Teaching Mathematics and its Applications, June 2009

The June issue of Teaching Mathematics and its Applications has appeared, and it contains a number of interesting articles:


Mathematics in and through social justice

Kathleen Nolan has written an article called Mathematics in and through social justice: another misunderstood marriage? This article was published in Journal of Mathematics Teacher Education on Tuesday. Here is the abstract of Nolan's article:
The current push to marry off mathematics with social justice compels one to ask such critical questions as “What is social justice?” and “How does (or can) mathematics look and act when viewed in/through the lenses of social justice?” Taking a critically reflective approach, this article draws the reader into a discussion of what is amiss in the currently promoted picture-perfect marriage of mathematics and social justice, presenting perspectives on both the content and context of mathematics teaching and learning. In this article, the author’s account of her experience in teaching a mathematics curriculum course for prospective middle years' teachers highlights a call to re-imagine the relationship between mathematics and social justice as more than a perfunctory integration of a “statistics and figures” approach. The author’s reflections acknowledge the complexity and potentiality of the relationship while challenging current status quo practices and paradigms in mathematics education.

Non-routine problem solving

Iliada Elia, Marja van den Heuvel-Panhuizen and Angeliki Kolovou have written an article called Exploring strategy use and strategy flexibility in non-routine problem solving by primary school high achievers in mathematics. The article was published online in ZDM on Tuesday. Here is the abstract of their article:
Many researchers have investigated flexibility of strategies in various mathematical domains. This study investigates strategy use and strategy flexibility, as well as their relations with performance in non-routine problem solving. In this context, we propose and investigate two types of strategy flexibility, namely inter-task flexibility (changing strategies across problems) and intra-task flexibility (changing strategies within problems). Data were collected on three non-routine problems from 152 Dutch students in grade 4 (age 9–10) with high mathematics scores. Findings showed that students rarely applied heuristic strategies in solving the problems. Among these strategies, the trial-and-error strategy was found to have a general potential to lead to success. The two types of flexibility were not displayed to a large extent in students’ strategic behavior. However, on the one hand, students who showed inter-task strategy flexibility were more successful than students who persevered with the same strategy. On the other hand, contrary to our expectations, intra-task strategy flexibility did not support the students in reaching the correct answer. This stemmed from the construction of an incomplete mental representation of the problems by the students. Findings are discussed and suggestions for further research are made.


Hands-on mathematics

The May issue of Science & Education contains an interesting article that is related to mathematics education. The article is written by Youjun Wang, and it is entitled: Hands-on mathematics: two cases from ancient Chinese mathematics. Here is the abstract of Wang's article:

In modern mathematical teaching, it has become increasingly emphasized that mathematical knowledge should be taught by problem-solving, hands-on activities, and interactive learning experiences. Comparing the ideas of modern mathematical education with the development of ancient Chinese mathematics, we find that the history of mathematics in ancient China is an abundant resource for materials to demonstrate mathematics by hands-on manipulation. In this article I shall present two cases that embody this idea of a hands-on approach in ancient Chinese mathematics, at the same time offering an opportunity to show how to utilize materials from the history of Chinese math in modern mathematical education.


Exemplary math instruction in East Asia

Yeping Li and Yoshinori Shimizu have written an interesting article about Exemplary mathematics instruction and its development in selected education systems in East Asia. The article was published online in ZDM on Saturday. In the article they enter into the discussion about teaching as a cultural activity, and they provide a structuring overview of several articles that are going to appear in a themed issue of ZDM. This themed issue definitely looks interesting, and it is something to look out for!

Here is the abstract of their article:
What may teachers do in developing and carrying out exemplary or high-quality mathematics classroom instruction? What can we learn from teachers’ instructional practices that are often culturally valued in different education systems? In this article, we aim to highlight relevant issues that have long been interests of mathematics educators worldwide in identifying and examining teachers’ practices in high-quality mathematics classroom instruction, and outline what articles published herein can help further our understanding of such issues with cases of exemplary mathematics instruction valued in the Chinese Mainland, Hong Kong, Japan, Singapore, South Korea, and Taiwan.

The role of prior knowledge

Jon R. Star, Bethany Rittle-Johnson, Kathleen Lynch and Natasha Perova have written an article called The role of prior knowledge in the development of strategy flexibility: the case of computational estimation. The article was published in ZDM on Saturday. Here is the abstract of their article:
The ability to estimate is a fundamental real-world skill; it allows students to check the reasonableness of answers found through other means, and it can help students develop a better understanding of place value, mathematical operations, and general number sense. Flexibility in the use of strategies is particularly critical in computational estimation. The ability to perform complex calculations mentally is cognitively challenging for many students; thus, it is important to have a broad repertoire of estimation strategies and to select the most appropriate strategy for a given problem. In this paper, we consider the role of students’ prior knowledge of estimation strategies in the effectiveness of interventions designed to promote strategy flexibility across two recent studies. In the first, 65 fifth graders began the study as fluent users of one strategy for computing mental estimates to multi-digit multiplication problems such as 17 × 41. In the second, 157 fifth and sixth graders began the study with moderate to low prior knowledge of strategies for computing mental estimates. Results indicated that students’ fluency with estimation strategies had an impact on which strategies they adopted. Students who exhibited high fluency at pretest were more likely to increase use of estimation strategies that led to more accurate estimates, while students with less fluency adopted strategies that were easiest to implement. Our results suggest that both the ease and accuracy of strategies as well as students’ fluency with strategies are all important factors in the development of strategy flexibility.

