ATM • Conference 2008 – Keele University
tags: conference, education, mathematics, research
Author: Reidar Mosvold
Essential skills for a math teacher
Education Week has an interesting article about the uncertainties about the skills that are needed to be a successful mathematics teacher. The point of departure for the article is the recent report by the National Mathematics Advisory Panel in the U.S. The report has several suggestions about the curriculum, cognition, instruction, etc. When it comes to the skills that are needed to become a good mathematics teacher, though, the answers were fewer:
Research does not show conclusively which professional credentials demonstrate whether math teachers are effective in the classroom, the report found. It does not show what college math content and coursework are most essential for teachers. Nor does it show what kinds of preservice, professional-development, or alternative education programs best prepare them to teach.
One of the panel members, Deborah Loewenberg Ball, was interviewed in the article, and she believed that it was in the area of improving teaching that the emphasis should be set in the years to come:
“We should put a lot of careful effort over the next decade into this issue so that we can be in a much different place 10 years from now.”
There appears to be a lot of work and research to do within this area. There is much agreement that the teacher is important, and the quality of the math teacher has an impact on the students’ results.
But the 90-page report also says it is hard to determine what credentials and training have the strongest effect on preparing math teachers to teach, and teach well. Research has not provided “consistent or convincing” evidence, for instance, that students of certified math teachers benefit more than those whose teachers do not have that licensure, it found.
So, the question that Ball and her team has focused a lot on in their research still remains important for researchers in the future: What kind of knowledge is it that teachers need?
The role of scaling up research
A new article has been published online at Educational Studies in Mathematics. The article is entitled: “The role of scaling up research in designing for and evaluating robustness“, and it is written by J. Roschelle, D. Tatar, N. Shechtman and J. Knudsen. Here is the abstract of the article:
One of the great strengths of Jim Kaput’s research program was his relentless drive towards scaling up his innovative approach to teaching the mathematics of change and variation. The SimCalc mission, “democratizing access to the mathematics of change,” was enacted by deliberate efforts to reach an increasing number of teachers and students each year. Further, Kaput asked: What can we learn from research at the next level of scale (e.g., beyond a few classrooms at a time) that we cannot learn from other sources? In this article, we develop an argument that scaling up research can contribute important new knowledge by focusing researchers’ attention on the robustness of an innovation when used by varied students, teachers, classrooms, schools, and regions. The concept of robustness requires additional discipline both in the design process and in the conduct of valid research. By examining a progression of three studies in the Scaling Up SimCalc program, we articulate how scaling up research can contribute to designing for and evaluating robustness.
When, how, and why prove theorems?
The full title of this new ZDM article is: “When, how, and why prove theorems? A methodology for studying the perspective of geometry“, and it is written by P. Herbst and T. Miyakawa.
Every theorem has a proof, but not every theorem presented in schools (not only in the U.S., although this is the focus of the article). Why is that? Here is the abstract of the article, which truly raises some important questions:
While every theorem has a proof in mathematics, in US geometry classrooms not every theorem is proved. How can one explain the practitioner’s perspective on which theorems deserve proof? Toward providing an account of the practical rationality with which practitioners handle the norm that every theorem has a proof we have designed a methodology that relies on representing classroom instruction using animations. We use those animations to trigger commentary from experienced practitioners. In this article we illustrate how we model instructional situations as systems of norms and how we create animated stories that represent a situation. We show how the study of those stories as prototypes of a basic model can help anticipate the response from practitioners as well as suggest issues to be considered in improving a model.
Blogged with the Flock Browser
Promoting student collaboration
Megan E. Staples wrote an article called: “Promoting student collaboration in a detracked, heterogeneous secondary mathematics classroom“. The article was published online in Journal of Mathematics Teacher Education on Wednesday. Here is the abstract of the article:
Detracking and heterogeneous groupwork are two educational practices that have been shown to have promise for affording all students needed learning opportunities to develop mathematical proficiency. However, teachers face significant pedagogical challenges in organizing productive groupwork in these settings. This study offers an analysis of one teacher’s role in creating a classroom system that supported student collaboration within groups in a detracked, heterogeneous geometry classroom. The analysis focuses on four categories of the teacher’s work that created a set of affordances to support within group collaborative practices and links the teacher’s work with principles of complex systems.
