LearningArithmeticinthe21stCenturyAndrewJasonLeonMyung
Last modified by Holger Dick on 2010/09/08 14:13
LearningArithmeticinthe21stCenturyAndrewJasonLeonMyung
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!
Dear Boulder Valley School Board,
When it comes to calculators in the classroom, We Love Peaches Incorporated believes we should avoid the use of the device until the student is successful at arithmetic without any help. After weighing the four options presented to us, we feel it is the most effective way to ensure your students are properly prepared for higher education. After presenting our reasons not to pursue the other three options we will then support our position.
Option 1: Ignore the device. We Love Peaches Inc. would never support such an extreme position, and finds the idea an empty option. Stated by WLP Inc. member Mr. Hepler, “If the student were to completely ignore the device, math problems that are more complex can't be done without a lot of strain.” He goes on in his response that to subject the students in your district to a lack of technology would set them behind nationally and prevent them from suceeding if they leave your district to take advanced science and math classes. This idea is seconded by WLP Inc. member Mr. Cockerham. Students taking the standardized tests of the SAT or ACT would also be at a disadvantage because those tests allow for calculators now. In a 1986 study in the Journal fo Research in Mathematics Education, Hembree and Dessart analyzed 79 studies of calculator use and found the following[1]:• Children who use calculators on tests have higher scores in both basic computation skils and problem solving. • Students who use calculators within a mix of instructional styles do not lose their paper and pencil skills. • Calculator use in the classroom improves the paper and pencil skills regardless of their ability • Those who use calculators in the class have better attitudes toward mathematics than children who do not use them.
Option 3: Invent New Curriculum Although a very novel idea, this one creates more problems than they solve. First, although we were hired for our knowledge in Human Centered Computing, we can't help but wonder how the Boulder Valley School Board can afford such a drastic change in curriculum. We also have not developed a new, novel calculator that could replace a run of the mill calculator available to most students today. Jason Cockerham agrees, “True, in theory students become independent of the devise later on. I don't think this will be the case in practice. If the students get comfortable using the devise, they will want to continue using it, because it's easier.” As a group, we are split, as member Mr. Hepler states, “The third choice to become independent of the device after it has been used as a teaching tool would be the best choice. If a person can become independent of the device after using it to help them with the work, rather than do the work for them, people will have the advantage that those who haven’t reached this advanced point in technology.”
Option 4: Distribute the work between students and calculators This solution has a huge uphill battle to make succeed in your district. WLP Inc. member Mr. Kim states, “I question myself that if those new technology would be any worth of spending lots of money or time. People in this world have [been] raised with this current system, and are still survived.” Mr. Hepler questions whether your faculty has the skills and training to execute such a shift in thought, “The problem with this is that there are so many different learning styles that it would be hard to determine how to enroll which students in which classes. This might work only if we find teachers that can teach in the various learning styles, to accommodate each individual student.” There are resources out there if the Boulder School Valley Board chooses. On Homeschoolmath.net they offer some helpful options for teaching with calculators[2]:• Let preschoolers or first graders explore numbers by adding or subtracting 1 repeatedly. • Let first through third grade children solve calculator pattern puzzles (ex. 7, 14, , , 35, __, 49) • Teach place values on the calculators after students build large 4-5 digit numbers. • Teach the size of one million by challenging students to add a number repeatedly until they reach it. • When teaching pi, have student measure the circumference and the diameter of several circular object, and calculate their ratio with a calculator.
But yet, these options, although viable teaching techniques, do not solve faculty training issues, nor provide grades 4-6 ways to integrate calculators in their arithmetic. Option 2: Let the students learn arithmetic and then introduce calculators Mr. Kim states that “learning the arithmetic is like learning how to drive. In other words, doing the arithmetic is like riding a bicycle; you will never forget.” The advantage of being able to teach the basics and principles behind mathematics without the automatic answer of a calculator is valuable to the development of your students. Each option stated above fell short in either they: removed calculators, unfeasible for your curricula, or weren't proven as effective for grades K-6. On HomeSchoolMath.net, Teacher David Iverson lends this comment[2]:“In Algebra 1, however, I don't allow students to use calculators at all. And, it my school, I find that most kids come to my course without a calculator or an inclination to use it. I feel that the basic rundown on the math in Algebra 1 should be: 80% of the numbers should utilize the basic information on a 12x12 multiplication table that kids should have memorized. 15% of the numbers should push beyond those limits. (example: what's 384/8?). And the last 5% should be things that they need a calculator for. “
Such a rough ratio of teaching could easily be followed by your faculty in the district and would not hamper your students abilities to learn arithmetic. The ideas presented above for teaching with calculators fits right in with Option 2 as they all require students till learn why they are using the calculator BEFORE they us it to prove those concepts. With the ideas presented above, we believe Option 2 is the most viable for your students. Again, Option 1 would not be beneficial and 3 and 4 leave too many holes to address before subjecting your students to a lack in arithmetic understanding. We encourage you buy very inexpensive calculators for your lesson plans after you've laid the foundation that prevents the students from using calculators as a crutch. Sincerely, Leon Gibson Myung Kim Jason Cockerham Andrew Hepler
[1]. http://www.sedl.org/scimath/quicktakes/qt9803.html [2]. http://www.homeschoolmath.net/teaching/calculator-use-math-teaching.php