IJSME, June 2009

The June issue of International Journal of Science and Mathematics Education has been published. The issue contains nine articles, several of which are related to mathematics education:


Slidecast from our AERA-symposium

It is hard to believe that a month has already passed by since the 2009 AERA Annual Meeting. I have already written about my presentation and the preparations for our symposium before, but I am now happy to finally be able to present the slidecast from our entire symposium session! Below, you find the embedded version of the slidecast (powerpoint slides with synchronized audio - just press the play button!):

Social justice and mathematics teacher education

The next issue of Journal of Mathematics Teacher Education is apparently going to focus on social justice and mathematics teacher education. In what appears to be an editorial, Peter Gates and Robyn Jorgensen presents the topic and talks about defining the term:
Reading the articles in this and the next Special Issue will very quickly show that social justice is difficult to define, in part because it not only depends on one’s own world view, but also it depends somewhat on the situation being analysed. Social justice is a relative concept; what is unjust to some, is not unjust to others; whether we consider something is socially unjust or relationally unjust will likewise differ.
In relation to this topic, three articles have been published online the last couple of days:
You can go to the links above to read more about these articles.

Mathematical problem solving and students' belief systems

María Luz Callejo and Antoni Vila have written an article that was published in Educational Studies in Mathematics last week. The article is entitled Approach to mathematical problem solving and students’ belief systems: two case studies. Most studies that focus on the role of beliefs in relation to problem solving are to some degree based on the works of Alan Schoenfeld, Günther Törner, Liewen Verschaffel, Erkki Pehkonen and several others. So does this. The theoretical part of the paper gives a nice overview of some of the most important earlier studies within this field. Personally, I would have included reference to some more critical perspectives, like Jeppe Skott, and when discussing belief systems, I also think the work of Keith Leatham provides an important contribution to the field. In their discussion, they consider inconsistencies between beliefs and actions, and in this connection, I think a reference to Leatham's work and his proposed framework of viewing beliefs as sensible systems would have been worthwhile.

Still, I think it is an interesting article to read if you are interested in problem solving or research on beliefs. Here is the article abstract:
The goal of the study reported here is to gain a better understanding of the role of belief systems in the approach phase to mathematical problem solving. Two students of high academic performance were selected based on a previous exploratory study of 61 students 12–13 years old. In this study we identified different types of approaches to problems that determine the behavior of students in the problem-solving process. The research found two aspects that explain the students’ approaches to problem solving: (1) the presence of a dualistic belief system originating in the student’s school experience; and (2) motivation linked to beliefs regarding the difficulty of the task. Our results indicate that there is a complex relationship between students’ belief systems and approaches to problem solving, if we consider a wide variety of beliefs about the nature of mathematics and problem solving and motivational beliefs, but that it is not possible to establish relationships of causality between specific beliefs and problem-solving activity (or vice versa).


Teaching mathematics for understanding

Edward A. Silver, Vilma M. Mesa, Katherine A. Morris, Jon R. Star and Babette M. Benken have written an article that was published in the most recent issue of American Educational Research Journal. The article is called Teaching Mathematics for Understanding: An Analysis of Lessons Submitted by Teachers Seeking NBPTS Certification. Here is the abstract of their article:
The authors present an analysis of portfolio entries submitted by candidates seeking certification by the National Board for Professional Teaching Standards in the area of Early Adolescence/Mathematics. Analyses of mathematical features revealed that the tasks used in instruction included a range of mathematics topics but were not consistently intellectually challenging. Analyses of key pedagogical features of the lesson materials showed that tasks involved hands-on activities or real-world contexts and technology but rarely required students to provide explanations or demonstrate mathematical reasoning. The findings suggest that, even in lessons that teachers selected for display as best practice examples of teaching for understanding, innovative pedagogical approaches were not systematically used in ways that supported students’ engagement with cognitively demanding mathematical tasks.


Mathematical modelling and medical students

Teaching Mathematics and its Applications has published an article by Zvi H. Perry about Change in senior medical students’ attitudes towards the use of mathematical modelling as a means to improve research skills. Here is the article abstract:
A PUBMED search for ‘mathematical models in medicine’ shows more than 15,000 articles covering almost every field of medicine. We designed a course with the goal of developing the students’ skills in computerized data analysis and mathematical modelling, as well as enhancing their ability to read and interpret mathematical data analysis. The study evaluated the acquisition of research skills and how to understand such data, as well evaluating the students’ feeling of competence. The course was structured as a 1-week (30-h) workshop for final year medical students. The study population consisted of 23 medical students who took the course in the 2005 academic year. Course evaluation used questionnaires that assessed the students’ satisfaction and mathematical knowledge. We found a significant change in the attitudes of our subjects, comparing their before and after attitudes towards their competence in the use of mathematical modelling, academically (i.e. their ability to read and understand articles using math models) as well as medically (i.e. their ability to implement theory that arises from math models to medical applications). We believe that the use of math modelling training in medical education significantly improved the students’ confidence in reading and applying math models in medicine; there is a tendency (albeit insignificant) towards superior results in attitudes of students towards math usage in medicine at large.


