Calculators, whether we like them or despise them, are here to stay—gone are the days when we had to tell pupils, “You won’t always have a calculator.” We should examine how to teach youngsters how to do basic math in the calculator age.
I’ve spent years figuring out how to use a math calculator in my instruction in ways that teach my middle college students critical talents like variety sense, estimate, and problem-solving. Through trial and error, I’ve devised and taught programs that use calculators as a key tool in developing students’ mathematical interest, conceptual knowledge, and procedural fluency. Two of my favorite subjects cover what many people overlook as fundamental central college concepts: possibilities and fractions.
PERCENTAGE
In this session, I normally begin by informing students that I would be providing them with a number of percent problems in addition to the solutions. The first thing that college students are surprised about is how I was able to provide them with the answers. Aren’t they supposed to be the ones who parent the ones who aren’t?
Not in this instance, I tell them: the goal isn’t to find the answer, but to figure out how the solution was discovered. The first issue we’ll answer is a basic one: what is 50% of 24? The pupils can usually yell “12!” sooner than I finish writing the problem on the board. “Excellent!” I’ll react. “Now, how should you parent that out on a calculator?” Students are holding a basic four-feature calculator at the time. I walk around and have students demonstrate their ways, and I remind them that dividing 24 by 2 isn’t what I needed. “But half is half,” they point out. “So you divide by the power of two.” “Certainly,” I responded. “However, we’re not frequently going to have anything as remarkable as 50%, therefore we need to find an exceptional solution.”
My college students, exasperated, attempt to parent out what I want. After enabling them to engage in ineffective conversation, I guided them to the thought that we will utilize the numbers 50 and 24 to get 12. Soon, they’re having thoughts like increasing the numbers by 1,200.
“That’s like a 12,” someone will comment. “However, I should get rid of those zeroes.”
My kids are beginning to recognize that in order to obtain the solution, we will multiply the percentage by the total number and then divide by one hundred. Some students even advocate that you convert one of the integers to a decimal before multiplying them (50 instances zero.24 or zero.50 instances 24). Others claim that you used a decimal factor in each number, but you should only use one digit in each (five. zero instances 2.4). Some recommend using the percent button on the arithmetic calculator, which will also convert their number on the screen to a decimal.
I next ask them to make educated guesses about why all of these strategies work and what they have in common. Soon, my pupils will be engaged in a mathematical discussion on the links between decimals and percents, how the number one hundred is inherent in all calculations, and how 50% equals zero. 50, 12, and 1/2 are all the same thing.
I continue the lesson with more difficult problems. Attempting to calculate something like 17.35 percent of 8.four using paper and pencil is overwhelming—however, with calculators, my students approach even purportedly terrifying problems like this with confidence, knowing that the connections remain constant regardless of the intricacy of the numbers. Using concepts such as percentage-decimal equivalence—along with green algorithms such as ” % multiply by n divide by 100,” my students build conceptual knowledge and procedural fluency with the use of calculators.
OPERATIONS WITH FRACTIONS USING A MATH CALCULATOR
To build on my pupils’ newly acquired knowledge of rational variety equivalency, I utilize math calculators to teach them multiplication and division using fractions and decimals. As with the shared problems, I begin by demonstrating to pupils known equal fractions and decimals, such as 1/2 = zero. five and 3/4 = 0.75. Students figure out how to create decimal forms using the numerator and denominator. They eventually figure out the department algorithm (numerator denominator). When they’ve mastered this skill, the real fun begins. I invite college students to see if they can apply their conversion strategy to make this process easier. After a few successful struggles, pupils arrive at zero.25, which they commonly interpret as equal to 1/4. Soon, they’re having a discussion about how they could have just accelerated the denominators without all that decimal nonsense.
“But how close are the numerators?” I inquire. Perhaps they multiply as well, but my pupils aren’t sure. That’s while we get rid of every other annoyance: 3/4 multiply by 2/5. The students initially hypothesize that they multiply the numerators and denominators, yielding 6/20.
“But how can we be certain?” I inquire. So, what if we converted our answer directly into a decimal? Finally, the academics are able to affirm that 6/20 is the solution, since 3/4 2/5 = 0.75 multiply zero.four, which equals zero.three, and 6 divided by 20 = zero.three.
Throughout the class, I give students challenging problems, such as those with incorrect fractions and mixed numbers, and all of their work can be verified with the use of calculators; they do not want me to continuously assess their work, which results in more independence in problem-solving.
The most amazing thing I discovered was how effortlessly college students could paint with repeated decimals. While it took some time or even more efficient effort, my college students were able to solve multiplication and department problems with all types of fractions that had repetitive patterns. They got started.
They began to realize that typing in a series of 3s represented zero. Three were supplied to them that were pretty close to the true answer for 1/3 divided by 1/4 (zero.3333333 divided by zero.25 = 1.3333332, a completely close approximation of the real solution of 1 1/3). I never learned how to operate with repeated decimals as well as my college students did throughout the rational variety subject, thanks to their usage of calculators.
It takes a lot of planning and forethought, as well as reconsidering what we believe is important for children to learn in math, but when you unleash the power of a math calculator, you provide pupils access to arithmetic in whole new ways. What comprises elementary mathematics must be defined.
What defines elementary mathematics must adapt to our changing reality. Our kids will spend their lives living in the twenty-first century, and calculators will be critical to providing them with a true twenty-first-century education that includes twenty-first-century arithmetic fundamentals.
Should calculators really be included in the class?
Without the use of a calculator, students may improve their fluency and mental math abilities. Visual models and number sentences assist children in locating solutions while also improving number sense, mental math, and problem-solving skills. When kids become overly reliant on calculators, their fluency and numerical awareness suffer.
Should students use calculators or not?
Calculators, on the other hand, serve an important part in increasing students’ familiarity with numbers and operations, as well as estimate abilities, when used effectively. Furthermore, the judicious usage of calculators promotes an effective learning environment that fosters a good attitude toward mathematics (Ellington, 2003).
When to allow students to use calculators?
They will need calculators to deal with the intricacies of college, but they should wait until they are advanced enough to estimate. So, in the United States, my response is somewhere between 8th and 12th grade.
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