The key question for mathematics educators is how can we engage our students in a meaningful way? While there are many ways to achieve this goal, I have found one approach that has worked particularly well for me. I call this approach Directed Discovery Mathematics (DDM) and I have outlined the key points of this approach below.

• Students learn best when they are actively engaged. Consequently, students should spend most of their class time working on problems. In order to make the learning process as active as possible, I generally do not start class with a lecture – a major shift from my practice during my early years of teaching. Instead, my students spend most of their class time working on problems sets.
• Since there is no lecture, the problem sets must guide students to develop the key ideas of each lesson themselves.
• The questions in the problem sets should be asked as clearly as possible. The challenge for the students should be answering the question, not figuring out what the question is asking. Just as importantly, the learning goals for each lesson should be unambiguous. When a student reaches the end of a problem set, she should feel that she knows exactly what she was supposed to have learned.
• There must be a balance between problems that are used to develop new ideas and problems that are provided for practice. Both are crucial!
• Problem sets must be edited and altered to meet the needs of a particular class. To facilitate this process, I have included the problem sets on the website as word documents which teachers can download and modify to meet the specific needs of their students. My hope is that this will represent a major advantage over textbooks that are printed on paper – and thus much harder to edit!