1st Edition
How to Solve A Problem Insights for Critical Thinking, Problem-Solving, and Success in College
This concise and accessible resource offers new college students, especially those in science degree programs, guidance on engaging successfully with the classroom experience and skillfully tackling technical or scientific questions. The author provides insights on identifying, from the outset, individual markers for what success in college will look like for students, how to think about the engagement with professors as a partnership, and how to function effectively in that partnership toward achieving their pre-defined goals or markers of success. It is an ideal companion for science degree prospects and first-generation students seeking insight into the college experience.
- Offers transferable problem-solving ideas and skills applicable for other disciplines and future careers
- Provides new students with support and inspiration for their college experience
- Includes guidance for successful interactions with professors, peers, professionals, and others
- Encourages thoughtful determination of desired outcomes from the college experience and shaping one's actions toward accomplishing those objectives
Preface and Acknowledgement
Chapter 1: On Encountering a Problem
What is a problem?
The Right to Propose a Problem
- The Implicit Faculty Commitment
- The Responsibility of the Problem Solver
- The Student’s Commitment
Preparing for Problems
Patience, Persistence, and Problem Solving
Knowing £ (The Battle) / 2
To Take on a Problem
- Study Strategies
- Assessments: Taking Tests or Exams
- Count your Blessing
Chapter 2: The Logic of the Problem: Good Thinking and its Rewards
Subject-Independent Logic (Subject-Specific Laws)
Scientific Laws ‘Do’ Nothing
General Logical Ideas in Science
Units – The Basics
Units and Meaning
Logic Above Memorization
Reading a Chemical Formula – Not only for Chemists
Chapter 3: Solutions in words: Answering Short Answer Question
Symbols and Words
Short Answers in Words
Chapter 4: Making Textbooks Pay
Chapter 5: Solutions in Numbers: Basic Mathematical Procedures
Some Mathematical Reminders
- Algebraic Manipulations and Useful Math Relations
- Trigonometric Ideas
- Beyond Triangles
- Other Interesting Relationships and Definitions
- Exponential Functions, e
More Emphasis on Logarithms and Powers
Linear (Straight-Line) Equations
Quadratic Equations.
Graphical Representations of Experimental Data
Simultaneous equations
- Option 1 – the exponential form: A = Aoe-kt
- Option 2 – the (straight line) ln form: ln(A) = ln(Ao) – kt
- An Extra Example
A Word on Matrices
- The Identity Matrix
- The Inverse of a Matrix
On the Shapes of Things
- Circles, Cylinders, and Spheres
- Triangles and (Triangular) Prisms
- Rectangles and Cuboids
Layer upon Layer
- A fun illustration from shapes
Chapter 6: Practical Solutions: Science in the Laboratory
Why Experiments Matter
Approaching Laboratory Activities
- Insist on high standards of logic and reasoning
- Be willing to think independently and to take on new challenges
- An Appreciation of Errors:
- Another suggestion to keep in mind
- The Unknown Possibilities
- Ethical Engagement
Chapter 7: Spreading the Word
Preparing Papers
Writing Abstracts
Preparing Posters
Preparing Talks
Chapter 8: Persisting Against Problems
Mindset and Anxiety about Belonging
Thoughts on Managing the Demands
On to the Next Problem
Appendix I: Additional Notes on Matrices and Matrix Algebra
- The Identity Matrix
- The Inverse of a Matrix
Appendix II: Thinking about Vectors: Basic Notes
- Adding and Subtracting Vectors
- Vectors in the Sciences – a qualitative example
- Vector Ideas in Introductory Chemistry
Appendix III: Safe Problem Solving
Biography
Kelling J. Donald is a professor of Chemistry, and currently Clarence E. Denoon Jr. Chair in the Natural Sciences, and an Associate Dean in the School of Arts and Science at the University of Richmond (UR). A theoretical chemist by training, he teaches students across the undergraduate Chemistry curriculum, in Introductory and Physical Chemistry courses, and mentors undergraduates in research, employing theoretical and computational approaches to solve chemical problems. Among other acknowledgments of his work with undergraduates, he has received the Distinguished Educator award from UR and the Henry Dreyfus Teacher-Scholar Award from the Camille and Henry Dreyfus Foundation. Born in Jamaica, he lives in Richmond, Virginia.
Donald provides a treasure trove of information applicable to students across the academic spectrum. For example, he presents the rationale for using logic, not rote memorization to solve problems, and he discusses the importance of getting the most from a textbook. Students will find the information in this book invaluable!
Professor Saundra McGuire, author of Teach Yourself How to Learn
Quantitative problem-solving skills are essential for success in introductory science courses. Prof. Donald’s text offers a helpful guide for first year undergraduate students on the necessary basic mathematics and general strategies, as well as explaining how students can more effectively study and communicate their scientific results.
Professor Joshua Schrier, Fordham University, New York
