Viewing posts tagged mathematics

Arthur Benjamin: Drop calculus, mainstream statistics

A short video with a compelling argument from TED:

Someone always asks the math teacher, “Am I going to use calculus in real life?” And for most of us, says Arthur Benjamin, the answer is no. He offers a bold proposal on how to make math education relevant in the digital age.

Study: Calculators okay in math class

…but, only if students know the math first.

Media guru Griffin Gardner forwarded this article from ScienceDaily, which suggests that calculators are useful tools in elementary-level mathematics classes.  Citing research by Bethany Rittle-Johnson and Alexander Oleksij Kmicikewycz at Vanderbilt, and recently published in the Journal of Experimental Child Psychology, ScienceDaily writes:

“So much of how you teach depends on how you market the material – presentation is very important to kids,” Kmicikewycz added. “Many of these students had never used a calculator before, so it added a fun aspect to math class for them.”

“It’s a good tool that some teachers shy away from, because they are worried it’s going to have negative consequences,” Rittle-Johnson said. “I think that the evidence suggests there are good uses of calculators, even in elementary school.”

From the JECP article:

The impact of prior knowledge on the benefits of generating information highlights an important constraint that teachers should consider. Initial practice in generating answers seems important to support procedure acquisition; once procedures are learned, the benefits of generating answers may be reduced or eliminated. This converges with teachers’ beliefs that ‘‘calculators should be used only after students had learned how to do the relevant mathematics without them” (Ballheim, 1999, p. 6). Reading answers from calculators does offer some potential benefits for higher knowledge students; it increases opportunities for practice of individual items and removes exposure to incorrect answers. Associative memory models predict that greater exposure to problems and their answers improves recall of the answers and that exposure to incorrect answers decreases recall of correct answers (e.g., Shrager & Siegler, 1998; Siegler, 1988). In the current study, using calculators increased the number of times the problems were practiced and decreased the number of errors during the study session. This may explain why higher knowledge students did not seem to benefit from generating answers. Over additional study sessions, benefits of calculator use for learning arithmetic facts may accrue. More generally, teachers should consider the potential trade-off in practice using procedures and frequency of exposure to correct information and should consider that this trade-off may vary for students with different knowledge levels. (p. 80)

The Chinese are using hand-held learning devices to help them pass English exams, and the U.S. is starting to see the benefits of the use of calculators in the classroom.  Is “ethical cheating” becoming mainstream?

The inconvenient truth about "Math education: An inconvenient truth"

I’m not sure how to comment on this one. The most efficient algorithm for me to solve the math problems she steps through is to use tools that are immediately accessible to me: by pressing the calculator button on my keyboard, using the calculator function in my cell phone, or use a standalone calculator. The most efficient method for me to understand what’s going on in the math problems is somewhat different. While the “standard” algorithms McDermott promotes are very effective in solving problems, they require very little understanding of the math involved.

The bottom line is that we have the tools to solve complex math problems easily. While the new methods try to emphasize on understanding the mechanics of the problems, I doubt the abilities of parents and most teachers to have enough of a full grasp of these mechanics to teach the underlying principles of mathematics effectively.

We need to decide if we want students to become better calculators or become better applied problem solvers. I prefer the latter. In that case, we should aggressively adopt the most efficient method for solving math problems by embracing calculators and other tools to solve these problems … even on tests. With the tedium of solving problems put aside, we can focus on building the capacities of learners to understand the underlying mathematics, and apply their creativities toward finding ways to solving new and complex problems that have meaningful applications for each learner.Картини