##### A MiddleWeb Blog

I have been thinking about the issue of calculators in the classroom for a long time. Up to now, I’ve chosen not to write about it because I’m still not exactly sure what I think is best. But I’d like to hear what other math teachers think.

When I first started teaching, I was so excited about using calculators. I thought back to when I learned my multiplication tables in elementary school. We had to take timed tests, and it was crucial to get a certain number of problems right.

To help me practice, my parents timed me at home. Even though I was able to memorize my multiplication facts with relative ease, it made a big impression on me and I remember it being a very stressful time.

I can only imagine what it would have been like if I had been a student who was having troubling memorizing those multiplication facts. As it was, I was really glad when the unit was over.

#### The wrong view?

As a teacher, my idea was that students would use their calculators to work their problems and they would learn their multiplication facts in due course without the tedious drill and practice that I went through. I now think that was probably the wrong view to take.

Even though I teach older students, many of them do not know basic multiplication facts. It’s not just multiplication, either. Many students struggle with combining positive and negative numbers, and fractions continue to be an area of weakness. I can’t help but wonder: is this a result of a dependence on calculators?

I have a classroom set of 30 TI-Nspire calculators, which we use almost every day. I’m grateful for the ease with which the calculators allow my students to explore a variety of concepts. However, I am concerned that using the calculators will hinder my students’ conceptual understanding.

#### Is getting the right answer enough?

Students can sometimes push the correct buttons on the calculator to get the “right” answer but still lack any real understanding. I’m also aware that some colleges and college classrooms do not allow the use of calculators, so I do not want to foster a dependence on calculators in my students.

Recently it became very obvious how dependent my students were when I removed the calculators from the classroom for a day.

When the students realized they would not be able to use a calculator, they were a little disheartened. They eventually recovered and actually did a great job on the activity. Even so, one student said, “This is the hardest thing we’ve done all year because I couldn’t use a calculator.”

It was good for me to actually see how much they relied on the calculator, even to perform very simple computations.

I have read many articles and studies which seem to provide somewhat conflicting information regarding the relationship between calculators and students’ achievement. Much of the research does seem to support a balanced integration for calculators in the classroom.

I certainly don’t advocate a no-calculator policy. I just need to find the right balance.

#### Maybe the problem is more about me

After consideration, I don’t think calculators themselves are the issue. In my case, I think it’s the way I have implemented their use. I was so enamored with their potential that I overlooked some of their limitations. The result was that I indiscriminately implemented the use of calculators for every lesson.

I am guilty of not taking the time during lesson planning to think about whether using a calculator will have a positive or a negative impact on students’ concept development and understanding.

From now on, I plan to be much more intentional with the use of calculators in my classroom. *Before *the lesson I plan to ask myself, what purpose will the calculator serve in this situation? Will the calculator help students deepen their understanding, or is it being used *in place of* actual understanding?

*After* a lesson, I plan to ask myself, what was the result of using the calculator? Did it improve students’ understanding, or did it just mask their lack of understanding? Also, were students so dependent on the calculator that they would be unable to function without it?

#### Common sense and timing

Here’s something else I have observed: Often students are willing to write down whatever is on their calculator screen, regardless of whether it makes sense in the context of the problem. Students seem to consider the calculator “all knowing.” For example, when solving for area, if the calculator shows a negative number the student will write it down, even though a negative number doesn’t make sense in the context of finding area.

As Kathleen Lynch-Davis (writing at the NCTM site) points out, calculators “do only what you tell them to do.” That’s a lesson that I need to impart to my students. I can do a better job of teaching them to judge the reasonableness of what the calculator tells them.

I’m also beginning to think that timing is a factor. Early on, when students are developing the foundations for a new concept, it may be better to leave the calculator out. Then, when students are exploring or looking to develop a deeper understanding, the calculator can help them dive in.

#### What is your experience with calculators?

I’m very interested in what other people think regarding the advantages and disadvantages of calculators in the math classroom. Also, what is the appropriate age or grade to first introduce calculators to students?

