I suppose it works better if I actually include the essays.

Describe the skills or attributes you believe are necessary to be an outstanding teacher.

An outstanding teaching is one who is knows the material he is teaching, knows how the material works in the real world, knows the skills that are necessary to learn the material, knows how the material fits into the next stage of learning, knows the most likely problems students will have, is ready to deal with those problems.
An outstanding teacher is predictable. Each unit will work along the same outline; each lesson will follow a basic outline. Students will know the objectives of each lesson and the objective will be reinforced throughout the lesson. Students will know that what they do in class and for homework will have a point.
An outstanding teacher will build knowledge. Students will start with the familiar and stretch towards the new. Students will build knowledge based on their own understanding first then connect their innate understanding to the formal skills they are learning.
An outstanding teacher will run a student-centered classroom, allowing students the time they need to explore. He will guide and mentor students using thinking time, writing time, and experimenting time until they can formalize their thoughts and observations into general principals.

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

There are too many ways to address a wide range of skills in the classroom to fit into one essay. I would start with cooperative groups. Use more real world logical problems. Allow students time to think. Use inquiry based education that allows students to build up skills. Use more manipulative. Build vocabulary. Have students talk, then write, then talk, and then edit what they wrote again and again. Allow students the opportunity to work with partners as often as possible, but requiring each to be accountable for their part of the work. Allow time for me to work with small groups or individually with students. Use real world projects or modeling that allows all ranges of students to show what they know. Spend some time each day with a formative assessment, short quiz, listening to groups, individual help, math journals, etc… Having students keep journals of what they learned what questions they have, and what they would like to learn.
Anything that helps me know as much as I can about each student so I can identify students who are struggling before they get too far behind. So I know what particular points they are struggling with and adjust for them. So I can group students better, at times it may be beneficial to group faster students together allow them to work deeper into a particular skill at other times it may be more advantageous to group different abilities together. Then again sometimes I might want to group students with different or similar learning styles together.
All students are expected to meet a minimum standard, but not all students will reach that standard at the same time. With a short teacher directed introduction most students can get started and begin working independently to explore the skill or concept for the day. For students who need more help this allows me to get to them and give them more individual time right away before they get bored and tune me out for the day. As some students or groups finish earlier I can show or ask leading questions that allows them to gain a deeper understanding of the skill or further the skill learned that day. As we close the class all student can write down in their journals what they learned and or answer a few quick questions, or participate in a discussion, or some other quick formative evaluation of the lesson of the day. I can then use this information to know which students I may need to spend more time with during class to make sure they understand and also which students I need to challenge more.

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