Finally… an assignment where I actually have used the technology before. Playing around with various “toon” programs was not only lots of fun, but guess what I am going to have my students due next time we are in the computer lab?
to enjoy the toons…..you have to click on the images page…
Theorizing
the Graphing Calculator
Since 1985 when Casio first introduced the fx-7000G, the graphing calculator has
become a staple in high school and university mathematics classrooms. Without reliable access to computer labs, this hand-held computer offers power and flexibility to both students and instructors. Open a suitcase containing a class set of calculators and
experience the excitement and anticipation as students gaze at the 30
viewing screen, wondering what the previous user has
left for them to explore, or what new direction they may follow today.
The graphing calculator does not replace mathematical content; rather enhances it
with the power of visualization. By changing components, students, individually or in groups, are able to study and classify the behaviour of functions, exploring possibilities and forming conjectures regarding similar situations.
The “what if” question, answered in real time, holds student interest
and promotes divergent thinking. Students become actively involved in problem solving; using tables for numerical results, supporting and confirming results graphically, solving
problems that cannot be solved with present analytical or algebraic
skills. The visual affordances offered by the calculator are applicable to all levels of math, offering a look at the simple concept of slope, right up to optimization problems in 3-Dimensions.
Technological advancements have enabled the graphing calculator to enjoy color screens and a seeming endless amount of memory. Using
pre-programmed or downloadable Apps, students have access to practice quizzes,
spreadsheets, and financial applications. Exploring the costs of buying a new or used vehicle quickly has tremendous impact on high school students.
Students can look at the interconnectivity of mortgages, changes in term
length, interest rates, frequency of monthly payments, and present values using
a few keystrokes. Concurrently graphingthe levels of interest paid vs principle paid over the course of a conventionalmortgage presents a visual impact students cannot ignore, nor are likely to forget.
It is not only their computational speed, widespread application base, or visual
impact on learning mathematics that has kept the graphing calculator in the
class-room for over 25 years; flexibility is also a contributing factor. The number of peripheral devices the calculator supports offers much to teachers and students. By attaching a calculator to an overhead projector, the teacher is able to introduce topics, lead discussions and regulate the pace of learning. This
scaffolding is essential to students new to the technology, or when exploring
unfamiliar problems. Data loggers, measuring time-distance relationships, Ph levels, temperature, decibel, and light levels not only give students access to real world information, but facilitate immediate visual representation of that same date, increasing the connectedness with the data, but also forming connections across math and
science. Watch with amazement at the engagement of students trying to create the first letter of their name on the calculator screen by walking towards and away from a motion sensor. By linking the calculator to a computer, the built in programming features are enhanced, extending the affordances offered by pre-built programs with student made programs.
Despite the affordances of graphing calculator, some trepidation exists. Access, comprehension and transfer cloud the seeming blue sky of calculator use in the classroom. Calculators are cheaper than computer labs, yet economics remain a factor. Schools must weigh the purchase cost; bore by the school or individual students, against the aforementioned advantages. Economically disadvantages school districts and communities may find access to this technology prohibitive. The visual
impact of the calculator offers much to students, but may also form a barrier
to true comprehension and understanding. If finding the roots of a quadratic equation, either by graphing or pre-programmed applications allows students ready access to such information, performance does not necessitate learning of the underlying concepts used in
such a task. Being able to copy the general shape of a function off the calculator screen may even inhibit knowledge transfer when the same tasks take a pencil and paper form. With no print button, all transfer into conventional print form may be rote, rather than conceptual.
The enduring use of the graphing calculator substantiates its positive impact on
learning in the mathematics classroom. But, like all technology, strong methodologies
and practices are essential to ensure that visualization enhances rather than
restricts mathematical comprehension and transfer.