Magazine article Montessori Life

Using Graphing Calculators in the Montessori Middle School Classroom

Magazine article Montessori Life

Using Graphing Calculators in the Montessori Middle School Classroom

Article excerpt

One of the greatest challenges facing educators in mathematics today is to stimulate and inspire as many students as possible to realize their potential, not only to master skills but to learn important mathematical ideas-without feelings of frustration and despair.

At the early ages, a child entering a Montessori environment is encouraged to explore and discover concepts, ideas, and patterns. As Montessori middle school educators, we operate on the principle of mastery learning; however, through the use of textbooks and programs that emphasize far too much mathematical skill mastery, we can often limit our students in the exploration of mathematics as an exercise in critical thinking. And, as we place more and more emphasis on skill mastery, we tend to decrease the importance of problem-solving strategies and other important content needed to cope with real-life problems.

As a result of the decrease in emphasis on problem-solving strategies atthe middle school level, we may tend to overlook vital content and problem-solving techniques our students will encounter in ahigh school environment. Real-life numerical values have little in common with the ones we often encounter in the textbooks we currently use. Real-life numbers are either very large or very small and are often seen as existing in a state of clutter and disarray.

It is often perceived that calculators threaten basic skill development. Thus some Montessori educators have either abandoned the idea of incorporating them into the current curriculum or limited their use to the point where they are rarely used in a meaningful way to promote higher order thinking. This view revolves around the idea that by allowing students to use calculators, their paper and pencil algorithm skills would be lost or replaced by dependency of the student on the machine.

Do calculators threaten basic skills? According to research (Suydam 1982), the answer seems to be no. If our students are allowed to develop their paper and pencil algorithms using a plethora of exploratory materials at the early ages, without the use of calculators, then there should be no fear of creating a harmful environment through the use of calculators in the middle school environment. Our current research indicates that 86% of the Montessori Middle Schools use simple calculators on a regular basis to complement the existing mathematics curriculum.

If we are to encourage and allow the use of calculators in our mathematics classes, it is my firm belief that graphing calculators should be used instead of simple calculators. Graphing calculators present an ideal instrument for learning mathematics. First, they incorporate a portable environment that may be used both at school and home. Second, if used correctly, they provide the students with a tool that fosters learning and thinking by providing immediate feedback that will support their reasoning.

Instead of simple handheld arithmetic machines, easily obtained for a few dollars through any office supply store, a graphing calculator is an ideal means of teaching complex mathematical concepts at the middle school level, for a number of reasons: the large screen, the graphics capabilities, the multiline display factor, and the ability to explore functions through graphing. Graphing calculators give students and teachers the ability to investigate, explore, compare, and discover concepts in a much more comprehensive way than simple calculators or no calculators at all.

Explorations

The majority of students using calculators typically rely on simple calculators. However, these calculators do not allow students to visualize their actions and learn from their mistakes. By middle school quite a few students have been introduced to the scientific calculator; buteven though it allows them to perform calculations based on an algebraic hierarchy, it still lacks the ability to display the entire operation. For example, if you compare the results of the following problem on a simple calculator to those of a graphing calculator, you can understand the difference. …

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