How to Solve A Problem : Insights for Critical Thinking, Problem-Solving, and Success in College book cover
1st Edition

How to Solve A Problem
Insights for Critical Thinking, Problem-Solving, and Success in College

  • Available for pre-order on March 21, 2023. Item will ship after April 11, 2023
ISBN 9781032203614
April 11, 2023 Forthcoming by CRC Press
62 Pages 6 Color & 14 B/W Illustrations

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Book Description

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 transferrable 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 ones actions toward accomplishing those objectives.

Table of Contents

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

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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