Do We Really Need to Learn to Carry the One?

I've been writing this post in my head all week and was going to post it to In Another Place, my other blog, but it seems a good way to get started at Classroom 2.0. Twice this past week, I heard two different people make essentially the same statement: the rise in the use of calculators has contributed to the deterioration of math skills in students. Because they can just punch in the numbers, they reason, they aren't really learning to do math.

I understand what they are saying, I guess, but I just don't buy it. Let's take learning to add as an example. There are two parts here: the concept of addition and the calculation of addition. The calculator doesn't replace the first part. You need a basic conceptual understanding that when you have three apple and someone gives you four apples, you are going to have to use addition to figure out how many apples you have. Assuming I've got that understanding, does it really matter what technology I use for the calculation part?

I don't think so. We learned to do addition the way we did because calculators were not ubiquitous. OK, OK, I can hear you saying, "But are calculators ubiquitous?" They certainly could be without too much trouble.

Here's my essential question: Are we far enough into the 21st century that we can completely abandon teaching students the old calculation method. Because I am bi-lingual with calculation, I can use a calculator OR use a pencil. I know how to carry the one. But, I remember when I couldn't do it and it was really frustrating. Long division was even worse. I understood the concept, grasped it pretty quickly in fact; I struggled with the calculation part, and even now, I'm not completely confident in my skills, so I will choose the calculator as the calculation tool.

I am definitely interested in what others think about this. Please comment or post your own entry. And, I'm wondering what other things we've always taught that we should be thinking about leaving behind (handwriting leaps to my mind).

Views: 19

Comment by Karen Richardson on June 3, 2007 at 10:57am
Is this an example of the adage, "Those who forget the past are condemned to repeat it"? You have a historical view of tool use that I don't think others consider when thinking about technology. They go for the gut instinct based on a much shorter time span: that isn't how we did it when I went to school.
Comment by Sylvia Martinez on June 3, 2007 at 11:42am
This is interesting. It really highlights the vast difference between "math" and "algorithms". We spend a lot of time teaching students to memorize ways to solve problems, sometimes using tools (like calculators, pencils, or slide rules) or sometimes using algorithms (FOIL, long division, carrying the one). That's not math, that's arithmetic.

Efficient computation is not math either.

Constance Kamai did a lot of research with children showing that teaching algorithms is actually harmful in their development of the mental models that help them grow in their own capacity to solve math problems. I saw her speak once, she showed videos and gave examples like first graders who could answer simple math problems easily, but after a year of "math" start to doubt their own knowledge, instead fall back on trying to guess what arithmetic operation is expected of them (saying things like, "do i plus or minus?" in response to the same simple math questions.)

Constance Kami research is hard to find online, but there are lots of great videos about her work that are often found in university lending libraries. Another person working hard in this vein is Tom O'Brien, here's his website:

He makes math games and software, writes puzzle books and also writes pretty amazing articles about math for young children. Read "Parrot Math" for sure.

Confusing calculator use with math ability is a symptom of this mistake.
Comment by Robert Ponton on June 6, 2007 at 10:16pm
This very controversy is being played out by various raconteurs both young and old on You Tube. The first video listed below is 15 minutes long but very interesting. Videos 2-4 are rebuttals and Videos 5-6 feature students with opposing viewpoints. My favorites are videos 8 and 9 which offer the best evidence for algorithms gone wild! Enjoy.


1. Math education: An Inconvenient Truth

2. A Response to Math Education: An Inconvenient Truth Part 1

3. A Response to Math Education: An Inconvenient Truth Part 2

4. Another Response

5. Math with Madeline

6. Math with Mason a Rebuttal to Madeline

7. The New Math

8. Abbott and Costello

9. Ma and Pa Kettle
Comment by Karen Richardson on June 7, 2007 at 7:31am
Thanks, Robb! The first video is VERY interesting, particularly coming from a NASA scientist. Well worth the time to get an understanding of a different perspective.


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