**Resources**

♦ Debunking the Calculator Myth

♦ Calculator Use in Elementary Grades

♦ Rethinking How We Use Calculators in Middle School

♦ What Impact Does Calculator Use Have On Test Results?

♦ Impact of Handheld Graphing Calculator Use on Student Achievement in Algebra 1

♦ The Calculator in the Elementary Classroom: Making a Useful Tool out of an Ineffective Crutch

**Photo credits**

♦ TI Nspire set – STEAM Middle School, Burleson, Texas

♦ Students using calculators – Ac2E Middle School Academy for Academic Enhancement Middle School, Rio Grande City, Texas

You bring up many good points. I have always thought that a calculator needed a extra step.

Student enters a problem

Student enters an estimate (if estimate is not in range another estimate is requested.

Calculator provides an answer.

I also find that students in HS classes have not done basic calculations. Once a week students took a 6 or 8 question quiz over basic calculations without using a calculator. These did not take long and provide students an opportunity to strengthen the those brain connections. Several students thanked me for this when applying for an after school job that required a “math” assessment.

Students do rely to much on calculators but so do adults. I do believe that during explorations such as looking at y = mx+6 and how the m changes slope calculator use is important.

Being intentional with calculator use is a good step.

Thank you for your comment! I love your idea about entering an estimate first! Students always need to consider whether their answer is reasonable. Great idea!

In the mid 90’s, I did a master’s thesis on calculator use and arithmetic skills. My study was controlled using one teacher (me) and 2 comparable classes of pre-algebra students. One class was forbidden to use calculators at any time, and was required to do all their computations by hand with paper and pencil evidence of the work (that took some parent cooperation, as well). The other class was required to do all their calculations with calculators, and comprehensive instruction on how to use calculators was part of the class structure. Other than calculator use, the instruction for the two classes was the same. Both classes were given the same pre-and post-test of arithmetic skills. Results were frightening to me. The class required to use calculators actually lost significant mental arithmetic skills in 6 months. The class forbidden calculators made incredible gains in arithmetic skills in those 6 months. I spent the remainder of the year in intense mental math remediation for those whose skills had deteriorated.

Since then, I have tried to use a calculator for computations that would be unnecessarily tedious by hand and discourage their use for basic arithmetic. I have been rather harsh toward that end when I see a student picking up a device to do basic arithmetic, and I continually remind the students that skills that are not consistently used deteriorate, rapidly. The hard part is convincing students that they need to be able to do the work without the ‘electronic idiot box’; after all, someone has to know how to be able to program the next generation of devices. It is an uphill battle.

I have been teaching for 26 years in middle school. I teach high school Algebra 1, Geometry Honors, sometimes Pre-Algebra, and this year I have picked up some accelerated 6th grade math.

Thank you so much for sharing your research! The fact that students lost “significant mental arithmetic skills in 6 months” is really alarming. Especially since, in my opinion, those skills are part of the foundation students need to be successful in math. However, I ‘m not surprised, I often see students use a calculator to perform a basic operation that should be almost automatic. Thanks again for sharing!

A very long time ago, I attended a mathematics teaching workshop/lecture by Dr. Lola J. May. She recommended not using calculators unless the students were doing word problems since we are assessing the students’ reasoning skills rather than their computational skills. Even then, the students need to write down what they put into their calculators. I have been using this method since that time with great success. Sometimes I let them check their answers after computational skill, but only with dividing with decimals.

Wow! That is a great suggestion! I hadn’t thought about the calculator being a tool for assessing reasoning skills. I like that! Going forward I am going to have to think carefully about why I am allowing students to use a calculator on an activity. Thank you!

I have to agree with all of the above. Michelle, thank you for your honesty and your reflective attitude. Linda, thank you for sharing your action research results.

