A gas station sells soda in three sizes. A 20-ounce cup costs 80 cents, a 32-ounce cup is 90 cents and a 64-ouncer goes for $1.25.
Traditional: What size offers the most soda for the money?
Connected: If the gas station were to offer an 84-ounce Mega Swig, what would you expect to pay for it?
A student, for instance, could argue that the 84-ouncer would cost what the 20-ounce and 64-ounce cups cost together. Another student could say that soda gets cheaper with volume, and then choose an answer based on some per-ounce price slightly less than what was given for the 64-ounce drink.
Or a student could skip calculating the per-ounce prices and just pick a number: $1.50 seems about right, based on my knowledge of real-life pricing strategies.
On one side, those who support Connected Math say that engaging students by presenting problems as real-life scenarios, often with no absolute solution or single path to arrive at an answer, fosters innovation and forces students to explain and defend their reasoning as they discover mathematical concepts.
The other side says the approach trades the clear, fundamental concepts of math, distilled through thousands of years of logical reasoning, for verbiage and vagary that may help students learn to debate but will not give them the foundation they need for more advanced mathematical study.
. . . University of Wisconsin-Madison math and computer science Professor Jin-Yi Cai began to become concerned with Connected Math when he saw the questions on his seventh-grade son’s test.
He went to the UW Math Library to investigate the textbooks, and he said that he was dismayed to find them “thicker than the collected works of Tolstoy.” Where the Chinese math books he remembers fondly were thin and contained concise explanations of math’s fundamentals, these books were cumbersome and full of long story problems and written passages.
“It goes around and around and things never really get down to the really crisp, elegant, basic fundamental principles,” Cai said of the Connected Math texts.
“It takes away the elegance, it takes away the beauty, it takes away the most basic logic structure. And the students are left with a vague, touchy-feely idea,” he said.
Cai and UW-Madison mathematician Melania Alvarez, who is running for school board, also object to all the essay writing required by Connected Math. Writing isn’t math, they say.
My algebra teacher, Miss Diedrick, said that math is a language of its own.
Update: Alvarez lost her school board race.