Mathematics Education in the Middle Grades Teaching to Meet the Needs of Middle Grades Learners and to Maintain High Expectations: Proceedings of a National Convocation and Action Conferences (2000) / Chapter Skim
Currently Skimming:
Action Conferences
Action Conferences
Pages 139-176
The Chapter Skim interface presents what we've algorithmically identified as the most significant single chunk of text within every page in the chapter.
Select key terms on the right to highlight them within pages of the chapter.
From page 141... ...
ACTION CONFERENCE ON RESEARCH IN THE TEACHING AND LEARNING OF MATHEMATICS IN THE MIDDLE GRADES Organized by Sandra Wilcox, Department of Teacher Education, Michigan State University The conference was clesignec3 around the question: What are the characteristics of research that would be helpful and informative for teaching mathematics in the micic3le gracles? ACTION CONFERENCE ON THE PROFESSIONAL DEVELOPMENT OF TEACHERS OF MATHEMATICS IN THE MIDDLE GRADES Organized by Deborah Ball, University of Michigan.
|
From page 143... ...
Thus, the agenda for the Action Conference was (lesigne(1 to bring some of these possibilities to light through presentations on various views of algebra anti on research in the teaching and learning of algebra, together with practical experiences of teachers anti (1istricts who have been implementing some version of algebra in the middle grades. Discus
|
From page 144... ...
The increase(1 availability of calculators and computers provides new ACTION CONFERENCE demands and opportunities for the teaching and learning of algebra. We may concentrate on the design and use of algorithms, on data modeling and predictions, or on analyzing anti projecting trends.
|
From page 145... ...
Algebra as the language of mathematics 2. If one thinks of algebra as the language of mathematics, then does the learning of algebra entail some of the same challenges encountered in the learning of reacling, ancl therefore call for a more cleliberate ancl focused attention to the task of teaching this formalization of mathematical expression ancl communication?
|
From page 146... ...
Fey closed by pointing out that these curricular goals should be implemente with consideration of the ways students learn. He suggested that the way students encounter these i(leas must be changed from the "demonstrate, imitate, ACTION CONFERENCE and practice" style that has dominated algebra instruction.
|
From page 147... ...
An(1 many important mathematical ideas, such as geometric series, the binomial theorem, and the number theory behind Pythagorean triples, require rather sophisticated symbol manipulation.
|
From page 148... ...
Typical graphs ACTION CONFERENCE -2 -3 3 2 y 1- l n ~3 -2 -1 ~ 1 ~ -1 Ad/ 1 Z x 6 Y4 -- - - 1 ha .
|
From page 149... ...
What (toes all this have to (lo with learning algebra in the middle grades? Learning is about constructing meaning.
|
From page 150... ...
Blanche Brownley, Secondary Mathematics Specialist from ACTION CONFERENCE the District of Columbia Public Schools, served as moderator for presentations about the Connected Mathematics Project (CMP) , University of Chicago School Mathematics Project (UCSMP)
|
From page 151... ...
. UNIVERSITY OF CHICAGO SCHOOL MATHEMATICS PROJECT Bonnie BuehIer discussed the use of the University of Chicago School Mathematics Project materials at Springman Middle School in Glenview, Illinois, a suburb of Chicago.
|
From page 152... ...
Support is the responsibility of the user, not of the curriculum (leveloper, she ACTION CONFERENCE thought, although the materials ought to provide guidance on the need for professional development. For information about the effectiveness of their program, BuehIer mentione(1 that on the Comprehensive Test of Basic Skills (CTBS)
|
From page 153... ...
Mathematics in Context introduces concepts within realistic contexts that support mathematical abstraction, with tasks and questions designed to stimulate mathematical thinking and to promote discussion among students. With more than 10 years of experience in efforts to improve their mathematics programs, Loftier was already familiar with some of the ideas behind Mathematics in Context and with the idea that all students can achieve higher standards.
|
From page 154... ...
Hake expressed appreciation for the lack of a national curriculum in the United States, because of the many varied approaches an(1 opportunities for experimentation. He argued that decisions in California and Texas are particularly worthy of attention, because those decisions shape the kinds of instructional materials that become available to the rest ACTION CONFERENCE of the county.
|
From page 155... ...
Why isn't my kid still special anymore? " Others say, "If this curriculum is good enough for the kids in inner-city Minneapolis, then it is not good enough for us in the suburbs." To overcome these beliefs, Barte} discussed various ways of marketing the message of "algebra for all" to other audiences: community advisory groups, brochures, parent meetings, posting student work in hallways, teacher to teacher conversation, and even cIassroom newsletters.
|
From page 156... ...
If you give them problems that they can't do in five minutes, they wall complain at first, but after a few months, they will ACTION CONFERENCE never go back. Algebra should be offered in 7th grade for gifted and talented students.
|
From page 157... ...
We also loose the greatest potential of democratic THE NATURE AND IMPACT OF ALGEBRA education which is our charge to address diversity with equity, to build discourse in that context, to create community and harmony where there is otherwise (livision. RESPONSES As Organizer of the action conference, Hyman Bass, professor of mathematics at Columbia University, led the closing (liscussion by focusing on several dilemmas and questions to be considered regarding the place of algebra in the middle grades.
|
From page 158... ...
CONCLUSIONS Although the participants were aware that the action conference was not designed to draft recommendations, many participants expressed a desire for help in making decisions back in their schools and districts. Thus, the remainder of the afternoon was devoted to discussing what kinds of statements would be reasonable and useful for schools and districts who were considering implementing algebra in their middle grades.
|
From page 159... ...
As for the organization of the mathematics curriculum in the middle grades, the typical high school courses (Algebra I, geometry) may be transplanted down a grade or two.
|
From page 160... ...
