Quotes and Excerpts - Management

Transformational MATH

See The Evolution of Math

In 1994, the standardized California Learning Assessment (CLAS) test used this question to assess the math knowledge of California's eight graders:

"A FOREST fire has destroyed 3,000 trees. To prevent erosion, new trees must be planted. Students from your school want to help replant the trees. Each student is given two trees to plant.... On the first day of replanting, one student plants both his trees in the forest. On the second day, two students plant their trees. On the third day, four students plant their trees, and so on. `

How many days will it take to replant the forest on this schedule?

Explain your plan to the principal so that you can convince her to help get students involved in replanting the forest."

Debra Saunder's editorial, There Is No One Answer, in the San Francico Examiner (2-1-1995) explained what happened:

"As I reported, the test's scoring guidelines awarded a lesser score to a student who got the right answer (10 1/2 days) but did not explain his answer well than its score for a student who gave the wrong answer (450 days) but a pretty note to the principal accompanied by a happy face....


"I received a letter from Susan Cottine, who headed the team that hatched the replanting question and scoring. Cottine explained that students received partial credits for incorrect answers because the question was '`an intentionally ambiguous problem in which no one pattern can be considered the absolute answer.'


Apparently, state educrats have decided that there isn't enough uncertainty in the world, so they needed to inject some extra ambiguity into junior high math. Why not one answer?


Cottine's letter explained her philosophy of teaching, which is evidently predicated on the belief that children will find answers to equations naturally if not hindered by pre-ordained methodologies. 'I validate different solutions that are mathematically appropriate,' she wrote, '`because I want my students to become more powerful problem-solvers and to be willing to risk exploring ideas in non-traditional ways.'


"...are they learning math? Not according to mathematics and computer science Professor Wayne Bishop, who said, 'Intentionally vague' questions are 'designed so that nobody gets penalized for not knowing much.'"


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