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 are supported.
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,
although 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 explorations.
Java-enabled browser is necessary. Recent versions of Netscape or Microsoft Explorer are recommended.
Evaluation and Observation
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 Standards.
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 activity. 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 shape.
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. For example,
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 represented, though.
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 equivalent fractions.
The function machines, Pacscal's triangle, fractals, clock arithmetic, etc. all provide materials that should raise interest in mathematics.