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Source: University of Chicago – 24 February 2009
Gesturing helps students develop new ways of understanding mathematics, according to research at the University of Chicago.
Scholars have known for a long time that movements help retrieve information about an event or physical activity associated with action. A report published in the current issue of the journal Psychological Science, however, is the first to show that gestures not only help recover old ideas, they also help create new ones. The information could be helpful to teachers, scholars said.
"This study highlights the importance of motor learning even in nonmotor tasks, and suggests that we may be able to lay the foundation for new knowledge just by telling learners how to move their hands," writes lead author and psychologist Susan Goldin-Meadow in the article "Gesturing Gives Children New Ideas About Math.”
Goldin, Meadow, the Beardsley Ruml Distinguished Service Professor in Psychology, was joined by Susan Wagner Cook, now Assistant Professor of Psychology at the University of Iowa and University of Chicago research assistant Zachary Mitchell in writing the article and doing the research.
For the study, 128 fourth-grade students were given problems of the type 3+2+8=__+8. None of the students had been successful in solving that type of problem in a pre-test. The students were randomly divided into three instruction groups.
One group was taught the words, "I want to make one side equal to the other side." Another group was taught the same words along with gestures instantiating a grouping problem-solving strategy--a V-shaped hand indicating 3+2, followed by a point at the blank (group and add 3 and 2 and put the sum in the blank). A third group was taught the words along with gestures instantiating the grouping strategy but focusing attention on the wrong numbers--a V-shaped hand indicating 2+8, followed by a point at blank. The experimenter demonstrating the gesture did not explain the movement or comment about it.
All of the students were then given the same mathematics lesson. On each problem during the lesson, they were told to repeat the words or words/gestures they had been taught.
After the lesson, students were given a test in which they solved new problems of this type and explained how they reached their answers. Students who repeated the correct gesture during the lesson solved more problems correctly than students who repeated the partially correct gesture, who, in turn, solved more problems correctly than students who repeated only the words.
The number of problems children solved correctly could be explained by whether they added the grouping strategy to their spoken repertoires after the lesson, Goldin-Meadow said. Because the experimenter never expressed the grouping strategy in speech during the lesson and students picked it up on their own as a new idea, the study demonstrates that gesture can help create new concepts in learning.
"The grouping information students incorporated into their post-lesson speech must have come from their own gestures," Goldin-Meadow said.
"Children were thus able to extract information from their own hand movements. This process may be the mechanism by which gesturing influences learning," she said.
Related research: Please see http://www.sciencedaily.com/releases/2007/11/071104191551.htm
(2) Major Topics of School Algebra--Videos and Transcripts based on the National Mathematics Advisory Panel’s Reports
Doing What Works is a Web site “dedicated to assisting teachers in the implementation of effective educational practices.” One section of this Web site covers the topic of algebra and is based on the National Mathematics Advisory Panel’s Final Report and the Reports of the Task Groups and Subcommittees. The following videos and transcripts are contained in this section (located on the Web site above):
(a) Multimedia Overview: National Mathematics Advisory Panel
Watch this overview to learn about the purpose and findings of the National Mathematics Advisory Panel, understand what the research can tell us about improving mathematics instruction, and find out why it's important for schools to focus on critical mathematics skills to better prepare students for entry into algebra. (3:25 min: http://dww.ed.gov/topic/topic_overview.cfm?PA_ID=8&T_ID=22)
(b) Multimedia Overview: National Math Panel - Major Topics of Algebra
Watch this overview to learn about the major topics of school algebra recommended by the Panel and two identified practices to support authentic algebra instruction for all students. (4:25 min: http://dww.ed.gov/topic/topic_overview.cfm?PA_ID=8&T_ID=22)
(c) The Major Topics of School Algebra
Improving the teaching of school algebra is best achieved
through enhancing teacher understanding of the major topics and the
development of instructional skills that focus on these topics and the
linkages among them. This visual diagram (http://dww.ed.gov/launcher.cfm?media/MathScience/MP2/TopicLevel/903_mp2_diagram.pdf)
illustrates the two algebra practices based on the findings and
recommendations presented in the Panel report. Use the diagram as a way
to engage school mathematics leaders in discussion about helping
students learn school algebra and providing multiple paths to ensure
that all students succeed. The diagram can be used to review key
findings and algebra topics recommended by the Panel.
