Taking Advantage of Technology
The computer can be a distraction and a frustration, but it can also be a teaching tool.
Such commonplace but abstract concepts as fractional equivalence and the "size" of large numbers can be made
visual through technology. And students can interact with virtual manipulatives to change algebraic variables
on a balance scale, or rotate a 12-sided solid to see its regularity and symmetry. These resources are examples
of the potential of the Internet as a teaching strategy.
This site shows arrangements of large quantities of U.S. pennies. It begins
with only 16 pennies, which measure one inch when stacked and one foot when laid in a row. The visuals build
to a thousand pennies and in progressive steps to a million and even a quintillion pennies! All pages have
tables at the bottom listing the value of the pennies on the page, size of the pile, weight, and area
(if laid flat). The site can be used to launch lessons on large numbers, volume versus area, or multiplication
by a factor of 10.
MSP full record
In this unit developed for middle school students, the lessons begin with a discussion of
why we study fractals and then provide step-by-step explanations of how to make fractals, first by hand and
then using Java applets—an excellent strategy! But the unit goes further; it actually explains the
properties of fractals in terms that make sense to students and teachers alike.
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This site invites learners to discover for themselves "an important relationship
between the three sides of a right triangle." Five interactive, visual exercises require students to delve
deeper into the mystery; each exercise is a hint that motivates and entices. The tutorial ends with information
on Pythagoras and problems that rely on the theorem for their solutions.
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This site offers numerous opportunities for online exploration of middle school mathematics.
The following two resources are examples. MSP
full record
Using this applet, the student represents two to four fractions by dividing and
shading areas of squares or circles and then ordering the fractions from smallest to largest on a number line.
The applet even checks if a fraction is correctly modeled and keeps score. A visual support to understanding
the magnitude of fractions!
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Another way to "explain" geometric transformations! Using this applet, students can explore the
world of translations, reflections, and rotations in the Cartesian coordinate system by transforming polygons
on a coordinate plane.
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In this impressive collection of applets, each applet presents a problem and prompts the
student for a solution. The ease of use and clear purpose of each applet make this a truly exceptional
site. Below is an example of an activity that fits well in the middle school curriculum.
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This virtual balance scale offers students an experimental way to learn about solving
linear equations involving negative numbers. The applet presents an equation for the student to illustrate by
balancing the scale using blue blocks for positives and red balloons for negatives. The student then solves the
equation while a record of the steps taken, written in algebraic terms, is shown on the screen. The exercise
reinforces the idea that what is done to one side of an equation must be done to the other side to maintain balance.
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The site was developed to illuminate the vision for school mathematics in NCTM’s
Principles and Standards for School Mathematics. The activities, lesson plans, and other resources are
designed to improve the teaching and learning of mathematics for all students. Below are two examples of
material for the middle grades level.
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Students explore the sum of the interior angles of triangles, quadrilaterals and
other polygons. To do this, they mark a midpoint on any side, then rotate the figure 180 degrees about that
midpoint. They eventually get all interior angles together at one vertex and consider what the figure suggests
about the angle sum. (From
Illuminations, National Council of Teachers of Mathematics Vision for School Mathematics -
MSP full record)
This tool allows learners to investigate various geometric solids and their properties.
They can manipulate and color each shape to explore the number of faces, edges, and vertices, and to answer
the following question: For any polyhedron, what is the relationship between the number of faces, vertices,
and edges? (From
Illuminations, National Council of Teachers of Mathematics Vision for School Mathematics) -
MSP full record)
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Copyright
December 2007 — The Ohio State University. This material is based upon work
supported by the National Science Foundation under Grant No. 0424671. Any
opinions, findings, and conclusions or recommendations expressed in this
material are those of the author(s) and do not necessarily reflect the views of
the National Science Foundation.
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This work is licensed under a
Creative Commons License.
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