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Dear Don, I am also teaching mathematics in California. I have corresponded to several people in email on this topic and I thought that you might find it interesting to read one of those: -=- -=- -=- -=- -=- -=- -=- I have several sources of information for you on the effectiveness of algebra instruction in the eighth grade. (1) From the Teacher2Teacher service http://mathforum.org/t2t/ hosted by the Math Forum I searched for letters/responses on the topic of algebra and I found this from one of the selections on http://mathforum.org/t2t/thread.taco?thread=856 From: Marielouise (for Teacher2Teacher Service) Date: 1998-12-02-22:17:13 Subject: Re: Algebra for all eighth graders >We are looking for data on school districts which offer "Algebra I" to all >eighth grade students. Currently only our accelerated students take >"Algebra I" in the eighth grade. We are concerned that our non- >accelerated students are ultimately being disadvantaged I do not have any specific data to share with you. However, I believe that if you contact the University of Chicago School Mathematics Project (UCSMP) at 5835 S. Kimbark Ave., Chicago IL 60637 (773)-702-1130 or email at: <ucsmp@uchicago.edu > and ask this same question they will have data to share with you. The UCSMP advocates teaching transitional math (prealgebra) to all seventh graders and algebra to all eighth graders. They have been doing this project for 15 years all across the country. Their winter 1998 Newsletter has a comparison chart showing percents of 8th graders studying various types of mathematics curricula. In the SIMS 1981 study 13% studied algebra. In the NAEP 1986 survey 16% studied algebra and in the NAEP 1996 survey 20% studied algebra. If you call or write UCSMP ask them to put you on the list for their free newsletter. It is very informative. -Marielouise, for the Teacher2Teacher service (2) Information from: Dr. James J. Kaput Department of Mathematics UMass-Dartmouth I met Jim last year at the NCTM Standards 2000 Electronic Format Group meeting in Washington D.C. The EFG invited 25 various educators from the U.S., Canada, the U.K. and France to present papers on the use of technology in teaching mathematics. The authors and the papers can be viewed here: http://mathforum.org/technology/papers/authors.taco This is Jim's response to your question: Have you seen the new NCTM Algebra Frameworks discussion book? It contains a number of relevant articles (including one by me). Also, the new draft Standards2000 middle school section has some explicit recommendations, basically saying that traditional Alg I in 8th grade is a bad idea. The draft of the NCTM Standards 2000 can be downloaded here: http://www.nctm.org/standards2000/download.html On the other hand, I don't have concrete research results to report - all algebra my work involves the elementary grades. Below I include some recent discussion material associated with that project taken from our YR 4 plan of work funded by the US Dept of Ed. OERI. Thanks for your interest, Jim K ---------------------- Overview: Background and Objectives Background: The Need to Solve the National Algebra Problem Just as algebra has acted as a constricted gateway to significant mathematics and all that follows from mastery of that mathematics, algebra reform is proving to be the gateway to K-12 mathematics education reform for the next century (Kaput, 1998). Across the country, the recognition that the traditional high school algebra sequence is highly dysfunctional and is inappropriate as the "algebra for all" has led to reform-attempts at the middle school level (NCTM, 1997a). These attempts have taken the form of pre- algebra courses or opportunities for 8th or even 7th graders to take the traditional Algebra I course, and they assume only minor modifications to high school algebra texts. Except in recent reform documents (NCTM, 1998) and new standards-based curricula, e.g., CMP (Lappan, et al, 1997) or MiC (National Center for Research in Mathematical Sciences & Freudenthal Institute, 1998), these attempts have not substantially involved changes at the earlier grade levels, and their appropriateness has been called into question in emerging standards. Indeed, the NCTM Standards 2000 draft document (NCTM, 1998) suggests that moving Algebra I into middle school is not a good idea, and indeed, "(O)ne negative consequence is that students are likely to have less opportunity to learn the full range of mathematics content, especially topics in geometry and data analysis, that are expected in the middle grades" (p. 214). The Draft Standards go on to suggest: "In fact, there is considerable value in connecting the learning of algebraic concepts and skills to the study of other mathematical content topics" (p.214). Goals and Research Objectives Our approach to the national algebra problem grows out of the prior Center's work, which is well reflected in the new Standards draft, and begins with serious development of algebraic reasoning in elementary school based on conceptual analyses of the nature of mature algebraic reasoning and its less mature forms. Our analyses acknowledge that mature algebraic reasoning takes several different forms and suggest that its development can transform the learning of most mathematics from the elementary level onward (Kaput, in press). If, in combination with changes at the middle school level, it is successful as a solution to the national algebra problem, it will: * Open curricular space for 21st century mathematics desperately needed at the secondary level, space locked up by the 19th century high school national curriculum now in place. * Add a new level of coherence, depth, and power to school mathematics, both as curriculum and as a habit of mind. * Eliminate the most pernicious curricular element of today's school mathematics - late, abrupt, isolated and superficial high school algebra courses (Kaput, 1998). Against the backdrop of such enormous potential payoffs, we formulated our primary research objectives: 1. To understand how the several different forms of algebraic reasoning and skill can be developed within the context of elementary school mathematics, and 2. To test models supporting this development that may be implemented on a large national scale. Making progress on the first primary objective will help us to build a coherent "early algebra story" that is broadly accessible to practitioners, teacher-educators, and policy makers - that can serve as the conceptual and practical basis for wide scale reform, a solution to the national algebra problem. The magnitude of this challenge and the need for multiple perspectives led to the formation of the Early Algebra Research Group (EARG), a collection of researchers who meet several times a year to share insights, jointly examine data, and comment on one another's' work. Prior work led to a five-part content analysis of algebra (see below), with a foundational role played by generalization and formalization, that is consonant with analyses produced by NCTM working groups. EARG has concentrated on expanding this five-part structure to analyses based in studies of cognition and learning, and to longitudinal analyses that account for the longer term development of these ideas and skills across grade levels. All of this work falls under primary objective (1). Making progress on primary objective (2) is the goal of our local work, especially the work planned for Year 4. -=- -=- -=- -=- -=- -=- I sincerely hope that others correspond to this topic. In my mind the most important thought is that "traditional Alg I in 8th grade is a bad idea." What is vital, in my opinion, is to develop methods that work to teach students algebraic concepts using a manipulative, technological and activity based approach rather than just assuming that because the Standards list algebraic concepts that the students must all be taught using the algebra text (mostly symbolic notation) and just plug away page by page. I have been noticing that teachers respond to Standards based curricula by thinking that we must all "go back to the book." Actually, I don't blame the teachers for this response because of the pressure that administrators and districts have been applying to the teachers. For some strange reason, using page numbers in texts seems safer right now than using interactive activities. You might find interesting some of the work that Frisbie Middle School has done recently to align activities to Standards: http://mathforum.org/alejandre/frisbie/math/ http://mathforum.org/alejandre/mathfair/index.html -Suzanne A., for the Teacher2Teacher service
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