All too often, I run into teachers (both preservice and inservice) lamenting that kids are using calculators to compute something simple, like 6 x 7. These teachers express their frustration by threatening to not let kids use any calculators until the kids prove that they know their facts. And there will be no calculators for any simple computations. I understand this thinking but I am not sure it will achieve the desired result - wise calculator use (i.e. phronesis).

Problem is, if teachers are the ones deciding when their students can or cannot use calculators, then students are not able to practice this critical-thinking skill for themselves. Consequently, whenever a calculator is available in the future it can be used because that was what the students learned in school. As an alternative to controlling calculator use, I suggest a couple of activities that can help students to decide for themselves when it is appropriate to reach for the calculator.

*John Henry - The Steel Driving Man*. This article suggests several different experiments involving routines that can be completed by human or mechanical effort (eg: sharpening pencils). Students are asked to predict which method will take longer, gather data, and compare the results using box-plots.

The experiment I am most interested in involves computing multiplication facts with and without a calculator. I give pairs of students four worksheets like the one shown below.

Each of the four worksheets is different. As one student completes the worksheet, the other one uses a stop watch to time the effort (errors add an extra five seconds to total time). This is repeated until each student completes two sheets - using the calculator for one but not the other.

Classroom data are gathered and typically show that the students complete the worksheets quicker without a calculator. Discussing the results can provide students with an opportunity to reflect on whether or not it is efficient to use a calculator for basic facts. In the few cases when it is faster to use a calculator, the issue is usually that the student has a lot of wrong answers when computing without a calculator. Teachers must decide an appropriate course of action in these instances.

A second activity that I use to develop students' wise use of calculators involves a worksheet of multi-digit multiplication items. Instead of assigning the entire worksheet, I ask students to pick four items to compute without a calculator, four items to estimate, and four items to use a calculator on. The students are also expected to explain why they selected the approach to use with each item.

Calculator phronesis, the wise use of calculators, requires opportunities for students to experience activities that involve metacognitive aspects. We teachers will not always be there to guide students' choices, but this is not to suggest that we do not have a responsibility to help students to develop this ability. It is my hope that through these classroom experiences, students will be able to ask and answer for themselves the question, "When is it okay to use a calculator?"

What a great, commonsense piece. I taught 7th grade math for two years--once, in the 1980s and again in 2005. In the 80s, calculators were considered a terrible form of cheating and confiscated. In 2005, my kids were using graphing calculators by following a "push this, push that" schematic in their books without understanding what their answer really meant.

ReplyDeletePendulum swing, neither helpful to conceptualizing. You also added a new word--phronesis--to my vocabulary.

Whenever I meet with a group of educators I try to talk about "phronesis." It has become one of my favorite words. For me, it captures what is central to teaching.

DeleteEmpowering students to decide for themselves! I think you've gotten to the heart of our job as teachers. Thanks.

ReplyDeleteI appreciate your comment. I'm glad you think this approach is at "the heart of our job as teachers." It is good to know that other teachers also see empowering learners as important.

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ReplyDeletetop most in realated post .

You have something here, putting the responsibility in the hands of the student and giving her the tools to decide whether to use the calculator. My administration routinely gave birth to farm animals when they walked into my room and saw me giving the students any control. They wanted ANSWERS. Correct ones. Ones that would result in graphite in the right bubble every time. That's partially why I'm now a writer and not an educator.

ReplyDeleteThere's a cognitive load issue here for students from deprived backgrounds. My students, many of whom relied on finger counting to solve the four function computation part of any math problem. This week, I took a look at the cognitive load placed on the student by math anxiety and by dyscalculia (www.mathnook.com/blog). Both stressors constrict working memory. Anxiety operates on the central executive, a top-down load, taking students with lots of working memory and reducing that attribute. Dyscalculia just stuffs more of a load on working memory - a bottom-up load - than the brain can handle effectively.

I used to think skeptically about computer-assisted instruction (CAI) for math. It seemed to me that if the student got addition and subtraction as fast counting, and multiplication and division as fast addition and subtraction, they would be motivated to know the facts. The problem for most of these students (hard to say what is organic dyscalculia and what occurs developmentally through poor teaching and home follow-up) is that they gave up on themselves too easily, saying that they "didn't have a brain for math," or some such rot. I am starting to be convinced that any child who gets MDAS handled at reaction speeds gives himself a gift that is measurable in terms of working memory untaxed by anxiety and the need to figure out 6+7. Until the student develops automaticity in these facts, he should be able to make an intelligent, informed choice about assists.

I really admire your approach to letting the students judge for themselves when it is okay to use it. They will see how much it actually helps them and how it can hinder them in the same way.

ReplyDeleteIn the same way a computer does not learn mathematical concepts by performing calculations, students will realize that they do not learn much mathematics my simply making calculations without making sense out of them.

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