Have you ever wanted to start an argument at a math teachers convention? Start by asking one simple question: “Should students be allowed to use calculators in math class?”
Most of us know all the ways calculators can be misused in math class. I’ve seen middle and high school students use calculators to answer questions like ‘7 x 0,’ or ‘4 + 1.’ When students use calculators for these questions, even the most permissive educators bristle.
But calculators can also be a useful tool. Adults use calculators all the time in the real world. Should we prevent students from using a resource that can make their lives (and ours) so much easier?
As with most questions in education, there is no single right answer. Calculators have the potential to improve the classroom experience for many students. But they can also prevent students from developing mathematical fluency.
How should educators decide when to allow calculators, and when to keep them tucked away?
Why You Should Allow Calculators in Your Math Class
There’s something that feels natural about allowing calculators. I rely a lot on mental math. But when I can’t solve a problem mentally, I don’t whip out paper and pencil and start doing long division. I take out my phone and get a quick and easy answer. One that’s guaranteed to be correct.
Most math teachers are familiar with the tyranny of the pacing guide. If we’re expected to teach algebraic expressions, we don’t have time to go back and teach “math facts” from all the prior grades. The year would be over before we finished the first unit.
So with that in mind, here are four reasons why teachers should allow students to use calculators in class.
1. Fewer Rules to Enforce
Schools have a lot of rules. The more we create, the more we have to enforce.
When we’re focused on enforcing rules, we create classrooms that are more teacher-centered and less student-centered. As a result, students feel less ownership of their learning. If we want students to become motivated, creative thinkers, we need to give them more opportunities to make decisions.
Some rules are necessary to create an environment that supports learning. Students can’t hit each other or throw things around the room. But limiting the number of rules saves our time. And it helps students understand which rules are most important.
2. Relevance and Authenticity
Math class has a relevance problem. Many students wonder whether the things they learn will benefit them in the outside world.
This problem relates closely to the authenticity problem. Does learning in schools match learning in the outside world? Do the ways we measure learning predict real-world success?
Allowing students to use calculators is one small way to address these issues. In the real world, having a calculator is an advantage. When I’m house-hunting, I want to know what my mortgage payment will be. And I’m certainly using a calculator to figure it out. I might even use an online mortgage calculator.
Learning to use tools appropriately is both a life skill and a mathematical practice standard. By incorporating technology, we can help students learn math while developing technology skills.
3. To Limit Memorization
The role of memorization in school remains a hotly debated subject.
At one extreme, you have strict traditionalists. They argue that we can’t teach students deep thinking until they have accumulated an arsenal of factual information. And they believe memorization is the way to accumulate this information.
On the other side are the beliefs that learning occurs naturally, and that students of any age are capable of conceptual learning.
There is truth to both sides. Remembering is important. But our brains are designed to remember the things we use on a regular basis. And to discard information that we don’t use regularly.
This is why memorization is mostly ineffective as a long-term learning strategy. If calculators save students hours of staring at multiplication tables, or anxiety over timed tests, I’m all in favor.
4. Speed and Efficiency
There’s no arguing that calculators are better at calculating than humans are. Whether working with big numbers or small numbers. Addition or square roots. The calculator has the edge every time.
Not only do calculators work more quickly, but they’re more accurate. The only time a calculator makes an arithmetic error is when we press the wrong button.
Why You Shouldn’t Allow Calculators in Your Math Class
While there are many reasons to allow students to use calculators, there are just as many reasons to avoid them.
Just as calculators feel like the right solution for finding a mortgage payment, I don’t like using them to calculate a tip. On a $40 check, I add $4 (one-tenth). Then I double it (assuming the service was adequate). Finding 20% is too easy to need a calculator.
And there’s a reason we teach math in school. If students are just punching numbers into a calculator, are they really learning anything?
Here are four reasons why you shouldn’t allow calculators in math class.
1. Conceptual Understanding
Once upon a time, math class was designed to teach students arithmetic. At least until eighth grade.
The reason states adopted the common core standards was to balance procedural with conceptual learning. (While many states are now rebranding the common core standards, the underlying concepts and progressions are nearly identical).
Concepts add richness to math. They help students access higher level math. And conceptual understanding is a key ingredient for application — understanding how to use math in everyday situations.
The use of calculators doesn’t support any of these.
2. Number Sense, Fluency, and Mental Math
Calculators are meant to calculate, or find answers.
But the goal of math class isn’t just to get answers. The goal is for students to develop skills that they can use later.
Students should become fluent with math in the way they are fluent with language. It’s fine to use a dictionary or a thesaurus to learn new words and definitions. But if you rely on them for every conversation, you aren’t really speaking the language.
Students can develop fluency and mental math skills without a calculator. Visual models and number sentences help students find answers while also developing number sense, mental math, and problem solving abilities.
3. They Don’t Always Work
There are also situations where calculators simply don’t work.
A standard calculator has a bear of a time with a simple fraction, like ⅓. Some savvy students may figure out that they can use division for a fraction. But if I ask for ⅓ + ½, I want ⅚, not 0.83 repeating.
And try entering a simple number sentence like “4 + _ = 10” into a calculator.
Students who are fluent in the language of numbers can handle these with ease. But students who rely too heavily on calculators lack the flexibility to adapt to novel situations.
4. They Short-Circuit the Learning Process
Learning math isn’t meant to be as efficient as doing math. When I give students a problem to solve, it’s not because I’m dying to know the answer.
I’m creating productive struggle, because that’s how students learn.
I can’t tell you how many times I’ve seen a student feeding answers from a calculator into an online platform. One hand on the calculator, one on the keyboard. I always ask the same question: “If the computer is asking the question, and the calculator is answering it, what do we need you for?”
