Question 1: High school graduates should understand that mathematics is useful in understanding the world around them and that math IS all around them. They need to know that math will help them

. make predictions based upon experiences and data

. find patterns to help them answer harder questions

. arrive at answers in a variety of ways and find a variety of answers to some problems

. become critical thinkers, questioners, problem solvers

Question 2: Curriculum for mathematics should:

. Include "big" questions (or long-term problems) with smaller questions that lead to, and help students discover, the tools for solving the larger problem. These questions should be interesting and meaningful.

. Call for communication skills- writing, speaking, presenting. These skills would show how the student thinks mathematically and how well they understand the problem at hand.

. Be constructivist, so students can gain confidence in their ability to solve problems and have a hands-on approach to learning. Students should be able to discover big concepts, like pi and areas of many-sided polygons, by seeing patterns and making comparisons.

. Be relevant to what they are going to encounter in the workplace, where they will be called upon to work in teams to solve problems, and be able to use technology.

. Allow for revision - so students know they can improve their work.

Question 3: A good indicator of how well a curriculum is working is by the students themselves. Is there a lower rate of failure? How long do students stay in mathematics? Do they do well in other subjects, like the sciences? Do they continue their mathematical studies in college? Do more students go into math/science-related fields? (These questions seem more relevant to me than: Will they score well on the SAT?)

Question 4: Teachers need to be able and willing to let go of their "control" in the classroom and let the students be in the spotlight. The learning has to be centered around the student rather than the teacher showing the way. Students need to learn how to enter a problem and figure out what the problem is asking, rather than be told. Then, the students have to figure out ways to solve the problem and also share them with the class. In this way, students (and the teacher!) will see the rich variety of problem-solving strategies available at arriving at the same answer. I feel a teachers attitude toward mathematics has to have a sense of newness and wonder. Otherwise, how else will the students be able to show new ways of solving problems? In the past, teachers have been too willing to say, this is the way to do the problem. There are too many other ways to solve that oftentimes lead to bigger concepts never realized before. So the teacher has to have that sense that there is going to be something new for them to learn as well as the student (I'm speaking from personal experience).