This paper comments on the expanded repertoire of techniques, conceptual frameworks, and perspectives developed to study the phenomena of gesture, bodily action and other modalities as related to thinking, learning, acting, and speaking. Certain broad issues are considered, including (1) the distinction between “contextual” generalization of instances across context (of virtually any kind—numeric, situational, etc.) and the generalization of structured actions on symbols, (2) fundamental distinctions between the use of semiotic means to describe specific situations versus semiosis serving the process of generalization, and (3) the challenges of building generalizable research findings at such an early stage in infrastructure building.
In this collection, I found the article by Chamberlin, Powers and Novak particularly interesting, so I will provide you with some more details about it. The study reported in this article is related to the No Child Left Behind initiative in the U.S. In relation to this initiative, several professional development courses in the U.S. are required to assess the teachers’ content knowledge. This article reports on the evaluation of the impact of these assessments. Although the article does not provide a very thorough theoretical background, it gives a good overview of the survey that were made to investigate the teachers’ perceptions about these assessments.
One of the results of this survey was that the teachers appeared to learn more because of the assessments. They explain it like this:
We surmise that these positive effects may be due to an important aspect of theassessment process in these PD courses – the assessment and learning of mathematical topics and material was on-going and demonstrating mastery of those ideas was expected.
Many teachers appear to be reluctant to be tested, and this study apparently describes a study which had positive experiences with assessing the teachers after a course, and this might be interesting for other teacher educators or providers of in-service courses to take a closer look at.
I started this blog in February this year, and in the welcome post on February 5, I wrote:
There are so many journals, so many conferences, so many web-sites that cover research in mathematics education. This blog will be my humble attempt to cover the most important ones. In the sidebar, you can find feeds from the most important scientific journals in mathematics education research. In this blog, I will comment on new and interesting (to me at least) articles in these and other journals. I will also try to follow some of the most important conferences in mathematics education, as well as sharing interesting bookmarks regarding mathematics education.
Now, ten months later, I think it’s appropriate to look back and see where I have come. The blog started out as a personal wish to get to know my own field of research better, and I personally feel that I have been extremely successful in this realm! I never advertised much for this blog, but when I started tracking the statistics with Google Analytics in late June, I realized that lots of people from all over the world actually read the blog!
Between July 1 and December 1, the blog had 5423 unique visitors, from 114 countries. I know this doesn’t sound like a lot, but for a niche blog like this, I think it is actually quite good. For me, it is also interesting to note that my own country – Norway – is only in the third spot when it comes to number of visitors.
Most of my time has been spent on covering articles from peer-reviewed journals in mathematics education, and I have also covered some conferences. This is something I intend to continue doing, but I have been thinking about different possible ways of doing this. First, I have thought about the possibility of writing more about some main articles in a way that people who are not researchers can relate to. I think it is important for researchers to communicate their results not only to fellow researchers. Unfortunately, but understandably, most teachers do not read our research journals! So, I have started thinking about writing some abstracts or impressions of research articles that teachers, parents and others who are interested but not researchers might relate to. I have also started thinking about making a stronger effort into providing an even better overview of the field (indexing journal articles, updating the conference calendar more, etc.). These are some of my own thoughts. But I am also interested in learning about your ideas! So, if you read this blog frequently, or if this is the first time you drop by … What do you think? What would be more useful to you? Please write comments to this post, or send me an e-mail to let me know!
I already know what an incredible learning experience this blog has been for me, but now I want to know how I can make it a better experience for you – the readers – as well!
The universal emphasis in mathematics education on teaching and learning for understanding can require substantial paradigmatic shifts for many elementary school teachers. Consequently, a pressing goal of teacher preparation programs should be the facilitation of these changes during program experiences. This longitudinal, mixed methods study presents a thorough investigation of the effects of a distinctive teacher preparation program on important constructs related to prospective teacher preparedness to teach mathematics for understanding, including mathematics pedagogical and teaching efficacy beliefs, mathematics anxiety, and specialized content knowledge for teaching mathematics. The results indicate that the programmatic features experienced by the prospective teachers in this study, including a developmental two-course mathematics methods sequence and coordinated developmental field placements, provided a context supporting teacher change. These shifts are interpreted through the nature and timing of the experiences in the program and a model of teacher change processes. The findings provide insights for mathematics educators as to the outcomes of these programmatic features.
