It is one thing for students to read portions of the book to seek information, and another thing for them to grapple with what they find. They need to know where they currently are as students, where they want to be, where they need to be, and how to get there. This is done through the exercises by asking for their opinions, thoughts, and feelings based on their experiences, what they read in the book, and their discussions with others.
Here is a sampling of phrases in the exercises: What did you do about ..., Are you prone to ..., Are you reluctant to ..., What would you have done..., How can this be applied to ..., Have you found it worthwhile to ..., Rate your feelings on ..., Give your experiences on ..., How would you react to ..., What are reasons for ..., Do you agree or disagree with ..., How did you take advantage of ..., List things that help you to ..., What criteria do you use to ..., Do you take time to ..., Give a convincing argument that ..., What do you intend to do about ..., What is your motivation for ..., What do you believe accounts for ..., Give a study behavior you ...., Give pros and cons of ..., What was your process for ....
Reading content with a purpose in mind enables students to probe it more deeply, thus understanding it better. Students are asked to explain, justify, support, or give rationale for their responses to most of the above questions or statements.
It is critical for students to get feedback, through discussion, on their responses to most exercises. Research shows that discussion nurtures these critically important learning objectives better than any other means of learning: (a) enhanced understanding and application of concepts and generalizations, (b) clarification of thinking and promotion of insight, (c) promotion of the development of problem solving skills, (d) increased ability to communicate (and as applied here, to communicate thoughts on mathematics and the learning of mathematics), (e) increased confidence through helping others, (f) changed behaviors, improved attitudes, and increased motivation, (g) promotion of active learning (thus increasing retention of knowledge), and (h) development of leadership qualities.
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He taught high school mathematics in Wisconsin for three years and college mathematics for the next thirty-six years. His first two years of college teaching were at the State University of New York, College at Buffalo. As a college professor of mathematics for thirty-four years at the University of Michigan, Dearborn, he taught all the courses in the calculus track lower-division mathematics program to students pursuing degrees in mathematics, engineering, natural sciences and business. At the upper-division level he taught linear algebra, abstract algebra, geometry from an advanced viewpoint, and specialized courses for students pursuing a major or minor in elementary school mathematics. He taught courses in problem solving in mathematics, and techniques of teaching secondary school mathematics.
His professional accomplishments are many. He has been an active conference presenter and workshop leader at local, state, and national conferences. He served two terms as chair of the Michigan Council of Teachers of Mathematics (MCTM) Teacher Preparation Committee, and served for many years as the National Council of Teachers of Mathematics representative to MCTM and the Detroit Area Council of Teachers of Mathematics. His writings and research have focused on issues associated with the learning and teaching of mathematics at all levels of education. He has published widely in academic journals on a variety of mathematics and mathematics education subjects.
Professor Dahlke is a strong advocate for college students, including their right to receive quality mathematics instruction. He believes that learning is a partnership among the student, the student s classmates, and the instructor, and that students efforts to organize and manage their time is critical to success in college. He further believes that students should enjoy college. In order for that to happen students should not get stressed out or too alarmed when things do not go well. They need to focus their energies on making necessary changes that will improve their college experience and lessen stress and anxiety. The end result will be successful college students with contented spirits.
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