LearningArithmeticinthe21stCenturyJonMai

LearningArithmeticinthe21stCenturyJonMai

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!

The proposed plan for the Boulder School District would be to develop new curricula and more intuitive calculators that would simultaneously require a more in-depth knowledge of the concepts and naturally lead the students towards the correct process that would be required to solve the equation. The obvious goal would be to lead students towards a natural understanding of the concepts so that they would not be reliant on the gadget, but instead use the gadget to speed up the already understood concepts and indeed as a tool for learning the concepts. The MAPS (Memory Aiding Prompting System), developed for people with cognitive disabilities at the University of Colorado, is one of these tools designed for learning and uses several types of scaffolding with fading (Carmien). We can relate this concept of learning to calculators. Homeschoolmath.net, which assists parents who are homeschooling their children in math, says this about calculators: “Calculators? should not be used for a random trying out of all possible operations and seeing which one produces the right answer.  It is crucial that the child understands the different mathematical operations so she knows WHEN to use which one - whether the actual calculation is done mentally, on paper, or with a calculator. (Using)” By developing calculators that lead to this knowledge of when to use the different functions and how they work, we can effectively teach students both the underlying mathematical concepts and how to utilize the technology at the same time. In a paper written by Bert K. Waits, a professor of Mathematics at Ohio State University, he states “We believe what is needed in the future is a university mathematics curriculum that takes advantage of computer technology to assist students in gaining mathematical understanding, in becoming powerful and thoughtful thinkers, communicators, and problem solvers. We seek a balanced approach to the use of technology in the future.(Bert)” When we use scaffolding with fading, we can use the calculator to bridge the gap to more advanced concepts that would be difficult to understand in and of itself, and by creating understanding of the concept we can fade away the bridge, using innovative curriculum to create the understanding of the proverbial water beneath the bridge. From personal experience, knowing when an answer is correct assists the learning process by teaching when the correct formulas or procedures are used. By utilizing this power to teach the students, we're reducing dependence on technology by using the technology as a learning tool. The technology effectively makes itself obsolete. Think of it as a plane that would fly itself, but in doing so teach the pilot how to fly. Therefore, if the plane ever fails, the pilot would have the knowledge to fly it themselves, or to fly other planes that do not have the same technological capabilities. We need to utilize technology to assist learning, but the underlying concepts are still extremely important for students to learn. Why not use technology in our favor?

Hiphophippotomi:

Jon Mai

Ariel Aguilar
References:

Carmien, S., & Fischer, G. (2005) "Tools for Living and Tools for Learning." In, Proceedings of the HCI International Conference (HCII), Las Vegas, July 2005, (published on CD). http://l3d.cs.colorado.edu/~gerhard/papers/tools-hcii-2005.pdf

Using calculator in elementary math teaching. (2003-2009). HomeschoolMath.Net Retrieved September 6, 2010 from the World Wide Web: http://www.homeschoolmath.net/teaching/calculator-use-math-teaching.php

Bert Waits. The Merging of Calculators and Computers: A Look to the Future of Technology Enhanced Teaching and Learning of Mathematics, Proceedings of ICTMT 3, 1997