For more than 20 years, belief research has been based on the premise that teachers’ beliefs may serve as an explanatory principle for classroom practice. This is a highly individual perspective on belief–practice relationships, one that does not seem to have been influenced by the increasingly social emphases in other parts of mathematics education research. In this article, I use the notions of context and practice to develop a locally social approach to understanding the belief–practice relationships. It is a corollary of the approach taken that the high hopes for belief research with regard to its potential impact on mathematics instruction need to be modified.
This paper starts from some observations about Presmeg’s paper ‘Mathematics education research embracing arts and sciences’ also published in this issue. The main topics discussed here are disciplinary boundaries, method and, briefly, certainty and trust. Specific interdisciplinary examples of work come from the history of mathematics (Diophantus’s Arithmetica), from linguistics (hedging, in relation to Toulmin’s argumentation scheme and Peirce’s notion of abduction) and from contemporary poetry and poetics.
How Does the Problem Based Learning Approach Compare to the Model-Eliciting Activity Approach in Mathematics? by Scott A. Chamberlin and Sidney M. Moon. Abstract: The purpose of this article is to discuss the similarities and differences in the two approaches referred to in the article title with an emphasis on implementation and outcomes.
Seeds of Professional Growth Nurture Students’ Deeper Mathematical Understanding, by Ji-Eun Lee and Dyanne Tracy. Abstract: This manuscript describes a group of middle school age students’ exploration of virtual mathematics manipulatives and the authors’ professional development process. In the manuscript, the authors share the experiences they had with middle school students and the process that they, as mathematics teachers, used to refine their own learning and teaching alongside the middle school students.
The State of Balance Between Procedural Knowledge and Conceptual Understanding in Mathematics Teacher Education, By Michael J. Bossé and Damon L. Bahr. Abstract: In this paper, we present the results of a survey-based study of the perspectives of mathematics teacher educators in the United States regarding the effects of the conceptual/procedural balance upon four concerns: the type of mathematics that should be learned in school, preservice teacher preparation, instructional conceptualization and design, and assessment.
An Exploration of the Effects of a Practicum-Based Mathematics Methods Course on the Beliefs of Elementary Preservice Teachers, by Damon L. Bahr and Eula Ewing Monroe. Abstract: Effects of a practicum-based elementary mathematics methods course on the beliefs of preservice teachers regarding conceptual knowledge in school mathematics were explored using a pre-post design. The intensity of those beliefs was assessed before and after the methods course using the IMAP Web-Based Beliefs Survey, an instrument constructed by the “Integrating Mathematics and Pedagogy” (IMAP) research group at San Diego State University.
What is Good College Mathematics Teaching? by Carmen M. Latterell. Abstract: This article attempts to answer the question “What is good college mathematics teaching?” by examining three sources of information: research, student course evaluations, and responses on the website RateMyProfessors.com.
This is the journal where I published my own article about Real-life Connections in Japan and the Netherlands: National Teaching Patterns and Cultural Beliefs, in July, and as always, all articles are freely available in pdf format.
When studying correlations, how do the three bivariate correlation coefficients between three variables relate? After transforming Pearson’s correlation coefficient r into a Euclidean distance, undergraduate students can tackle this problem using their secondary school knowledge of geometry (Pythagoras’ theorem and similarity of triangles). Through a geometric interpretation, we start from two correlation coefficients rAB and rBC and then estimate a range for the third correlation rAC. In the case of three records (n = 3), the third correlation rAC can only attain two possible values. Crossing borders between mathematical disciplines, such as statistics and geometry, can assist students in deepening their conceptual knowledge.
If you are interested, you might want to check out the information about the book in Google Books (which includes links to where you can buy the book), and you might also be interested in taking a look at this page about Early Algebra.
Reidar Mosvold 