Dr. Faulkner discusses the Panel's key recommendations,
especially focused on important messages for teachers, such as
providing a strong foundation for children's success in algebra and
future mathematics achievement, strengthening teachers' knowledge of
mathematics, and ensuring mathematics proficiency for all students. He
also addresses the Panel's hopes for how the research findings will be
used. (6:03 minutes: http://dww.ed.gov/launcher.cfm?media/MathScience/MP2/TopicLevel/911_mp2_video_faulkner.mov)
Listen to Dr. Schmid provide a brief overview of the Panel's
recommended major topics and implications of the Panel's findings for
algebra instruction, including the importance of strengthening teacher
knowledge and building student understanding of the topics and the
connections among them. (7:11 minutes: http://dww.ed.gov/launcher.cfm?media/MathScience/MP2/TopicLevel/904_mp2_video_schmid.mov)
The mission of The Futures Channel is threefold:
- To produce and distribute high quality multimedia content which educators in any setting can use to enliven curriculum, engage students and otherwise enhance the learning experience.
- To connect mathematics, science, technology and engineering to the real world of careers and achievement, providing a context and purpose for what students are learning, allowing them to envision their own successful futures.
- To provide a channel through which professionals from the sciences, engineering and technology sectors can reach their future workforce prospects and interest them in their fields.
The Amgen Tour of California (http://www.amgentourofcalifornia.com/) recently concluded and, coincidentally, the Futures Channel Web site featured several lessons related to bicycles:
(a) Engineering Faster Bikes
(b) Building and Testing Wheels
(c) Bicycle Design
Two weeks prior to last Sunday's Academy Awards ceremony, a dinner was held at the Beverly Wilshire to honor those receiving Scientific and Technical Awards from the Academy of Motion Picture Arts and Sciences. The Academy's Web site (http://www.oscars.org/awards/scitech/about/) states:
In recognition of the critical role played by science and technology in the moviemaking process, the Academy has, almost since its inception, honored the achievements of pioneers in these fields whose work has advanced the motion picture industry.
First presented at the 4th Academy Awards ceremony in November 1931, Scientific & Technical Awards are conferred in recognition of original developments that result in significant improvements in motion picture production and exhibition.
Scientific and technical achievement is awarded on three levels: Technical Achievement Award (certificate), Scientific and Engineering Award (bronze tablet), and Academy Award of Merit (Oscar statuette)...
Presentations of each year’s honors are made at a formal dinner held prior to the Oscar ceremony, which has become a highlight of the Academy Awards season. If one or more Scientific and Technical Academy Awards of Merit are awarded in a given year, the event is videotaped and portions are edited into the Oscar telecast...
[http://www.oscars.org/awards/scitech/winners.html] Among the awards voted by the Academy’s Board of Governors, the Gordon E. Sawyer Award (an Oscar statuette) was presented to Ed Catmull for his lifetime of technological contributions to the industry.
Mark Kimball was awarded the John A. Bonner Medal of Commendation for his "dedication to his craft and service to the Academy."
Information about each of these computer scientists is presented below:
The Academy’s Board of Governors voted the Gordon E. Sawyer Award to Ed Catmull, a computer scientist, co-founder of Pixar Animation Studios, and president of Walt Disney and Pixar Animation Studios, for his lifetime of technical contributions and leadership in the field of computer graphics for the motion picture industry.
"Ed is one of the rare individuals who can bridge the space between science and art," said Academy President Sid Ganis. "His vision, ingenuity and groundbreaking designs have made the impossible possible--for filmmakers and movie audiences around the world."
Catmull, currently president of Walt Disney and Pixar Animation Studios, founded three of the leading centers of computer graphics research--the computer graphics laboratory at the New York Institute of Technology, the computer division of Lucasfilm Ltd., and Pixar Animation Studios.
In 2000 Catmull, Rob Cook and Loren Carpenter received an Academy Award of Merit (an Oscar statuette) for their significant advancements to the field of motion picture rendering as exemplified in Pixar’s "RenderMan." The software, which produces images used in motion pictures from 3D computer descriptions of shape and appearance, has been used in 45 of the last 50 films nominated for an Academy Award in the Visual Effects category.
Catmull previously received two Scientific and Engineering Awards: in 1992 as part of a team for the development of "RenderMan" software, and in 1995 as part of a team responsible for pioneering inventions in Digital Image Compositing. He also shared a Technical Achievement Award in 2005.
While at Lucasfilm Ltd., Catmull managed development in the areas of computer graphics, video editing, video games and digital audio.
Catmull earned Bachelor of Science degrees in computer science and physics and a Ph.D. in computer science from the University of Utah. In 2005 the University of Utah presented him with a honorary doctoral degree in engineering.