Several researchers have addressed the issue of collaboration and group work, and Staples analyzes the role of one teacher in this respect. Staples observed 39 lessons in the study, and data was collected through field notes, reflective memos, and 26 lessons were also video-taped. She also conducted interviews with most of the students and the teacher, and she collected curriculum documents, etc. During the data analysis, four categories emerged that were critical for understanding the teacher’s role (p. 8):
- Promoting individual and group accountability
- Promoting positive sentiment among group members
- Supporting student–student exchanges with tools and resources
- Supporting student mathematical inquiry in direct interaction with groups
These categories are used as point of departure for the organization and presentations of the results in the article.
The classroom is a complex system, and this is something Staples discuss a lot in the article. Understanding this complexity and being able to analyze it, is something she emphasizes as being important for both future and current teachers.
And interesting article. In the theoretical foundations, she refers (among others) to the works of researchers like E. Cohen and J. Boaler.
Norma 08 – final program
The final program of the Norma 08 conference has arrived (download as pdf). I am not going to repeat the entire program here, but I will point at the plenary lectures that will be presented at the conference:
- Monday, April 21, 16:30-17:30 – Jeppe Skott (Theme B)
- Tuesday, April 22, 11:00-12:00 – Paul Drijvers (Theme C)
- Wednesday, April 23, 11:00-12:00 – Eva Jablonka (Theme D)
- Thursday, April 24, 11:00-12.00 – Michèle Artigue (Theme A)
JMTE, April 2008
The April issue of Journal of Mathematics Teacher Education has been published. The following articles are enclosed:
This is an interesting collection of articles, addressing a multitude of perspectives from the use of video in teacher education in the article by Jon R. Star and Sharon K. Strickland to Jesse L.M. Wilkins’ focus on the relationship between content knowledge, attitudes, beliefs and practices by elementary teachers. I find the latter article especially interesting, since it aims at analyzing relationships between knowledge, beliefs, attitudes and practices at the same time. All four are large fields of research, and this is therefore a brave attempt. I would like to question the choice of investigating the teachers’ practice through self-reporting in a survey though.
National Mathematics Advisory Panel
In the U.S., the National Mathematics Advisory Panel (on request from the President himself) has delivered a report to the President and the U.S. Secretary of Education. This final report was delivered on March 13, and is freely available for anyone to download (pdf or Word document). I know this is old news already, but I will still present some of the highlights from the report here. Be also aware that there will be a live video webcast of a discussion of the key findings and principle messages in the report. The webcast will be held tomorrow, Thursday March 26, 10-11.30 a.m. Eastern Time. This discussion will be lead by Larry R. Faulkner (Chair of the Panel) and Raymond Simon (U.S. Deputy Secretary of Education).
A key element of the report is a set of “Principal Messages” for mathematics education. This set of messages consists of six main elements (quoted from pp. xiii-xiv):
- The mathematics curriculum in Grades PreK-8 should be streamlined and should emphasize a well-defined set of the most critical topics in the early grades.
- Use should be made of what is clearly known from rigorous research about how children learn, especially by recognizing a) the advantages for children in having a strong start; b) the mutually reinforcing benefits of conceptual understanding, procedural fluency, and automatic (i.e., quick and effortless) recall of facts; and c) that effort, not just inherent talent, counts in mathematical achievement.
- Our citizens and their educational leadership should recognize mathematically knowledgeable classroom teachers as having a central role in mathematics education and should encourage rigorously evaluated initiatives for attracting and appropriately preparing prospective teachers, and for evaluating and retaining effective teachers.
- Instructional practice should be informed by high-quality research, when available, and by the best professional judgment and experience of accomplished classroom teachers. High-quality research does not support the contention that instruction should be either entirely “student centered” or “teacher directed.” Research indicates that some forms of particular instructional practices can have a positive impact under specified conditions.
- NAEP and state assessments should be improved in quality and should carry increased emphasis on the most critical knowledge and skills leading to Algebra.
- The nation must continue to build capacity for more rigorous research in education so that it can inform policy and practice more effectively.
During their 20 month long work, the Panel split in five task groups, where they analyzed the available evidence in the following areas:
- Conceptual knowledge and skills
- Learning processes
- Instructional practices
- Teachers and teacher education
- Assessment
These groups are visible in the main chapter headings of the report.
