LearningArithmeticinthe21stCenturyStormDrain

LearningArithmeticinthe21stCenturyStormDrain

To-Do

Develop principled arguments (backed up by: research, empirical findings, your personal experience, hypotheses about resulting cognitive developments, and the topics discussed in class) which of the four positions YOU will favor!

Principled argument which of the four positions YOU will favor!

Learning Arithmetic in the 21st Century:
Students Must Learn Arithmetic Before Using Calculators

 
As the technology and education experts for the Boulder Valley School Board, we have come to a decision concerning the use of hand-held calculators in the classroom:
 
Teach students how to do arithmetic first, not press buttons
 
Although calculators can be a useful resource, they shouldn’t be the primary learning method for early elementary-aged students studying arithmetic for the first time. Basic math is a skill that every person should have. For example, if an individual is in a situation where he or she needs to do some quick addition, having mastered basic arithmetic at an early age, he or she would just calculate the answer and give it back in a matter of seconds. If he or she couldn’t do basic math without a calculator, there would be several steps involved, including retrieving the device, turning it on, punching in the numbers, and reading the screen. These added steps would not only take much longer than doing it mentally, but students who rely on technology for basic computations might also find their abilities have slowed when their devices aren’t available.
 

A person who all the time uses a calculator gradually loses his/her mental computational skills… Their brains slowly but surely get accustomed to walking on crutches and became indolent to use mental computational abilities… In certain cases it leads to difficulties in math learning.
http://www.eslteachersboard.com/cgi-bin/articles/index.pl?page=3;read=1784

 
Basic math is a skill individuals use every day. Whether it’s calculating the tip at a restaurant or doubling a recipe, math is a fact of everyday life. If students are taught to depend on technology for simple algebra, they risk becoming so dependent on calculators they’ll need to carry the devices with them everywhere. Teaching someone how to press a button is not even close to teaching them how to do basic math.
 
In addition to the problems above, students who fail to learn arithmetic without technology first may have grown up trusting their devices will provide them correct answers. What happens, though, when the device produces an inaccurate response?
 

One of the problems experienced with children who have used calculators from an early age without proper integration is that they have not had the opportunity to develop good "number sense". This is sometimes referred to as a "feel for numbers". The importance of estimating an answer before or after calculating is not understood. Why estimate, when the calculator will give you the exact answer? After all, a calculator is never wrong. That is virtually true, but the operator of the calculator is capable of error. http://www.math.wichita.edu/history/topics/calculators.html#calc

 
The ability to detect incorrect answers is therefore hindered when a student doesn’t have a complete grasp of numbers before integrating technology with the process of problem solving. How would a student know the relationship between addition and multiplication if they only knew how to press buttons on a calculator? It is crucial that students learn arithmetic before being introduced to calculators and other computational devices.
 

There is nothing wrong with using calculators after the concepts are learned
 
That said, once students are capable of performing simple arithmetic, calculators can become a useful resource. There are times, especially in a student’s high school or college math career, when having a calculator can be very useful. For example, if a student is doing a basic physics problem and has to multiply 8.39E12 by 4.08E-11, it’s important to know the methods by which this problem is done by hand, but using a calculator makes it possible to do the calculation much faster with less chance of error. If a student had to do this sort of problem multiple times without a calculator, the calculation would not only become tedious, but it might take away from understanding a larger concept.
 

If students use calculators to figure out the relationship between the circumferences and diameters of many different round objects, they can get beyond problems of correct division and watch the concept of pi emerge.
http://www.sedl.org/scimath/quicktakes/qt9803.html

 
 
In order to avoid technology dependency, why don’t students learn it all by hand, without calculators? 
 
This argument favors the banning of calculators altogether. While the fear of over-dependence on technology is a valid concern, applying it to every level of academia has the potential to limit student’s exposure to and ability to solve more complex problems.  The ability to do basic arithmetic operations, such as addition, subtraction, multiplication, and division, are skills that require learning by rote at early elementary-school age.  These basic skills would then be applied at later stages of a student’s education as solving for problems which require detailed graphs or more complex operations could be solved efficiently and accurately by a calculator.  Requiring students to do these complex problems by hand would consume vast amounts of time and effort, both of which would be better spent learning new concepts.  Although some educators advocate for the banning of calculators and other technology in the classroom, it is clear that in later stages of a student’s education, this approach hinders a student’s ability to solve certain problems:
 

Prior to the wide spread use of graphing calculators, we observed that students hadvirtually no understanding about the use of graphing as a tool to do mathematics. For example, even our best calculus students did not initially know what it meant to solve an equation of the form f x ( )=0 graphically. Their understanding about graphs was so minimal that creating a graph by hand to solve the equation was an impossibly time consuming task.
www.math.ohio-state.edu/~waitsb/papers/reformbacklash.pdf?

 
The drawbacks of banning technology from the classroom are significant, and it is clear this position is too drastic to appropriately prepare students for their future academic and professional careers.

 
Can students use calculators to learn arithmetic and later become independent of the technology?  Why should students learn the basics first?
 
One problematic approach involves allowing the use of technology in the classroom at all stages in the learning process with the hopes that eventually the student will become independent of the devices.  This view is debatable since it is unlikely students will gain this independence.  In the same way that an individual using a GPS navigation system in his or her car doesn’t recall directions as easily or retain a clear mental map of his or her location, a young student who hasn’t learned how to do basic arithmetic before using a calculator or other technological aids will find more difficulty in recalling and performing basic arithmetic:
 

A September 2000 Brookings Institution study found that calculator use decreases student math achievement. Analyzing national test data, Brookings concluded that students who used calculators every day scored lower than students who used the devices less frequently.
Calculating the Cost of Calculators by Lance T. Izumi, Capital Ideas, December 21, 2000.

 
It is clear, then, that while technology can contribute positively to classroom learning, it also has the potential for becoming a handicap for students who haven’t mastered the basics.
 
 
 
 
Resources:
 
Bright, G. W., Waxman, H. C., & Williams, S. E. (Eds.). (1994). Impact of calculators on mathematics instruction. Lanham, MD: University Press of America.
www.math.ohio-state.edu/~waitsb/papers/reformbacklash.pdf?
 
Calculators in the Classroom.
http://www.math.wichita.edu/history/topics/calculators.html#calc
 
 Lance T. Izumi. Calculating the Cost of Calculators by Capital Ideas, December 21, 2000.
 
SEDL, Quick Takes:Calculators in the Classroom, March 1998, http://www.sedl.org/scimath/quicktakes/qt9803.html
 
The Hazard of Using Calculators at School by Victor Guskov. http://www.eslteachersboard.com/cgi-bin/articles/index.pl?page=3;read=1784