Response to: NCTM Position Paper on Technology

The article Teaching Strategies for Developing Judicious Technology Use by Lynda Ball and Kaye in the 67th NCTM yearbook (2005) discusses the judicious use of CAS and technology in the classroom. The article begins by taking the position that technology, when used effectively, can "extend the mathematics that can be taught and enhances students' learning" (Ball & Stacey, 2005, p. 1)  The article further states that "banning technology is not necessary" (Ball & Stacey, 2005, p. 3) and is in response to the "frequent calls to ban the use of calculators and computer software that "do mathematics (especially arithmetic or algebra) in schools or a particular grade levels."

One particular point that I found interesting in the article was the brief summary of a recent work by Heid - 2002, who is an "opponent of the use of CAS in American schools.  There are practical arguments about cost, ease of use, and inadequate preparation for unchanged college courses and tests." which I touched on during my last response to CAS in the classroom.  I stated this exact point, that although the adaptation in secondary school is beneficial, and may allow more time for examining underlying concepts rather than methodical manipulation, that we are in fact doing a disservice by delivering students to a VERY teacher centered university environment.

Continuing on with the current article of discussion, a teacher "Lucy" of "fourth-year high school students who were taking a college preparatory"in Australia was surveyed about her judicious use of technology in the classroom. The classroom had access to CAS calculators full-time during their final two years including assessments. Lucy's view on technology for the classroom is summarized well by the following, "she often stated that her main goal for the use of technology was improving the mathematical understanding of students, not the learning of technology."

Lucy employed a "white box-black box" approach which involves presenting material by pencil and paper and then later incorporating technology for more difficult problems.  The CAS allows the students to focus on the topic of concern and not difficult mathematical manipulation.  I find that this approach closely aligns with my current teaching philosophy, where students will learn underlying concepts before they are permitted to utilize technology to perform more difficult operations.  Lucy reflected on her own changes in teaching style as a result of using CAS in the classroom:

Lucy emphasized when technology use is an efficient and effective method for solving problems and when it is unnecessary. In fact, Lucy commented for solving problems that this emphasis was perhaps the greatest change in her teaching that had resulted from having constant access to CAS technology over two years (Ball & Stacey, 2005, p. 7).

I can however, see particular exercises where students may utilize technology to discover and form their own conjectures about new concepts and material, then through reinforced lecture and formal presentation of material students will begin making connections about their recent discoveries. The article further examines how teachers can produce judicious user of technology by creating "An environment where students are usually given the responsibility to make their own selections of mental, pencil and paper, and technology approaches" (Ball & Stacey, 2005, p. 12).

The main take away for me of the article is that as educators we have the ability to "confidently deliver programs that result in students using technology to increase their mathematical understanding instead of randomly pressing buttons in the hope that an answer may appear by magic" (Ball & Stacey, 2005, p. 14).

References:

Ball, L., & Stacey, K. (2005 Teaching strategies for developing judicious technology use. In W. J. Malaski & P. Elliot (Eds.), Technology-Supportoted Mathematics Learning Environments 67th Yearbook.