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Teaching Children to Love Problem Solving: A Reference from Birth to Adulthood

Terri Germain-Williams
World Scientific
Publication Date: 
Number of Pages: 
Problem Solving in Mathematics and Beyond 6
Problem Book
[Reviewed by
Peter T. Olszewski
, on

Teaching Children to Love Problem Solving provides the reader with a collection of best practices for any math educator teaching a child problem solving skills. For any age bracket, this book offers the developmental information, relevant mathematical concepts, sample problems with multiple solutions, and activities for student engagement. In the introduction, Terri Germain-Williams references George Pólya’s problem solving work How to Solve It, which outlines for four-step process:

  1. Understand the problem.
  2. Devise a plan.
  3. Carry out the plan.
  4. Examine the result.

The problem solving addressed in this book is presented in the context of the various stages of human development. Anyone with a child can use it to understand the range of a child’s potential at each age. Every chapter opens by describing the child’s cognitive ability at a certain age range. There is then an overview of mathematical ideas that students are learning at that age range, which run from infancy through age 23.

As pointed out by Williams, the brain of a newborn is rapidly changing and absorbing new information. Incorporating numbers to daily routines is vital for development. This can be as simple as counting how many birds are in a book or how many pencils are on a table top. What should be avoided is having toddlers under the age of two looking at screens, TV, tablets, cell phones. On page 6, Williams references the American Academy of Pediatrics (2001),

Television and other entertainment media should be avoided for infants and children under age 2. A child’s brain develops rapidly during these first years, and young children learn best by interacting with people, not screens.

Pages 10–14 present puzzle progressions ranging from non-connecting puzzles with large knobs through interlocking puzzles. These puzzles are an excellent resource for a toddler’s developing brain, building logical thinking skills.

In “Grade School Gurus” (chapter 5), we learn as children enter the 3rd grade they start to develop concrete thinking skills. Conversations are increasingly fully understood at this age. Students can understand that even though items such as pencils maybe arranged in different ways, can still add to the same amount, whether they be in a jar or in a row on a table. In addition, Williams points out that fractions are developed at this stage of growth. Pages 45–46 present fractions on a number line as well as Tape Diagrams.

The book moves forward to discuss Teenage Thinking (Chapter 7) and Post-Secondary Problem Solvers (Chapter 9). Here, students will be exposed to topics such as Venn Diagrams, systems of linear equations with applications, and Matrix Logic. In addition, students can be asked how mathematics is used in their daily lives. For example, on page 102, Activity 9.3 (Mindful Living), asks students to make a list of the top ten priorities by analyzing money on what the student believes should be spent on certain things. This is problem solving that gets students involved and makes them think about their futures.

This book presents how adults can make an important and life-long interest in children with problem solving. Problem solving skills are a vital part of everyone’s lives and the sooner we develop these ideas on our children, the better. They will need these skills not only in school, but also for their jobs, family, and life, in general.

The Common Core State Standards developed eight Standards for Mathematical Practice, outlined on page 105, which can lead to a reduction of stress when solving a problem in mathematics. By developing these skills with students, we are instilling a love of mathematics, solving problems, and are promoting best practices for teaching our students. In turn, students will have more confidence and motivation for problem solving.

We all know that word problems are the most challenging for students. Following these helpful tools and resources presented in the book should help you and your students achieve a higher level of satisfaction for problem solving.

Peter Olszewski is a Mathematics Lecturer at The Pennsylvania State University, The Behrend College, an editor for Larson Texts, Inc. in Erie, PA, and is the 362nd Chapter Advisor of the Pennsylvania Alpha Beta Chapter of Pi Mu Epsilon. His Research fields are mathematics education, Cayley Color Graphs, Markov Chains, and mathematical textbooks. He can be reached at Outside of teaching and textbook editing, he enjoys playing golf, playing guitar and bass, reading, gardening, traveling, and painting landscapes.

  • The Earliest Years: Babies into Infancy
  • Developing Toddler Thinking
  • Preschool and Problem Solving
  • Early Childhood Problem Solving
  • Grade School Gurus
  • Middle School Minds
  • Teenage Thinking
  • Preparing Late Teens
  • Post-Secondary Problem Solvers
  • Conclusion