Saturday, October 18, 2008

Calculators ... Warning of Possible Harm - use wisely

Paul Dunham writes:

I've been cleaning up some of my work areas at home, and have come across a few things.
An eon ago (it seems) while preparing a paper during my credential program, I came across this article:

"Impacts of Using Calculators in Learning Mathematics"
by Tingyao Zheng


This paper argues that using calculators in learning mathematics may have negative effects if they are used inappropriately:

1. Students may lack conceptual understanding;
2. The procedural perception of a mathematical problem of those students who did not go through a successful structural development in learning algebra could be reinforced;
3. Sometimes the calculator delivers misleading information;
4. Students may develop undesirable problem solving behavior;
5. Differences from conventional notation and notation used with calculators may confuse students.

Suggestions aimed at reducing those problems are advanced.

from the conclusion:
" The discussion above together with the examples show us that concern for the negative impact of using calculators, especially graphing calculators, is very real. Because calculators are generally numerical in nature, students may not acquire solid conceptual understanding. Their view of mathematics will probably be more procedural and accordingly their problem solving skills may be limited. The development of their structural view about mathematics could also be hindered. Moreover, because of it design, a calculator may deliver misleading information and create confusion in learning notation."

I remember how odd it struck me that this conclusion was in stark opposition to the majority of the other "scholarly" papers I found. It was one of the first glimmers I had of how something was really amiss in the math ed world.



Anonymous said...

One argument that has not been raised against calculators, especially with the TI-84's are that students, primarily in middle school, are unfamiliar with the interface and cannot use them with the proficiency that is expected. Teachers spend more time debugging than teaching. It is impossible as math reform advocates claim to use graphing calculators at this age level and teach a class as rigorous as algebra. The graphs on a calculator display, look nothing like the sketches students are required to draw of lines and parabolas. Calculators are absolutely useless in a first year algebra class and should not be used except in college after students have some math proficiency. Augmenting instruction is fine, but calculators are not a replacement for thinking.

dan dempsey said...

I would disagree about the effort to enable students to use TI-82 83 or 84. It does not require a lot of instruction to get kids going efficiently.

I found these TI products to be much more user friendly than the TI 85 or most of the H-P professional grade stuff.

I certainly do not disagree that these calculators are creating an environment where a lot of mathematics is not being effectively learned. Without the TIs etc. there would be no Core-Plus and that would be fabulous.
Given international results and current post secondary remediation rates many of the NSF and NCTM actions of the last decade are not creditable.

Those deep conceptual understanding that Dr Ruth Parker et al have touted did not occur with the materials and philosophy she pushed.

She is yet another PhD expert on math with no undergrad degree in math. District offices are filled with math curriculum decision makers who know politics and the Club Ed game but do not know much math. The results of their actions are usually defective. They like to hire math coaches who like themselves are Ed Game experts but not math experts.

If you are looking to spend a whole lot of money and accomplish very little .... then look no further than Denver, Colorado or Seattle, Washington for a math plan. ... If you want a larger scale example try Dr Bergeson's Math leadership in Washington State ... now there is a waste of money without results.

Anonymous said...

That's interesting because my experience with the TI's was dramatically different.

There were actually two groups. First period was with a group of ninth graders that had taken Core 1 without calculators in eighth grade and then took it a second time with calculators in high school (extended algebra).

Students did not have the ability to make an appropriate sketch. Their sketches looked exactly like the display and they could not derive anything useful from it. Their answers were at best approximations to the nearest millionth (nonstandard).

The second group were mostly ELLs these kids did not know which keys to press. Also, we spent serious time debugging calculators. Mind you, I was forced to teach this filth.

Not surprisingly, this school has created a serious public relations problem with the community, much like Bergeson. Naturally, kids and parents steer clear of it. I'd call it a creationist's dream school (the almighty pumpkin's faithful elite).