced. Specific attention was also given to the textbooks’ uses of content constructs including examples, representations, and exercise problems in order to show their approaches for the teaching and learning of fraction division. The results provide a glimpse of the metaphors of mathematics teaching and learning that have been employed in Chinese, Japanese, and US textbooks. In particular, the results from the textbook analyses demonstrate how conceptual underpinnings were developed while targeting procedures and operations. Implications of the study are then discussed.