Tag: Conclusion

Children Don’t Need Calculators To Learn Math!

I received a request to share an article with all of you from NannyPro.com. They’ve published an article and thought it would be a good fit for you, the readers of our blog. I read through it and agree that it is appropriate and a good fit. So without further ado, here it is:

Why Every Kid Should Be Able to Do Math Without a Calculator

by Michelle

In a highly-advanced technological age where every child seems to have a smartphone complete with a powerful calculator in their pocket, it may seem silly to make sure that they still are able to do math without the assistance of a calculator. However, there are plenty of reasons why children should know how to solve basic equations without a computer’s intervention. Regardless of how ubiquitous calculators and calculating software seem to be, there are things that a child simply can’t learn from plugging numbers in and instantly receiving an answer.

Learning to Operate in the Real World

While it’s quite likely that your child will almost always have access to a calculator of some sort in his adult life, it’s still important that he have at least a basic understanding of how to work out simple mathematical equations. Technology isn’t infallible, and there may come a time when he needs to come to a numerical conclusion and has no access to a calculator. When children rely on technology to do all of their work for them, they’re missing out on necessary life skills.

Learning Real Skills Versus Learning to Operate Software

A 2007 report by the Institute of Education Sciences and the National Center for Education Evaluation and Regional Assistance to Congress shows that 16 of the best and most powerful reading and math learning software programs had no measurable effect on test scores. Students learned how to operate the software to obtain the desired affects, but not to apply the underlying concepts in daily life. No matter how well your child learns to solve equations on his calculator, he will essentially be missing the most important part of the exercise: how the solution is found. Kids can’t watch a calculator perform equations in real-time or observe the various steps in between. They simply enter a set of numbers, and another is returned to them. Manipulating a calculator with speed and accuracy doesn’t necessarily indicate that your child has the first idea of how to complete that same equation with a pencil and paper.

Obtaining Higher Education

Kids as young as those in elementary school are given calculators as a part of their curriculum, a practice that’s often continued all the way up to high school. What parents may not realize, however, is that many university math departments do not allow the use of a calculator. When a high school honors student is struggling merely to pass his first math classes in college, the hit to his self-esteem alone could affect his performance in the realm of higher education. Introductory collegiate mathematics classes generally ban calculator use, largely because in higher math the numbers are secondary to the abstract equations. For a science or mathematics-based major, the ability to understand the basic parts of an equation is essential. A calculator is of absolutely no use beyond introductory calculus, nor will it help a physics student find the answers they’re looking for. Instilling basic, core competency in these areas from a younger age and actively using those skills throughout high school far better prepares a young student to explore an education beyond the walls of that high school.

In an educational environment that relies largely upon calculators in the classroom, figuring out a way to instill basic mathematical principles and an appreciation for arriving at a solution through figuring it out independently isn’t easy. As long as calculator use is encouraged, and even required as part of a public curriculum, the responsibility to teach and reinforce basic equation-building and mathematical skills will fall upon the shoulders of parents. When your child protests that calculators are everywhere and he’ll never need to know how to work out a problem manually, explaining all of the reasons why he should still acquire these skills may help to soothe his indignation.

If you’d like to see the article at NannyPro.com’s  site, you can view it here: http://www.nannypro.com/blog/why-every-kid-should-be-able-to-do-math-without-a-calculator/

Of course if your child needs a boost in their math proficiency confidence – we are always ready to help them at Mathnasium.com/cherryhill.

Have a great day!

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Learning Math with the Abacus

abacus

So you’ve all seen an abacus, right?

I thought you might be interested in knowing a little about its history and how it’s used.

So I looked for an article that would do just that and found this one!

Learning Math With Manipulatives — The Abacus

The abacus has been around in various forms for over 2300 years. It was used for various counting and operational tasks. One might even call it the original math manipulative (unless you count fingers and stones). In my younger years, abaci were relegated to the bottom shelf or used as a toy for the kinesthetic kids. These days, abaci can meet the same fate that the abaci of my youth did. The first known abacus, the Salamis tablet, collected dust for over 2100 years. For all those lonely and banished abaci on dusty shelves everywhere, I dedicate this article on how to represent, add and subtract whole and decimal numbers.

