Over the buzz of excited voices and the distinctive clatter of dice on nearby tables, Jamie Cortez mutters a time-honored invocation before rolling his “bones.’'
“Daddy needs a new pair of shoes,’' he says with a grin.
When the first die tumbles to a halt, he notes his score and draws a matching number of circles on a piece of paper.
Then he rolls again, notes his score, and sketches stars within each circle corresponding to the dots on the face of the die.
His opponent, meanwhile, glumly suggests that she is fated to roll lower numbers than Mr. Cortez.
At first glance, the game seems less like a professional-development seminar for teachers than something akin to the action taking place not far away in the casinos that line the Las Vegas strip.
But Mr. Cortez and the other teachers of the Clark County school district’s Mathematics and Science Enhancement (MASE) program, gathered here at the Kirk L. Adams Elementary School, are playing for very different stakes.
Unlike the city’s “high rollers,’' they expect their big payoff to come over time, as they learn to help their peers develop the mathematical acumen needed to replace rote arithmetic lessons with a rich math pedagogy.
This morning’s lesson, for example, is designed to illustrate how the seemingly simple game of “circles and stars’’ can be the starting point for lessons in addition, multiplication, probability, and pattern recognition.
Proponents say MASE seems to be generating, often for the first time, excitement among elementary teachers about teaching math.
“I just came out of the university and, basically, the university showed me what could be possible, but not how to do it,’' Mr. Cortez says. “So when a slot opened up for our school [in the MASE program], I thought, ‘What an opportunity to learn what I didn’t learn.’''
If successful here in the nation’s ninth-largest district, the MASE approach to staff development could have important implications for reform in other large urban areas.
‘Constructivist’ Learning
MASE is an ambitious multiyear effort designed to produce two groups of mathematically and scientifically adept teachers, according to Linda Gregg, the MASE program coordinator.
The first, a group of 70 “teacher leaders,’' will eventually shoulder the responsibility for introducing new ways of teaching math to teachers in the district’s 127 elementary schools. A second group of site-based teachers will work with their colleagues at each school to help implement the program.
Before that work can begin, however, the prospective teacher-leaders will have spent at least two years attending hands-on workshops to learn the techniques of effective math instruction.
Although MASE is designed to improve the quality of both math and science instruction in grades K-6, staff development in science has lagged behind the math program.
In math, MASE is designed to help teachers apply the curriculum and teaching standards developed by the National Council of Teachers of Mathematics, which favor teaching critical thinking over rote computation.
It also builds on a “constructivist’’ model of learning, which holds that students come to the classroom with a host of personal experiences that help shape their learning and the ways in which they make sense of information. (See Education Week, Oct. 9, 1991.)
In the constructivist model, teachers act more as guides to help children build their understanding than as traditional dispensers of knowledge.
“A lot of children come to us without having an opportunity to think,’' Ruth Parker, an independent consultant to the MASE program, tells teachers of grades 3-6 during one workshop. “What we’re trying to do is build a memory bank [from which] the child can draw to solve problems.’'
Rocked Out of the Old Ways
But the MASE program also emphasizes that teachers must not only abandon their traditional classroom techniques, but also must be offered the chance to learn the math they need in ways that amplify the constructivist model.
Hence, the staff-development workshops concentrate on hands-on lessons in exercises like “circles and stars.’'
Ms. Parker often teaches model lessons during staff-development sessions to allow teachers to observe and learn from her mistakes.
“It’s really risky [to teach a lesson] in front of 40 kids that you’ve never given before,’' Ms. Gregg remarks.
Such rapid and sweeping change is demanding, particularly for teachers with limited math backgrounds, Ms. Parker adds.
Under the MASE structure, the teacher-leaders will each be assigned to a group of schools to conduct in-service training.
“By design, we won’t have leaders in-service their own school,’' Ms. Parker notes.” Their job is to rock people out of their old ways of doing things, and that’s terribly difficult to do with their own peers within the school.’'
MASE also is designed to train a group of “site specialists’'--teachers who will act as school-based liaisons between the teacher-leaders and their classroom colleagues, helping to ease the transition to new ways of teaching.
Another unusual feature of the program is that principals also have been invited to attend the staff-development sessions.
‘101 Reasons Not To Change’
Before the district launched MASE, Clark County’s approach to elementary math and science differed little from the national norm, Ms. Gregg observes. Elementary teachers focused heavily on simple arithmetic, and, if they taught science at all, generally read from a textbook.
Although the district’s staff-development programs in math and science frequently received federal funding, they produced “pretty sporadic’’ results, Ms. Gregg says.
“The idea came to me that in a [145,000-student] district, we did not have enough teachers that were able to give leadership,’' she says.
As an alternative, Ms. Gregg and others designed the MASE approach and applied for funding from the National Science Foundation’s teacher-enhancement program.
The foundation agreed in 1992 to support the four-year project, and the district began its first training sessions shortly afterward.
But while many teachers seem enthusiastic about the new approach, acceptance of the constructivist philosophy of the program is hardly universal.
Ms. Gregg discussed some of the lessons learned from the first full year of the MASE program at a meeting of urban districts committed to elementary math and science reform held in Inverness, Calif., last month. (See story, this page.)
While many prospective teacher-leaders are embracing change, she noted in a briefing paper that others “are finding 101 reasons not to change anything.’'
MASE is also designed to fill a need for competent math teachers in the early grades that is being exacerbated by the district’s ballooning enrollment.
Clark County officials estimate that the district will have to build roughly 100 new schools by 2000.
The goal of the MASE program is to insure that even if new teachers come to the district with minimal math skills, an organizational structure will be in place to help them learn both math content and successful pedagogy.
That aspect of the program could also have important national applications, because most districts lack any comprehensive means of upgrading teacher skills.
A number of critical reports have decried the level of math training required of most prospective elementary teachers. Experts contend that the generally weak math backgrounds of elementary teachers have hurt the math education given to most students.
‘Circular Problem’
An article in the January issue of the The American Mathematical Monthly, a publication of the Mathematical Association of America, argues that the solution to improving the math ability of elementary teachers lies in changing the attitudes of college professors toward teaching basic math to students who are not majoring in the subject.
In the article, titled “Future Elementary Teachers: The Neglected Constituency,’' Thomas W. Hungerford, a math professor at Cleveland State University, argues that the current difficulty in math education is a “circular problem,’' in which college professors criticize the weak math backgrounds of their students without recognizing that they are in large measure responsible for producing poorly educated teachers.
“Considering what is being done to improve other [math] courses, the lack of attention being paid to courses for prospective elementary teachers is astounding,’' Mr. Hungerford asserts.
But Ms. Gregg and Ms. Parker maintain that much work also needs to be done to help teachers already in the field.
"[Teachers have] learned, through school, that [math is] a horrible subject and they hate it,’' Ms. Gregg says. “Through MASE, they’re learning a lot of the mathematics themselves that they never learned before.’'
Mr. Cortez concedes that his math education ended in high school, and that he never really grasped the importance of math in everyday life.
But his work in the MASE program, he says, has caused him to abandon his “by the book’’ approach to math teaching.
“My students ask for math now,’' he says. “And I enjoy teaching it.”
