Response to: Deciding When to Use Calculators

The article Deciding When to use Calculators by Anthony Thompson and Stephen Sproule presents a framework that will help "middle school mathematics teachers..." to "...decide when to use calculators with their students" (Thompson & Sproule, pg. 127).  Thompson and Sproule present this framework in  what they call a "cartesian representation" which includes two dimensions and four categories.  The first dimension is student oriented and is divided into the subcategories essential and nonessential.  They define essential as "the activity would be too complex for the students to complete without using a calculator" and nonessential as "the mathematics activity can be completed without using a calculator" (Thompson & Sproule, pg, 127). The second dimension of the framework is the goal oriented dimension, which "focuses on two possible pedagogical goals: (1) for the students to find a computational solution and (2) to engage students in problem-solving processes" and thus the two subcategories of the second dimension are product and process (Thompson & Sproule, pg, 128).  The authors describe process oriented as "the goal of the activity is for students to understand the processes associated mathematical exploration and problem solving," similarly product oriented means "the goal of the of the activity is for students to determine a computational solution or end product" (Thompson & Sproule, pg, 128).

The framework presented by Thompson and Sproule appears to be a good tool for a quick decision as to whether calculators should be incorporated in a particular activity. However, I believe the decision requires further consideration then the four categories presented in the framework and that there are  variables Thompson and Sproule do not address in this brief article.  One of which we have not discussed at great length but certainly is worthy of consideration is whether or not students are allowed  to utilize advanced calculators on standardized tests.  Although this may seem to be a stretch from an article that addresses whether calculators should be used in a classroom, teachers cannot neglect the direct relationship, mainly from a comfort and confidence aspect, that students develop a dependency as a result of using calculators to perform desired tasks.  I would argue that Thompson and Sproule failed to consider the dimension of whether a calculator is allowed on gateway standardized tests (i.e. SAT, ACT, AP examinations) to perform specific functions.  If it is not, then in my opinion the students should not be exposed to the calculators ability to perform such function to prevent the above mentioned dependency.  To clarify, I understand the framework is for middle school teachers but  believe that students who form a dependency early may have difficulty on standardized test, where middle school mathematics serves as a foundation.

I agree with the authors on the concept that calculators should be used when the difficulty of a problem lies in the mathematical manipulation, which would consume time and consequently detract from the overall learning goal of the practice problem. However, I would challenge the intent of incorporating such a difficult problem, as it seems somewhat convoluted that we as teachers create problems which detract from the overall goal/task and simply allow students to utilize a tool to eliminate the barrier we just created. Why not just provide simple questions and eliminate the use of a calculators to ensure the students understand the main objective?


Thompson, A. D., & Sproule, S. L. (2000). Deciding when to use calculators. Mathematics teaching in the middle school, 6(2), 126-129.