Mark Kimball, a computer scientist and motion picture technologist with more than 28 years experience in the movie industry, was voted the John A. Bonner Medal of Commendation by the Academy's Board of Governors...
Kimball’s career began in 1978 at the Jet Propulsion Laboratory as a system engineer with the Deep Space Network. In 1980 he moved to Walt Disney Productions, transferring in 1985 to Walt Disney Feature Animation, where he spent nearly two decades as the CAPS logistics system lead, a senior software systems specialist, a consulting engineer and finally as chief technologist. From 2004 through 2007, Kimball was director of digital production for The Walt Disney Company. Currently Kimball works as an independent media technology systems expert.
Kimball’s feature credits include "Tron," "Beauty and the Beast," "Aladdin," "The Lion King," "Pocahontas," "Dinosaur" and "Atlantis: The Lost Empire"...
Kimball earned a Bachelor of Science degree in engineering from UCLA and a Master of Science degree in computer science and distributed systems from West Coast University in Los Angeles.
Two educators who are now fully trained NASA astronauts will make their first journey into orbit on space shuttle Discovery's upcoming mission to the International Space Station. During the STS-119 mission, Joseph Acaba and Richard Arnold will step outside the station to conduct critical spacewalking tasks. Acaba taught at Melbourne High School and Dunnellon Middle School in Florida. Arnold taught science and mathematics at several schools in the U.S. and overseas, including John Hanson Middle School in Waldorf, MD.
Discovery is targeted to launch from NASA's Kennedy Space Center in Florida on March 12 for a 2-week mission. The shuttle will deliver the space station's fourth and final set of solar arrays, thus completing the complex's backbone, or truss.
The arrays will provide enough electricity to power science experiments and support the station's expanded crew of six. Altogether, the station's arrays can generate about 120 kilowatts of usable electricity--enough to provide about forty-two 2,800-square-foot homes with power.
The 14-day flight will include four spacewalks, each lasting about 6.5 hours, to help install the S6 truss segment to the right side of the station.
STS-119 is the 125th space shuttle flight, the 28th flight to the station, the 36th flight of Discovery, and the first flight in 2009.
Detailed interviews were conducted with teachers Joseph Acaba
and Richard Arnold, discussing their backgrounds, teaching experience,
and the current mission. Transcripts of these interviews are available
at the Web sites below:
Video messages by these astronauts for teachers are available at the following Web sites:
For an overview of the current mission, visit the following Web site:
Each of the three sections of the California Mathematics Council sponsors an annual conference. Information on these conferences is provided below:
= CMC-Central Section (CMC-C): CMC-C's Algebra Symposium will be held on March 13-14, 2009 at the Embassy Suites in Seaside (Monterey County). Information about registration and room reservations can be found at http://www.cmc-math.org/SLOreg (early registration rates are available through March 1).
CMC-C President Mike Lutz writes: "The timing of our Algebra Symposium could not be better. Following is a description of the keynote address that will be given by David Foster at the banquet on Friday, March 13: 'California eighth graders are in limbo! There is a rising failure rate in college prep mathematics. The state financial health is seriously impacting schools. All this comes at a time when schools are already struggling, with mixed success, to meet the needs of an ever-increasing student population in algebra. There aren’t any silver bullets or easy remedies for this challenge, but we do know from research and experience what it does take to significantly increase the achievement of students in mathematics. This presentation will share lessons learned and statewide data. We will share information about high leveraged assessments, intensive professional development and support strategies for struggling students. In crisis state, teachers need to take the lead and do what is right for students.' Saturday's sessions will follow up with grade-specific strategies.” Visit http://www.cmc-math.org/SLOreg for a preview of conference speakers and topics.
= CMC-Southern Section (CMC-S): The CMC-S conference (http://WWW.CMC-MATH.ORG/PS) will be held in Palm Springs on November 6-7, 2009. This is the largest of CMC's three conferences. The Palm Springs Convention Center is the hub of the conference, along with the Hilton, Spa, Wyndham, and Zoso hotels. Speaker applications for the CMC-S conference are expected to be available at http://www.cmc-math.org/PSspkr next week.
= CMC-Northern Section (CMC-N): The 2009 CMC-N conference (http://WWW.CMC-MATH.ORG/ASIL) will be held on December 4-6 on the Asilomar Conference Grounds (Monterey Bay Peninsula). Those interested in speaking at this conference should visit http://WWW.CMC-MATH.ORG/ASILspkr for more information. Proposals are due by April 10.
COMET is sponsored in part by a grant from the California Mathematics Project.
COMET is produced by:
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