As most teachers know, the use of manipulatives by younger elementary students helps them to understand the concepts of place value and operations later on. In my search for a variety of manipulatives to teach number sense, addition and subtraction, I came across a convenient tool in the abacus. I’m sure it was no coincidence that each row on the abacus included exactly ten beads, but there was no operators manual with the abacus I found. When I found an instruction manual several years later, I found that the manufacturer of the abacus saw it as no more than a counting device and had no idea of the place value power inherent in the design.

Representing Numbers With a Dusty Abacus

When I first started using an abacus as a manipulative in math class, I was teaching grade six. In the grade six curriculum, students were supposed to represent whole numbers greater that one million and decimal numbers to thousandths. If you count the number of places from one million down to thousandths, you get ten places. Coincidentally, the abacus had ten rods of ten beads each. I’m sure what I discovered was discovered long ago, and some manufacturers probably even send out better instruction manuals that make note of this, but at the time, it was a completely new discovery.

To make a long story short, I assigned each row a specific place value starting with millions at the top, and thousandths at the bottom. One could use a strip of tape or an indelible marker to label the rows. To represent a number, a student would simply move the number of beads for the value of each place in the number they were given. For example, the number 325,729 was represented by moving three of the hundred thousands beads, two of the ten thousands beads, five of the thousands beads, seven of the hundreds beads, two of the tens beads and nine of the ones beads.

I didn’t have a class set of abaci, so I made up little sketches of an abacus (six or so per page) and students showed representations of numbers using these.

Adding and Subtracting Numbers With a Polished Abacus

Once students are familiar with representing numbers using an abacus, they can move onto adding and subtracting numbers. The idea of adding using an abacus and place value is quite a simple process. Begin by representing the first number. Add the value of each place value in the second and subsequent numbers one at a time beginning with the lowest place value and regroup as necessary.

Consider this simple example, 178 + 255. The student would represent 178 on the abacus to begin. She would then add five to the ones row. Since there aren’t five more beads to add, this first move would also involve regrouping. The student would move the two remaining ones, then regroup by sliding all ten ones back and replacing them with a ten. She would then move three more beads since she already moved two of them for a total of five. Since there was some regrouping, there would now be eight tens. The students needs to add five more, so there would be another regrouping, this time of ten tens to make a hundred. Finally, the student moves two additional hundred beads; this time regrouping isn’t necessary. If everything was done correctly, the student would end up with four hundreds beads, three tens beads and three ones beads.

A variation on addition is to add the second and subsequent numbers from the highest place value to the lowest place value.

Subtracting is much the same as addition, but it involves “removing” beads. The procedure for subtracting is to represent the first number then to subtract the value of each place value in the second and subsequent numbers beginning with the highest place value.

Consider this example, 3.252 – 1.986. The student would first represent 3.252 using the abacus. He would begin by subtracting one one. This is fairly straight forward because there are enough ones available. In the next step, though, the student has to subtract nine tenths from two tenths. He begins by subtracting two of the nine tenths, but he then has to regroup one of the remaining ones into ten tenths. Once he has ten more tenths, he can subtract the remaining seven tenths. He continues by subtracting eight hundredths from five hundredths, and again, he has to regroup, this time, one of the tenths into ten hundredths. The final step also involves regrouping since six thousandths must be subtracted from two thousandths. In the end, the student hopefully ends up with one one, two tenths, six hundredths, and six thousandths (1.266).

Subtraction could also be accomplished by subtracting the lowest place value first, but this sometimes means more manipulations of the beads which means more chance for error.

Conclusion

The use of the abacus takes a little bit of time to master. It is important that the teacher and the students use the correct place value terminology (e.g. “regroup ten hundreds to make one thousand” instead of “turn ten green beads into one blue bead”), so the concepts of place value, addition, and subtraction can be transfered to mental strategies and paper/pencil algorithms. Remember, the best way to dust and polish an abacus is with little fingers!

By: Peter Waycik – Peter Waycik is an elementary teacher and a reading specialist. He supplies thousands of free math worksheets to teachers and parents every day at www.math-drills.com.  He also runs www.edarticle.com where you can find information on a variety of education topics.

So are you ready to go buy an abacus!?!?

Hope you have a great day.

 

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