Instructional Science, November 2009

The November issue of Instructional Science has been released (Volume 37, Number 6, 2009). Here is a list of articles that is published in this issue:

New IJMEST articles

A couple of new articles have been published online in International Journal of Mathematical Education in Science and Technology. Several are so-called classroom notes (see this link for full list), and then there are these two original articles:

  • Pilot study on algebra learning among junior secondary students, by Kin-Keung Poon and Chi-Keung Leung. Abstract: The purpose of the study reported herein was to identify the common mistakes made by junior secondary students in Hong Kong when learning algebra and to compare teachers’ perceptions of students’ ability with the results of an algebra test. An algebra test was developed and administered to a sample of students (aged between 13 and 14 years). From the responses of the participating students (N = 815), it was found that students in schools with a higher level of academic achievement had better algebra test results than did those in schools with a lower level of such achievement. Moreover, it was found that a teacher’s perception of a student’s ability has a correlation with that student’s level of achievement. Based on this finding, an instrument that measures teaching effectiveness is discussed. Last but not least, typical errors in algebra are identified, and some ideas for an instructional design based on these findings are discussed.
  • Student connections of linear algebra concepts: an analysis of concept maps, by Douglas A. Lapp,  Melvin A. Nyman and John S. Berry. Abstract: This article examines the connections of linear algebra concepts in a first course at the undergraduate level. The theoretical underpinnings of this study are grounded in the constructivist perspective (including social constructivism), Vernaud’s theory of conceptual fields and Pirie and Kieren’s model for the growth of mathematical understanding. In addition to the existing techniques for analysing concept maps, two new techniques are developed for analysing qualitative data based on student-constructed concept maps: (1) temporal clumping of concepts and (2) the use of adjacency matrices of an undirected graph representation of the concept map. Findings suggest that students may find it more difficult to make connections between concepts like eigenvalues and eigenvectors and concepts from other parts of the conceptual field such as basis and dimension. In fact, eigenvalues and eigenvectors seemed to be the most disconnected concepts within all of the students’ concept maps. In addition, the relationships between link types and certain clumps are suggested as well as directions for future study and curriculum design.

Insight into the fractional calculus via a spreadsheet

David A. Miller and Stephen J. Sugden have written an article called Insight into the Fractional Calculus via a Spreadsheet. The article was published in the most recent issue of electronic journal Spreadsheets in Education. The article is freely available as a pdf download, but here is a copy of the abstract:

Many students of calculus are not aware that the calculus they have learned is a special case (integer order) of  fractional calculus. Fractional calculus is the study of arbitrary order derivatives and integrals and their applications. The article begins by stating a naive question from a student in a paper by Larson (1974) and establishes, for polynomials and exponential functions, that they can be deformed into their derivative using the μ-th order fractional derivatives for 0<μ<1. Through the power of Excel we illustrate the continuous deformations dynamically through conditional formatting. Some applications are discussed and a connection made to mathematics education.

JMTE – October 2009

ZDM, November 2009

ZDM – The International Journal on Mathematics Education – has published the November issue of 2009 (Volume 41, Number 6). The issue contains the following nine articles:

The article by Karen C. Fuson and Yeping Li is an Open Access article, so that one should be available to all, even non-subscribers 🙂

Mathematics curriculum: a vehicle for school improvement

Christian R. Hirsch and Barbara J. Reys have written an article entitled Mathematics curriculum: a vehicle for school improvement. This article was recently published online in ZDM. Here is a copy of their article abstract:

Different forms of curriculum determine what is taught and learned in US classrooms and have been used to stimulate school improvement and to hold school systems accountable for progress. For example, the intended curriculum reflected in standards or learning expectations increasingly influences how instructional time is spent in classrooms. Curriculum materials such as textbooks, instructional units, and computer software constitute the textbook curriculum, which continues to play a dominant role in teachers’ instructional decisions. These decisions influence the actual implemented curriculum in classrooms. Various curriculum policies, including mandated end-of-course assessments (the assessed curriculum) and requirements for all students to complete particular courses (e.g., year-long courses in algebra, geometry, and advanced algebra or equivalent integrated mathematics courses) are also being implemented in increasing numbers of states. The wide variation across states in their intended curriculum documents and requirements has led to a historic and precedent-setting effort by the Council of Chief State School Officers and the National Governors Association Council for Best Practices to assist states in the development and adoption of common College and Career Readiness Standards for Mathematics. Also under development by this coalition is a set of common core state mathematics standards for grades K-12. These sets of standards, together with advances in information technologies, may have a significant influence on the textbook curriculum, the implemented curriculum, and the assessed curriculum in US classrooms in the near future.

