Time and Time Again, Again
Time and Time Again
After her interaction with Andy and Sarah, Sally turned to look at the work of a third group of studentsLiz, Greta and Andrew. She noticed they had yet a third set of points because their container was a different size from the other groups.
Sally felt better about working with this group because they usually had the right answers and seemed to be strong in their computational skills. She could see that they, at least, were making the transfer to functional notation in their work. "What'd you get for your equation of the line?" Sally asked.
"We got something like y = (.45/7)x + 4 2/5 for the rational form and y = .064x +4.4 for the decimal," Andrew replied.
"Good. So what do x and y represent?" Sally asked.
"x is how many marbles you put in," answered Liz.
"And y, Greta?"
"How much the water goes up when you put the marbles in." Greta responded.
"How much did the water rise when you added 7 marbles?" Sally pressed a little bit, remembering Igor's instruction to push students until you were certain they really understood.
"4.85 cm," Greta answered.
"Sounds right," Sally accepted the answer but continued, "Are you all sure of Greta's answer?" for confirmation.
"No," replied Liz honestly, "but I think so. I don't see what else it can be."
"Well, Greta's right," Sally stated cheerfully and with relief that at least one of the groups in her class seemed to be getting the point of the exercise. "x is the number of marbles and y is how much the water rises."
Back at the Ranch
Alison stared out the window of her office at the gray November day. The sky matched her mood. "I need strong research studies as well as local data on math achievement in order to prepare my report for the Superintendent and the School Committee. I need to look at the new math program objectively and acknowledge that a few single-school studies find it does not work so well, but weren't those studies subsequently shown to be flawed?" she asked herself. "I've got to present information in a way that everybody can understand--and not take too much time doing it. I need a teacher who loves the program, and a teacher who has been won over. Should I invite Igor Strome? He certainly knows the state and national scene " She was mulling over how his presence might put off some parents when a phone call came in from Jack Mann. It didn't make her feel any better.
"Al, we gotta talk about the math workshops," he said. He recounted what he had learned in the last hour. At lunchtime, Jack asked Iris and Nicole how things were going in the math workshop sessions, and he had gotten an earful. Part of what he heard worried him. Nicole blurted out that the new math materials they were adopting were far worse than the old ones in terms of covering basic math skills. She predicted students would fare even more poorly on the TABS test as well as the Iowa test in the eighth grade. "Maybe they'll know how to think mathematically about probability and statistics," she told him, "but the problem is, they won't be able to double a recipe. Ha! This spells disaster. It's a terrible curriculum," she said. "Watch my words, this is a mistake. Parents won't stand for it," and she wagged her index finger at him for emphasis.
Iris, on the other hand, seemed delighted with the potential of the graphing calculator to convey the meaning for many students. "I've already seen the light bulb go on for a bunch of kids in my classes," she told him, excitedly. "I'd never have gotten this far if Igor, that's the workshop leader, hadn't pushed me. But he's a tough guy. Honestly I think he pushed Sally Elmore over the edge in the last session. He doesn't have a lot of patience, you know, and he just assumes that we know it all already. Don't tell Sally I told you, but I think she was crying in the bathroom during the workshop. She left at lunchtime because of Igor."
Jack pointedly asked Alison. "Is it true, Al? Is it true these materials don't teach the basics and won't help us get our test scores up? GAWD! I can just hear the parents now, let alone Superintendent Gross And where in the HELL did you find this Igor guy?" Jack's voice was rising, he was furious. "Who is he? I don't want Sally to be upset. She's new to West and I want her to stay to convey that caring ethos of the elementary schools that we need up here." She had been strong-armed into attending yesterday's session, by himself and by Alison. Professional development was great, but not at the cost of losing a caring teacher. "Time and time again, Al, we do the wrong thing for what seems to be the right reasons. We're not helping but hurting teachers."
Alison's heart sank. She didn't know what to do. How would she ever convince Sally and the other teachers, let alone her Superintendent and Jack Mann, that this new math program was best for kids? Furthermore, how realistic was it to think that a few in-service workshops would help prepare math teachers teach a math they never had, in ways they never experienced? Were these new standards-based curriculum ideas really worth it? She thought about a statement she once read in graduate school "Teachers are both the objects and the agents of reform." Could be both in Barberton, she wondered?
(1) Katherine K. Merseth and Molly V. Schen prepared this case for the National Science Foundation Teacher Enhancement Program and the Merck Institute for Science Education. Any viewpoints expressed in this case do not represent the views of NSF or the Merck Institute for Science Education. The names and places are fictional, though based on real experience. Arthur Proulx, Darien Lauten, Karen Graham, Melisa Collins and Steve Bensen of the University of New Hampshire developed an earlier version of sections of this case. A complete version of their case will appear in Windows on Teaching: Cases in Secondary Mathematics, edited by Katherine K. Merseth and published by Teachers College Press.