Question 2: Working knowledge of a calculator (either scientific or graphing).

Estimation skills for distances, weights, time. Many students cannot make comparisons between two numbers because of weak estimation skills. Examples: weight of a head of cabbage, length of a room, time to drive from town to another place.

Develop a willingness in students to attempt new problems, using problem-solving skills learned and/or developed in the mathematics curriculum (guess/test, look for patterns, working backwards, etc.). Many students often give up too easily. They read a problem, decide it is too hard, and will not attempt it because they feel they will not succeed.

Develop decision-making skills based on data gathered and analyzed. Students should learn probability and statistics (on a very concrete level with models they can understand) and apply what they learn to make good decisions.

Develop a ``joy of mathematics''. So many students are turned off to math, feel they are dumb when it comes to math, and, even worse, feel that it is okay to feel this way. The curriculum should provide students opportunities to be successful in math and to enjoy doing math.

Develop mental math skills so that students can do simple calculation in their head without the use of pencil and paper. Estimation is part of this area.

Question 5: I always had an easy time doing arithmetic, but not necessarily mathematics as we know it today. I had an easy time memorizing and regurgitating back to the teacher, getting A's in math classes, and feeling good about my math ability. I also had teachers in middle school, high school, and college that I admired and respected and who were approachable. All of these things made me major in mathematics in college. It was not until I was finishing up my master's degree in mathematics that I decided to go into education.

Question 6: I want my students to be able to really understand mathematics conceptually. I do not want them to be good memorizers as I was when I was a student. I want colleges to allow students time to participate in class discussion on math topics rather than continue the lecture-by-teacher/take-notes-in-class environment. I would like to see classes offered where students work together on problem sets, learning math by doing, and using the instructor as a mentor-coach.

Colleges need to allow prospective teachers an early opportunity several years before their senior year to experience a high school or middle school math classroom. They may not realize until they have invested too much time and money in their education courses that they were not meant to be teachers.

Colleges need to expose students to new teaching philosophies, techniques, and pedagogy and be allowed time to see good teaching done by master teachers. They need to see different techniques incorporating collaborative learning, integrated mathematics programs, manipulatives, and visual models. Otherwise, the newly graduated teacher will teach her/his students the same way s/he was taught.

New teachers discover reality when they step into their very own classroom, teaching a full load of five to six classes of 25-35 students per class. This can be overwhelming to many of them. Colleges need to provide a support system to help teachers adjust to full-time teaching, either with weekly or monthly seminars or with college staff members visiting new teachers in their classrooms on a regular basis.