My Educational Philosophy

The hiring season has begun: schools in New Jersey have started posting open positions for high school math teachers for the 2012-2013 school year. In preparation, I dusted off a draft of "My Educational Philosophy" that I wrote for Larry at Traders-to-Teachers and cleaned it up for use on applications. I still consider it a working document, but it does express what I think are key points:

• Learning is neurologically based: education must be based on a sound theory of cognition. This is the old cognitive scientist coming out in me.
• There is an inherent tension between the needs of society and the needs of an individual, and a good teacher in the classroom does not avoid this tension.
• I teach for understanding, and my definition of "understanding" owes a lot to Howard Gardner. 

OK, here it is:

Number Theory for Teachers

This summer I'm taking a course in Number Theory designed for secondary school math teachers, specifically those of us who went through the Traders-to-Teachers program at Montclair State University. As such, it will cover a subset of the topics usually found in introductory number theory courses, with, I suspect, less rigor. From the syllabus: "Our class discussions will relate number theory topics to middle and high school level curriculum."

At the beginning of the first class the instructor asked what we hoped to get out the course. I kept silent, as my situation - unemployed - and interests differ from the rest of the class. However, I continued to ponder the question and hope to answer it here. Aside from the obvious and trivial response - to satisfy a requirement for full teacher certification - here's what I want to get out of the course:

The Role of Technology in Education

A question on a recent job application asked about technology in education. Such questions often force me to reflect on the topic and focus my ideas; this one was no different. I take the standard view of "technology as a tool" and consider four kinds of tool use: 

1. Technology as a tool for communication and collaboration. This use is well-known and includes e-mail, using the web for access to information, collaborative software and social media for group projects, etc.
2. Technology as a tool for the expression of ideas. My best example is from mathematics: software that allows you not just to visualize mathematical ideas but to increase the number of dimensions through 3-D and animation; to emphasize or discriminate features using color and pattern;  to show the development of complex ideas using selective hide/show, etc. The best software makes this expressiveness available to students as well as teachers.
3. Technology as an extension of self. Through digitization and storage, technology enables a teacher to provide differentiated instruction both in the classroom, by increasing the number of modalities by which material is presented; and outside the classroom, by providing extra help or extended topics for which class time is not available.
4. Technology for ubiquitous data-gathering and number-crunching. This use of technology opens up possibilities for extended, fine-tuned assessments of learning and teaching; it also raises ethical issues.

In addition to all of these uses, exposure to the technology that will be encountered in higher education and the workplace is a necessary part of secondary education.

My original answer to the question follows.

Why I want to teach mathematics

I recently applied for a teaching position whose application included the following questions:
Why do you wish to join the XYZ school system?
How do you feel you can contribute to XYZ's educational excellence?

Here are my answers. Arriving at them required some thought, which I describe below.

Why do you wish to join the XYZ school system?
With a background in business and technology, I'm looking to work in a school district where professionalism, quality, and teamwork are valued, and where a need to make secondary education relevant to today's society is recognized. As a parent and student, I also value personal growth, individual differences and preferences, and a questioning attitude. I found similar values in [XYZ]'s Mission and Belief statements. In addition, I got to know a little of the community and surrounding area while my son attended the local college (class of 2010) so I know it's a location where I'd enjoy working.

How do you feel you can contribute to XYZ's educational excellence?
First and foremost, I can bring technology into the classroom, both as an instructional tool and as an introduction to the technologies that students will encounter in higher education and the workplace. Second, as a lifelong learner who re-entered the educational world only recently, I can bring a different set of experiences and a fresh perspective to the community's pursuit of excellence.

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Another Job Application Question

The second standard question on AppliTrack applications for teaching positions concerns differentiated instruction: Here's my standard answer.

How would you address a wide range of skills and abilities in your classroom? 

1. Thoroughly assess individual needs, abilities and preferences at the beginning of the school year. Consult with more experienced teachers who have had the students previously.

2. Use available technology to give multi-modal presentations in the classroom, so that information is communicated is as many different styles (verbal, visual, aural, haptic, etc.) as possible.

3. Encourage expression of mathematical thoughts in different ways. Show that there is often more than one way to reach a desired result.

4. Make time for all students. As classroom time is limited, be available outside of class. Where appropriate, provide supplementary material tailored to individual needs.

5. Explore the use of project-based learning that allows students to bring their individual strengths to a group activity.

6. Consider supervised peer-based tutoring, in which the tutor also benefits by learning to communicate mathematical ideas clearly.

Technology, both in and out of the classroom, can aid many of these efforts, such as multi-modal presentations, supplemental work tailored to individual needs, assessment and record-keeping.

What does it mean to be an outstanding teacher?

This is a standard question on AppliTrack applications. It took me a couple of weeks to draft and polish my answer. My approach was to list what I believe is necessary to be a competent teacher, then extrapolate. In other words, an outstanding teacher must be more than just competent.