Calculator in the classroom
Why They're Necessary, and When They're Not
Calculators are now in use in mathematics classrooms everywhere. They are used often in elementary classes, regularly in Junior High mathematics courses, and in every Senior High math and Science class.
This page will attempt to explain some of the reasons why calculator use has become such an integral part of the mathematics classroom, and what benefits and drawbacks exist for students as a result.
First, you need to be aware that calculator use is built into the courses which are offered to students. Teachers are expected to provide opportunities for students to use them, and students must become proficient in their use. High School mathematics courses are designed around the use of a scientific/graphing calculator. As a result, students in lower grades must know how to use a calculator properly. This is not to say, however, that calculators are to be used for all operations.
Junior High School:
Students in grades 7, 8, and 9 are exposed to many new ideas in mathematics, including the topics of integer and fraction operations, and measurement formulas. We'll use these topics to help explain where calculators are helpful, and when they should not be used.
One important benefit of using a calculator in the Jr. High mathematics classroom is that it lets students cover more material during the year. And there is more material to cover ... students in these grades learn far more mathematics than their parents or grandparents did at an equivalent level.
For example, the notion that formulas can be used to evaluate an area or volume requires that students perform many calculations, some of which would be quite lengthy if done with pencil and paper.
For instance, a typical calculation at the grade 8 or 9 level might look something like this:
when working out the volume of a cylinder. Multiplying decimals is a skill learned in grades 5 and 6, and is one that (hopefully) all Jr. High students can do, even a three-step problem like this one. However, the process is time-consuming, especially when you remember that errors will be made occasionally, so every step must be checked.
The rationale for using calculators to do these calculations is that the considerable amount of time saved using a calculator will enable the teacher and students to explore many more formulas, relationships between formulas, and real problems, ... that they wouldn't have had time for otherwise.
In other words, if doing a cylinder volume problem calculation by hand takes five minutes, but using a calculator requires only one minute, students will have more time to make sure they understand how the formula works, and more time to explore formulas for spheres, cones, and pyramids! More mathematics can be learned, because the calculator is doing the time-consuming drudgery of the arithmetic!
This premise holds true in all math courses, right through to the end of grade 12. In fact, the amount of material in those courses is such that it is assumed that students will be using calculators to do the multiplying and dividing ... the courses could never be completed if they weren't!
This immediately suggests to some that students may be losing skills. Surely if students are no longer doing multiplication or division with big numbers after grade 6, they will lose these skills.
In fact, this is true. Students are losing skills.
Here's how the argument goes. It's a trade-off. If you assume that calculators will always be available for our use, then let's use them a lot. Once you understand the principles of long division, for instance, in grades 5/6, and can do long division by hand, it's no longer necessary to actually do it. In Jr. High, all long division (eg: 875.4 Ã· 7.9) is done on a calculator. The extraction of square roots on paper isn't even taught any more ... the square root of 678.92 is done on a calculator.
By freeing students from these time-consuming arithmetical calculations, more time in the classroom can be devoted to learning more mathematics. Lots more mathematics.
Does a student need to practice long division after grade 6, in order to be ready for the 'real world'? Of course not. We all use a calculator. We'll always be able to use a calculator for those types of calculations, so it's a skill we don't need to be good at! And it doesn't matter! These are skills that aren't needed any more.
A parent of a Pure Math 20 student might be faster at multiplying 6.78 by 11.134 by hand than their son or daughter. That's because the parent spent a lot of their years in school practising arithmetic operations, and not so much time learning mathematics! Today's student knows far more mathematics than the parent did even after grade 12, and can solve far more complex problems! And that's what it's all about.
However, this is not to say that some skills are not still useful, and the distinction is very important. Both 'real world' problems and Sr. High school math courses require students to be able to be good at 'mental math'. You can't expect to pull out your calculator every time you need to multiply 6 times 8, and if you have to use a calculator in grade 10 math to do problems like -6 + 8, you won't finish the tests!
In Jr. High math, we still require students to be proficient at some basic skills; operations that they can do in their head without a calculator. These include, for example, the times tables, integer operations, simple powers, and the order of operations. Students are not allowed to use a calculator when practicing these skills.
In addition, some paper and pencil skills are important because they carry over into algebra, where most calculators can't (yet) operate. So in grades 7 through 9, students are expected to be able to do fraction operations by hand, and may not use programmed formulas to solve problems.
Students in grade 9 who are not proficient in these mental calculations don't often succeed in the advanced level Sr. High mathematics courses.
Senior High School:
The past twenty years has seen huge changes to the Sr. High mathematics curriculum, most especially in the area of relations and functions. Where students in Math 10 and 20 previously studied just the line and the parabola, they now are exposed to a wide range of functions, including graphs of the exponential, sinusoidal, absolute value, reciprocal, and cubic functions. This broadening of the curriculum is a direct result of being able to use scientific and graphing calculators in place of the cumbersome calculations that were formerly necessary, involving paper and pencil graph plotting, as well as logarithmic and trigonometric tables. In fact, the graphing calculator makes possible the study of relationships between functions that could never be done in high school before, due to the immense amount of time required to plot relations by hand. As mentioned already, present day math students are exposed to much more information than their parents were. This is a direct result of using calculators in the classroom.
Nevertheless, it is important that students use their calculators properly. While using a calculator's graphing capability to study the similarities between functions can broaden a student's grasp of relationships in mathematics, relying on that calculator to to basic operations like times tables facts and integer operations has exactly the opposite effect. Students are slowed in their work, often making assignments take much longer to do than they should. As well, the concepts which should be evident from appropriate use of the calculator, become lost in a maze of unnecessary calculator operations.
Students who are enrolled in advanced Sr. High math courses who are not able to perform basic calculations successfully without a calculator very seldom do well. Often they fail.
It is for this reason that the Jr. High mathematics teacher must carefully choose when to allow the use of a scientific calculator, in order to allow students to become familiar with its operation, ... and when to not allow its use, so that students gain a set of skills that will free them to use the calculator to its best advantage.