ICMI-News, May 2009

A new newsletter has arrived from ICMI (International Commission on Mathematical Instruction), and it contains lots of interesting news! Here is the table of contents:
  1. Editorial: The Relevance of Mathematics Education in India
  2. ICMI Study 20: Educational Interfaces between Mathematics and the Industry (EIMI)
  3. ICMI Study 20: Discussion document (short version)
  4. ICMI has a new website!
  5. Exhibition "Experiencing Mathematics" in southern countries
  6. Calendar of Events of Interest to the ICMI Community
  7. Historical vignettes: David Eugene Smith, the proponent of ICMI
  8. Subscribing to ICMI News
The entire newsletter is freely available online, and you can also read previous newsletters from the archive.


March issue of NOMAD

The March issue of NOMAD has been published. The issue is introduced by a very interesting editorial about Quality criteria in mathematics education research. This editorial is followed by three articles:
By following the links above, you can read the abstracts of the articles. Unfortunately, the entire articles are only available in the printed version of the journal.


IJCML, April 2009

Euler and structural steel design

David M. Boyajian has written an article that was published in International Journal of Mathematical Education in Science and Technology a couple of days ago. The article is entitled Euler teaches a class in structural steel design. Here is the abstract of the article:
Even before steel was a topic of formal study for structural engineers, the brilliant eighteenth century Swiss mathematician and physicist, Leonhard Euler (1707-1783), investigated the theory governing the elastic behaviour of columns, the results of which are incorporated into the American Institute of Steel Construction's (AISC's) Bible: the Steel Construction Manual. Each semester as the author teaches the introductory undergraduate 'Structural Steel Design' course, when arriving at the subject of compression members, he insists on first explaining in detail the mathematical contributions of Euler to the theory of elastic buckling, based on the subject of differential equations-the contents of which constitute this article-before commencing with issues pertaining to engineering design.


"Gender games"

Anna Llewellyn has written an article called ‘Gender games’: a post-structural exploration of the prospective teacher, mathematics and identity. The article was published online in Journal of Mathematics Teacher Education on Tuesday this week. Here is the abstract of Llewellyn's article:
In this article, I draw on post-structural and feminist epistemologies to analyse interview data from two prospective teachers on a primary education degree. Specifically I use Foucauldian critical discourse analysis to discuss the competing discourses of the masculine mathematician and the feminine primary school teacher. The initial purpose of the article is to deconstruct the themes of control, choice and confidence, which I argue are prevalent within mathematical discourses within our current neoliberal society. A further aim of the article is to explore the representation of discourse and data within educational texts, which I do by experimenting with the language used throughout.


Does policy influence math teachers?

Teachers College Record features an interesting article related to mathematics education this week (the article is freely available): Does Policy Influence Mathematics and Science Teachers' Participation in Professional Development, by Laura Desimone, Thomas M. Smith and Kristie J.R. Phillips. Here is an abstract of the article:
Using a national sample of high school mathematics and science teachers from the Schools and Staffing Survey (SASS), we find that authority (teacher leadership and control over school and classroom policy), not power (frequency of evaluation of teachers and professional development, and ease of dismissal of teachers), is associated with teachers taking the kind of professional development that we know improves teaching and learning-activities focused on subject matter content and instructional strategies, as well as active interactions with other teachers around curriculum and instruction. Similarly, we find that stability (measured by reduced teacher turnover), not the consistency of professional development with other reforms, is associated with taking effective professional development.


Multiple representations

Amy E. Ryken has written an article that was published online in Journal of Mathematics Teacher Education on Friday. The article is entitled Multiple representations as sites for teacher reflection about mathematics learning, and here is the abstract:
This documentary account situates teacher educator, prospective teacher, and elementary students’ mathematical thinking in relation to one another, demonstrating shared challenges to learning mathematics. It highlights an important mathematics reasoning skill—creating and analyzing representations. The author examines responses of prospective teachers to a visual representation task and, in turn, their examination of school children’s responses to mathematical tasks. The analysis revealed the initial tendency of prospective teachers to create pictorial representations and highlights the importance of looking beyond the pictures created to how prospective teachers use mathematical models. In addition, the challenges prospective teachers face in moving beyond a ruled-based conception of mathematics and a right/wrong framework for assessing student work are documented. Findings suggest that analyzing representations helps prospective teachers (and teacher educators) rethink their teaching practices by engaging with a culture of teaching focused on reading for multiple meanings and posing questions about student thinking and curriculum materials.