Introduction
3 methods
My background
why I teach
AVID Math 7
curriculum
Teacher's Role
changing
Instruction
ideas
Assessment
rubrics
Equipment
one computer
... or a lab
Notes
from others

As I have worked with my students this year, following a 7th grade mathematics curriculum, my belief in the importance of teaching lessons using more than one method of presentation has been reinforced. Here are methods I have found to be valuable:
 activities  kinesthetic, manipulative, cooperative
 technology  the Web, software or graphing calculators
 revisiting and formalizing the mathematics
I first introduce a lesson as an activity. The students are arranged in groups of four and work through the activity using manipulatives. Often there is movement. There is no initial expectation that the student will master the mathematical objective of the lesson.
We sometimes think that students will "learn" immediately or as a result of something that the teacher says; however,
I find that students don't learn unless they choose to learn. It is important to create an environment that offers students ways of experiencing how to work through a problem that requires the use of mathematics.
In my classes, directions are made available by means of a text or a handout. I introduce the topic, but give the group time to ponder, absorb, and follow the directions. My main role is to walk around the classroom as a facilitator, not spending a great amount of time with any one group.
My goal at this point is to create an environment where students are engaged in learning. They need to be encouraged to get involved in the activity. Hints here and there for how to start can make the task attainable. The students, however, have to make the choice to become involved.
If the class cannot begin working without further explanation, I stop the activity, review the directions, and begin again. Students must realize that they are responsible for understanding the task. They are to read the directions and
follow them to complete the activity.
Once the first presentation of an activity has been completed, a different way of presenting the same topic can be undertaken. Technology is an excellent tool at this point. Either the Internet or software can be used to present the same activity. If possible, the students work individually on computers but with partners working sidebyside or as pairs on a computer.
In my computer classroom I have one classroom rule: everyone facilitates. I remind the students that there are three parts to facilitating:
 to help the teacher by following directions
 to help themselves by doing their best
 to help their classmates by sharing information
Finally, we regroup in a classroom and discuss the activity, to make certain that the mathematics has been understood by all. This often involves looking at the problem algebraically or symbolically, so that the mathematics is formalized. This step is vital for students to be able to take the experience of an activity or the use of technology and make use of that experience on a standardized test. In California we are increasingly measured as teachers by student performance on standardized tests. Unless we teachers help students to make the "jump" from enjoying engaging experiences to how the mathematics will look on standardized presentations, we will miss an opportunity to help our students perform well.
Recently a teacher wrote to me saying that it was hard for her to believe that the lessons I display on the Web are really for my seventh grade students. She says she can't get past the basics, because her students just can't seem to master them, and won't do any work. I find, however, that my students will try many things when the basic skills are embedded in activities rather than being the sole objective of a lesson. Seventh grade students love to work in groups, they love new challenges (as long as these are attainable), and they love technology and manipulatives. The lessons that I continue to design incorporate all of these components.
Students  all of us for that matter  want to succeed at their work. It is important to create lessons with attainable goals. Projects should be designed that have a range of entry levels. Directions should be clear and simple so that tasks are within reach.
I believe strongly that all students can learn. Students who have reached middle school and have not mastered arithmetic need to see arithmetic in a different context. Some need to have spatial experiences in order to understand concepts fully. Others need kinesthetic experiences that can be had through working with manipulatives. Some students don't really understand a concept until they have explained it to someone else. Traditional mathematics classes have not fully explored these different kinds of experiences.
Through presenting an activity with the three components (activity, technology, formalizing) we not only give students with different learning styles different ways to see a problem, we give them the extra time they may require for learning. When I think in terms of varied presentations of the same problem, I can't help but allot more time to the material. Time and experience in class enrich an activity: students can learn from their experiences and connect the mathematics to those experiences. Such a foundation helps them to understand and appreciate mathematics.
