11/23: Modern School observations

For those who are interested, below is the document I gave to the principal of Modern School on my observations and recommendations for the Middle School Math teachers.

Math observations 6th, 7th and 8th Standards
by Robert Lee-Engel

From my limited interactions and observations of the math teachers of the 6th, 7th and 8th standards at Modern School, this is what I have observed:
1) The teachers are of the highest quality.
2) They are very well prepared.
3) They understand their subject material very well.
4) They expect high standards from their students.
5) They have trained their students very well to show their work, step by step, and the reasons for each step.
6) The students have very strong computational skills because there is no calculator use.

From my limited understanding of India and its educational system, the biggest different I see from the system I work in are:
1) The emphasis on testing, especially at the 12th standard, puts incredible pressure on the teachers to "teach to the test," limiting their freedom to be creative.
2) The national government mandated curriculum hinders the teacher's autonomy and creativity to meet the specific needs of the students.
3) The number of students in a math class (45 to 48 per class at Modern School, as compared to 10-14 at The Evergreen School, where I teach) limits the teacher's ability to meet specific needs of a student, especially those students at either extreme on the continuum. The class size also forces teachers to evaluate students on a limited criterion - testing, as opposed to a multitude of criteria - daily work, projects, and testing - in schools where class sizes are more manageable.

As I have reflected on my teaching methods, which I have developed over my 23 years of teaching , and 22 years at The Evergreen School, this is what I have come to believe are best practices for teaching math at the 6th, 7th and 8th standards (in no particular order of importance):
1) Everything should be invested with meaning. Ask the students "why" and expect the students to ask the teacher "why."
2) Classes should be interactive. Get the students to talk, ask questions, teach each other, come to the board, share ideas.
3) There should be a joy in teaching. Teachers should love what they are doing, modeling for their students their love of learning.
4) Teachers should have fun. Especially when teaching math, we need to be performers.
5) Include group work: students working with each other learn from each other. They also learn how to articulate ideas. Also, it removes the teacher from being the sole "holder of knowledge" in the class.
6) Teachers need to be well prepared. They need to know their subject material well.
7) It is okay to make mistakes. This may actually be the most important element for creating an environment where students take risks. Fear of making a mistake is the biggest detriment to learning. Most learning occurs from our mistakes. The deepest learning occurs when students are challenged.
8) It is important to use "open ended" questions and assignments. This provides for a multitude of solutions. It also builds self esteem and independent thinking skills.
9) There should be a focus on the process more than the product. We teachers are helping students to become thinking, problem solving human beings, so the process of being a learner is most important.
10) Accuracy is important. While process is very important, we cannot forget that accurate computational work is a very valuable tool.
11) We need to expand the students' definition of math. Math is not just computational skills. it also involves problem solving skills. So conceptual understanding is just as important as computational algorithms.
12) We need to help the students develop their ability to articulate. As social animals we need to learn to communicate well with others, whether it be working together, teaching each other, or just sharing of an idea.
13) Differentiation - students have different abilities. We need to challenge the most advanced students and give extra support to those students who are struggling.
14) We need to protect our students' self esteem. Try not to embarrass students. Students perform better when they feel good about themselves. It is a matter of respecting each individual.
15) Hold high expectations of your students, and they will rise up to your expectations.
16) Use an inductive approach whenever possible. It embeds the learning with the student's personal experience, thus there is more meaning for the student, instead of mere memorization.
17) Use project-oriented curriculum. It is a good way for the students to prove their understanding of the concepts through their application in their project. It is open ended - allowing the students to choose topics of their particular interest. And it is another form of evaluation.

Below are my suggestions/recommendations for Modern School math teachers, based on my limited observations. I believe these recommendations are manageable, even with the restraints previously mentioned.
1. Teachers should "spice up" their curriculum by supplementing the standard curriculum with activities that encourage students to think -to apply the information they have learned, adding an emphasis on application.
2. Teachers should find or create curriculum that is fun for the students - games, puzzles, etc. that require the application of concepts, or even teach concepts through these activities.
3. Teachers should use an inductive approach whenever possible -investigations that teach concepts - instead of a deductive approach of merely giving the students conjectures or properties.
4. Teachers should respect the students by not embarrassing them publicly (when they have not done their work). Intimidation may work for some students, but for others it shuts down the learning process, creating an atmosphere of fear instead of joy in learning, which is not conducive for growth.
5. Teachers should allow for more interactive learning through group activities. This does a number of things: it encourages communication, students learn by teaching each other, and it empowers students when they realize that they can teach each other.
6. Teachers should incorporate more open-ended questions. This encourages students to think, as well as providing opportunities for student creativity.
7. Teachers should foster a classroom atmosphere of risk taking. An environment must be created where it is okay to make mistakes. This is especially important in a math class.
8. Teachers can find or create material that requires thinking"outside of the box." I have found that often, Modern School students had difficulty when ever I asked them to do this.