The calculator is a good tool and can take the drudgery out of math computations, but too much of a good thing is definitely not a good thing. As an instructional coach I get into many classrooms. More than once this year, I have seen students, even students in advanced math courses, pick up a calculator to do basic computations that would be faster, easier, and likely more accurate if they took a moment to think. Computations such as 16 x 10 or 214 x 0.5 or 3000 – 50 should never require a calculator.

In situations where a calculator would be warranted, I require students to FIRST estimate a solution. Without this step, they fail to question the accuracy of the answer, the calculator gives them. And when asked how they arrived at a solution, I hear, “I did it on the calculator.” Wrong answer! Limiting the use of calculators will increase number sense in our student mathematicians.

Thank you for sharing your experience! I like the way you put it, calculators “can take the drudgery out of math”. That is the right use for a calculator, not as a substitute for reasoning or thinking. Also, the suggestion to estimate first is a great idea!

I stress multiplication table memorizing for all of my students because it it is often faster than a calculator and allows for an easy estimate to know if your result is close. It helps the student progress if the have some number sense as well as unit sense. Like hours per mile as opposed to miles per hour. I digress. My son was not allowed to use a calculator until second semester of Algebra 1. It helped him with math and many other courses which require number sense. I agree with not using them until the student can demonstrate a understanding of numbers and operations. They do need to learn how to use calculators too. I use mine almost every day.

Thank you for a great comment! You are so right, if a student doesn’t know their multiplication tables they don’t know if their answer makes sense. I also agree students need to use calculators, I just need to get better at knowing when they should use them.

I have fought this battle for 20 years. I have personal experience with calculator use from past work as an accountant. Using the calculator so much actually hindered my own ability too do basic math calculations in the grocery store, at dinner, etc. I have always stressed to my students the importance of using “the greatest calculator ever devised”, their brain. I don’t let them use it in the classroom unless it is a complex problem for the sake of time. I also stress to my students that the calculator is only as good as the person operating it. I find that even though I don’t allow them in class, they automatically use them at home for homework. We can’t control everything, but those who believe us impress the class everyday with their mental math capabilities.

Thank you for your comment! You made so many good points, I especially appreciated you sharing your experience as an accountant. Also your comment on “mental math” is something I’ve been thinking a lot about lately, because without some mental math ability it’s hard for a student to be successful. Thanks again!

You wonder if calculators contribute to not knowing facts, not being able to work with positive and negative numbers, difficulty with fractions, etc. i can tell you, as someone who began teaching in the 70s when most students did not have calculators, these problems have always been around. I did not notice them getting particularly worse with calculators with the exception of knowing multiplication facts.

Thank you for sharing! It’s so helpful to have input from someone who has had experience teaching with and without the use of calculators. I wondered if some of the deficiencies I noticed were problems that had existed before calculators- so thank you for addressing that!

Calculators work really well, as you pointed out, when the lesson is specifically designed to use the technology. Just using the calculator because it’s there isn’t appropriate. The issue I have is to meet CCSS standards at the high school level there isn’t a language that has students learning how to do basic calculations. Students are “magically” all ready for more rigorous problems and concepts. I cannot find in the standards where secondary students use rote practice of multiplication tables, or addition/subtraction timed exercises. Administrators require that we meet today’s standards but students are ill-prepared for the rigors of secondary standards. I allow them to use the calculators so that we can get to the “fun” or “deep” stuff required of today’s students.

I’m curious about calculator usage in other countries where students do better than us on the PISA tests. Does anyone know of a comparability study on this?

I have always required my urban students (ranged between 7th and 12th grade) to do all mental math. It has been a fight at the beginning of each of my 19 years as a teacher, but by December most students made significant improvement with them. Number sense only comes from practicing the relationships between numbers.

I have two decades’ worth of anecdotal evidence that my students, compared to other teachers’ “calculator-dependent” students in the same grade level, do much better at end-of-year tests; this includes students that receive special services and accommodations. Also, most of the students who go on to graduate from my district come back to me to report that if it weren’t for my requirement of them to do the mental math, they never would have done so well.

Math works. Mental math works for each student.