After having presented their principle messages, the panel present 45 main findings and recommendations for the further development of mathematics education in the U.S. These 45 findings and recommendations are split in the following main groups (strongly resembling the list of task groups above):
- Curricular content
- Lesson processes
- Teachers and teacher education
- Instructional practices
- Instructional materials
- Assessment
- Research policies and mechanisms
These are the main issues in the forthcoming video webcast. All in all, it is an interesting report, so go ahead and read it!
Mathematics Teacher, April 2008
The April issue of Mathematics Teacher has arrived, and it contains the following three articles:
- Digital Images + Interactive Software = Enjoyable, Real Mathematics Modeling by Andy Ventress
- <!– Investigating the Mathematical Process with Nonlinear Asymptotes
Michael J. Bossé, Karen A. DeUrquidi, David L. Edwards and N. R. Nandakumar –> Investigating the Mathematical Process with Nonlinear Asymptotes by Michael J. Bossé, Karen A. DeUrquidi, David L. Edwards and N.R. Nandakumar - Using Technology to Promote Mathematical Discourse Concerning Women in Mathematics by Lyn Phy
The last article is a free preview article, and is downloadable for everyone. The author has a focus on women in mathematics, and she discusses her use of cooperative groups, Blackboard (a course managment system) and the internet as means to facilitate meaningful mathematical discourse. The venue for examining these types of mathematical discourse is a course called “Women in Mathematics”, which the author developed in her university. They studied the following women mathematicians in the course:
All in all, this is an interesting description of an interesting university course. At a meta-level, this article also address issues of how to use history of mathematics in your teaching. At the end of the article, the writer proposes that anecdotes and activities about women mathematicians can be used in “ordinary” mathematics courses, and this indicates a certain “direct” use of history.
Useless arithmetic
Linda Pilkey-Jarvis and Orrin H. Pilkey have written an article in Public Administration Review about the use of mathematical models in environmental decision making. Mathematical models are used extensively in the context of environmental issues and natural resources, and when these methods were first used, they were thought to represent a bridge to a better and more foreseeable future. There has also been much controversy in this respect, and the authors pose the question whether the optimism about the use of these models were ever realistic. In this article, they review the two main types of such models: quantitative and qualitative.
Although both present us with a generalized perspective on a natural problem, they are not equal in terms of predictive power. The first type—quantitative models—can be used as a surrogate for nature, whereas the second—qualitative models—do the same but with less accuracy.
After a review of these types of models, they provide a list of ten lessons that policy makers should learn when it comes to quantitative mathematical modeling:
- The outcome of natural processes on the earth’s surface cannot be absolutely predicted.
- Examine the excuses for predictive model failures with great care and skepticism.
- Did the model really work? Examine claims of past “successes” with the same level of care and skepticism that “excuses” are given.
- Calibration of models doesn’t work either.
- Constants in the equations may be coefficients or fudge factors.
- Describing nature mathematically is linking a natural flexible, dynamic system with a wooden, inflexible one.
- Models may be used as “fig leaves” for politicians, refuges for scoundrels, and ways for consultants to find the truth according to their clients’ needs.
- The only show in town may not be a good one.
- The mathematically challenged need not fear models and can learn how to talk with a modeler.
- When humans interact with the natural system, accurate predictive mathematical modeling is even more impossible.
These points are directed at policy makers, but I think several of them are also relevant for students at university level (and perhaps also upper secondary). In a simplified form, I think some of these points might even be relevant for younger pupils.
In the wrapping up of the article, they clarify their main argument:
Our argument in this article has been that mathematical models are wooden and inflexible next to the beautifully complex and dynamic nature of our earth. Quantitative models can condense large amounts of difficult data into simple representations, but they cannot give an accurate answer, predict correct scenario consequences, or accommodate all possible confounding variables, especially human behavior.
Reference:
Pilkey-Jarvis, L. & Pilkey, O.H. (2008). Useless Arithmetic: Ten Points to Ponder When Using Mathematical Models in Environmental Decision Making. Public Administration Review 68 (3) , 470–479 doi:10.1111/j.1540-6210.2008.00883_2.x
Reidar Mosvold 