Turning on to math Math teachers explore new ways to reach students by Bob Mullin Traditionally. the "good math student" has tended to be of a particular type. Quite skilled at "memorizing and rcgurgilaling" textbook concepts, 10 use words of Portland State mathematics professor Marjorie Enneking, such a student could excel on tests and easily make hiS/her way through a typical public school math curriculum. HOwever, something was lacking. "Most exercises in lextbooks, even the so-caffed story problems, I don't consider real problems," says Enneking. "I would call them practice problems." Real problem-solving involves seeking answers in a way that isn't immediately obvious, she explains. "The dilemma in mathematics is thai ... kids art' nol bad in arithmetic skills-they have the basic facts all right-bul they don'l know what 10 do with them" says Enneking. "They don't know how to use them in any practical and creative way." This problem has been compounded by the increaSing numbers of students now laking math to meet .upgraded high schoof graduation and college entrance requirements. Many of these students lack the degree of abstract thinking skills thai marks the traditionally successful math student. In addition, according to Enneking, "very often, and rightfully so, these students don't see much connection between school math and real math thaI is used in the world." In response to this situation, Enneking gal together last summer with J. Michael ShalJghnessy, associate professor of mathematics at Oregon State University. to aHack the problem with 60 of the best middle, junior high and high school math teachers in Oregon, Washingron, Idaho and northern California. Their task: to find new ways of teaching math that would turn kid$ on to a subject Ihal all too often has turned them off. After spending three weeks sharing ideas-30 at PSU and 30 at OSU-the teachers returned to their schools during the past Scil001 year to implement these ideas with a variety of programs thai generally were built around one or more of the following alternative approaches: • A less formal introduction to geometry thaI begins with spatial visualization , a tudy of shapes and their properties that "relies heavily on physical models, hands-on activities, and application of geometry." • A new context for general math which uses a p r o b l e m ~ s o l v i n g approach and incorporates probability and statistics and the use of computers. • Inserting p r o b l e m ~ s o l v i n g into the traditional Algebra I and Algebra II curriculum, where p r o b l e m ~ s o l v i n g in a variety of content areas takes up at least two days a week and traditional algebra skills "not more than" three days a week. • New statistics and probability courses with an emphasis on "descriptive statistics" at the junior high (Grades 7 to 9) level and on "exploratory data analYSis, simulations of experiments on computer, and some hypothesis testing" at the senior high (Grades 11 and 12) level. • Increased use of computers in math, especially in p r o b l e m ~ s o l v i n g . During d break from semindr5, PSU math professor Mdrjorie Enneking (center, standing) O ~ f 1 I e d teachers from iJlI over the NOl'thwest as ,hey experimented with math games in d reslJUl'Ce room set up (01' the PSU workshops, fuoof'd by the Nationdl Science fouooa'ion. This summer, funded by a $356,314 grant from the National Science Foundation. the teachers met again on the two campuses, only this time they brought 60 new teachers wilh them. While the new teachers went through a similar i d e a ~ s h a r i n g experience, the old teachers served as mcntol'5 10 t h ~ new whire reaming leadership skills designed, according to Enneking, "to give them tools to be able to make changes in their school programs," "Suddenly the 'good math studenr' wasn't the best anymore. It was a very healthy thing to have happen." "The culminating activity will be to get the leaders' group bade again in the faU of 1987, hopefully with an administrator from each of their districts," says Enneking. "We think we need to make the administrators more aware of the good things happening so they can be more in tune with what their teachers are recommending . .. As for what was happened so far, Enneking says, "by and large the teachers who participated in the program last s u m m ~ r were very, very excited about the things they did." For example, Gwen Waite of Hermiston High School used spatial visualization techniques learned in last summers worksnop to help create what she calls a GEMS (Getting Enthusiasm in Mathematics) approach in her basic math classes, and her success became the topic of a newspaper article published in the East Oregonian newspaper. The article described how students used "bright-colored wooden cubes and sticks of varying lengths, plastic tape measures and M&Ms" to learn math concepts formerly taught "by rote." When Waite asked the students to place colored wooden rectangular pieces onto paper patterns, some students completed the assignment in a few minutes, but others found difficulty in fitting the pieces in the allotted space. "Research indicates some of us use the left side more than the right side of the brain, SO we will retrain the brain with this exercise, which gets both sides working together," the article Quoted Wai(e as telling her class. "You can see the problem instead of just putting it down on paper," said one student. "It makes it a lot easier because, somehow, iI's explained in mOre depth." Other teachers elsewhere reported similar success stories using techniques learned at the workshop. In addition, many participants began to share their work with others in in-service workshops and educational articles. The ideas of this new "folk math," as one staff member calls it, were catching on everywhere. The alternative approaches were nol without their frustrations, however. Enneking reports that teachers found some of the best math students under the old methods of teaching ran into difficulty dealing with hands-on materials. while other kids who were considered not SO bright in math were now succeeding, "Suddenly the 'good math student' wasn't the best anymore," Enneking says. "Actually, it was a very healthy thing 10 have happen." Another healthy aspect of the program has been its effe<::t on teachers. AI a lime when a shortage of math teachers is developing across the country, in part because existing teachers were finding other more profitable Or creative places for their talents, those teachers involved in the workshops have been energized by their discovery that other teachers care, too. "We found that the network and the support group that developed among teachers was a very important Outcome of this process," says Enneking. "They're talking to one another on the phone, they're helping one anolher, they're making arrangements to get to conferences. Many of them are already doing other workshops. These are very committed teachers." (Bob Mullin is a Portland free-lance writer who also teaches English at Aloha High School.) PSU Perspective, SUmmer 1986 1 ~ g t ! 7
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