The National Convocation on Middle Grades Mathematics Education (which preceded the Action Conference) drew over 400 educators to Washington to consider the following question: What might a mathematics program look like that is developmentally responsive, academically excellent, and that seeks social equity for all students?
|
From page 161... ...
· If research is situ ate(1 in, grows out of, and informs theory and practice, how can we better articulate the relationship or interface among theory, research, and practice? The Action Conference brought together approximately 30 professionals including mathematics educators and teachers, mathematics education researchers, curriculum (levelopers, administrators, and representatives from the National Science Foundation and the Department of Education.
|
From page 162... ...
Hiebertidentified three sources of the tensions: · perceptions of minimal impact of research on solving problems of practice, fueled by inadequate communication to interested audiences, particularly the challenge of talking to the general population about what we know, · confusion between values, which research cannot settle, and empirical issues; and · a genuine dilemma that is inherent in the research process, the tension between addressing daunting, complex problems anti (1oing good research. Hiebert suggeste(1 a framework to better understand and resolve tensions by moving research from: · what works to understanding what works; · critical experiments to continuing programs of research; ACTION CONFERENCE · feature-base(1 to system-base(1 class room research; · researcher-driven to a teacher-driven research anti (1evelopment enterprise.
|
From page 163... ...
Mary Kay Stein drew on her work in the QUASAR project to highlight how research often grows out of and attempts to solve problems of practice (Stein, Grover, Henningsen, 1996; Henningsen and Stein, 1997; Stein and Lane, 19961. Drawing on her study of teachers' use of cognitively challenging problems as a case of linking research on teaching to research on learning, Stein argue(1 that cIassroom-base(1 research can: · uncover anti illuminate patterns of teaching practice that may be problematic in terms of student learning, · contribute to better un(lerstan(ling anti (1escribing these practices, an(l, in turn, · be helpful in (resigning interventions to reshape practices that better support student learning.
|
From page 164... ...
Fey noted that many theoretical ideas (e.g., constructivism, conceptual and procedural knowledge, multiple representations, research on coopera ACTION CONFERENCE five learning, teacher change and school change) guided the development of the grade 6-S Connected Mathematics curriculum.
|
From page 165... ...
Judith Sowder presented findings from a twoyear project aimed at having teachers explore some of the complex mathematical ideas that are typically a part of the middle grades curriculum (Sowder, Philipp, Armstrong & Schappelle, 1998; Sowder & Philipp, in press; Fennema, Sowder, & Carpenter, in press; Thompson, 19951. While the outcomes of this stu(ly were very encouraging (e.g., teachers began to see questioning as a teaching approach and started to listen to their students more closely)
|
From page 166... ...
Student learning 1. We know a lot about student thinking in some domains of the middle grades curriculum.
|
From page 167... ...
(1998~. Middle grades teachers' mathematical knowledge and its relationship to instruction.
|
From page 168... ...
With a focus on mathematics at the mi(l(lle gra(les, the structure of the Action Conference was groun(le(1 in analysis of the practice of teaching middle grades mathematics, considering the major tasks teachers
|
From page 169... ...
Ball pointed out that the focus of the discussion throughout the workshop would be from the vantage point of teacher educators, and would consider sites through which teachers might most profitably learn mathematics content needed in teach ing, based on tasks which teachers regularly do as part of their teaching. Participants observed that the diagram helps make clear that the content to learn becomes more complex at each level.
|
From page 170... ...
Ball, together with Joan FerriniMun(ly, Center for Science, Mathematics and Engineering Education at the National Research Council, led an activity designed to engage participants in considering mathematics knowledge as it is used in one task of teaching. Ball ACTION CONFERENCE presented a mathematics problem and asked participants to solve the problem and to describe the mathematical territories into which it might head.
|
From page 171... ...
. OPPORTUNITY TO LEARN SITUATED IN SITES OF PRACTICE The Action Conference explored the promise and potential problems of situating opportunities for teachers' learning in practice.
|
From page 172... ...
To learn more about what people are trying and how it is working, anti to sharpen the ability to examine their own designs and practices as professional developers, participants engage(1 in several examples of professional development projects. WRITTEN CASES Margaret Smith, Pennsylvania State University, engage(1 the participants in a case study of student work The Case of Ed Taylor; Smith, Henningsen, Silver, & ACTION CONFERENCE Stein, 1998)
|
From page 173... ...
questions for rejection and discussion: How might curriculum materials such as these offer professional development opportunities for leachers? How might these materials influence or support a teacher's daily decisions?
|
From page 174... ...
REFLECTIONS ON THE IMPROVEMENT OF PROFESSIONAL DEVELOPMENT A panel, moderated by Mark Saul, from BronxviDe Public Schools, consisting of ACTION CONFERENCE Iris Weiss, Horizon Research; Stephanie Williamson, Louisiana Systemic Initiative; and John Moyer, from Marquette University, reacted to the issues raised at the Conference through the lens of their experiences. Weiss, from the perspective of large scale research about implementation, argued for the need to help teachers develop some way to filter and make decisions.
|
From page 175... ...
At the close of the panel, Nora Sabelli from the National Science Foundation discussed the new opportunities for research on middle grades mathematics in the Department of Education/ National Science Foundation Research Initiative. She indicated that the focus of the initiative will be on long-term agendas, strategic plans for implementa tion, and ensuring that there is the human, methodological and institutional capacity for converting schools into learning communities.
|
From page 176... ...
Educational Evaluation and Policy Analysis, 1562}, 129-151. ACTION CONFERENCE National Council of Teachers of Mathematics.
|
Key Terms
This material may be derived from roughly machine-read images, and so is provided only to facilitate research.
More
information on Chapter Skim is available.