||Jul 25, 2003 by Teacher Education
|| These Java-applet activities are designed for either group or individual
exploration into concepts from middle school mathematics. Each activity includes
a rationale, instructions for the activity, a lesson plan, and a curriculum
context for each. Additionally, discussions are connected to the lessons,
providing content and pedagogy. There are also links to textbooks used at the
middle school level. Currently,
?Math Thematics, published by McDougal Littell
* Interactive Math, published by the Glencoe Division of McGraw-Hill
* Mathematics in Action, published by Macmillian/McGraw-Hill
* Middle Grade Mathematics, published by Prentice Hall
The Shodor Educational Foundation has put together a remarkable set of
interactive mathematics explorations for middle school mathematics. Most are
user friendly and encourage high level thinking. The collection has added links
for those who wish to expand their knowledge. There are also exploratory
questions. There are explanations answering what, how, and why each concept
addressed is connected to the NCTM Standards.
All of activities are activated by Java applets. For many of the questions
posed, the ability to find answers is greatly enhanced by the actions
demonstrated with the applets. This is truly a case where technology is
enhancing what can be understood.
The activities are also special because many of them are adaptable for use at
different levels of difficulty. This would allow them to be used with all levels
of students. Because the difficulty level can be raised to be more challenging,
advanced students would be able to explore on their own. This is something
that is lacking in many materials.
|| The major learning goals are to present activities which explore mathematical
concepts, to connect these activities to mathematical discussions and to the
NCTM standards. The site provides support for teachers in both content and
pedagogy. It links to texts, provides a dictionary, and support tools that can
be used with the activities and lessons or independently.
Students and teachers will have hands on experiences with models that make many
of the math concepts come alive. They will be able to make strong connections
between language, symbols, and models. These activities could prove useful to
parents trying to help their students with their math.
|Target Student Population:
|| The site is designed for preservice and inservice teachers. It would also be
useful for middle school through university students.
|Prerequisite Knowledge or Skills:
|| Knowledge of middle school mathematics concepts is helpful,
definitions, explanations, and curriculum contexts are provided. This material
is not in lieu of a curriculum, but it enhances what is being taught.
|Type of Material:
|| Interactive Java-applet activities, lesson plans, and discussions
|| Preservice or inservice teachers could develop lessons based on these examples.
Mathematics methods classes could use the material as a demonstration or review
of content materials.
Use for group and individual explorations based on concepts found in the middle
school mathematics curriculum. The activities are used to make basic concepts
more concrete through models that give multiple ways of undertanding. At the
same time, students who are more advanced are encouraged to do advanced
|| Java-enabled browser is necessary. Recent versions of Netscape or Microsoft
Explorer are recommended.
|| These activities stand alone as excellent examples of connections to the NCTM
standards. Additionally, they are accompanied by clear instructions, by a
curriculum context, and by a set of discussions which enable teachers to learn
how to introduce each of the topics. The activities are organized by the NCTM
Each activity is an interactive, computer application designed to teach students
about a concept through hands-on experimentation. Activities usually present
good opportunities for group work as well as individual investigation. Support
materials, which include handouts, tables, worksheets, etc., are available for
many of these activities and can be accessed from the why page for that
The content of the material in these interactive activities is superior. There
is a richness to the subjects selected and the types of explorations supported.
There are many opportunities to ask "what if" I tried this number or this
The range of topics and the links to enhanced explorations are impressive. Most
activities serve to enhance what can be done in a classroom, which is what
technology should do.
The inclusion of the rationale for each activity is useful for teachers who wish
to add some of these activities to their lessons. It raises them beyond the
realm of "cute tricks."
|| The decimal, fraction converter is not at the level of the other activities. A
calculator does the job equally or even better. Pictorial modeling and a
connection to percents would be helpful.
The Pascal's Triangle model could be clearer.The activity is much richer when
you actually code all of the spots based on their remainder from the multiple.
coloring in the multiple of five could have the other squares
labelled from 1 to 4 to get the point across. The patterns are visually
I think a good case for fractions represented on the number line or as shaded
parts of the same whole has been made. However, fractions as part of a set
should also be included in some way.
In terms of the iteration of the fractals. instructors using them should know
enough to be able to ask about perimeters and areas where appropriate.
Spreadsheets could be introduced here.
Some activities are more complete than others. For example, Pattern Finder
is minimal, even though patterns are a major part of understanding mathematics.
Potential Effectiveness as a Teaching Tool
|| The use of these activities, both in the classroom and as outside of classtime
learning could be invaluable. Not every institution will have access to
materials to demonstrate each of these concepts, but Shodor provides this access
via the Java applets. The strength of this site is in the accompanying
materials to clarify and extend the activities.
|| The usefulness of this site would be diminished were it not used as a package--a
great deal of thought and work has been put into the accompanying materials.
The instructor has to know enough about the math behind these activities so they
are used as the enhancements for understanding they are supposed to be.
Otherwise they can be reduced to "neat" things to see. For example, it is
interesting to see the iterations that change a triangle into a snowflake, etc.
However, there should be understanding about what the changes are and how they
affect the area and the perimeter at each stage.
Ease of Use for Both Students and Faculty
|| Navigation of the site is simple. It is arranged logically, defines each of its
sections, and provides a search engine.
Most activities were user friendly. In the instance where questions arise, the
"How" page is available.
|Other Issues and Comments:
|| This is a rich site, providing both activities, lessons, background information,
and tools for the preservice, inservice, and higher education instructor of
mathematics or mathematics methods. It is well integrated, clear, and each
visit brings new, useful information to site visitors.
This is an ambitious set of activities that provide enhanced understanding of
complex mathematical concepts. In some cases, especially in the modeling of
fractions, they help remove the fog students often find around subjects such as
The function machines, Pacscal's triangle, fractals, clock arithmetic, etc. all
provide materials that should raise interest in mathematics.