When math class turns into ‘data entry class,’ something has gone terribly wrong.
Given the benefits and drawbacks of calculator usage, many teachers just pick a side and go with it.
But reflective educators judge each situation on its own merits. At the end of the day, we should allow calculators when they support our learning goals.
The following questions can guide you in deciding when to use calculators and when to put them away.
Would You Use a Calculator?
This is the first question I ask myself when deciding if calculators are appropriate.
My parents tell me how they used to use tables to look up logarithms and trigonometric functions when they were in school. Today this seems insane.
I enjoy mental math. When I’m figuring out a tip or splitting a check, I do it in my head. If it’s too complicated to do mentally, I will use a calculator. If there are too many steps, I’ll make notes.
One thing I never use is the traditional algorithm. These were developed centuries ago because they made efficient use of ink, but they are fast-becoming obsolete. Traditional algorithms are tedious. They don’t promote understanding or fluency. They make students dislike math. And it’s too easy to make mistakes with them.
I know some students still need to learn the algorithms for state tests. But unless there’s a state test consideration, I would allow a calculator over an algorithm.
What is the Learning Objective?
The other question we should ask ourselves with any learning activity is “What do I want students to learn?”
If we’re just trying to get through the book or “cover” the standards, we may use calculators when they don’t make sense. Or we may ban them when they do.
By approaching each lesson with intention, the question becomes fairly simple. “Does a calculator support the learning objective? Does it detract from it?” If the answer is ‘neither,’ let the students decide.
But be sure to recognize that a standard is not a learning objective. When teaching ‘slope,’ for example, I think it’s important to put the calculators away. Sure, we can plug points into a formula and find the slope using a calculator. But does that mean students get the concept?
Slope is a complex concept that asks students to combine several foundational concepts. They need to understand the coordinate plane. They have recognize subtraction as the difference between numbers, and the change in ‘x’ and ‘y’ as examples of such a difference. And they need to understand that the differences represent a proportion. Finally, they need to understand how proportionality can be expressed as a fraction or as division.
As students are connecting all these concepts, I don’t want them to rush to the calculator. They need to take the scenic route, by working these out mentally, drawing visual models, or writing number sentences.
On the other hand, if a student is finding the area of a 45.78” by 2.06” rectangle, I want them to focus on the concept of area. Not waste working memory on a lengthy calculation. Here, I’d allow the calculator.
Is it a Scaffold or a Crutch?
A scaffold allows construction workers to perform repairs or renovations on a building. When the repair is complete and the scaffold removed, the building stands on its own.
A crutch helps us keep weight off a broken bone. But in doing so, it also prevents the muscles from working. When the bone heals, we take away the crutches and begin the work of rebuilding the muscles that have atrophied.
Too often in upper-elementary and middle school, calculators are used as a crutch. We may feel students “should have learned their facts earlier.” Or we may worry that we won’t have time to cover “the basics.”
But this is the exact situation where we should not use calculators. One way or another, these students need to build their number sense. If we rush them through content to pass a test, we are sabotaging their growth as mathematicians.
That doesn’t mean students who struggle with arithmetic should never use calculators. But the calculator needs to be part of an overall strategy. If they use calculators today, what am I doing tomorrow or next week to address their needs?
Does the Calculator Teach a Skill?
A calculator can be used to teach specific skills. Have the class to add ‘7’ to itself thirty times. Or have them compare ⅓ to “1 divided by 3” on a calculator.
Scientific calculators can help students develop a deeper understanding of how altering an equation impacts its graph. In upper level math, learning to use the calculator becomes an end in itself.
In these cases, students learn valuable skills by using a calculator. Skills they might not be able to learn without one. In those cases, it’s easy to justify using a calculator.
Alternatives to Calculators
If your students struggle with basic operations, a calculator can seem like a quick fix. But if we fail to address the underlying issues, the problems keep rising to the surface.
I remember working with a 6th grade teacher whose students struggled with ratios and proportions. Before addressing the grade-level challenges, we introduced an adaptive online platform.
Even though his students were working on content from 2nd and 3rd grade, it made a difference. One day, he came to me and said, “It’s amazing. My students suddenly understand what I’m talking about when I teach my lessons.”
Mathematical concepts connect across grade levels. When we help students develop foundations, it’s easier for them to learn grade-level skills.
Visual Models: Incorporating visual models is an excellent way to build fluency. Arrays, area models, and number lines help students understand the relative size of numbers and the meanings of operations. This helps them improve computation in a way that sticks.
Number Sentences: Where visual models build numeracy, number sentences support flexible thinking. Instead of using an algorithm or a calculator, students can rewrite “99 x 8” as “(100 x 8 ) – 8.” This ability to reason can support mastery of basic facts and complex calculations.
The Sieve of Eratosthenes: Introducing this simple tool is one of my favorite lessons. It’s a fun activity that helps students develop base-10 understanding, learn times tables, and perform two-digit addition.
Personalized Learning: Students need time and space to work at their own levels. Dedicating as little as 30 minutes a week to personalized learning can revolutionize your math class. With an adaptive platform such as IXL or Khan Academy, students can develop fluency. All without any additional grading or planning on the part of the teacher.
The Teaching Makes the Difference
Calculators can be a valuable tool in support of high-quality math instruction. Or they can be a crutch that prevents learning and hides misconceptions.
As with any classroom tool, the teaching is what makes the difference.
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Jeff Lisciandrello is the founder of Room to Discover and an education consultant specializing in student-centered learning. His 3-Bridges Design for Learning helps schools explore innovative practices within traditional settings. He enjoys helping educators embrace inquiry-based and personalized approaches to instruction. You can connect with him via Twitter @EdTechJeff