CAS calculators in algebra instruction

S. Aslι Özgün-Koca has written an article called Prospective teachers’ views on the use of calculators with Computer Algebra System in algebra instruction. This article has recently been published online in Journal of Mathematics Teacher Education. Here is the abstract of the article:

Although growing numbers of secondary school mathematics teachers and students use calculators to study graphs, they mainly rely on paper-and-pencil when manipulating algebraic symbols. However, the Computer Algebra Systems (CAS) on computers or handheld calculators create new possibilities for teaching and learning algebraic manipulation. This study investigated the views of Turkish prospective secondary mathematics teachers on the use of advanced calculators with CAS in algebra instruction. An open-ended questionnaire and group interviews revealed prospective teachers’ views and beliefs about when and why they prefer three possible uses of CAS—black box, white box, or Symbolic Math Guide (SMG). The results showed that participants mainly preferred the white box methods and especially SMG to the black box method. They suggested that while the black box method could be used after students mastered the skills, the general white box method and SMG could be used to teach symbolic manipulation.

MTL, Volume 11, Issue 4

Teachers’ perceptions about the purpose of student teaching

Keith Leatham from Brigham Young University in Utah, U.S., is one of the scholars who have made important contribution to research of teachers’ beliefs in mathematics education research in the last couple of years. I very much like his proposed framework for viewing teachers’ beliefs as sensible systems (from his 2006 article in Journal of Mathematics Teacher Education). Now he has written a new article with focus on beliefs (or this time it is referred to as perceptions), and he has co-written this article with a colleague from Brigham Young University: Blake E. Peterson. Their article is entitled Secondary mathematics cooperating teachers’ perceptions of the purpose of student teaching, and it was published online in Journal of Mathematics Teacher Education last week. Here is their article abstract:

This article reports on the results of a survey of 45 secondary mathematics cooperating teachers’ perceptions of the primary purposes of student teaching and their roles in accomplishing those purposes. The most common purposes were interacting with an experienced, practising teacher, having a real classroom experience, and experiencing and learning about classroom management. The most common roles were providing the space for experience, modeling, facilitating reflection, and sharing knowledge. The findings provided insights into the cooperating teachers’ perceptions about both what should be learned through student teaching and how it should be learned. These findings paint a picture of cooperating teachers who do not see themselves as teacher educators—teachers of student teachers. Implications for mathematics teacher educators are discussed.

A case study in Rwanda

I haven’t read many scientific articles in mathematics education from or about Rwanda, but here is one! Alphonse Uworwabayeho from Kigali Institute of Education in Rwanda, and University of Bristol, UK, has written an article entitled Teachers’ innovative change within countrywide reform: a case study in Rwanda. The article was published online in Journal of Mathematics Teacher Education on Wednesday. This is even an Open Access article, so everyone should have full access to it! Here is the abstract of the article:

This article presents practical perspectives on mathematics teacher change through results of collaborative research with two mathematics secondary school teachers in order to improve the teaching and learning of mathematics in Rwanda. The 2006 national mathematics curriculum reform stresses pedagogies that enhance problem-solving, critical thinking and argumentation. Teachers need to use new teaching strategies. This article is a case study looking at issues around developing teachers’ use of interactions in mathematics classrooms independently of the national programme. Outputs of the study include teachers’ awareness of the need for change and their increased flexibility to accept learners’ autonomy in shifting from teacher-centred to learner-centred pedagogy. Geometer’s Sketchpad challenged teachers’ practice and then provoked reflection to improve student learning.